Hypnosis and Analgesia - ETH E-Collection

Transcription

Diss. ETH No. 14070
Feedback Control of
Hypnosis
and
Analgesia
in Humans
A dissertation submitted to the
Swiss Federal Institute of
Technology (ETH)
Zürich
for the
degree
of
Doctor of Technical Sciences
presented by
Andrea Luca Gentilini
Dottore in
Ingegneria
Chimica
Politecnico di Milano
born 10.12.1972 in
Livorno
accepted
on
Prof. Dr. Manfred
the recommendation of
Morari,
examiner
PD Dr. med. Thomas Walter
co-examiner
Prof. Dr. Adolf Hermann
co-examiner
Schnider,
Glattfelder,
March,
2001
©
2001
All
Rights
Reserved
Foreword
The purpose of this section is threefold.
issues that
proposing
a
a
Second,
who
significantly
An easier
through
stay
the final
Third,
coupled
was
I would like to
success
some
degree,
with
a
structured
acknowledge
of this thesis.
start-up
training for marathons during the first
at the Automatic Control
at that time because
they finally
it.
contributed to the
I conceived these few lines while
years of my
obtaining
I would like mention how this thesis
and how should the reader go
people
I would like to address
tentative solution to the avoidable difficulties
Ph.D. program.
the
First,
Ph.D. candidate must face towards
looking
at the former
obtained their Ph.D.
degree
Laboratory. I decided to
graduate students' smile
made
me
two
do
so
when
think that I would have
been too excited towards the end to be able to draw rationale conclusions
about such
an
important period of
The path towards obtaining
though this is known to all
my life.
the researchers who
always straight. Even
successfully completed a
Ph.D. program, few of them decided to share their
experiences for the benefit
of future Ph.D. candidates.
answer
to two crucial
researchers
a
Ph.D.
degree
I will try to do
questions, which
is not
so
here
by giving
my
personal
may be of interest also for senior
supervising Ph.D. candidates.
What
are
Ph.D.
program?
the avoidable and unavoidable difficulties encountered
How
can
the avoidable difficulties be removed?
3
during
a
4
Let
by setting obvious premises: the goal of every Ph.D. candi¬
something new and to communicate it to the scientific
community through scientific publications in high quality journals. Hard
challenges convey big troubles, some of which may be easily avoided with a
Not withstand¬
new approach to the management of the human resources.
us
start
date is to discover
ing the fact that
research labs
ture to
-
-
for the limited
the institute I
perform outstanding
up these words: because such
best to get the
highest
put into building such
A
experience that I have from visiting other
was
working
an
excellent
return to the
an
in
provides
And this is the
research.
background
excellent infrastruc¬
why I speak
exploited at
which was visibly
reason
must be
strong investment
infrastructure.
period of the Ph.D. program is represented by the
a specific research goal is not yet outlined and the igno¬
the
field
often total, presuming that one has not been previously
in
is
rance
the
research direction. Other apparently less relevant un¬
in
same
engaged
certainties may disorient. They are associated to questions like which type
of journal should I target for my publications, which conferences and lec¬
tures should I attend, which institutions may be worth a visit during my
Ph.D. program. These latter, which seem to be more burocratical details
than anything else, may interact in a dangerously synergistic way with real
research problems and ultimately increase confusion. As a result, the first
real research contributions are delayed in time. Very often, one is reaching
particularly
delicate
first months where
the end of the Ph.D. program with
directions which may be worth to be
the last round bell
rings
a
very detailed map of
pursued.
and the time to
lacks.
bewildermentoftheinitialperiodmaybeamentorforthestart-upintheresearchwork,aVirgilioguidingthegraduatestudentthroughthehellofthefirstmonths.Inmypersonalview,thisguidemustnotbethePh.D.advisor,whosemaindutiessuchasreviewing,teaching,travelingandmanagingtheresearchinstitutedonotallowher/himphysicallytobeconstantlyafterthePh.D.candidate.Moreover,etymologycallyspeaking,herorhisroleismoretogive'advice'thantoleadtheway.ThepersonIampointingatcouldbeanybodylikeaseniororpost-docresarcherorevenagraduatestudentapproachingtheendofher/his
One feasible solution to the inevitablePh.D.
move
At that time
new
research
though,
often
from intentions to actions
5
program who has been
to
do,
working
in
know how to do it but
tual interest in
a
a
similar field. Those persons know what
they
lack time and manpower.
collaboration between
'fresh' Ph.D. student is
defined.
quickly
an
experienced
The senior researcher may
seeing the development of her/his idea without losing
The young researcher
activities.
the way
through daily
The
mu¬
researcher and
a
enjoy
contact with other
enjoys the experience of the senior, learns
technical
difficulties, acquires discerning capabilities
an investigation and the ones which
are not, experiences the importance of the communication of scientific re¬
sults. The concrete goal of such a tight teamwork may be anything which
can be considered as a 'research output' such as a journal or conference
paper and/or a postgraduate thesis. Needless to say, the success of such
a collaboration strongly depends on the characteristics of the individuals.
Particularly important keys to success beyond the technical skills may be
the natural disposition to teamwork, the will to share knowledge and the
commitment to solve conflicts in view of the big picture. At the end of the
mentorship program, a cross evaluation of the respective partner may also
be bénéficiai for both: the young researcher would receive important feed¬
back about the strengths she/he may want to exploit further and the lacks
which need to be compensated. The senior researcher may benefit from the
feedback about her/his leadership and management capabilities, which may
help her/him further in the career.
about the directions which
I
firmly believe that the
single individuals.
of the
moving
consequentlyis
worth
people potentiates the strengths
however, that the Ph.D. is ultimately
herself/himself and nobody else. Becoming aware
interaction among
It is also true,
of the candidate
isamajorachievementduringthegraduateprogram.Togiveanswerstothequestionsstatedinitially,theinitiallackoforienta¬tionofthePh.D.programisanavoidabledifficulty.Assigningaseniorre¬searcherasamentorforthePh.D.candidatemaybeasolutiontotheprob¬lem.DefiningaresearchoutputsuchasacommonpublicationasthegoaloftherelationshipenablesthePh.D.candidatetocommunicateresearchresultsduringaperiodwherenormallynooutputisproduced.Further,itallowsthementortotesther/hisleadershipcapabilities.Anexampleoforganizationswherementorshipprogramsaresuccessfullyusedareconsult¬ingcompanies,forthesimplereasonthattherichestskillsofaconsultantcomefromtheirexperience.Andoneofthemostfruitfulofthoseskills
a success
of this and
are
6
opportunities. A recently hired consultant not only lacks
experience, but could create damage for the company trying to establish
the intuition for
Further,
one.
it would
afford to pay. The
certainly
reasons
take
a
period of time the company cannot
adoption of a mentorship pro¬
which motivate the
consulting companies
Mentorship programs may be
gram in
may hold also for the academic environment.
an
easier
start-up for Ph.D. candidates.
For the reader
Chapters 1,2,3 and 4 of the present thesis are partially modified stand-alone
publications. A foreword section is given at the beginning of each chapter
to inform the reader about where she/he can find the original publication
and how does the present chapter relate to others in the big picture of
the thesis. After having summarized the main achievements of the thesis,
chapter 5 provides an outlook for future research directions.
Acknowledgments
This work would not have been
possible without the help and the support
people. Among my colleagues at IfA, I am particularly thankful
to Christian Frei, Marco Derighetti, Prof. Adolf Hermann Glattfelder and
Konrad Stadler who have been precious partners during several research
discussions. To Marco Sanvido, whose wide expertise in computer science
often prevented the real-time platform from collapsing. Finally, a special
acknowledgment to Gianni, Eleonora, Francesco, Alberto, Domenico and
of many
Milos with whom I lived many critical and
exciting
situations and to
with whom I shared the office with the most gorgeous
I
am
indebted to Marco Rossoni
I would also like to mention the
partners
ical
at the
impact of
Inselspital
automatic
Fabio,
of town.
Gerosa, Christoph Schaniel and
supervised during Semester and Diploma projects
contribution they gave to this thesis.
Grieder that I
consistent
sight
Pascal
for the
precious help and collaboration from our
Bern, who allowed us to demonstrate the clin¬
control in anesthesia. A rewarding acknowledgein
7
ment must be
their close
given to Dr. Thomas Schnider and Dr. Rolf Wymann for
supervision of the project, to Dr. Marting Luginbühl, Prof. Alex
Zbinden and Daniel
Leibundgut for the support and to Dr. Christian Birecently brought into clinical investigations.
presented in the thesis was partially supported by Swiss National
eniok for the vital energy he
The work
Science Foundation SNSF 32-51028.97.
I
am
professionally
and
humanly
indebted to my advisor Prof.
Morari for his endless commitment to research and the
strated both
as
a
research leader and
as a
sharpness
Manfred
he demon¬
manager.
Finally, I would also like to thank the many people who were running,
cycling, rollerblading during summer and winter, night and day besides me
while I was training for marathons: Gabriela, Oliver, Jan, Markus, Jacques,
Daniel, Hannes, Gianni, Pamela, Anna, Luca, Sybille, Eleonora, Olivier, my
father and my
dog
Nuur.
8
Abstract
The main contribution of this thesis is the
two novel feedback control
Both
systems
to the
design and the application of
practice of general anesthesia.
improve the patient
The first
care during and after general surgery.
patient's degree of unconsciousness by continuous
administration of volatile hypnotics.
The second aims at regulating the
patient's analgesic state by means of continuous opiates infusion. Another
contribution of the thesis consists in the development of a new modeling
framework to quantify anesthetic drug synergies.
aims at
regulating
In the introduction
the
thoroughly analyze all the potential benefits of au¬
an example, two control strategies are presented
for the particular cases of Mean Arterial Pressure (MAP) and Bispectral
Index (BIS) regulation with isoflurane. Further, we describe the real-time
platform which allows us to apply closed-loop control in the operating room.
In particular, we discuss the mandatory safety measures that cope with the
clinical safety standards and the software architecture.
we
tomation in anesthesia. As
Chapter
2
describes the model-based
closed-loop system which delivers
as assessed through Bispectral In¬
model-based closed-loop controller of
isoflurane to guarantee unconsciousness
dex
(BIS).
hypnosis
This has been the first
with volatile agents
controller
was
practice. BIS
triggered by
monitors
Drug Administration
itors
were
on
increasing
humans. The
use
conception of this
of BIS monitors in the clinical
the first clinical devices to receive Food and
clearance
compensate for the lack of
since the first successful
tested
ever
the
as
a
surgical
monitors for unconsciousness. BIS
reliable
sensor
for awareness,
a
intervention with anesthesia in 1846.
9
mon¬
deficiency
10
The results of the clinical validation of the controller
sented.
The patent for the control strategy to
both the
European Community
Chapter
3 describes
a
control
closed-loop
The ideal
input
closed-loop system
analgesics.
strategy to regulate analgesia
patient
are
pre¬
pending
in
for the
intraoper¬
This has been the first model-based
for the control system is still
assessed while the
humans
BIS is
and the United States of America.
model-based
ative administration of
on
regulate
ever
missing,
is unconscious. Therefore
controller which has two
On
tested
since
we
on
pain
humans.
cannot be
developed
a
closed-
it maintains the
one hand,
loop
goals.
patient's
hemodynamic stability assessed through MAP, a possible candidate indica¬
tor for the analgesic state. On the other hand it tracks predicted analgesic
concentrations in the plasma, allowing anesthesiologists to titrate opiate
infusion on the basis of clinical signs of inadequate analgesia.
In
chapter 4 the problem of anesthetic drug interaction is addressed. Pre¬
cisely, we present a modeling framework which is suitable to quantify and
test anesthetic drug synergies. Even though several synergy models were
already presented in other medical fields such as cancer therapy, they are
The main assumption which is violated for
not adequate in anesthesia.
anesthetics drugs is that all the compounds in the mixture investigated
must have an effect on the considered clinical endpoint if given alone. The
novel modeling framework is able to describe mixtures of two and three
anesthetic drugs. Further, single drug parameters can be embedded in the
model equation without the need to be re-estimated.
In
chapter
5
we
summarize the main achievements of the thesis and outline
future research directions.
Zusammenfasssung
Entwicklung und die Anwen¬
geschlossenen Regelkreisen im Gebiet der Anästhesie.
Der erste hat das Ziel, eine bestimmte Hypnosetiefe des Patienten mit¬
tels kontinuierliche Dosierung von flüchtigen Hypnotika zu erreichen. Der
zweite regelt den Analgesiezustand des Patienten mittels intravenöser Opi¬
In dieser Dissertation beschreiben wir die
dung
ate.
von
zwei
neuen
Zudem führen wir ein
neues
Modell
ein, das die Interaktion zwischen
Anästhetika beschreibt.
möglichen Vorteile der Automatisierung¬
Beispiel nehmen wir die Regelstrategien,
die den Mittleren Arteriellen Druck (MAP) und den Bispektrale Index
(BIS) mit Isofiuran reglen. Dann beschreiben wir die technischen Lösungen,
welche die notwendige Sicherheit unserer Geräte garantieren und die Ar¬
chitektur unserer Software Applikationen, mit welchen wir die Regler in der
Im
Kapitel
1
analysieren
wir die
stechnik in der Anästhesie.
Als
Klinik anwenden können.
Im
Kapitel 2 beschreiben wir die erste je am Menschen getestete modell¬
Reglerstruktur, welche eine gewünschte Hypnosetiefe erreichen und
halten kann. Die Hypnosetiefe wird durch die Messung des Bispektral-Index
abgeschätzt und durch die reglerkontrollierte Verabreichung des flüchtigen
Anästhetikums Isofiuran erreicht.
Die zunehmende Verbreitung der BIS
Monitore im klinischen Bereich hat den Anstoss zur Entwicklung eines
solchen Reglers gegeben.
Die BIS Monitore sind die ersten Geräte für
die Messung der Hypnosetiefe, die von der 'Food and Drug Administration
(FDA)' zur Verwendung der Klinik zugelassen wurden.
basierte
Für die
Regelungsstrategie
wurde ein Patent bei der
11
Europäischen
Union
12
angemeldet.
Im
3 stellen wir einen modellbasierten
Regler für die intraopera¬
Analgetika vor. Die hier beschriebene Struktur
entspricht dem ersten geschlossenen Regelkreis, der die intraoperative Ve¬
rabreichung von Schmerzmitteln regelt. Da keine objektive und spezifis¬
che Messung der Schmerzempfindung existiert, fehlt unserem Regler ein
passendes Messsignal. Der Grund dafür ist, dass Schmerz für einen bewusstlosen Patienten nicht definiert ist. Unter gewissen Umständen, kann jedoch
der Mittlere Arterielle Blutdruck (MAP) als Indikator für die Analgesie be¬
trachtet werden. Deshalb haben wir einen Regler entwickelt, der gleichzeitig
MAP und die Konzentrationen des Analgetikums in bestimmten Grenzen
Kapitel
tive Administration
von
halten kann.
Im
Kapitel
4 stellen wir ein
neues
Modell für die Interaktion
von
Anästhetika
Andere
Interaktionsmodelle, welche schon in verschiedenen biomedi¬
zinischen Gebieten verwendet werden, sind für die Anästhesie nicht geeignet.
Diese Modelle gehen nämlich davon aus, dass jedes Anästhetikum, welches
einzeln verabreicht wird einen Einffuss auf den klinischen Endpunkt hat.
Dies trifft besonders in der Anästhesie nicht zu, da sich gewisse Wirkungen
vor.
erst bei der Kombination mehrerer Anästhetika
haben wir ein
von
Im
bis
zu
neues
Modell
drei Anästhetika
entwickelt,
zu
zeigen. Aus diesem Grund
welches in der
Lage ist, Synergien
beschreiben.
Kapitel 5 fassen wir die Kernpunkte dieser Dissertation zusammen
mögliche Richtungen für die zukünftige Forschung vor.
stellen
und
Prefazione
Questa
tesi descrive due nuovi
cati nel campo dell'anestesia
paradigmi di controllo ad anello chiuso appligenerale. Il primo controllore regola il grado di
ipnosi del paziente mediante la
volatile. Il secondo
ne
trazione continua di
nuovo
Nel
somministrazione continua di
mantiene lo stato di
analgesici
intravenosi.
analgesia
un
anestetico
mediante la somminis¬
Nella tesi inoltre si propone
un
modello per descrivere le interazioni tra farmaci anestetici.
capitolo
introduttivo si esaminano i
tomatici nella
potenziali benefici dei controlli aupratica clinica dell'anestesia. Come esempi si considerano i
particolari di un controllore della pressione arteriosa media (PAM) e
bispettrale (BIS) con l'ipnotico isoflurano. Si discutono inoltre
sia l'architettura software che tutti gli schemi di sicurezza introdotti nella piattaforma di controllo che consentono l'applicazione di algoritmi automatici
casi
dell'indice
in sala
Nel
operatoria.
capitolo
2 si descrive il controllore ad anello chiuso che
ponente ipnotica
dello stato di anestesia del
controllore basato
su
modelli dinamici per la
anestetici volatili che sia mai stato utilizzato
dei monitor per il BIS nelle sale
per lo
sviluppo
del sistema
diregolazione.ImonitorperilBISsonostatiiprimiadaverricevutoI'approvazionedella'FoodandDrugAdministration(FDA)'comemonitordiipnosidurante1'anestesiageneraleecompensanounamancanzaesistentesindallaprimaanestesiageneraleavvenutanel1846.Siriportanoesidiscutonoinlineirisultatidell'applicazionedelsistemadicontrolloinsalaoperatoria.LoschemaperlaregolazionedelBISèinattesa13
uso
paziente.
regola
la
Si tratta del
com-
primo
regolazione dell'ipnosi
su
operatorie è
esseri umani.
con
II crescente
stato lo stimolo
principale
14
di brevetto presso la comunità europea
Nel
capitolo
analgesici
primo controllore basato
stato di
esiste il
parlare
analgesia
sensore
di
negli
Stati Uniti.
3 si illustra il sistema di controllo ad anello chiuso per la
ministrazione continua di
del
e
del
paziente
modelli dinamici per
che sia stato utilizzato
ideale di questo sistema di
percezione
per defmizione
su
durante anestesia
som¬
generale. Si tratta
la regolazione dello
su
esseri umani. Non
controllo, poiché
di dolore durante anestesia totale.
è
improprio
Il dolore è difatti
esperibile solamente da un soggetto cosciente.
capitolo un sistema di controllo che mira
effetti
della
stimolazione
a sopprimere gli
chirurgica sulla PAM, un possibile
indicatore di una insufficiente analgesia. Lo scopo non prioritario del con¬
trollore è anche quello di regolare le concentrazioni di analgesico nel plasma
predette da un modello dinamico. In questo modo si consente all'anestesista
sia di dosare la somministrazione di analgesici in base ai segni clinici di una
insufficiente analgesia sia di minimizzare il consumo di droga.
una
sensazione
Con queste premesse si discute nel
capitolo
4 si propone
farmaci anestetici.
diversi ambiti della
un nuovo
modello per
quantificare
Diversi modelli di interazione
biomedicina,
dei farmaci anestetici.
Difatti
l'ipotesiprincipalesecondolaqualeognifarmaco,sesomministratosingolarmente,hauneffettosullavariabileclinicadiinteresse,nonèsoddisfattaingeneraledaifarmacianestetici.Nelcapitolo5siriassumonoiprincipalicontributidellatesi.Inparticolaresievidenzianoleproblematichechelaricercafuturadovràaffrontareaffinchéschemidicontrolloautomaticopossanoessereordinariamenteapplicatiinsalaoperatoria.
Nel
ma non
si possono
le interazioni fra
già proposti in
estrapolare al dominio
sono
stati
Contents
Foreword
3
Abstract
8
Zusammenfassung
11
Prefazione
13
1
Automatic Control in Anesthesia
1.1
1.2
19
Introduction
22
1.1.1
Problem formulation
1.1.2
The benefits of feedback controllers in anesthesia
1.1.3
The
1.1.4
Closed-loop
challenges
of the
22
operating
room
control of anesthetic effect
Modeling
...
23
24
26
27
1.2.1
The
1.2.2
Modeling
the effect of anesthetic
1.2.3
Modeling
for control of MAP
27
respiratory system
15
drugs
29
30
Contents
16
1.2.4
1.3
1.4
1.5
Controller
2
2.2
2.3
2.4
32
35
1.3.1
MAP Control
35
1.3.2
BIS Control
37
Clinical validation ol the controllers
39
1.4.1
MAP control
39
1.4.2
BIS control
42
Supervisory fonctions
46
Artilact tolerant controllers
Experimental setup
Feedback Control of
2.1
control ol BIS
design
1.5.1
1.6
Modeling for
52
Hypnosis
Introduction
55
58
2.1.1
Assessment ol anesthesia
2.1.2
Closed-loop drug
2.1.3
Goal olthis
Volunteer
49
administration and BIS
study
58
58
59
study
60
data
2.2.1
Demographic
2.2.2
Experimental setup
61
2.2.3
Study design
61
61
Modeling
2.3.1
Distribution model
2.3.2
Effect compartment
Control
design
62
63
modeling
66
73
Contents
2.5
2.6
3
76
2.5.1
Smooth transfer
76
2.5.2
Respiratory parameters update
77
2.5.3
77
Test ol the controller
81
Analgesia
85
Introduction
88
3.1.1
Intraoperative analgesic
3.1.2
Goal olthis
administration
study
88
89
3.2
Modeling
91
3.3
Control
96
3.4
5
Implementation
Feedback Control of
3.1
4
17
design
3.3.1
Controller
3.3.2
Explicit MPC
3.3.3
97
tuning
Controller
Test olthe Controller
Modeling
of Anesthetic
100
105
112
Drug
Interactions
121
4.1
Introduction
125
4.2
Isobolographic methods
126
4.3
Logistic regression
129
4.4
The two
131
4.5
The three
Conclusions
drugs
interaction model
drugs
interaction model
134
141
Contents
18
5.1
Main achievements
142
5.2
Automatic control in anesthesia
143
5.3
5.4
5.5
5.6
5.2.1
Main achievements
143
5.2.2
Outlook
143
Feedback control of
hypnosis
144
5.3.1
Main achievements
144
5.3.2
Outlook
145
Feedback control of
analgesia
146
5.4.1
Main achievements
146
5.4.2
Outlook
147
Modeling
of anesthetic
drug
interactions
149
5.5.1
Main achievements
149
5.5.2
Outlook
149
The
advantages
Bibliography
of model-based controllers
149
152
Chapter
1
Automatic Control in
Anesthesia
19
Plutarch,
nology (ETH)
collaboration
This
project
ferent scientific
methodshavethecommoninteresttoimprovethequalityoflife.Regardlessofthecausesofanapparent,yetperceivableincompati¬bility,themutualresearcheffortwhichsupportedthisthesiscontributedtobridgethegap.Theforefrontcontrolengineeringconceptscombinedwiththeultimatetech¬nologyavailablenowadaysfortheanesthesiologistsintheoperatingroommadeitpossibleforourgrouptoachieveresultswhichwerebarelyconceiv¬ablejustadecadeago.Butmoreconcretely,wheredoestheopportunityliefordisciplineslikeauto¬maticcontrolandcomputersciencetodevelopnewconceptsandproductsfortheclinicalpracticeofanesthesia?Threeinnovatingfactorsmotivateautomaticcontrolintheclinicalpracticeofanesthesia:newsensorsforthepatientmonitoring,newactuatorsforthedrugadministrationandnewshort-actingdrugs.Automaticcontrolisthescientificframeworkcoordi¬natingthethreeabovecitedelements.Duringtheinitialphaseoftheproject,severalclosed-loopcontrollerswhich
20
1 Automatic Control in Anesthesia
^.trpjujviapbévov Se tov MaxsSoisixov Spâparoa,
LP<jjpoäxov a'KEiaarjarjeïv.
The Parallel Lives
bers of both the medical and
was
that poetry and
supported by
-
lüpa
Demetrius and Antonius.
to
53,
10.
Foreword
The Automatic Control
Laboratory at the Swiss Federal Institute of Tech¬
developing a multi-task autonomous anesthesia system in
with the University Hospital in Bern.
is
the strenuous commitment of excellent
engineering community. Heidegger
philosophy reside on tall, separated mountains, yet be¬
longing to the same geographical chain. The same holds for apparently
separated disciplines like medicine and engineering, which despite the dif¬
believed
mem¬
21
regulate inspired
and
expired
anesthetic gas,
have been used in clinical studies
on
O2 and CO2
humans.
In this
concentrations
chapter
two
more
compared: control of Mean Arterial
Pressure (MAP) and control of hypnosis through Bispectral Index (BIS).
The first controller was conceived and implemented by two former members
of the institute, Marco Derighetti and Christian Frei towards completion of
complex
controllers
are
discussed and
their Ph.D. programs. The second controller is
one
of the main contribution
of the author of the present thesis. Both controllers
use isofiurane as input,
hypnotic drug inducing hypotension. MAP was considered as the main
indicator for depth of anesthesia before alternative monitoring techniques
were introduced such as BIS. One of the goals of this chapter is to demon¬
strate how the introduction of a new sensor may go as far as to trigger
radical changes in the paradigms for drug administration. BIS monitors did
already open new possibilities for clinical research. It is a strong belief of
the author that the benefits which we demonstrated in this chapter must
a
also be demonstrated in the clinical
Provided that
to
surgical
hypnosis
analgesia. It
with intravenous opiates.
described in chapter 3.
The
be assessed with BIS
can
stimulation may be
insufficient
following chapter
functions which
are
in the
room.
was
alternatively
The steps towards
also
monitors, MAP
considered
as
therefore natural to try and
gives
a
achieving
an
reactions
indicator of
regulate MAP
goal are
this latter
qualitative overview of the supervisory
application of automatic controllers
necessary for the
This
topic has been the
artifacttolerantcontrolschemesarepresented.Theexperimentalsetupandtheresultsoftheapplicationofautomaticcontrolduringclinicalstudiesarealsodiscussed.Thischapterappearedwithminormodificationsasapublicationinthescientificliteratureas:Gentilini,A.,Frei,C.W.,Glattfelder,A.H.,Morari,M.,Sieber,T.J.,Wymann,R.andSchnider,T.W.:2001,Multitaskedclosed-loopcontrolinanesthesia,IEEEEngineeringinMedicineandBiologyMagazine19,
operating
practice.
tian Frei's Ph.D. thesis. In
particular,39-53.
main contribution of Chris¬
22
Introduction
1.1
Problem formulation
1.1.1
Adequate
anesthesia
can be defined as a reversible pharmacological state
patient's muscle relaxation, analgesia and hypnosis are guaran¬
teed. Anesthesiologists administer drugs and adjust several medical devices
to achieve such goals and to compensate for the effect of surgical manip¬
ulation while maintaining the vital functions of the patient.
Figure 1.1
depicts the Input/Ouput (I/O) representation of the anesthesia problem.
The components of an adequate anesthesia are labeled 'unmeasurable' be-
where the
i.V. anesthetics
hypnosis
»
volatile anesthetics
manipuiated,
variables
%
analgesia
muscle relaxants
>
|
relaxation
unmeasurable
outputs
ventilation parameters
Nacf
EEG pattern
heart rate
>
surgical
e
disturbances
CQxonc.
stimulus
>
-
>
blood pressure
blood loss
insp/exp
Figure 1.1: Input/Output (I/O) representation
Adapted from the literature (Frei, 2000).
they
must be assessed
measurements,
as
depicted
by correlating
Fig. 1.1.
them to available
problem.
physiological
in
Muscle relaxation is induced to facilitate the
depress
outputs
cone.
of the anesthesia
movement responses to
surgical
access
stimulations.suoicn
Thedgroflax¬tincbsmyuvSwFDp()V-M.,20Aéqkj
cause
measurable
to internal organs and to
1.1 Introduction
23
(Prys-Roberts, 1987).
that clinical
Another
signs such
macing (Cullen
et
as
source
of
complexity
tearing, pupil reactivity,
al., 1972)
results from the fact
eye movement and
partially suppressed by
are
muscle
gri¬
relaxants,
vasodilators and vasopressors.
is
operative
recall of events occurred
a
general
indicating unconsciousness and absence of post
during surgery (Goldmann, 1988). Some
distinction
between conscious and uncon¬
sharp
Hypnosis
term
authors believe there is
scious states
a
In this respect it would be
improper to
However, the patterns of the electroen¬
which is the only non invasive measure of central
show gradual
nervous system activity while the patient is unconscious
modifications as the drug concentrations increase in the body. Nowadays
about
of anesthesia.
speak
depth
cephalogram (EEG)
-
-
the EEG is considered
of
as
the
major
source
of information to
assess
the level
hypnosis.
Better
accepted
measure
Mean Arterial Pressure
exist for the vital functions. Heart Rate
(MAP)
are
considered the
principal
(HR)
and
indicators for
hemodynamic stability, while O2 tissue saturation or endtidal CO2 concen¬
trations provide useful feedback to anesthesiologists about the adequacy of
the artificial ventilation.
To achieve
adequate anesthesia anesthesiologists regularly adjust the set¬
drug infusion devices as well as the parameters of the breath¬
tings
to
modify the manipulated variables listed in Fig. 1.1. This is
ing system
done based on some patient spécifie target values and the monitor readings.
Thus anesthesiologists adopt the role of a feedback controller and it is nat¬
ural to ask whether automatic controllers are capable of taking over and/or
improving parts of
acomplexdecisionprocess.1.1.2ThebenefitsoffeedbackcontrollersinanesthesiaSeveralauthorshaverecognizedtheadvantagesassociatedwiththeuseofautomaticcontrollersinanesthesia(SchwildenandStoeckel,1995;Chilcoat,1980;O'Haraetal.,1992;Derighetti,1999).First,iftheroutinetasksaretakenoverbyautomaticcontrollers,anesthesiologistsareabletoconcentrateoncriticalissueswhichmaythreatenthepatient'ssafety.
of several
such
24
Second, by exploiting
both accurate infusion devices and
monitoring techniques,
newly developed
provide drug
automatic controllers would be able to
administration profiles which, among other advantages, would avoid over¬
dosing. Moreover, they may take advantage of the drug synergies, for which
now a proper modeling framework was developed (Minto et al., 2000). The
ultimate advantage would be a reduction in costs due to the reduced drug
consumption and the shorter time spent by the patient in the Post Anes¬
thesia Care Unit
(PACU).
if tuned
properly,
Further,
sate for the interindividual
profile
to the
(Linkens
variability
and to tailor the
stimulation
drug administration
surgical procedure
of each
particular
intensity
Hacisalihzade, 1990). Ultimately, automatic controllers
research as a 'reference' anesthesiologist in clinical studies.
and
be used for
The
1.1.3
automatic controllers should be able to compen¬
challenges
of the
operating
can
room
Several
complexities were faced when designing the real-time platform to
closed-loop controllers in the operating room. The issues and the solu¬
tions adopted are summarized below.
test
•
Sensors and actuators: To
patient's
several
time
sensors
an
provide
easy
an
access
adequate monitoring of the
to the drug infusion devices
and actuators had to be assembled in the mobile real¬
platform depicted
in
Fig.
1.2.
Safety critical system: All the implemented closed-loop controllers
physiological signals which are potentially corrupted by artifacts.
They may result either from routine manipulation or calibration of
use
the
measuring devices and may cause, if not considered in the control
schemes, considerable damage to the patient (Frei, 2000). A super¬
visory system and fault tolerant controllers were embedded in the
real-time platform to detect sensor failures and/or other abnormal
Amoredetaileddescriptionofthesesafetyfeaturesoftheplatformwillbegiveninalatersection.•Modeluncertainty:Amajorsourceofdifficultyresultsfromthehighuncertaintyassociatedwiththepublishedmodelsforthe
•
vital functions and
operations.drug
t"
gah
Figure
1.2: The real-time
platform
Nevertheless, anesthesiologists are able to
variability by tailoring the drug ad¬
ministration to the single subject's needs, therefore guaranteeing an
adequate performance across the population. In order to reproduce
this, feedback controllers must be designed with robust and/or adap¬
tivetechniques.Robusttechniquestendtoleadtocontrollersforthe'worstcase'situation,whichtendstomakethemsluggish.Adaptiveschemesrelyontheexcitabilitybytheinputsignal,whichisoftenlimitedbyethicalconstraints.Ourapproachwastousebothdatacollectedfromordinarypatientsduringanesthesiaanddataacquiredfromyounghealthyvolunteersforthedesignandthevalidationoftheproposedcontrolstrategies.Clinicalvalidation:Theimprovementsfortheclinicalpracticeandthepatient'scarewhichareenvisionedfromtheuseofautomaticcontrollersinanesthesiacannotbequantifiedunlessextensiveclini¬calvalidationisperformed.ThereforetheETHprojecthasbeenputonsolidfoundationsbyestablishingaclosecooperationbetweena
1.1 Introduction
25
let t rouie
ni aima
«lifting
mm-rgmey
shui-ficjH'n
llI'i'ÄtljlJIg
for clinical studies.
distribution and effect.
compensate for interindividual
26
clinic
(University Hospital of Bern) and an anesthesia workplace
(Dräger Medizintechnik. Lübeck, Germany.). Among
ufacturer
advantages, the partnership with
directly from young healthy
data
the
hospital
technology
us
to
acquire
volunteers for model identification.
The support from the industrial partners
available
enabled
man¬
other
provided
us
with the latest
the market.
on
Up to now, six different control strategies have been tested by the ETHUniversity Hospital team on more than 150 patients during general anesthe¬
sia. These controllers regulate O2, CO2, inspired and expired anesthetic gas
concentrations in the breathing system as well as MAP and depth of hypno¬
sis derived from the EEG (Derighetti et al., 1996; Frei, Derighetti, Morari,
Glattfelder and Zbinden, 2000; Sieber et al., 2000; Gentilini et al., In press,
2001.; Derighetti, 1999; Frei, 2000).
Closed-loop
1.1.4
control of anesthetic effect
Among the several controllers presented in the last section, two Single Input
Single Output systems (SISO) extracted from the Multiple Input Multiple
Output (MIMO) control problem depicted in Fig. 1.1 will be described
extensively here: Mean Arterial Pressure (MAP) and Bispectral Index (BIS)
control.
Both feedback systems
and aim at
input
controlling
reasons
1999).
MAP decreases with
anesthetic.retal
efct.Byondha,psilumzbrgv(F195)M¬APwq'-T28HE
the
the volatile anesthetic isofiurane
as
during surgery (Frei, 2000; Derighetti,
increasing isofiurane concentrations in the in¬
motivate MAP control
Several
ternal organs.
use
the anesthetic effect.
As
such, MAP
can
be considered to be
a
direct
measure
of
1.2
Modeling
27
Hypnosis can be assessed with the Bispectral Index (BIS Index, Aspect
Medical System. Newton, Massachusetts). The BIS index is derived from
the EEG by combining the higher order spectra of the signal with other
univariate indicators such as Spectral Edge Frequency (SEF) and Median
Frequency (MF) (Schwilden et al., 1987; Schwilden et al., 1989; Shüttler
and Schwilden, 1995). This combination of indicators is necessary since,
for instance, SEF and MF can provide an estimate of the hypnotic state
at deep levels but are likely to fail in the region of light sedation (Ghouri
BIS can reveal, unlike simple Fourier
et al., 1993; Kochs et al., 1994).
analysis, the synchrony of cortical brain signals which characterizes un¬
(Rampil, 1998).
consciousness
BIS values lie in the range
100 is associated with the EEG of
awake
an
0-100, where
and 0 denotes
subject
an
iso¬
predicts accurately return of consciousness (Doi
et al., 1997; Glass et al., 1997; Kearse et al., 1994; Sebel et al., 1995) and is
the first clinical monitor for hypnosis which to date has received FDA clear¬
BIS has been developed and validated based on EEG recordings of
ance.
5000 subjects. More than 600 peer-reviewed articles and abstracts provide
electric EEG
a
signal.
BIS
clinical evaluation of BIS.
The
modeling
trollers.
issues and the control
The additional
operating
safety
design will be
required for
issues
outlined for both
the
application
con¬
in the
will also be described. Clinical results will be discussed for
room
both controllers.
Modeling
The model
required
for control has to account for two
systems: the medical devices
involving drug distribution,
1.2.1
The
A schematic
Fig.
1.2 is
(actuators
and
qualitatively different
and the physiology
effect in the human body.
sensors)
metabolism and the
respiratory system
drawing of
in Fig.
given
the
respiratory system depicted
1.3. A pump forcesof
theairintothepatients'lungswhileunidirectionalvalvesimposeafixedorientationforthecirculation
1.2
at the bottom of
28
Figure 1.3: Schematic representation of the closed-circuit breathing system.
Typical ranges for the parameters of the respiratory system (see Eq. (1.1)
for a detailed description) are : Qq
1-10 1/min, Jr
4-25 1/min, Vt
0.3-1.2 l,V
4-6 1, AQ
0.1-0.5 1/min, C0
0-5 %, expressed as isoflurane
=
=
volume percent in the
breathing
mixture.
This gas flow
through
(Qo
branch and excessive air leaves
1/min),
high
> 4
the
a
constant flush.
dynamics introduced
by the respiratory system may be neglected since a change in the fresh gas
composition is effective for the patient almost immediately. During minimal
flow anesthesia (Qo < 1 1/min) the fresh gas flow only compensates for gas
taken up by the patient and the eliminated COi through the absorber. At
such low flows the system is economically more efficient and safer for the
patient. In fact, due to recirculation, the patient breathes a gas mixture at
almost constant humidity and temperature. The expired gases are now re¬
circulated, which introduces considerable dynamics. A first principles model
of the minimal flow breathing system was derived
a
fresh gas flow is used
on one
the system leads to
tocapurehbvisfymndl(Dg,19).AwkF20IzCqj'
If
the other.
=
=
the gases. The fresh gas stream enters
on
=
=
1.2
Modeling
29
breathing parameters through
dC
V^F=QoC°where V
[1]
the
following equation:
(g° -Ag) Cmsp
-
fn{yT -A) (Cmsp -c^
(li)
respiratory system. C\ [%] is the alveolar
concentration, measured as volume percent of the
is the volume of the
concentration
or
endtidal
breathing mixture. Jr [1/min] is the respiratory frequency, Vt [1] is the
tidal volume, A [1] is the physiological dead space. AQ [1/min] represents
the losses of the breathing circuit through the pressure relief valves. Qq
and
the
Co [%]
are
the fresh gas flow and its anesthetic concentration
respiratory circuit, respectively. Cd
control system. We will refer to
Co
as
the
is the
manipulated
"vaporizer setting"
entering
variable in
in the
our
following
sections.
1.2.2
Modeling
the effect of anesthetic
The
drugs
physiological mechanisms regulating drug distribution and drug effects
only partially known. Therefore first principles modeling is almost im¬
possible. Thus one has to select from approximate first principles physiologi¬
are
(Bischoff, 1975),
black-box identificationgeneric
schemes(Jacobs,1988),andknowledgebasedmodeling.Allapproachesexhibitcertaindrawbacks.Inphysiologicalmodelsparametersarehighlyuncertainandcollectedfromdifferentsourceswhereexperimentsmayhavebeenperformedunderverydifferentconditions.Black-boxmodelsandknowledgebasedmodelssufferfrompoorextrapolationproperties.ForthedesignofbothBISandMAPcontrollers,weusedphysiologybasedmodels.Theyconsistofapharmacokinetic(PK)partdescribingthedrugdistributionintotheinternalorgansandapharmacodynamic(PD)partdescribingthedrugeffectonthephysiologicalvariablesofinterest.ThestructureofthePKpartiscommontobothcontrollers,sincebothuseisofiuraneasinput.ThePDpartdiffersinthetwomodelsandwillbediscussedinthenexttwosections.AnyPKmodelconsistsofdifferentialequationsresultingfrommassbalancesforthedrugarounddifferentcompartments(Jacquez,1985).Forthe
cal models
ith compartment
between internal
is the vector of
is the
pharmacological
properties of isofiurane were extensively documented (Eger II, 1984; War¬
ren and Stoelting, 1986; Yasuda, Lockhart, Eger, Weiskopf, Johnson, Preire
and Faussolaki, 1991; Yasuda, Lockhart, Eger 1986).
drug
we
drug
may write
Vt-^
dC
at
Cly0
(Ct)
(Zwart
=
Qt(C) (Ca
=
Ct/Rt
and outflow
et
-
(Clo)
concentration in the arterial
Ch0)
-
pool.
II,Weiskopf,Liu,Laster,TaheriandPeterson,1991),someoftheparametersinEqs(1.2,1.3)werederivedfromtheliterature.Theotherswereestimatedfromthedatacol¬lectedduringgeneralanesthesiawithisofiurane.Forfurtherdetailsontheidentificationprocedurethereaderisreferredtothepublishedliterature(Derighetti,1999;Frei,2000).Inspiredandendtidalconcentrationsaremeasuredon-lineandprovideareliableindicationofthepatient'sdruguptake.Thisrepresentsaclearad¬vantageoverintravenousdrugs,forwhichnomeasureofdrugconcentrationinthecentralcompartmentisavailable.Thisadvantagewasexploitedinbothcontrolschemesbyimposingconstraintsonendtidalconcentrationstopreventoverdosing.Inourmodelsventilationandbloodflowaredescribedasnonpulsatilephe¬nomena.Sincetheequilibrationtimeofthedrugisgreaterthantherespira¬torycycleandtheperiodofHR,thisassumptiondoesnotaffectperformanceofthecontrollers.1.2.3ModelingforcontrolofMAPTomodelthePDeffectofisofiuraneonMAP,weassumedthatthereactionofthehemodynamicsystemtothedrugdoesnotchangeduringprolongedadministration(Derighetti,1999;Frei,2000;WarrenandStoelting,
30
al., 1972):
kt(C)Ct
concentrations in the different
concentration
Since the
(1.2)
(1-3)
where
of the
Qt is the blood flow bathing the organ, Vt is the distribution volume
drug, kt is the elimination rate, Rt is the apparent partition coefficient
which macroscopically describes drug absorption and metabolism as a ratio
(Bischoff, 1975).
compartments and
C
Ca
In other words
to isofiurane
though HR is known to be strongly
coupled with MAP, it was not taken directly into account into our model.
Several tachycardie episodes have been reported during isofiurane anesthesia
and may suggest the need to model those effects (Shimosato et al., 1982).
However, it is not clear whether those episodes depend on beta sympathetic
In fact, at moderate to deep levels of
activation of barorefiex activity.
isofiurane anesthesia, two clinical investigations have reported contradictory
results concerning the activity of the barorefiex, leaving the issue unresolved
(Seagard et al., 1983; Kotrly et al., 1984).
were
no
time
considered.
varying phenomena due
modeling structure describing the hemodynamic effects of halothane
(Zwart et al., 1972) was adapted to the characteristics of isofiurane. While
halothane decreases Cardiac Output (CO), reducing thethe
perfusiontoin¬ternalorgans(Gelmanetal.,1984;SmithandSchwede,1972),isofiuranedecreasesmainlysystemicresistancethroughdilatationofthebloodvessels(EgerII,1984).WeassumedthatMAPandCOcanbedescribedthroughthefollowingPDrelationship:MAP=â(C)(1.4)Eilift(C)wheregtrepresentstheconductivityoftheithorgan,increasedbythepres¬enceofisofiuraneandQa=J2l=1Q%representsCO(Derighetti,1999;Frei,2000).Conductivitiesgtsareassumedtodependexclusivelyontheanes¬theticconcentrationinthesamecompartmentwhereasQaisassumedtodependonthearterial(A),graymatter(G)andmyocardial(M)concen¬trationsthroughtheaffinerelationships:Qa=Qa,o{^-+aACA+aGCG+aMCM)(1.5)ff,=ff,,o(1+&.crO-(1-6)QaoandgtQarethebaselineCOandconductivityintheithorgan,respec¬tively.Accordingtothepreviousdiscussion,theeffectsofisofiuranecon¬centrationsaremorepronouncedinEq.(1.6)thaninEq.(1.5)(Frei,2000).MAPmustbekeptwithinphysiologicallimitsduringanesthesiadespitesurgicalstimulations.Therefore,aphysiologicalmodeldescribingtheeffectsofskinincision,skinclosureandintubationonthesystemiccirculationwasderived(Derighetti,1999;Frei,2000).Surgicalstimulationsactivate
1.2
Modeling
31
Even
to sensitation
The
or
tolerance
32
sympathetic part
of the autonomous
nervous
stress, infection and hemorrhages do.
system,
as
other situations like
The
sympathetic system triggers a
neural and a humoral reaction. The first causes the release of norepinephrine
in the synaptic cleft, whereas the second is associated to the discharge of
norepinephrine and epinephrine from the adrenal medulla into the blood
stream. The two reactions show significantly different time constants, one
in the order of few seconds and the other in the order of a minute, which
is the characteristic time constant of blood circulation. It is expected that
the MAP reactions show the
same
distinct time constants.
These effects
during our clinical studies. A typical
example where both effects are clearly visible after a tetanus stimulation
MAP measurements expressed as deviations from
is shown in Fig.
1.4.
the value before stimulation are plotted versus time immediately after the
stimulus for one patient.
The solid line represents the prediction of the
model (1.5,1.6). This model was validated during clinical studies and the
possibility of suppressing the effects of surgical stimulation by a feedforward
compensation with isofiurane were investigated (Frei, Derighetti, Morari,
experimentally
Glattfelder and
Even
a
though
great
Zbinden, 2000).
the model for MAP
amount of uncertainties.
and sites of
surgical
pain (Petersen-Felix
1.2.4
observed
was
extensively validated,
stimulation and the different
et
Modeling
it still contains
These may result from the different types
subjects'
sensitivities to
al., 1998).
for control of BIS
To model the PD effects of isofiurane
20
unteers and have
isofiurane.
put them under
on BIS, we enrolled
general anesthesia with
consenting vol¬
AtthetimetherewerenopublishedPDmodelsdescribingtheeffectofisofiuraneonBIS.Foramoredetaileddescriptionofthestudydesign,thereaderisreferredtochapter2ofthepresentthesis.Weassumedthattheoveralldynamicmodelfromisofiuraneinspiredcon¬centrationstoBISislimitedbythedrugdistributiontotheorgans.Oncethedrugfacesthereceptorsoreffectsite,wecanassumethatthebindingoccursinstantaneously.Then,attheeffectsite,therelationbetweenBISandlocalanestheticconcentrationsisrepresentedbyastaticnonlinearity.NoneofthecompartmentsofthePKmodelcouldbeconsideredtheef-
have been
1.2
Modeling
33
Neuronal reaction
Humoral reaction
%
S
o0
o
&
c^g
8
8
°
8°8
n9^S
o
JO
°9
°^°
oôgo*
-88
o°8
o
°8n2oO°®>0 qO
a8o00oOg°0
time
ted
1.4:
versus
MAP deviations
time after
a
concentration of isoflurane.
peak)
from values before stimulation
The neuronal
components of the MAP reaction
Adapted
from the literature
feet compartment in
effect compartment
den
(o)
tetanus stimulus for
dynamics.
light
was
one
subject
(first peak)
are
at 0.5
are
distinguishable
plot¬
% endtidal
and humoral
(second
from the
plot.
(Frei, 2000).
of the arguments above.
Therefore
an
artificial
added to the model to compensate for this hid¬
The effect compartment
can
be regarded
asanadditionalcompartmentwithnegligiblevolumeattachedtothecentralcompartment.Thisassumptionensuresthatitspresencedoesnotperturbthemassbal¬anceequationsofthePKmodel.Effectsiteconcentrationsarerelatedtoendtidalconcentrationsbyafirst-orderdelay:dCedtkeO(Ci-Ce).(1.7)Theparameterkeoisreferredtoastheequilibrationconstantfortheeffect
Figure
[min]
34
site. As PD
relationship
adopted
we
ABIS
the classical
^
ABISMAx
=
Emax model:
(1.8)
where
ABIS
ABISmax
BISq
is the baseline
mum
achievable BIS.
or
=
BIS
=
BISMAX
awake state
ECso
(1.9)
-BIS0
-
(1.10)
BIS0.
value, BISmax represents
for which the effect is half of the maximum achievable.
to small concentration
subject's sensitivity
be regarded as an index
and
BISmax
=
0 since
tric EEG. In such
The
cases
of the model
high
BIS
7
represents the
at the effect site.
changes
nonlinearity. We
assumed
BISq
concentrations of isoflurane lead to
=
an
It
=
can
100
isoelec¬
0.
modeling assumptions together
with the available identification pro¬
cedure for the effect site compartment
are
discussed with
more
details in
(Yasuda, Lockhart, Eger II, Weiskopf, Liu, Laster,
Peterson, 1991; Schnider et al., 1994). It is worth
mentioghavrblyfsdPDpu¬K(G.,I201)Tc-BSF5w'zx4OjA
project.
the literature
and
the mini¬
represents the concentration at the effect site
Taheri
1.3 Controller
design
35
\\
-
M
N
-
i
^K.
-
~-^
-
05
1
vol
05
1
vol
[%]
[%]
relationships for two patients who underwent general anes¬
closed-loop BIS control. In both plots BIS values versus effect
site concentrations are represented. The solid line (
) and the dash dot
line (—
) represent the optimal fit obtained for the individual and for the
population of volunteers, respectively. Note how the patient represented in
the right plot differs from the average subject in the population.
Figure
1.5: PD
thesia with
•
—
Controller
1.3
In this section the control
1.3.1
design
to
regulate MAP
and BIS is discussed.
MAP Control
Control of MAP is
back
design
(OBSF)
performed by
means
of three Observer Based State Feed¬
controllers whose interconnection is illustrated in
where y\ and j/2 represent MAP and endtidal isoffurane
Fig.
concentrations,
1.6,
re-
36
The
spectively.
underlying
idea of the control structure is that the main
Upper Endtidal
V2,ref
Vl,ref
V2
u
p
2/1
V2,ref
ci
MAP
Lower Endtidal
Figure
1.6: Block
diagram
of the override structure to control MAP. y\ and
2/2 denote MAP and endtidal concentration measurements,
regulates MAP
under normal conditions whereas
upper and lower limit for endtidal concentrations,
C|*
u
and
respectively. C\
C|
enforce the
represents the
vaporizer
setting. Adapted from the literature (Frei, 2000).
controller
C\ regulating MAP
constraints have to be
because
orevencardiacarrest.TocomplywiththeupperlimittheoverridecontrollerC",whichisinitselfacompleteOBSFcontroller,wasintroduced.TheminimumselectorappliedtothecontrolsignalsofC\andC|*ensuresthattheupperlimity"retiscompliedwith.Aminimumendtidalconcentrationy^retmustalsobeguaranteedtopre¬ventlightanesthesiaandawareness.Thereforewealsointroducedanover¬ridecontrollerC|toensureaminimumendtidalconcentration.Thestabil¬ityanalysisoftheoverridestructurewasdoneaccordingtothepublishedliterature(Glattfelderetal.,1983;GlattfelderandSchaufelberger,
high
arrhythmias,1988).
is active under normal conditions.
imposed
on
y^.
An upper bound
isofiurane concentrations may lead to
y"ret
However,
is needed
hypotonic crisis,
cardiac
1.3 Controller
design
37
(Kwakernaak and Sivan,
1972) was modified with the additional blocks represented in Fig. 1.16
(Derighetti, 1999). A feedforward compensation term for MAP as well as
The classical state feedback controller with observer
integral
action
for the effect of
were
added for better
surgical
setpoint tracking and
stimulations and
modeling
errors,
to
compensate
respectively.
The
saturation shown in
thecontrollerparameterson-linewithoutgoingthroughthewholeLQRdesignprocess.1.3.2BISControlTocontrolBISweadoptedthecascadedInternalModelControl(IMC)depictedinFig.1.7,wherethemastercontrollerregulatesBISandtheslavecontrollerregulatesendtidalconcentrations.ThemodelofthepatientMasterSlavePatient-c62eiFigure1.7:BlockdiagramofthecascadedInternalModelControl(IMC)structuretocontrolBIS.y\andy2denoteBISandendtidalconcentrationmeasurements,respectively.ThemastercontrollerQiprovidesendtidalconcentrationreferences2/2,re/totheslavecontrollerQ^.ThesaturationblockafterQ\wasintroducedtoenforceupperandlowerlimitsfory^.2/1re/iVve/r1Pi
Figs 1.6 and 1.16 limits the fresh gas concentra¬
tions between 0% and 5%, expressed as isofiurane volume fraction in the
fresh gas flow. Therefore, an anti-windup compensation was added to cope
with the input constraints, which was not depicted in Fig. 1.16 for the sake
of simplicity. The parameters of the controller were obtained as the solu¬
tion of a linear quadratic regulator (LQR) problem (Bryson and Ho, 1975).
The controllers were parametrized with the fresh gas flow Qq, the patient's
weight and the respiratory frequency Jr such that it is possible to compute
input
38
is
split
in two
parts. The PK model P2 relating inputs
to endtidal concentrations yi and the effect
to y\
2/2
is
or
the PD
(Gentilini
controller
u
nonlinear, where the nonlinearity
relationship relating effect site concentrations to
press, 2001.). According to Fig. 1.7, the master
et al., In
Q\ provides endtidal
slave controller.
2/2,re/
vaporizer
BIS. The overall model is
represented by
BIS
at the
compartment model P\ relating
This control
the master
specified by
concentration reference values 2/2,re/ to the
forces yi to reach the reference value
loop
loop.
The theoretical
background and the tuning guidelines for IMC control sys¬
are reported in the literature (Morari and Zaflriou, 1989). Input satu¬
ration was also added to the parallel model P2 as an anti-windup prevention.
The saturation block after Q\ limits endtidal concentration references be¬
tems
tween
are
0.4% and 2.5%.
not
violated,
Constraints
but also represent
bandwidth. To compensate for
The
a
2/2,re/ ensure that the limits for j/2
clear limitation on the controller's
this, anesthesiologists
are
the range of the constraints at their convenience
parallel
model in the master
PD model around
concentration.ThisconfigurationprovedtobemorerobustwithrespecttoPDparametricuncertaintiesthanthefullnonlinearmodel.Theoffsetconcentrationsintheblockdiagramwereomittedforthesakeofsimplicity.ThetransferfunctionsoftheparallelmodelsP2andP\wereobtainedbyusingtheaverageparametersidentifiedfromthepopulationofvolunteers.ThetransferfunctionsoftheIMCblocksQ2andQiwerechosenasthefilteredinversesofthenominalmodelsP2andPi(MorariandZaflriou,1989).ThechoiceofacascadedarrangementwithIMCcontrollerscontributedsignificantlytotheacceptanceofthecontrollersintheoperatingroom.Infact,thecascadearrangementmimicstheprocedureadoptedbyanesthesi¬ologistsiftheywereaskedtocontrolBISmanually.Namely,duetolackofclinicalexperienceincontrollingthehypnosisthroughBISvalues,ananesthesiologistwouldfirsttargetaspécifievalueforendtidalconcentra¬tions.Thenshe/hewouldadjusttheendtidalconcentrationreferencesonthebasisoftheBISvalues.Inthedevelopedcontrolschemebothtasksareachievedatthesametime.Also,thedesignisaccomplishedbytuningjusttwoparameters,whichhaveadirect,clearinterpretation.Thesepa¬rametersaffecttheapproximateclosed-looptimeconstantoftheslave
narrow
on
a
referenceand
loop
is
a
able to
during
enlarge
or
anesthesia.
linearization of the nonlinear
1.4 Clinical validation of the controllers
39
controller, respectively. Further, in the ideal case when there is no
plant-model mismatch, the closed-loop trajectory tracks reference changes
with no overshoot, therefore preventing overdosing. The time constants of
the IMC filters were set to achieve nominal settling times for such con¬
trollers (defined as 90% of the steady-state value) equal to ts
2 min for
master
=
the endtidal controller and ts
=
4 min for the overall BIS controller.
Another
advantage of the IMC strategy is that the control transfer functions
can
adjusted on-line when the operating conditions of the closed-circuit
breathing system are changed. This is not unusual during surgery since
/h, Vt, Qo are often modified for several reasons. For instance, short periods
at high flows (Qo > 5 1/min) are normally used when a quick wash-out of
the drug is needed towards the end of the operation. Further, increasing
alveolar ventilation /r(V^
A) is a standard procedure to reduce high
be
—
levels of endtidal
al., 1985).
If
CO2
respiratory.enod
parmetschngdbyiolu,vwP2Qk.14CfMAFS-I065T^%Y
et
which result from
an
increased metabolism
(Chapman
40
g
i
100
8°
Strong stimulus
[
I'
-
i
-
^60
20
^1
5"
1
1-
30
40
Upper override
50
60
70
80
90
80
90
-
"05-
0^_
^
20
30
40
50
60
70
30
40
50
60
70
30
40
50
60
70
tune
[mm]
Automatic MAP
regulation during liver surgery. The first plot
references, respectively. The second plot
represents endtidal concentration measurements yi together with the upper
and lower limits y"ret an(i
y^ref- The third plot represents the vaporizer
settings during the study. In the fourth plot the active controller is depicted,
Figure
1.8:
from above
where
depicts MAP
1 denotes
C|
is
and MAP
active,
-1 denotes C%* is active and 0 denotes
active. Note that the upper override controller becomes active when
surgical
stimulation starts at t
=
50 min.
Adapted
from the literature
C\
is
heavy
(Frei,
2000).
The clinical
duration of
and type of
65
mmHg
,
performance is evaluated based on several criteria such as the
periods with MAP within ± 10% of the target value, number
critical incidents in both groups. These are periods with MAP<
systolic blood pressure BP> 160 mmHg or HR> 110 bpm.
representstheendtidalconcentrations2/2togetherwiththe
Figures 1.8,1.9 and 1.10 show a clinical evaluation of the MAP
In all figures the upper plot represents the MAP profile during
The second plot
controller.
the
study.
upper
the
vaporizer settings and the
V2*ref
notation in
and lower
Fig. 1.6,
the controller
y\rer
active and 0 denotes that
C\
the lower endtidal
C\ would tend
limits.
active
-1 denotes that
C|
is
to reduce isofiurane
settings and
endtidalconcentrationsbelowtheacceptedlimit.Atroughlyt=50min,aheavysurgicalstimulationoccurs.Tocompensateforthis,anendtidalconcentrationlargerthany"retwouldberequired.ThisactivatestheupperoverridecontrollerC",asdepictedinthefourthplotofFig.1.8.Figure1.9showsacomparisonbetweenmanualandautomaticcontrol.Uptot=192minanesthesiawasconductedmanually.Accordingtotheanes¬thesiologist,duringthisphasejustminoradjustmentsofthevaporizerset¬tingwereneeded.Att=210minautomaticcontrolstarts.Thisphaseisdominatedbyaheavydisturbancestartingatapproximatelyt=220minandaperiodofgoodregulationfromt=250minon.NotefromthesecondplotinFig.1.9thatthecontrollertendstomakemoreuseofthebandwidthofallowedendtidalconcentrationsthantheanesthesiologist,alsoasare¬sultoftheheaviersurgicalstimulationsinthesecondpartoftheoperation.Figure1.10showsaclinicalevaluationwherethecontrollerwasabletosup¬presstheeffectofsurgicalstimulationsoccurringatt=82minandt=115min,respectively.Theperiodbetweent=50minandt=80minwasnotcharacterizedbyanysignificantstimulations.Duringthisphasethelowerendtidalcontrollerwasactivetodeliveraminimumamountofisofiurane.Thefollowingconclusionscanbedrawnfromtheabovediscussion.ThecontrollerissuccessfullyabletocompensateforlightdisturbancesasshowninFig.1.8.Thelimitedcontrolactionandthefastdisturbancedynam¬icsseriouslylimittheabilitytocompensateforheavydisturbances.Theselimitationsalsoapplyformanualcontrol.Thereforeweexpectthatthe
41
The third and fourth plots represent
controller, respectively. According to
is active.
active, +1 denotes that C|*
=
the override selector often switches between the MAP controller
consequently dif-
is
In
is
Fig. 1.8 the MAP profile under automatic control during a liver surgery
represented. The controller is able to achieve good performance during
the periods of light surgical stimulations occurring at t
38 min and t
89 min. Note that during the period of light stimulation (t
20-35 min)
=
=
C| even though
acceptable range. Presumably, this is a result of the particular sensitivity of
the patient's MAP to isofiurane during the unstimulated period. In this case
endtidal concentrations lie within the
C\ and
42
^100
-
Strong stimuli^
K
"
g
80
>^
60
-
140
1 b
160
180
L
'
-
200
220
240
/~"'\
'-
"
--
,
V
~-^.
*~
0 L
4
-"'
*
^
2Î
'
1
05
CT
260
_
„
^
^~~~
,
-
,
180
200
220
240
260
280
180
200
220
240
260
280
220
240
260
280
-
o
25
2
-
oL_
1
-
^
140
160
180
200
[mm]
time
Figure
1.9:
Comparison
of manual and automatic
tomatic control starts at minute t
the variables in each
plot
plot,
see
=
the
heavier
surgical
regulation
a
caption of Fig.
that automatic control makes
concentrations than the
210 min. For
of
use
anesthesiologist.
a
detailed
1.8.
of
Note in the second
wider bandwidth of endtidal
This
presumably
stimulations in the second part of the
from the literature
of MAP. Au¬
description
results from the
operation. Adapted
(Frei, 2000).
ference between manual and automatic control will not be substantial. An
intuitive way for
improving blood
troller with information about
(Frei, Derighetti, Morari,
now
being
1.4.2
tested in first
pressure
major
Glattfelder and
pilot
regulation
is to
provide
the
con¬
future disturbances like skin incision
Zbinden, 2000).
This
approach
is
studies.
BIS control
Forty ASA-class I to
dominal, orthopedic,
III
patients aged
thoracic
or
20 to 65 scheduled for elective ab¬
neuro-surgery
are
enrolled in the clinical
I
80
^
60^
|*
50
o
L
60
,
,
,
70
80
90
100
43
|
,
,
,
110
120
130
140
,_
150
i
i
i
i
i
i
i
i
i
i
i
50
60
70
80
90
100
110
120
130
140
150
50
60
70
80
90
100
110
120
130
140
150
time
z
[min]
regulation of MAP during neurological surgery
episodes
regulation were performed. For a detailed
description of the contents in each plot, refer to the caption of Fig. 1.8. Note
that the lower override controller C| is active during the first period (t
50-80 min) of light surgical stimulation to guarantee a minimal anesthetic
Figure
1.10:
for which
Automatic
no
of manual
=
administration.
evaluation of the BIS controller.
The goal of the study is to determine
closed-loop titration of isofiurane to target spécifie values of BIS
improves the quality of anesthesia. Time to eyes opening after interruption
of drug administration, average time spent by the patient in the PACU
will be recorded together with episodes where BIS was outside the range
30-70. These periods indicate excessive and insufficient level of hypnosis,
respectively. The study is in progress. Figure 1.11 shows the performance
of the controller during a discus hernia removal. To the best of the authors'
knowledge, this is the first model-based closed-loop controller for hypno¬
whether
sis assessed with BIS
humans.
using volatile anesthetics which has been tested
The controller
was
able to
keep
on
BIS in the range 40-50 and to
44
100
120
140
160
180
200
220
100
120
140
160
180
200
220
_
/
_
i
t
i
t
±
t
100
120
140
160
180
200
220
time
plot
the
follow
[min]
In the upper
are
•
changes
in the reference
the first and second
uncertainty
plot
This is
1.11.
was
expected,
are
less
was
started at t
decreased from
Qo
=
3
=
70 min.
1/min
to
Qo
At t
=
1
=
comparing
since the model
dynamics
Further,
to
a
higher level,
at low flow conditions.
The auto¬
80 min the fresh flow
1/min
to minimize
consumption. The supervisor recognizes the changes
setting increased immediately
of
noisy than the BIS.
system and updates the model in the controller. As
slower
performance
apparent when
1.12 shows another clinical validation of the controller.
matic controller
thetic
Fig.
as
is lower for the PK model than for the PD model.
endtidal measurements
rate
in
The
signal appropriately.
the slave controller is better than the master,
Figure
:
plot BIS and BIS reference values during closedrepresented. In the second plot endtidal reference concen¬
) and measurements 2/2 (• •) are depicted. In the lowest
2/2,ref (
vaporizer settings are represented.
Figure 1.11:
loop control
trations
-•
I
0
a
anes¬
in the
breathing
the
vaporizer
result,
which compensates for the
Note also that the
input
at the
45
60~
-
>7
'V'VI
40 ;
'
"'; "''"i~<:
''
'
20100
110
120
130
140
150
160
100
110
120
130
140
150
160
130
140
150
160
25
=3
2
5
1 5
""
1
05
,
Bumpless
transfer
Flow reduction
£1
2-
60
70
80
90
100
110
time
Figure
1.12: The
tion of
Fig.
plots
illustrate the clinical
1.11. Automatic control
120
[mm]
was
study
as
started at t
described in the cap¬
=
70 min and the fresh
3 1/min to Qq
1 1/min at t
80
Qq
min. The supervisor implements instantaneously a higher vaporizer input
to compensate for the slower dynamics of the actuator at low flows.
gas flow rate
was
vaporizer does
trol at t
a
=
not
reduced from
=
=
=
change across the switch from manual to automatic con¬
bumpless transfer procedure was designed to provide
70 min. A
smooth transition between manual and automatic anesthetic administra¬
tion.
The mathematical details of the
procedure
are
reported
in
chapter
2.
comparing the performance of
Namely surgical stimulations are not
and therefore the hypnotic state
as much as they do af¬
affecting BIS
fect MAP. This is expected, since consciousness is depressed with lower
anesthetic concentrations than the stress response and particularly hemo¬
dynamic reactions. The question is then whether isofiuranedesu
Interesting
conclusions
can
be drawn when
the MAP and the BIS controller.
-
shouldbe
-
46
regulate
natural to
use
or
it to
BIS.
regulate
Supervisory
1.5
The
BIS
MAP. Isofiurane
being a hypnotic, it would seem more
However, this also depends on the anes¬
thesiologists' confidence in the BIS values. A meaningful control objective
would be to administer isofiurane to regulate BIS while maintaining MAP
within specified limits.
to
functions
supervisory functionality
may be
regarded as the superposition of all
wrapped around the basic feedback
routinely applicable in the operating room.
the necessary functions that have to be
control
algorithms
to make them
Even
though the need for supervisory functionality for automatic control
application in anesthesia has clearly been recognized by a number of re¬
searchers, not all of them implemented them in real practice (Furutani
Often just a brief outline of the neces¬
et al., 1995; Kwok et al., 1997).
sary supervisory functions is presented (Fukui and Masuzawa, 1989; Mar¬
tin, 1994; Martin et al., 1992; O'Hara et al., 1992; Isaka and Sebald, 1993;
Woodruff, 1995). A supervisory system was implemented in our real-time
platform according to the scheme represented in Fig. 1.13. Four main layers
can
be identified.
D
Input and output conditioning: The measurements pass an input
conditioning stage as they enter the anesthesia system. This includes
preprocessing of the signals, selection of the most trusted one out of a
set of multiple measurements and rejection of measurement artifacts.
Similarly, the control signals pass through a comparable output condi¬
tioning stage. Typical tasks of this part are the shaping of test inputs
for Fault Detection and Isolation
override controller
or
(FDI),
the min-max selection of
an
the switch from manual to automatic control.
state of the process
stored,includingcontrollerstates.Typically,thisinformationisstoredindatabanks.Fromtherethedataareaccessedforstorageorfor
C Process information: At this stage all the data available about the
aredisplay.
1.5
Supervisory
functions
47
Anesthesiologist
Level
Signal conditioning
D
Input
Output
Control variables
Measurements
Figure 1.13: The different layers of supervisory functions. At the lower
level physiological measurements and output for the actuators pass through
a signal preprocessing stage. For instance artifacts in the measurements are
rejected during this phase. At the top level, the Man Machine Interface is
represented. Adapted from the literature (Frei, 2000).
B
Algorithmic layer: This incorporates feedback controllers, Super¬
Logic Control (SLC), Fault Detection and Isolation (FDI) al¬
gorithms, as well as decision support functions. The separation into
layers Bl and B2 separates dynamic from logic control. At this stage,
visor
for
instance,
ogist
transition conditions
are
checked to allow the anesthesiol¬
to switch to automatic control. FDI functions
detecting
faults in the system. This may include
disconnected
are responsible for
equipment faults like
sensors or leaks as well as the detection of critical phys¬
iological patient states like excessive blood losses. Decision Support
(DS) makes suggestions to the anesthesiologist on how to optimize the
anesthetic procedure. It provides information that can not be directly
read off from monitors. Typical examples are the display of the esti-
48
mated time required for the patient to wake up
drug application or the estimated concentration
after termination of
of anesthetics in the
different compartments.
A Man Machine Interface
layer
(MMI):
and it is therefore drawn
structure.
and vice
Every
versa
plemented by
This is the most
the top
layer
graphical
through
user
is also
part of the MMI. As
during
BIS control is
depicted
in
oriented
supervisory
anesthesiologist
typically im¬
the MMI. The MMI is
interface
an
user
of the
information from the system to the
has to pass
a
as
(GUI)
example the
Fig. 1.14.
but any acoustic alarm
control
panel adopted
Operating panel for closed-loop regulation of hypnosis, (a)
which displays parameters of the breathing system, BIS and
the actual control action; (b) buttons for the switch between passive, manual
and automatic control; (c) buttons to inform the controller about significant
events such as skin incision, skin closure and intubation; (d) BIS controller
panel, where the reference BIS is selected together with tolerable limits
Figure
Central
1.14:
panel
for the endtidal anesthetic
troller and
reliability
concentration; (e) information about
active
con¬
of both BIS and endtidal concentration measurements.
1.5
Supervisory
functions
49
The detailed discussion of all the
of the present
we
will focus
supervisory functions is beyond the scope
chapter but can be found in the literature (Frei, 2000). Instead
on a particular aspect of the supervisory system which is the
treatment of measurement artifacts.
Artifact tolerant controllers
1.5.1
4-
3-
2
1
S
time
Figure
1.15:
Example
of
an
10
[mm]
untreated artifact
control of endtidal anesthetic concentrations.
isofiurane concentration references
(—
•
—
)
occurring during
In the upper
automatic
plot,
and measurements
(
endtidal
)
are
plot, vaporizer settings are represented. Note that
the short disconnection of the sampling line is interpreted by the controller
It therefore reacts
as an absence of anesthetic in the breathing system.
by injecting instantaneously a large amount of anesthetic which delays the
settling time of the step response. Adapted from the literature (Frei, 2000).
plotted.
In the lower
Several authors listed the undesirable
implications
of
non
proper artifacts
50
handling during closed-loop control in anesthesia for the patient (Ruiz et al.,
1993; Reid and Kenny 1987; Fükui and Masuzawa, 1989). A minor conse¬
quence is illustrated in Fig. 1.15. Here a model-based endtidal controller
is supposed to lower endtidal isofiurane concentrations from 1.3% to 0.7%
as indicated by the dashed line.
During this maneuver an automatic cali¬
bration of the monitor occurs during which a zero value is provided for the
concentration measurement. This sudden change in the controlled output
causes the controller to fully open the vaporizer. Although the artifact ter¬
minates after 20 s,
enough isofiurane has been supplied to the system to
considerably overshoot and prolong the maneuver. Fortunately, this situa¬
tion only deteriorates the controller performance but there are no critical
consequences for the patient here. On the other hand artifacts in the blood
pressure signal might lead to sharp decreases of blood pressure during MAP
control. An example of such critical transients is documented by Fukui and
Musuzawa (Fukui and Masuzawa, 1989). Luckily, we have not encountered
such
a
situation.
I
w
5
-A,B,C,D
V
L
k/s
i,
-A,B,C,D
K
Vi
1.16:
Feedback
Artifact tolerant control schemes for Observer Based State
(OBSF)
the residuals which
controllers.
are
The nonlinear functions
corrupted by
tp
and
-01
artifacts and which may lead to
exclude
degradationofthecontroller'sperformance.Adaptedfromtheliterature(Frei,2000).Beforepresentingoursolutiontotheartifactproblemweinvestigatehowartifactsdeterioratecontrollerperformance.Figure1.16representsa
Figure
seriousclassi-
In
be
Supervisory
cal OBSF controller where
imation of the
developing
In
states
x
e.g. with
a
The artifacts
the strategy
Fig.
v(t)
w(t)
spectively. S(t) represents the
1.16
and
computed considering
Kaiman filter
S(t),
integral
system represented by the
we
will work with
of the system. The matrix L for
a
unlike white measurement
thecontrollerintwoways.First,throughtheoutputinjectionmatrixLartifactsleadtoamismatchbetweenobserverstatesandsystemstates.Second,theyleadtoanoffsetoftheintegralpartofthecontroller.Thismismatchbetweencontrollerstatesandrealitycanbeviewedasacontrollerwind-up(Kothareetal.,1994).AnaturalremedytopreventartifactsfromdegradingthecontrollerperformanceistomakesurethattheartifactsS(t)donotentertheobserverequations.Inastochasticframeworktheerrorsignaley(t)=y(t)—y(t)representsavectorvaluedzeromeanandwhitestochasticprocess(Bar-ShalomandFortmann,1988).Ifv(t)andw(t)arezeromeanwhitenoiseprocessesandanartifactoccurs,ey(t)isnotzeromeanbuthasameanofS(t).Thusthedetectionofanartifactbasedontheinnovationssignaley(t)isequivalenttodetectingasuddenshiftinthemeanofey(t).Thetestforthezeromeanhypothesismaybeformulatedasastatisticaldecisionbasedontheactualvalueofey(t).IncaseofanartifactthecorrespondingoutputinjectionvectorissettoLi=0whichpreventstheartifactfromenteringtheobserverequations.Thestatisticaldecisionmayberepresentedbyadiagonalnonlinearblockf(ey(t))multiplyingtheinnovationsey(t).Thatis:UeyM)-eyM={e0yM;£$^|(LH)whereTtisaspécifiethresholdvalue.WithamoregeneralnonlinearityV'(ey(t))=diag(V'i(eyi(t)),...,VP(eyp(t)))
1.5
functions
51
V have been introduced.
action and the feedforward
artifacts. The observer
update
or
serves
process and measurement noise
process
compensator
state space matrices
linear time invariant approx¬
represent process and measurement
A, B, C,
noise,
of the observer states
design.
noise, affect(1.12)
D.
to estimate the
re¬
characteristics,
can
52
the observer
dynamics
it(t)
Typically i>i(eyji(t))
analogous approach
become:
=
Ax(t)
+
is such that
Bu(t)
V'j(O)
+
=
LV>(ey(t))ey(t).
1 and
tpt(—oo)
(1.13)
V^00)
=
may be taken to exclude artifacts from the
=
0.
An
integrator
equation.
With the nonlinear modification introduced in
the feedback system must be checked
trasformed into the
following
anew.
Eq.
To do
(1.13)
this,
the
stability
the system
can
of
be
form:
ey
è
=
G(s)ë+
=
A(ey)+z2
(1.14)
zi
(1.15)
G(s) incorporates the linear time invariant parts of the closed-loop
system and A contains the nonlinear weighting functions. Using Integral
where
Constraints
when time
(IQC)
varying
or
The nonlinear modifications
such that the
case.
More
one can
uncertain
4>l{eyz)
check the
systems
stability
are
of the output
of
Eqs (1.14,1.15)
included in the A-block.
injection have
to be chosen
of the observer does not suffer in the artifact free
performance
precisely they must
be chosen such that the
noiseonthesignal(eyJdoesnotleadtoaninactivationoftheobservercorrections.Theartifactsuppressionschemewasextensivelytestedduringtheclinicalvalidationofthemodel-basedendtidalcontrolleraswellasforMAPandBIScontrol.InthislattercasetheconceptswereadaptedtotheparticularstructureofthecascadedIMCcontroller.Figure1.17showstypicalcaseswhereartifactswereproperlydetectedwithoutperformancedeterioration.Inparticular,thelowerplotinFig.1.17showsthecorrectbehaviourforanartifactlastingforapproximately5min.1.6ExperimentalsetupWhenitcomestotheroutineapplicationofautomaticcontrollersonpa¬tients,considerableattentionmustbepaidtoaproperHardware/Software(HW/SW)platform.Intheearlyphaseoftheprojectthecontrollerswere
Quadratic
even
normal
Experimental setup
1.6
53
Sensor disconnetion
time
Figure
1.17: In both
(
trations
(—
)
)
as
plots
well
as
measured
[min]
inspired (
endtidal concentrations
)
and endtidal
predicted by
concen¬
the observer
represented. The plots demonstrate the successful suppression
during sensor calibration and disconnection, where no endtidal
measurements are available. Adapted from the literature (Frei, 2000).
•
—
are
of artifacts
implemented
under Modula II
the necessary
platform
A/D
and
suffered from
a
D/A
on an
MS DOS
number of
shortcomings,
real-time and multi
adequate
user
supported
conversion boards
industrial PC with
(Derighetti, 1999).
such
as
poor
support of
tasking features, lack of software components
interfaces and compiler limitations.
to
design
host (PC) computer system provides
experimental platform (Frei, 2000). The oper¬
ating system XOberon from the Robotics Institute of ETH provides the
required real-time and multi task features (Wirth and Gutknecht, 1993).
The applications are implemented using the object oriented programming
language Oberon, a member of the Pascal-Modula family (Kottmann et al.,
Currently
a
target
(VME PowerPC)
This
the hardware basis for the
-
54
2000). Making use of the object oriented technology a framework has
developed which efficiently allows to write new control applications.
The
platform
is
depicted
in
puter system equipped with
thesia workstation from
Fig.
a
1.2. The
compact integration of the
touch-screen
Dräger Germany
on
a
standard CiceroEM
contributes
acceptance of this prototype system in the
general
the platform
is endowed with
an
significantly
operating
been
com¬
anes¬
to the
room.
Also,
emergency shut-down button which cuts
any active controller off and transfers the
to the
been
regulation of the breathing system
dosing. Recently an i.v. pump has
infusion of analgesics.
manual
anesthesiologist through
integrated for the continuous
The design of the MMI aimed at reproducing closely the standard moni¬
toring systems for anesthesia. This way anesthesiologists are able to run
closed-loop controllers without any engineering support. An example
operating panel was already presented in Fig. 1.14.
of
an
Chapter
Feedback Control of
2
Hypnosis
2 Feedback Control of
56
Vous les connaissez?
Hugo.
Hoederer.
Oui. Tu
Hugo.
Non.
Jean-Paul
Hypnosis
Sartre,
entendu
as
(Ils écoutent.)
Les
mains
un
bruit de moteur?
Non.
sales. IV
Tableau,
Scène III.
Foreword
In this
chapter the model-based closed-loop control system which regulates
hypnosis with the volatile anesthetic isofiurane is discussed in detail. Hyp¬
nosis is assessed by means of the Bispectral Index (BIS), a processed pa¬
rameter derived from the electroencephalogram (EEG). Isofiurane is admin¬
istered through a closed-circuit respiratory system. The model for control
was identified on a population of 20 healthy volunteers. It consists of three
parts: a model for the respiratory system, a pharmacokinetic (PK) and a
pharmacodynamic (PD) model to predict BIS at the effect compartment.
A cascaded Internal Model Controller (IMC) is employed. The master con¬
troller compares the actual BIS and the reference value set by the anes¬
thesiologist and provides expired isofiurane concentration references to the
slave controller.
concentration
Several
advantages
factor for the
•
•
The slave controller
of the model-based
success
the controller is
anti-windup
of this controller
designed
measures
the fresh gas anesthetic
to
approach
are
adapt
which revealed to be
worth to be mentioned
to different
a
key
:
respiratory conditions
protect against performance degradation in the
event of saturation of the
•
maneuvers
entering the respiratory system.
input signal
fault detection schemes in the controller cope with BIS and
expired
concentration measurement artifacts.
The results of 4 clinical studies
are
presented
performed
in the thesis. Two of them
in the
were
operating room on humans
already discussed in chapter
57
1. In the
following chapter
two other clinical validations
control structure is under patent
pending
in both the
are presented. The
European Community
and the United States of America.
This
chapter
can
be found with minor modifications
scientific literature
as a
publication
in the
as:
Gentilini, A., Rossoni-Gerosa, M., Frei, C, Wymann, R., Morari, M.,
Zbinden, A., Schnider, T.W.: 2001, Modeling and closed-loop control of
hypnosis by means of Bispectral Index (BIS) with isoflurane, IEEE Trans¬
actions on Biomedical Engineering, In press.
58
Hypnosis
Introduction
2.1
Assessment of anesthesia
2.1.1
We
already discussed the définition of anesthesia as an adequate combina¬
hypnosis, analgesia and muscle relaxation in the introductory section
of chapter 1. We briefly outlined how to measure muscle relaxation and we
pointed out the difficulties in assessing analgesia intraoperatively. This lat¬
ter aspect will be discussed in more details in chapter 3. This chapter will
be devoted to the methods to measure and control the patient's hypnosis
intraoperatively.
tion of
is associated with unconsciousness and absence of
Hypnosis
tive recall of
intraoperative
events
(Goldmann, 1988).
post
opera¬
With the electroen¬
cephalogram (EEG) the brain activity can be measured non-invasively.
Anesthetics change the pattern of EEG. These changes can be quantified
and correlate with the drug concentration. The EEG has been used as a
measure of depth of hypnosis.
However, several difficulties are associated
with the use of EEG as a measure of the degree of unconsciousness (McEwen
et al., 1975). Unlike the electrocardiogram (ECG), the EEG has no cyclic
patterns and statistical techniques must be used to extract useful infor¬
mation. Moreover, while most anesthetics affect the EEG, they do so in
different ways (Stanski, 1990): for instance, high doses of opiates produce a
slow paced, high voltage EEG whereas hypnotic agents induce 'burst sup¬
pression', short periods of time where the EEG is isoelectric (Muthuswamy
et al., 1999).
2.1.2
Closed-loop drug
administration and BIS
Several feedback controllers for anesthesia have been
ature.
of the
physiological signal
andLinkens,1997;MahfoufandLinkens,1998;Rossetal.,1997;Ritchieetal.,1985).Concerninganalgesia,wherenoreli¬ablemeasureexists,itwasnotedthatthepatient'sautonomicresponsestopainfulstimulationsarepresentbothintheawakestateandwithhypnotic
bility
proposed in the liter¬
strongly depends on the relia¬
controlled, as in the case of muscle
The effectiveness of such controllers
relaxation
(Mahfouf
to be
2.1 Introduction
59
analgesic agents (Pinsker, 1986). A pragmatic task would be to deliver a
drugs to obtund them. Hemodynamic variables such as
Mean Arterial Pressure (MAP), Cardiac Output (CO) and Heart Rate (HR)
have been considered in this respect (Isaka and Sebald, 1993). MAP control
is also crucial during surgery to improve surgical visibility and to guarantee
adequate perfusion to internal organs (Furutani et al., 1995). Since most
volatile hypnotics also depress MAP (Warren and Stoelting, 1986), yet by
different mechanisms of action (Murray et al., 1992; Monk, 1988), they
and
sufficient amount of
used as input variables in several feedback schemes (Prys-Roberts and
Millard, 1990; Millard et al., 1988; Frei, Gentium, Derighetti, Glattfelder,
Morari, Schnider and Zbinden, 1999).
were
Concerning hypnosis,
quency
(SEF)
several univariate parameters like
and Median
Frequency (MF)
can
Spectral Edge
Fre¬
be extracted from the spec¬
tral characteristics of the EEG and have been used
as
controlled outputs in
closed-loop system (Shüttler
Schwilden, 1995;
al., 1987;
al., 1989). All the mentioned quantities can provide an esti¬
mate of the hypnotic state at deep levels. However, they are likely to fail in
the region of light sedation (Ghouri et al., 1993; Kochs et al., 1994). Bispectral analysis computes higher order spectra of EEG which can reveal phase
couplings of single waveforms. Together with multivariable statistical analy¬
sis this feature is the main foundation for the Bispectral Index (BIS,
a
and
Schwilden et
AspectMdialSymIn.Nwo,hu)TBEG¬rvbf(R198D7;K45g0j6-23
Schwilden et
60
Hypnosis
one hand, the use of volatile
complexity of the respiratory system. On the
other hand expired concentrations provide a useful indication of the drug
concentrations in the body.
intravenous
agents
are
used for control. On the
anesthetics introduces the
To the authors' best
knowledge
this work describes the first
system to control BIS with volatile anesthetics.
model identified from
In this
experiments
on
closed-loop
The controller based
on
a
humans.
study which provided the
dynamic model to predict BIS. It is followed
by an analysis of the data and a description of the model structure. Subse¬
quently, the control design is outlined. Not withstanding its increasing pop¬
ularity, BIS is still under development and evaluation. Therefore we must
guarantee the patient's safety in those situations where BIS is corrupted
by artifacts and therefore not unreliable as a feedback signal. To achieve
this, a cascade arrangement was used which maintains expired anesthetic
concentrations between acceptable limits. When switching from manually
administered anesthetic to closed-loop control the continuity of the control
action is guaranteed providing a smooth transition. Moreover, we discuss
the procedures which guarantee safe performance of the controller in the
presence of artifacts in both BIS and expired concentration measurements.
chapter
we
data necessary to
Finally,
patients
2.2
The
first describe the volunteer
identify
a
the results obtained from two
are
presented
particular
tests of the controller
on
and discussed.
Volunteer
study
were designed to explore the effects of the hypnotic isofiuanalgesic alfentanil on several clinical end-points such as BIS,
Another goal of the study was to
raw EEG and hemodynamic variables.
determine the reactions of such end-points to experimental painful stimuli,
which may be used to define depth of anesthesia (Petersen-Felix et al., 1996).
rane
experiments
and the
2.2 Volunteer
2.2.1
study
61
Demographic
data
Twenty consenting volunteers of physical status ASA I were enrolled for
study. The age group considered was 25 ± 3 years, weight was 68± 13
kg. The subjects were randomly assigned to two groups. In the first group
alfentanil targeted concentrations were varied whereas endtidal concentra¬
tions of isofiurane were kept constant. In the second group isofiurane was
varied and alfentanil was kept constant.
the
2.2.2
Zipprep®
Experimental setup
electrodes
ommended
by
were
secured
on
the
subjects
in frontal
the manufacturer of the BIS monitor.
position,
as rec¬
Raw EEG and BIS
monitored with Aspect A-1000 monitor (Aspect Medical Systems Inc.
Newton, Massachussets). The electrodes' impedance was kept under 3 kil.
The sampling frequency of the raw EEG signal was 128 Hz. The sampling
frequency of BIS was 5 s. Arterial pressure was measured invasively with a
catheter cannula inserted into the radial artery. Electrocardiogram (ECG),
O2 saturation in the tissues, gas concentrations in the breathing system
were recorded at 100 Hz with a Compact AS/3 monitor (Datex-Ohmeda
Division. Helsinki. Finland). Inspired and endtidal O2, CO2, sevofiurane
and isofiurane concentrations were also calculated during every breathing
cycle and stored as volume percentages by Compact AS/3 monitor. Mus¬
cle relaxation was monitored continuously with the Train Of Four (TOF)
procedure. A high frequency (128 Hz) event marker was used to track sig¬
nificant events during the study such as the begin and end
ofeachpainfulstimulation,occurrenceofmovementresponsesandbloodsampling.Hemo¬dynamicdata,aswellasrawEEGandBISwereacquiredwithLabview5.0underWindowsNTforoff-lineanalysis.2.2.3StudydesignBeforeinduction,baselinevalueswererecordedforapproximately10minwhilethesubjectswerebreathingpureO2withafacemask.Generalanes¬thesiawasinducedbythesinglebreathtechniquewithamixtureof7%
were
62
60 %
N2O Bolus doses (0
sevoflurane
in
urium were
administered after loss of
15
eyelid
Hypnosis
mg/kg body weight)
of
mivac-
reflexes to facilitate intubation
Respiratory parameters during assisted ventilation were adjusted to main¬
CO2 partial pressures between 35 and 40 mmHg Fresh gas
flow was set to 6 1/min Body temperature was kept in the range 36 5-37 C
Hypnosis was maintained by continuous administration of isofiurane with
tain endtidal
°
the autonomous closed-circuit respiratory circuit Cicero
(Drager
Medizin-
Lübeck, Germany) Alfentanil was delivered through the in¬
Harvard Apparatus 22 Targeting infusion policies algorithms
techmk GmbH
fusion pump
maintained
DOS
constant level of
a
The infusion
policies
is
was
defined
alfentanil and
a
concentration
in
the
plasma
software STANPUMP under
wereappliedinarandomizedsequenceArterialsamplesofisofiuraneandalfentanilwerecollectedThesamplingoccurredduringboththetransientphaseswhenthetargetconcentrationsofboththeanalgesicandthehypnoticweremodifiedandduringsteady-stateAttheendofthestudy,alfentanilinfusionwasstoppedandthefreshgasconcentrationofisofiuranewassettozeroatthesametimeThesubjectswereextubatedassoonastheyopenedtheireyesaftertheirnameswerecalled2.3ModelingThemodeldevelopedforcontrolconsistsofthreeinteractingpartsade¬scriptionoftherespiratorysystem,amodelfortheuptakeanddistributionofisofiuraneandaneffectcompartmentmodeltodescribethetimecourseoftheBISThemodelfortherespiratorysystemwasalreadypresentedinchapter1Thedynamicsoftheclosed-circuitrespiratorysystemare1STANPUMPisfreelyavailablefromtheauthor,StevenLShafer,MD,Anesthesi¬ologyService(112A),PAVAMC,3801MirandaAve,PaloAlto,CA94304
by
a
at 7 different
steady-state combinations of hypnotic
phase lasting for approximately 20 mm Each com¬
constant level of predicted plasma concentration of
constant level of endtidal concentration of isofiurane
physiological
mental stimuli
kept
with each
analgesic,
bination
the
predicted drug
computed with the
1
Each volunteer
and
were
variables reached the
steady-state values,
When
different experi¬
2.3
Modeling
63
Parameter
Table 2.1:
and
Mammillary
colleagues.
described
2.3.1
mean±SD
[min 1]
kn
1.26 ±0.204
ki3
0.402 ±0.055
ku
0.243 ±0.072
kis
0.0646 ±0.0414
&20
0.0093 ±0.0137
kii
0.210 ±0.082
hi
0.0230 ±0.0156
k41
0.00304 ±0.00169
hi
0.000500 ±0.000119
rate constants of the PK model
published by
Yasuda
by Eq. (1.1).
Distribution model
Isoflurane is carried to the internal organs
by
the
systemic circulation and
depress
activity. As a result, the
of
isoflurane
concentrations
uptake
high
might be slower
than at low concentrations. Several publications report the pharmacologic
properties of isoflurane (Eger II, 1981; Eger II, 1984). Isoflurane decreases
most volatile anesthetics
cardiovascular
and distribution at
arterial pressure to the
same
extent
as
halothane and Enffurane do
(Warren
al., 1992). However, with isoflurane the
decrease is the result of a reduction in systemic resistance (Graves et al.,
1974) whereas for halothane it is mainly a result of a lowered Cardiac Output
(CO) (Prys-Roberts et al., 1974; Lynch, 1986). In fact, at 2.6% endtidal
concentrations of isoflurane, the CO is reduced by only 10% relative to the
and
Stoelting, 1986; Murray
baseline value
(Collins, 1996).
characteristics of isoflurane
colleagues
are
Therefore
have identified
for the distribution of isoflurane
we
not affected
Lockhart,EgerII,Weiskopf,Liu,Laster,TaheriandPeterson,1991).ThecompartmentsaredepictedinFig.2.1.ThemammillaryrateconstantsarereportedinTab.2.1.
Yasuda and
et
(Yasuda,
a
assume
that the distribution
by hypotension.
mammillary compartmental
model
64
Îr(Vt
—
A) (Cinsp
—
Hypnosis
C\]
Figure 2.1: The mammillary compartment model published by Yasuda and
colleagues (Yasuda, Lockhart, Eger II, Weiskopf, Liu, Laster, Taheri and
Peterson, 1991). The concentrations in the central compartment (1) rep¬
resent endtidal
expiration cycle
concentrations,
or
equivalently
i.e.
the concentrations at the end of the
alveolar concentrations.
In their
experimental setup young healthy volunteers received a mixture
composed by 1% sevofiurane, 0.6% isoflurane, 34.4% O2 and 64% N2O for
30 min. Synergies between volatile anesthetics at the distribution level can
be neglected (Vuyk, 1997). Endtidal samples were collected during the ad¬
ministration, in the following 23 hours and every morning for the next 6-7
days. The number of compartments was established by statistical testing
on
the model residuals to avoid
partments
were
overparametrization. A posteriori, the
associated with groups of internal organs
their time constants.
on
com¬
the basis of
Compartments 2 and 3 have fast dynamics and are
Group and the Muscles, respectively. Com¬
partments 3 and 4 are notably slower and are associated with fat compart¬
ments. By using the published partition coefficients of isoflurane (Yasuda
et al., 1989), it is perfusing
possibletoestimatethevolumesV3andthe
associated with the Vessel Rich
2.3
Modeling
65
1
Table 2.2:
suda and
[1] (meaniS'.D)
Volumes
Compartment
2.31±0.71
2
7.1±2.5
3
11.3±5.6
4
3.0±0.7
5
5.1±4.1
Volumes of the
mammillary compartments
as
published by
Ya-
colleagues.
blood flows
Qj
of the internal organs
y3
as:
_vLkll
(2.1)
=
Rj kji
(2.2)
Qj-- V3 R3 k3l
=
The volumes of the compartments
inspection of the data
are
reported
in Tab. 2.2. Based
the
mass
assumed that alfentanil does not
on
visual
modify the distri¬
bution characteristics of isofiurane. Therefore we adopted the distribution
model described by Yasuda and colleagues as a PK model. With Eq. (2.1)
we
balance for isofiurane in the central compartment is:
^r E(^^-^)
=
For the general
jthcompartment(j^2)weobtain:dC>krVlk3XC3whereasforj=2dC2dtki2G\k2\C2-k2oC2.(2.3)(2.4)(2.5)Anopen-loopvalidationofthemodelwiththedatacollectedinourvol¬unteerstudyisrepresentedinFig.2.2.InspiredconcentrationsduringthestudywereusedasinputtothePKmodeltopredictendtidalconcentra¬tions.Thecomparisonwithmeasuredendtidalconcentrationsisreported
J=2
+
ÎR (Vt
Vi
-
A)
(Ct
insp
d)
66
Hypnosis
-
-
-
-
-
„n^n
'i
i
Ä^BW9
-
-
-
1
f'rVJ"
T
,
0
50
100
150
time
Figure
2.2:
Open-loop
tion of isoflurane.
upper
(
endtidal
)
200
300
validation of the Yasuda PK model for the distribu¬
The administration
and lower
(
) point
profile
series
for
subject
6 is
depicted.
prediction
The
represent measured inspired and
concentrations, respectively. The thick solid line (
the model
di
250
[min]
) represents
for endtidal concentrations.
Fig. 2.2, showing excellent agreement between measurements and model
predictions. The model is able to predict endtidal concentrations with suf¬
ficient accuracy also during closed-loop experiments, as we will discuss in
the last section of the chapter.
in
2.3.2
The
Effect
adopted
isoflurane.
compartment modeling
PK model is not able to describe the time
As
an
example,
let
us
isoflurane for volunteer 11 and the BIS time course,
Blank data windows in
Fig.
2.3
course
of BIS with
consider the administration
correspond
to
depicted
periods where
as
profile of
Fig. 2.3.
the subject
in
2.3
Modeling
67
Mw
IT > (
100
iii«)»
120
140
160
120
140
160
180
200
220
240
£115- I'
II
•7!
1
-
05-
time
[min]
Figure 2.3: In the upper plot, the BIS profile for subject 11 during the study
is plotted. In the lower plot, the corresponding PK profile of isoflurane
The upper (
is depicted.
) and lower (
) point series represent
measured inspired and endtidal concentrations, respectively.
received
this
experimental painful stimuli. Those periods were excluded from
analysis since they belong to the disturbance response of the subject.
In
Fig. 2.4 BIS is plotted versus measured endtidal and second compartment
predicted concentrations. If time is considered in the plot of the endtidal
concentrations, the data describe a clockwise hysteresis. In the second plot,
they describe a counterclockwise hystheresis. This demonstrates that the
dynamics of BIS must lie between the time course of the concentrations in
these two compartments. This also means that, when endtidal concentra¬
tions are at steady-state, the concentrations at the effect compartment are
not at steady-state yet. These delays can be attributed to transportation
at the site of effect
as
well
as
diffusion resistances.
68
'"x*
'
-
\
1
hI
//
I
^\J
vol
2.4: In the left
concentrations for
-
vol
[%]
plot,
subject
BIS values
are depicted versus measured endtidal
right plot, BIS values versus predicted
compartment are plotted.
To compensate for this unmodeled
al., 1994)
was
[%]
11. In the
concentrations in the second
et
-
/
\
Figure
Hypnosis
dynamics,
an
effect compartment
linked to the central compartment,
as
shown in
(Schnider
Fig.
2.1.
The effect compartment does not represent any
physiological organ or group
of organs in the human body. Rather it models the drug transportation de¬
lays from the lungs to the site of effect. By assumption, the volume of
the effect compartment is negligible. As a consequence, its introduction
in the model does not affect the mass balances in Eqs.
(2.3,2.5). Effect
compartment concentrations
are
related to concentrations in the central
compartment by the following first order model:
dCe
dt
keO (Ci
-
Ce).
(2.6)
theoretically
ß/5o
The
is the baseline
compartment.
have to be identified.
whereas 7 is
assumed
constants
ß/5o
a
=
equilibration constant
ECô and 7 2.3
canbeestimatedbycollapsingthehysteresisloopintheplaneofBISversuseffectsiteconcentrations.Loopcollapsingwastransformedintotwonestednonlinearregressionproblems.Firstatentativevalueforkeoisassumed.ThentheoptimalECsoand7wereestimatedas:{EC50,opt,7oPt}=argmina2(2.10){EC50,l}where1NBIS,-BIS,(2.11)Inthepreviousequationß/5jdenotestheithmeasurementandß/5jde¬notesthecorrespondingmodelprediction.NisthenumberofBISmeasure¬mentscollectedforthatparticularvolunteer.Ifwedenotetheminimumof2t,wecaniterateonkeoa2asa2t,wecaniterateonk„osuchthatkeo,opt=argmin{a20J.fceOEstimatesofthemeasuredendtidalconcentrationsatagivenBISmea¬surementwereobtainedbylinearinterpolation,whichintroducesnegligibleerror.TheresultsoftheidentificationschemearereportedinTab.
2.3
Modeling
69
At the effect compartment
ABIS
or
measure
100 and
an
=
Emax model
ABISMAX
Aß/5
Aß/5MAx
of the
=
BIS
=
BISMAX
awake state
BISmax
degree
=
-
of
is assumed
CJ+EC2,
C}
-
nonlinearity
of the effect compartment
as
keo
the PD model:
,
(2.7)
where
BISo,
(2.8)
BIS0.
(2.9)
achievable with infinite isofiurane concentrations at the effect
value, BISmax represents
in
Eq.
as
well
the BIS
ECso and
7 are the two parameters of the PD model that
ECso represents the subject's sensitivity for the drug
0.
(2.7).
as
We
the PD
70
Table 2.3:
[min-1]
EC50[vo\%]
7
1
0.6492
0.8243
1.127
2
0.6248
0.5880
1.274
3
0.1463
0.5980
1.969
4
3.027
0.7118
1.144
5
3.489
0.5146
1.577
6
0.3453
0.5262
1.431
7
2.895
0.9612
1.453
8
0.4581
0.7032
1.677
9
0.8728
0.7494
1.000
10
5.000
0.4959
1.369
11
0.3684
0.9220
2.913
12
0.211
0.8015
1.590
13
0.5914
0.5976
2.210
14
0.1754
0.8270
1.940
15
1.000
0.6690
1.378
16
0.3273
0.6130
2.351
17
0.8537
1.047
2.219
18
0.08044
1.094
0.7915
19
0.02477
0.7699
5
20
5.000
0.6915
1.402
pooled
0.3853
0.7478
1.534
Volunteer
Estimated
keo
ke0
,
ECô and
7 for each volunteer.
reports the estimates obtained from the pooled analysis.
Hypnosis
The last
row
0 <
keo
Subject
low. Those
for subjects 4,5,7.
pooled analysis,0.217
wherethedatafromallsubjectsofthestudywereana¬lyzed.Thekeovalueobtainedfromthepooledanalysisis0.3853[min-1],indicatingamorerobustestimatewithrespecttooutlyingsubjects.Itisworthnoticingthatthecoefficientofvariationforkeo(cr/n=1.1426)isoneorderofmagnitudehigherthananyofthecoefficientsofvariationforthePKparametersreportedinTab.2.1.ThereforespecialcaremustbeusedtotunethecontrollerstoberobusttouncertaintiesinthePDparameters.TheaverageECsointhepopulationis0.7495±0.1771[vol%],whiletheresultfromthepooledanalysisis0.7478.Thenegligibledifferencebetweenthetwoestimatedvaluesisaconsequenceofthesymmetricdistributionofthesingleindividualparametersaroundtheirmean.ForECsotheco¬efficientofvariationwaslower(<r//x=0.2362)thanforthekeoestimate.Theaverage7inthepopulationwas1.60±0.5437,whiletheresultfromthepooledanalysiswas1.534.Inthiscasethemeanvalueisslightlyinfluencedbythehighvaluesestimatedforsubjects11,13,16and17.ThedatapointstogetherwiththefittedPDrelationshiparedepictedintherightplotofFig.2.5.Inthiscasethebeneficialeffectsoftheeffectcompartmentmodelforthefitimprovementarehiddenbytheinterindividualvariability.Underdifferentexperimentalconditionswhichdeserveattentionwhencom¬paringtheresults,OlofsenandDahanhaveidentifiedaneffectcompartmentmodeltodescribetheeffectsofisofluraneontheBISfromendtidalconcen¬trationmeasurements(OlofsenandDahan,1999).Theyreportkeo=
2.3
Modeling
< 5
The average
keo
71
the effect compartment is
for each volunteer of the
study. The improvement in the fit introduced by
depicted in the left plot of Fig. 2.5 for subject
11. At the effect compartment the hystheresis observed in the left plot of
Fig. 2.4 has almost completely disappeared. For the optimization we used
[min-1]
20 received
subjects
and 0 < 7 < 5
The upper constraints
and 20.
were
high
are
estimate biased towards
in the
as
constraints.
Subjects
10,19
input during the whole study. This did
10 and 19 received anesthesia at constant isoflurane
active at the end of the
not
population was
high values, as
a
Table 2.3 also reports the
optimization for subjects
doses of isoflurane and BIS remained
produce significant
0.9480±1.0831
result of the
BIS
changes.
constantly
excluded from further discussion.
keo values identified
[min-1] (/z±<r),
optimal parameters
an
for the
72
Hypnosis
100
90
80
70
m
60
50
40
30
02
04
06
vol
08
0
05
1
vol
[%]
15
2
25
[%]
Figure 2.5: In the left plot, BIS values versus effect site concentrations for
subject 11. In the right plot, BIS values versus effect site concentrations
in the pooled analysis. In both plots, the solid line (
) represents the
estimated PD relationship.
min-1, ECso
=
0.6% and 7
lation examined. The
=
5.8
as mean
values identified from the popu¬
higher average keo estimated with our data might be
the result of several factors. First, our data set was collected from volunteers
and not from patients. Second we explored a broader range of isofiurane
endtidal concentrations (0.4%-2.2% compared with 0.6%-1.6%) and we per¬
formed randomized changes between the levels to be explored. Finally, a
In partic¬
reason may be the use of the analgesic alfentanil in our study.
ular, a comparison of the two estimated A;eos would suggest that alfentanil
accelerates BIS equilibration.
Although this hypothesis would have rele¬
vant medical implications, it was not considered relevant for the purpose of
control design. In addition, in our data set alfentanil neither increased nor
decreased BIS consistently. An example is depicted in Fig. 2.6. For this
particular subject, none of the changes both in targeted as well as in mea-
2.4 Control
design
73
sured alfentanil concentrations
considerations led
W
us
produced
a
noticeable BIS variation. These
to exclude alfentanil in
%
W*
"i*fc
our
model for BIS control.
»fl*^
250
200
Is
o
150
100
50
100
150
time
200
[min]
Figure 2.6: In the lower plot, alfentanil target () and measured ( o )
plasma concentrations for subject 4. In the upper plot, BIS is represented
at the corresponding time instants. Isofiurane endtidal concentrations were
kept at 1 % all throughout the study.
2.4
Control
The overall
design
dynamic system
the effect compartment is
systems. Both systems
are
a
from
vaporizer setting
to concentrations
at
series connection of two linear time invariant
Single Input Single Output (SISO).
Let
us
denote
74
the system
were
and output,
A2
x2
=
A2x2
y2
=
C2x2
(2.12)
B2u
+
(2.13)
vaporizer settings and endtidal
respectively.
concentrations
Eqs (1.1,2.3,2.5)
From
-kR
kiR
0
km
-ki
*2lg
0
0
-k20
0
0
we
*15
f
0
0
[ Qo/v
Bt
0
[0
Co
1
0
0
0
k21
0
0
0
-&31
0
0
0
0
-^41
0
0
0
0
-k5i
0
]
0
(2.14)
(2.15)
0]
0
input
*3l£ *41^ *5l£
-
0
the
0
0
0
are
have:
=
0
Hypnosis
(2.16)
where
kR
=
(Q0
kiR
=
fR (VT
kw
=
fR (VT
ki
=
kw
AQ
-
+
-
-
k12
+
/fl (1/T
-
A)) IV
A)/V
(2.18)
A)/l/i
+
k13
(2.17)
(2.19)
+
ku
+
k15.
(2.20)
The above system is connected in series with the effect compartment de¬
scribed
by Eq. (2.6),
output
yi is the BIS. We have:
where the
X\
denotesthenonlinearityinEq.(2.7).ThecontrolstructuretoregulateBISwasalreadydiscussedinchapter1.InthefollowingwewillrefertothenotationintroducedinFig.
Vi
where
/(•)1.7.
input
is the endtidal concentration and the
A-ix-i
+
Biy2
(2.21)
(2.22)
2.4 Control
design
75
The transfer functions of the
P2 and P\ blocks
Qo kw (s
P2{S)
V
(s
+
kR)
Y\J=1 (s
-
+
Xj)
k21
-
+
are
k20) n,=3 (s
k1Rkw (s
+
k21
+
+
k]i)
&20)
rij=3 (s
+
k]i)
(2.23)
PiW
=
s
where
can
^-
Aj
(2.24)
+ fce0
are
the
eigenvalues
be shown that
X3
< 0
V
of the
j
=
mammillary compartmental matrix. It
5 (Jacquez and Simon, 1993). The
1,...
,
Eq. (2.23)
obtained from
Similarly, _f\
Eq. (2.24) with keo from the pooled analysis whose results are reported in
Tab. 3. The transfer functions of the IMC blocks Q2 and Q\ are.1
with
mean
parallel
model
P2
parameters from Tabs 1 and 2.
was
obtained
from
was
thefilrdnvsomap:Q2()=FP-1.5S^6wIMCc7T]—W3\gub,kEqzB0J_V+/y48x¬A
transfer function of the
ating
2.5
2.5.1
a smooth transfer procedure must be
guaranteed to provide an optimal administration profile for the patient.
That is, the first control action of the controller must be equal tothe
thelastinputactionspecifiedduringmanualcontrol.Thisisautomaticallyguar¬anteedinourreal-timeplatformifreferenceendtidalconcentrationsaresetequaltomeasuredconcentrations(y2,ref=Vi)duringopen-loop.LetusassumethattheblockdiagramisopenaftertheoutputoftheblockQ2andletusdenoteasuconandumantheinputsspecifiedbytheblockandtheanesthesiologist,respectively.Wehave:UCon=<?2[V2,ref~(V2~£2)]=Q2-P2Uman=F2Uman.(2.29)Analogously,wemustguaranteethattheoutputoftheQiblockconvergestothemeasuredendtidalconcentration.Todoso,wesetyiêf=Vi-Then:V2,ref=Qi[yi,ref-(yi-yi)]=QiPiy2=F1y2.(2.30)SinceforbothfiltersFt(0)=1(i=1,2),uconwillconvergetoumanandy2ireftoj/2,providedtheinputumanisasymptoticallyconstant.Theanesthesiologistisnotallowedtoswitchfrommanualtoclosed-loopcontrolbeforetheinputcomputedbythecontrollerhasreachedthevalueshe/heimposedwithatoleranceof±10%.ThecontrollerwillbereadytobestartedwithinatimeequaltothesettlingtimeofthefilterF2.DuringthisphasethetimeconstantsoftheIMCfiltersaretemporarilyreducedtoshortenthewaitingtime.Thepresentedinitializationschemewasacceptedbyanesthesiologistsatthisstageoftheproject,becauseumanisnotoftenchangedpriorto
76
Hypnosis
Implementation
The controllers were implemented in a discrete state space form. The sam¬
5 s, corresponding to the
pling times of the controllers were set to AT
sampling frequency of the BIS. Three additional features were implemented
to improve performance and cope with the safety requirements in the oper¬
=
room.
Smooth transfer
When the controller is switched on,
2.5
Implementation
beginning
of surgery.
would allow
published
2.5.2
in
A
77
more
perfect tracking
a
accurate
future work.
Respiratory parameters update
The parameters of the closed-circuit
changed during
As
bumpless transfer procedure which
a negligibly small time will be
of ucon within
surgery for several
respiratory system fn, Vt, Qo
may be
reasons.
example, surgical stimulations may induce arousal reactions in the
patient which are not promptly captured by the BIS, since BIS values dis¬
played on the monitor at a given time result from calculations on the previ¬
ous 15-30 seconds of raw EEG data. In this case short periods at high flows
(Qo > 5 1/min) are often used to guarantee a faster equilibration of endtidal
concentrations because of the higher mass flow rate of fresh anesthetic. In
an
this
manner
the arousal reaction is
compensated.
In another scenario it may be necessary to reduce
the blood
et
pool by increasing
alveolar ventilation
levels of
high
Jr(Vt
—
CO2
in
A) (Chapman
al., 1985).
For these
reasons we allow the respiratory parameters to be changed by
To enhance the
anesthesiologist at any time during automatic mode
controller performance, we automatically update the model P2 and the Q2
block in Eqs (2.23) and (2.25), respectively. The effectselec-
the
ofafreshflowchangeandtheconsequentmodelupdatewerealreadypresentedanddiscussedinFig.1.12.2.5.3ArtifacttolerantcontrollersOccasionally,themeasuredsignalsusedforfeedbackcontrol(endtidalisofiu-raneconcentrationsandBISvalues)arecorruptedbyartifacts.Sucharti¬factsmaybeintroducedintheconcentrationmeasurementsbydevicecali¬brationand/ordisconnectionofthesamplingline.BISartifactsmightcomefromthehighimpedanceoftheelectrodes,corruptionoftheEEGwiththeelectromyographysignal(EMG)andaccidentaldisconnectionofthe
.
(Reid and Kenny, 1987; Ruiz et al., 1993; Frei, 2000)
recognized that such artifacts must be handled appropriately not to
seriously degrade the controller's performance or threaten the life of the
patient. An elegant framework to design artifact-tolerant controllers for the
observer-based feedback controllers was proposed (Frei, Bullinger, Gentilini,
Glattfelder, Sieber and Zbinden, 2000; Frei, 2000). The error residuals be¬
tween measurements and the observed predictions serve as a basis for the
artifact detection and prediction problem. The same approach for artifact
handling cannot be appliedl).
inthiscase.Infact,eventhoughparallelmodelsareusedintheblockdiagramdepictedinFig.1.7,theyarenotobservers.However,theerrorresidualsmaystillbeusefulintheartifactdetectionproblemforendtidalconcentrationmeasurements.Infact,inthisparticularcaseartifactsresultfromthecalibrationofthemeasurementdeviceandtemporarydisconnectionofthesamplinglineand/ortheYpiece.Thefirstsituationisautomaticallytriggeredbythemeasuringdevice,whereastheothersmayoccurduringrepositioningofthepatient.Inallcasesy2—0andconsequentlye2=V2—V2——§2Lete2,N={e2(k-N),...,e2(k-l)}(2.31)bethecollectionofNresidualsacquiredwheny2hadnoartifacts.Lete2denotethearithmeticmeanoftheresidualsine2jjv.Assumefurtherthate2(k—i)~J\f(e2,a2)Vi=1,...,N.Theproposedtestforartifactdetectionis:H0:e2{k)=e2(2.32)Hi:e2{k)<e2.(2.33)Ifatthesamplingtimekthenullhypothesisisrejected,thenweconsidery2(k)corruptedbyartifacts.Thealternativehypothesisisone-sidedbecauseallartifactsourcestendtodecreasee2(k).Hoisrejectedataconfidencelevela=0.01if:C2(fc)"e'2<*(«)=-2.33(2.34)awhere$(a)isthecumulativedistributionfunctionofastandardizednormalvariable.IfHoisnotrejected,thene2(k)updatesthevectorofresidualsinEq.(2.31).Otherwisethesamevectorisusedfortestingtheresiduale2(fc+
78
trodes. Several authors
have
Hypnosis
2.5
Implementation
We set
a
=
0.1 in
is described in
which
study,
(2.34)
Eq.
Fig.
was
manual control
79
aimed at
(Sieber
on
the basis of off-line tests.
We used
2.7.
data set collected
a
comparing endtidal
al., 2000).
Such
during
a
test
clinical
a
concentration control
versus
plot from above depicts
endtidal concentrations and reference values during closed-loop (first part)
control and during manual adjustment (second part) of the vaporizer by
the anesthesiologist. The second plot depicts the residuals e2(k) together
et
The first
Calibration
y-
1
Disconnection
V
05
L'
\
Calibration
A
^rv^
1
"
x
.
r^^n ^
^
40
0
20
60
40
60
80
time
100
120
140
160
100
120
140
160
100
120
140
160
[mm]
signal (
)
plotted during closed (first half) and openloop (second half) control. In the middle plot, the error residuals &2
2/2—2/2
(—|—) are plotted together with the lower bound for artifact detection.
In the lower plot the vaporizer settings are depicted. All artifact episodes
were properly detected.
Figure
2.7: In the upper
and measurements
(
plot,
)
endtidal concentration reference
are
=
Eq. (2.34). Finally,
vaporizer settings of the experiment which were used
in
the third
as
input
plot
the
sequence for the model in
Eqs (2.12,2.13)
whereendtidalconcentrationmeasurementshadartifactscanbe
with the lower bound for acceptance defined in
are
plotted.
Three
periodsrecognized
80
Hypnosis
The first and
28 min, t
36-39 min and t
156 min.
roughly t
correspond to calibration of the measuring device whereas the second
corresponds to a 3 min disconnection of the sampling line. Figure 2.7 shows
that all artifacts were correctly identified.
at
=
=
=
last
The artifacts in BIS
unlikely to occur
during the study.
arising from the corruption of EEG with EMG
since the
patients
In all other
receive
such
high
are
doses of muscle relaxants
low electrode
impedance or
electrodes, we use the Signal Quality Index
(SQI) as a basis for the detection. The SQI is an auxiliary value delivered
by the BIS monitor at each sampling time. It is expressed as a percentage
value, with 100% denoting a high quality measurement. Together with the
staff from Aspect Medical System, we decided that BIS is unacceptably
corrupted by artifacts when SQI < 20.
cases
as
accidental disconnection of the
artifacts the
reliability of
meaningful input actions.
the system is
The
following
guaranteed
decision
ruleswereadopted(seeFig.1.7):1.ifj/2hasartifacts,thenwesete2=0andtheinputofPibecomes§2insteadof2/2•Duringthisphasetheclosed-loopsystemisequivalenttoasingleIMCloopcontrollingBIS;2.ify\hasartifacts,thenwesete\=0.Inthiscasejusttheslavecontrollerremainsactive;3.whenboth2/2andy\haveartifacts,e2=0ande\=0.Inthiscasethesystemwilloperateinopen-loop,whichistheonlyoptionwhenthereisnomeasurementavailable.Letusexamineinmoredetailthedynamicsofthesysteminthepresenceofartifacts.Specifically,assumethatartifactsoccurintheBISand/orendtidalconcentrationmeasurementsatthesamplingtimek.Supposefurtherthatnoartifactsoccuredbeforethat,whichimpliesthatfork<k,e\(k)^0ande2(k)^0.Settinge\=0and/ore2=0canberegardedasasetpointchangeinthemasterand/orslavecontroller.SincebothQ\andQ2arestrictlyproper,thisproceduredoesnotresultindiscontinuitiesofthecontrolaction.Letusassumetheworstcasesituationwhereartifactspersistbothiny1and2/2Vk>k.Thecontrollerwillstartanadministration
During
delivers
if the controller
2.6 Test of the controller
81
profile which ultimately converges to a constant, safe vaporizer setting. This
steady-state value is the input which would nominally result in a BIS equal
It can be calculated
to yi,ref for the average subject in the population.
by first inverting Eq.(2.7) to obtain the corresponding concentration at the
effect compartment:
X\
=
100
EC,
2/1,re/
(2.35)
50
Vl,ref
Then from
Eqs (2.14,2.5)
1
Qo
we
obtain desired
fR (VT
-
A) k21
vaporizer setting
+
h
Qo &21
20
as:
+
^20
(2.36)
For
a
typical
anesthetic
[1] Qo
the typical subject
ur =0.71 [%1.
A
=
2.6
0.15
=
1
procedure
[1/min], AQ
of the
with
=
population
0.2
we
=
10
[1/min], Vr
0.6
[1],
50 and for
[1/min] and yhref
obtain from the above expression
=
Test of the controller
Two clinical tests of the BIS controller
were
already presented
in
We showed that the controller is able to target and maintain
level of unconsciousness
assessedbyBIS.Inthissectionwereportanddis¬cusstwoparticularcasesshowingtheperformanceoftheartifactdetectionsystemandthecontrollerbehaviourwithapatientwhoexhibitedtolerancetoisoflurane.Further,weshowthepredictionaccuracyofthePKmod¬elsduringclosed-loopexperiments.Thedetailsconcerningtheadmissioncriteriatothestudiesandthepremedicationtakenbythesubjectswerereportedinchapter1.TheclinicalstudyshowninFig.2.8depictsanab¬normalpatient'sbehaviourthatwascorrectlyhandledbythecontroller.A60yearsoldmanundergoingcraniotomywasenrolledforthestudy.Figure2.8depictstheBISandMAPsignalsduringtheoperation,togetherwiththeinputatthevaporizer.Bloodpressurewasmeasurednoninvasivelywithapressurecuff.Automaticcontrolwasactiveduringthewholeperiodconsidered.Duringtheinitialperioduptot=205min,thesubjectexhib¬itedavividtolerancetoisoflurane.Precisely,BISvaluesfluctuatedaround
1.
/#
a
chapter
desired
82
Hypnosis
Bolus dose of alfentaml
„'
o—
170
/
190
'
200
Blood pressure
E
E
40
170
210
220
230
240
250
260
220
230
240
250
260
220
230
240
250
260
increase
—
190
200
210
190
200
210
0^170
time
[nun]
Figure 2.8: In the upper plot BIS and BIS reference values during closedloop are represented. In the middle plot systolic, mean and diastolic arterial
pressures acquired with a blood pressure cuff are represented. In the lower
plot the vaporizer settings determined by the closed-loop controller are plot¬
ted. The controller was active during the whole period represented in the
figure.
50 while BIS reference values
kept increasing during
of alfentanil
that
were
phase.
set to 40.
At
The
roughly
t
=
input
at the
206 min
a
vaporizer
bolus dose
a sharp increase of blood
regarded as a sign of inadequate analgesia. Shortly af¬
ter, BIS values dropped to around 10. It is not certain, even though highly
probable, that such drop was a consequence of the bolus dose of analgesic.
Let us recall that the effect of alfentanil on BIS was not completely ruled out
by the data collected from the study on volunteers. The controller promptly
reacted to the sudden drop in BIS values by reducing the vaporizer setting
was
pressure, which
almost to 0.
administered to compensate for
was
At t
Symmetrically
=
251 min the BIS reference value
to the initial
phase,
the
was
increased to 60.
patient remained unresponsive
to
2.6 Test of the controller
changes
in the
83
vaporizer settings.
BIS electrodes disconnection
^
50;
0—
145
4
2
=
^>^
0
1 15
150
155
„
160
time
A
165
1"
[mm]
Figure 2.9: In the upper plot BIS and BIS reference values during closedloop are represented. In the middle plot endtidal concentration references
and measurements are depicted. In the lower plot the vaporizer settings
are plotted. The solid line in the lower plot indicates the period where the
controller
Figure
was
active.
2.9 illustrates the controller's behaviour
tifact in BIS measurements.
The
hernia removal is considered.
of
BIS,
roughly
case
Figure
endtidal concentrations and
BIS electrodes
of
a
2.9
during
occurrence
represents the
vaporizer settings.
an ar¬
undergoing
operative profile
At t
=
159 min
accidentally without anybody in
the operating room noticing the fact.
During this transient the master
controller operates without feedback signal. As a result, the endtidal con¬
centration reference signal did converge to a constant value which is capable
of achieving the specified BIS reference in the average patient. Such value
is approximately 0.6%, as calculated from the pooled PD relationship rep¬
resented in Fig. 2.5. When artifacts disappeared, the master controller was
were
disconnected
of
63 years old female
84
switched
on
again by the supervisory system. Consequently,
concentration references
were
computed
on
Hypnosis
new
endtidal
the basis of BIS values.
f
100
120
140
120
140
160
180
200
220
180
200
220
1 5
"o
>
05
0
100
160
time
Figure
2.10:
In the upper
plot
[min]
measured
(
isofiurane concentrations whereas in the lower
endtidal concentrations
In the
are
)
plot
and
predicted (
)
predicted
measured and
represented.
cases where isofiurane was administered through the control plat¬
form, the states of the parallel model Pi can be regarded as estimates of
the corresponding measurements. Figure 2.10 shows excellent agreement be¬
tween predicted inspired and endtidal concentrations and their correspond¬
ing model predictions. It is worth noticing that the plot shows comparisons
flowrates.Pciy=130mnhgdQ2[/]\TpuKvb-^•*
at different fresh gasinA^'r
Chapter
Feedback Control of
3
Analgesia
86
Aunculam Mario graviter
Tu
facts
hoc: gams,
mirans
Nestor,
Marziale, Epigrammata. Ill,
in
Analgesia
olere.
aunculam.
28.
Foreword
In
compared two approaches for the closed-loop administration
hypnotics: either to regulate Mean Arterial Pressure (MAP) or
to regulate Bispectral Index (BIS). In chapter 2 we thoroughly investigated
the second approach, both from a control theory and a clinical perspective.
From both treatises one can conclude that BIS may be used with advantage
chapter
1
we
of volatile
as a
guide
What do
for
we
hypnotic
administration.
do with MAP now?
MAP is not
only an indirect indicator to assess depth of anesthesia or ade¬
quate perfusion to internal organs. The signal itself and its fluctuations in
correspondence to surgical stimulation are signs of responsiveness of the au¬
tonomic
for the
drugs
system. The reactions of the autonomic system
patient's
sake and to
may be used with
In the
improve
advantage to
the
operating
achieve this
must be minimized
conditions.
Analgesic
goal.
following chapter a new paradigm for the closed-loop administra¬
analgesics during general anesthesia is presented. The manipulated
variable in the control system is the infusion rate of the opiate alfentanil,
administered intravenously through a Computer Controlled Infusion Pump
Theoutputstobecontrolledarethepatient'sMeanArterialPres¬sure(MAP)andthedrugconcentrationintheplasma.MaintainingMAPwithinappropriaterangesimprovestheoperatingconditionsforsurgicalin¬terventionandprovidesoptimaltreatmentofthepatient'sreactionstosurgi¬calstimuli.Maintainingplasmadrugconcentrationswithinrangesspecifiedbytheoperatorenablesanesthesiologiststotitrateanalgesicadministrationtoqualitativeclinicalend-pointsofinsufficientanalgesia.MAPisacquiredbothinvasivelyandnon-invasivelythroughacathetercannulaandablood
tion of
(CCIP).
87
cuff, respectively. Since plasma drug concentrations cannot be
on-line, they are estimated via a pharmacokinetic (PK) model on
the basis of the infusion profile. An explicit Model Predictive Controller
(MPC) was designed to achieve the above mentioned objectives. An upper
constraint on predicted drug concentrations was imposed to avoid overdos¬
pressure
measured
on the MAP were introduced to trigger a prompt
during hypertensive and hypotensive periods. Artifacts
in the MAP measurements are rejected to prevent harmful misbehavior of
the controller. Finally, the results of the application of the controller to 6
patients are presented and discussed.
ing, whereas
constraints
controller reaction
This
chapter
can
be found with minor modifications
scientific literature
as a
publication
in the
as:
Gentilini, A., Schaniel, C, Morari, M., Bieniok, C, Wymann, R. and
Schnider, T.W.: 2001, A new paradigm for the closed-loop intraoperative
administration of analgesics in humans, IEEE Transactions on Biomedical
Engineering, Submitted for publication.
88
Introduction
3.1
3.1.1
Opiates
the
the
Analgesia
Intraoperative analgesic
used for
are
intraoperative and postoperative pain
postoperative setting,
level.
patient's pain
can regulate
the
drug
infusion rate is
With Patient Controlled
the administration of
patient
the medical staff
administration
(Scherpereel, 1991;
treatment.
In
adjusted according to
Analgesia (PCA), the
opiates without supervision of
Liu and
Northrop, 1990;
Johnson and
Luscombe, 1992).
The
intraoperative administration of opiates
is not directly related to pain
spécifie measure of pain are available when the subject is
unconscious (Habibi and Coursin, 1996). The International Association for
the Study of Pain defines pain as an 'unpleasant sensory and emotional ex¬
perience associated with actual or potential tissue damage'. Consequently,
it may even be improper to speak about "pain" during general anesthesia
when the patient experiences unconsciousness (Petersen-Felix et al., 1998).
treatment, since
Opiates
surgical
are
infused because
stimulation
they decrease autonomic stress
al., 1988; Kaplan, 1993), such
(Ausems
et
(HR)
Heart Rate
surgery
no
For several
increases.
reactions to
as
MAP and
These reactions must be minimized
SISO controller for MAP with
during
is clinically not
hemodynamically
the plasma generally do
not decrease MAP. If the MAP is elevated because of pain, opiates generally
decrease MAP. Secondly, it was shown that even high doses of opiates may
not be able to suppress MAP reactions to noxious stimulation completely
(Wynands et al., 1984; Hynynen et al., 1986; Phibin et al., 1990). Conse¬
reasons a
Firstly, opiates are generally considered
stable, that is increasing opiate concentrations in
acontrolsystemwhichpurelyadjuststheopiateinfusionrateonthebasisofthepatient'sMAPmayleadtoprolongedrespiratorydepres¬sionattheendofsurgery(ShaferandVarvel,1991).Thirdly,MAPcanbelowindependentlyfromopiateconcentrations,forinstancewhenvolatilehypnoticorvasoactivedrugsareused.Inthiscasethecontrollermayleadto
feasible.
quently, underdosing.
opiates
to be
3.1 Introduction
89
Several open- and
the
closed-loop approaches have been investigated to improve
intraoperative administration of analgesics. Ausems and colleagues
titrated
Rate
opiate infusion
(HR),
to several clinical
endpoints
somatic responses and autonomic
such
as
MAP and Heart
signs of inadequate anesthesia
as sweating and lacrimation (Ausems et al., 1986). In their clinical pro¬
tocol, the infusion rate of alfentanil was gradually decreased in the absence
of signs of inadequate analgesia as a remedy to prevent overdosing.
such
Schwilden and Stoeckel tested
closed-loop controller which administers
patient's Median Frequency (MF) of the elec¬
2-4 Hz (Schwilden and Stoeckel, 1993). Despite
at
troencephalogram (EEG)
the adequate performance of the control system, it is questionable to look
at the MF of EEG as the clinical end-point for analgesic drugs. Further, if
used in combination with analgesics, hypnotics compromise the reliability
of MF by inducing burst suppression episodes in the EEG (Rampil, 1998).
Moreover, from clinical data it is not clear whether and how noxious stimuli
affect the EEG (Rampil and Laster, 1992; Kochs et al., 1994).
a
alfentanil to maintain the
colleagues tested a closed-loop fuzzy controller for MAP and
during gynecological surgery (Carregal et al., 2000). The
light level of stimulation for such surgical procedures and the slow sampling
rate of the controller do not allow to extrapolate the reported performance
to periods of intense stimulation and more invasive surgical procedures.
Carregal
and
HR with alfentanil
Both studies
encouraging because they
are
ing good hemodynamic
control with
optimal closed-loop system aiming
a
means
freedomtoadjusttheinfusionratebasedonotherqualita¬tivesignsofinadequateanalgesia.Noneoftheseissueshavebeenembeddedinacontrolsystemsofar.3.1.2GoalofthisstudyInthefeedbacksystemfortheadministrationofanalgesicdrugsthatwepresentinthischapter,thepatient'sMAPandthepredicteddrugconcen¬trationsintheplasmaaretheoutputstobecontrolled.Wedesignedthecontrolalgorithmtoachievemultipleclinical
must include
some
degree
of objectives:
confirm the
of achiev¬
an
They
MAP
of
with
regulation
opiates
drug consumption and must offer
opiates.
at the
to minimize the
possibility
also suggest that
90
•
during
stable
Analgesia
where both outputs lie within constraints, the
adjust the infusion rate mainly to keep MAP
value specified by the anesthesiologist;
periods
control system must
around
•
a
reference
the controller must maintain
value
specified by
beyond MAP regulation;
erence
•
the controller must react
Also, it
siveness, since
lated.
Alfentanil
the
plasma drug concentrations around a ref¬
anesthesiologist as a secondary objective
promptly
when output constraints
are
vio¬
must treat constraints violations with different aggres¬
not all violations have the
same
clinical
severity.
as the opiate for this study because of its relatively
equilibration and the moderate pharmacokinetic (PK) vari¬
ability (Shafer and Varvel, 1991).
was
chosen
fast blood-brain
In this
design principles and the clinical validation of
analgesic administration. First, we outline the model
used for control. It consists of a pharmacokinetic (PK) model adapted from
the literature and an approximate pharmacodynamic (PD) model whose pa¬
rameters were defined on the basis of anesthesiologists' experience. Second,
the control algorithm is described. It consists of an explicit Model Predictive
Controller (MPC), which is the only control strategy capable of handling
both multiple control objectives and constraints prioritization in a consis¬
tent way. In particular, we discuss the choice of the optimization weights,
the weights on the output constraints and the horizons lengths and their in¬
fluence on the closed-loop performance. Third, we present an algorithm for
the rejection of artifacts in the MAP signal, which was added to make the
controller applicable in the operating room (OR). Fourth, the closed-loop
performance of the controller, when applied during general surgery on hu¬
mans, is presented and discussed, together with some suggestions for future
chapter
we
describe the
the control system for
administra¬tionofanalgesicdrugs.Totheauthor'sbestknowledgetheonedescribedhereisthefirstmodel-basedclosed-loopcontrolsystemtoregulateMAPwithopiates.
research.
We
designed
a
novel feedback
paradigm
for the
intraoperative
3.2
Modeling
91
Modeling
3.2
The linear
three-compartment mammillary PK model depicted in Fig.
adopted to describe the distribution characteristics of alfentanil.
3.1: Three
Figure
keo
[min-1]
mass
is the
balance
compartment.
3
=
EMC,
=
-
d)
-
*10Ci
2
+
û
(3.1)
C\ [ng/ml] and C3 [ng/ml] represent plasma and auxiliary compart¬
where
concentrations, respectively. V\ [ml]
central
5
•
[min/h]
k\3 [min-1] (j
2,3)
is the volume of the central
com¬
drug transfer rates between the
and the auxiliary compartments, kô [min-1] is the elimination rate,
105 [ng/ml] is the alfentanil concentration in the syringe, k
60
partment,
=
A
equation for the central compartment gives:
J
p
constant of the effect
equilibration
^f
ment
3.1
compartment PK model for the distribution of alfentanil.
=
are
the
=
is
a
normalization constant and
concentrations in the
rlC
_±
Note that
Eqs (3.2)
u
[ml/h]
auxiliary compartments
and
=
kjl{Cl-C3)
(3.1)
implythat,foraconstantinfusionrate,thesteady-stateconcentrationsinallthecompartmentsareequal.
was
are
j
=
is the infusion rate.
described
2,3.
The
by:
(3.2)
duringthevolunteerstudy,whichwasalreadydescribedinchapter2.Inthatstudythat20younghealthyvolunteerswereanes¬thetizedwithisofluraneforapproximately5h.Alfentanilwascontinuouslyinfusedduringthestudytoachieveandmaintainconstantlevelsofpredictedplasmaconcentrationbetween25ng/mland400ng/ml.Targetcontrolledinfusion(TCI)algorithmswereimplementedusingSTANPUMP1softwarewithShafer'sPKmodelforalfentanil.Approximately20alfentanilsamplesweretakenpersubjectduringtransientandsteady-statephases.AccordingtothestandardtechniquestoevaluatepredictionperformanceofCCIP(Varveletal.,1992),wecalculatedforeachdrugsamplethepercent¬agePredictionError(PEtJ)as:Gml3—Cp.Jl3~Cp~.pE=^»».3w3.100(33)whereCptJandCml3representthepredictedandmeasuredalfentanilcon¬centrationsatthejthsamplefortheithsubject.Additionally,wecomputedtheMedianPredictionError(MDPEt)andtheMedianAbsolutePredic¬tionError(MDAPEt)as:MDPEt=median{PEl3lj=1,...,Nt}(3.4)andMDAPE,=median{|P^j|,j=1,...,Nt}(3.5)respectively.InEqs(3.4)and(3.5)Ntisthenumberofsamplesforsubjecti.MDPEtisanindexforthebiasofthemodelforaparticularsubject,whereasMDAPEtisanindexforthedispersionofthemodelresiduals.Finally,wecomputedWOBBLEtas:WOBBLE,=median{\PEn-MDPEt\,j=1,...,Nt}(3.6)1STANPUMPisfreelyavailablefromtheauthor,StevenL.Shafer,M.D.,Anesthesi¬ologyService(112A),PAVAMC,3801MirandaAve,PaloAlto,CA
92
trations collected94304.
prediction performances of the following published models for alfentanil
compared to select the best candidate for control design: Scott (Scott
and Stanski, 1987), Scott weight-adjusted, Maitre (Maitre et al., 1987),
Hudson (Hudson et al., 1991) and Shafer. The parameters of Scott's weightadjusted and Shafer's models were obtained from the source code of the
software STANPUMP1. As a measure of performance, we computed the
prediction errors between model estimates and measured alfentanil concen¬
were
The
Analgesia
3.2
Modeling
93
which represents
a bias free measure of the variability of PEtJ
prediction accuracy of Maitre's and Hudson's models was
remarkably lower compared to the other models. No significant differences
in all the performance parameters were found between Scott's and Scott's
weight-adjusted models. Therefore we excluded Maitre's, Hudson's and
Scott's models from further discussion. Figure 3.2 shows the profile of pre-
individual.
51
The
150-
0
50
100
150
200
time
250
300
350
[mm]
Figure 3.2: alfentanil infusion profile for subject no. 3 in the study. The
subject is a 30 years old female of 67 kg weight and 167 cm height at the time
of the study. Continuous lines represent the predictions of Shafer (
) and
Scott weight-adjusted (—
) models. Alfentanil measured concentrations
in the plasma ( o ) are also reported.
•
dieted and measured
—
plasma
concentrations for
a
subject
in the
study.
The
step behaviour of plasma concentrations predicted by Shafer's model follows
was chosen for the TCI algorithm (Bailey and
Shafer, 1991). Shafer's model is strongly overpredicting plasma concentra¬
tions, as confirmed by comparing the average MDPE among the subjects
for the two different models: Scott weight-adjusted (-14.29) and Shafer (-
from the fact that this model
94
31.49).
No substantial differences
were
Analgesia
observed in the average MADPE
Despite the bias,
provides a more uniform performance among the popula¬
tion, as deducible by visual comparison of the boxplots represented in Fig.
3.3 for Shafer's and Scott's weight-adjusted models. We decided to adopt
or
in the average WOBBLE for the different models.
Shafer's model
Shafer
Scott
weight-adjusted
1,11
1
1
,
j
5
10
15
Subject no
1
1
II
20
5
10
Subject
15
20
no
Boxplots of the Prediction Errors (PEtJ) for Shafer's (left)
weight-adjusted (right) models and every subject in the study.
Despite the bias, the variability of the Prediction Errors in Shafer's model
is more uniform among the population of subjects.
Figure
3.3:
and Scott's
Shafer's model
the
prediction
as
bias
the PK model in the MPC scheme.
we
To compensate for
re-estimated the volume of the central compartment.
This heuristic
procedure reduced the prediction bias without significantly
performance parameters. The volume of the central
compartment in the PK model depends on the subject's Body Surface Area
deteriorating
the other
3.2
Modeling
(BSA) through
95
the
following relationship:
Vx
where
c
=
0.825 in the
where
[kg]
0.007184
[cm] represent
(3.7)
BSA.
parameters. BSA is computed
w0425 h°
725
as
(3.8)
subject's weight and height, respec¬
tively.
subjects with respect
1.1028.
to the c parameter in Eq. (3.7), obtaining as an optimal value
copt
The fact that copt > 0.825 was to be expected since larger volumes decrease
the concentrations predicted by the model. Figure 3.4 depicts MDPE
w
and h
=
c
set of
published
BSA
=
the
We minimized the average MDPE among the
=
,
MDAPE and WOBBLE with
notice that
c
=
increasing values of
1.1028 is also close to the value
MDAPE and that WOBBLE is
just slightly
c.
It is
interesting
minimizing the
to
average
worsened relative to the
orig¬
inal value.
There is
no published PD model quantifying the effects of alfentanil on
Consequently, an approximate PD model was tuned to reproduce the
anesthesiologists' clinical experience. An effect compartment was linked to
the central compartment, as depicted
inFig.3.1(Schnideretal.,1994).TheconcentrationsattheeffectsiteCe[ng/ml]arerelatedtoplasmacon¬centrationsbythefollowingequation:-£=ke0(Ci-Ce)(3.9)wherekeo[min-1]istheequilibrationconstantattheeffectsite.ThevalueforkeoinEq.(3.9)wascalculatedinordertoreproduceanobservedtimetopeakeffectonMAPafterabolusinjectionofalfentaniloftpeak=1.5min.Intheestimation,weadoptedShafer'sPKmodelwithc=coptandweassumedanaveragesubjectwithw=70kgandh=180cm.Weobtainedkeo=0.4[min-1].SincetheMPCalgorithmrequiresalinearmodel,weassumedalinearrelationshipbetweenMAPandeffectsiteconcentrationvariationswithagainofk=—0.0881[mmHg/(ng/ml)].ThegainvaluewasderivedthroughlinearizationofanapproximatePDrelationshippostulatedbyanesthesiologists.Eventhough-aswediscussedintheintroduction-opiatesmaynotaffectMAP,thesignofthegainguaranteesthattheinfusionratewilldecreasewhenMAPistooloworincreasewhenMAPistoohigh.Table3.1summarizesthePKandPDparametersofthemodelusedintheMPCcontrolalgorithm.
MAP.
96
Analgesia
200
180
160
140
120
100
MDAPE
^
/
80
60
MDPE
40
__---" 'wobble
20
0
05
1
15
2
25
3
c
Figure
versus
3.3
3.4:
\MDPE\ (
different values of
Control
)
c
in
,
MDAPE
(
)
and WOBBLE
(
)
Eq. (3.7).
design
depicts the block diagram adopted for the closed-loop adminis¬
alfentanil, where P represents the patient, M represents Shafer's
adjusted PK model, C is the MPC controller and K represents the observer,
where artifacts are rejected according to the algorithm described further. M
computes predictions of the drug concentration in the plasma y\ from the
infusion rates of the syringe u. As mentioned earlier, the dynamic system
M has two roles: on one hand, it provides anesthesiologists with a patient's
weight and height adjusted estimate of the drug levels. On the other hand,
it provides the MPC controller with the second output measure which must
be regulated during closed-loop administration. yi,ref represents plasma
Figure
3.5
tration of
concentration references,
x
MAP measurements and
references, respectively.
represents the observer states,
yi an(i 2/2,re/
are
3.3 Control
design
97
Parameter
Value
[1]
v,
1.1028 BS A
ku
[min^1]
0.142 [min"1]
0.231 [min-1]
0.0185 [min-1]
0.4 [min-1]
0.515
hi
ki3
&31
keO
k
[mmHg/(ng/ml)]
-0.0881
Table 3.1: PK and PD parameters in the MPC controller.
2/1
WËgmtmtÈi
2/2
u
P
-
^
X
-
c
K
*-
2/1, ref
2/2,1" et
Figure
3.3.1
3.5: Block
Controller
actions
of the
explicit
MPC controller.
tuning
At every discrete time step
input
diagram
k,
the MPC
{u(k\k),... ,u(k
+
m
—
algorithm computes
l\k)}
the
m
which minimize the
following
objective
oftheMPCalgorithm(Leeetal.,1994;Garciaetal.,1989).ThequadraticobjectivecriterionexpressedinEq.(3.10)aimsatminimizingbothcontrolerrorse3=yJtref—Vjaswellasinputsu,inputratesAmandconstraintviolationeforthefuturepstepsahead.Notethatthecontrolerroratthegenericfuturetimestepk+iiscomputedasdeviationoftheoutputreferencefromthepredictedoutputvalue.Precisely,e3(k+i)=ytiref—yj(k+i).ThecontrolactionscomputedbytheMPCalgorithmareimplementedinaso-calledrecedinghorizonpolicy.Namely,ateverytimestepkjustthefirstofthem
98
subject
Figure
Figure
3.6:
u(fc|fc),
3.6
Schematic
min
to the
diagram
,Ati(m-l+fc|fc)^^
Vl I
+
following
Vl
y\
yi
yi
—
—
depicts schematically
of the MPC
lywu\\u(k
+
(k
+
i
+
l\k)
'i=0
w^\\[y2(k
+
i
+
l\k)
i\k)\\2+wAu\\Au(k
+
i\k)\\2
yhref(k
+
i
+
1)}\\2
+
y2,ref(k
+
i
+
1)]||2
+
yi,max
yi,mtn
V2,max
2/2,mm
the
^
>
•
^
•
<
—e
e
principlescomputed
•
•
-
-
0i^max
0\rri%n
b2,max
&2,mm-
Analgesia
predicüonhorizffli
(3.10).
optimization problem
in
+
Eq.
function
p-i
(3.10)
pee2
constraints:
(3.11)
(3.12)
(3.13)
(3.14)
(3.15)
input
measurement
actions is
Eq. (3.10)
is
implemented. At the
updates the states of the
repeated.
end of the
Eq. (3.10) p and m are usually defined prediction and control horizons,
respectively, whereas {wAu,wu,wyi ,wy2} are the weights on input incre¬
ments, input and outputs respectively, e is a 'slack' variable introduced to
guarantee feasibility, whereas pe is the weight on the output constraintstheir
intheoptimizationalgorithm(Garciaetal.,1989).{&i,mm,blimax,b2,min,b2,max}representtoleranceweightsforconstraintviolation.Precisely,thehighertheparametercorrespondingtoacertainconstraint,thelessaggressivewillthecontrollerbewhensuchaconstraintisviolated.InEq.(3.11)wehaveUrmn=0andumax=1000ml/h.TuningoftheMPCcontrollerinEq.(3.10)requirestospecifythehori¬zonlengthspandm,theoptimizationweights{wAu,wu,wyi,wy2,pe}aswellastheoutputconstraints{yiâx,yi,min,y2,max,!/2,mm}-Thetoleranceweights{6i,mm,b^max,b2,mm,b2,max}andtheinternalmodeltopredictthefutureoutputestimatesmustalsobespecified.Therationalebehindthechoiceofthemodelwasdiscussedintheprevioussection.Inordertobetterunderstandtheroleoftheweights{wAu,wu,wyi,wV2,pe},letusobservethattheMPCcontrollercomputestheinfusionratetomain¬tainbothy\andy2attheirtargetlevel,despiteMAPreactionsinducedbysurgicalstimulation.Sincethecontrollerusesoneinputtoregulatetwooutputs,theinfusionratewillbecomputedbytheMPCalgorithmtoreal¬izeadynamictrade-offbetweenminimizingthecontrolerrore=yref—yforthefirstandthesecondoutput,respectively.Theaggressivenessofthecontrollertominimizey\ref—Viratherthany2yref—ViortheotherwayroundisdeterminedbytheratioofthetwooutputweightswyiandwV2.InthelimitingcasewherewVl/wV2—>0,thecontrolstrategyre¬ducestoasimpleSISOcontrollerforMAP.Conversely,ifwVl/wV2—>oothecontrolalgorithmresultsinopen-loopinfusionpoliciestotargetplasmaconcentrations(Gentilinietal.,2000;BaileyandShafer,1991).Tuningoftheoptimizationweightswasperformedtoachievetwospecificclinicalgoals.First,thecontrollershouldnotaimattightlymaintainingtheref¬erencevaluey2irefforMAP.Rather,itshouldreactmoderatelyify2lieswithinconstraintsandmoreaggressivelyiftheconstraintsarehit.Thesamepromptcontroller'sreactionisdesiredifpredictedconcentrationshit
3.3 Control
design
99
observer and the
sampling time, a new
optimization in
In
100
respective
constraints. As
a
second
priority the anesthesiologist
must have
during automatic control
That is, the con¬
to other qualitative indicators of insufficient analgesia.
troller should react moderately to changes in yiêf during stable periods
where y 2 lies within the constraints. To achieve the above discussed goals,
we set wyi
< wV2 < p. Particularly, we adopted wu
10~4, wAu
0.5,
a
degree
of freedom to
Analgesia
adjust
the infusion rate
=
=
0.004,
w^
=
2,
pe
=
2
The output constraints for both MAP and
are
chosen
by
the
=
104.
anesthesiologist
predicted plasma
concentration
before induction of anesthesia-noc
acordingthep'svulyf.Hwbmzx32EMPC-(T=5)q10,IFAk—¬\{BL6[]9<KR
wvi
3.3 Control
troller
design
101
partitions the
space 6 C
R8
belongs to the polyhedral region
Subsequently, the update of the infusion
Au(k) =Ft
where the matrices
region
and
(Bemporad
m
controller's
nR
=
{Fl,Gl}
In the worst
i.
case
Eq. (3.16) states
by the matrices {Ht,Kt}.
computed as
in which 0 may vary.
that 0
rate is
6 +
define the
situation,
defined
(3.17)
Gt.
piece-wise affine control
ur may increase
action in
exponentially
with p
al., 2000).
complexity while guaranteeing adequate performance, obtaining
We chose p
et
=
10 and
m
=
3 to minimize the
127.
100
120
140
160
180
200
220
240
260
280
300
260
280
300
110-
P2
H
4
TO
100
120
140
160
180
200
2/1,=/
240
State-space partition of the MPC controller for two different sets
weights. We set the observer states x(k) to represent a constant
3.7:
of output
concentration in all the
compartments
ofC=200ng/mlandaconstantMAP=90mmHg.Further,wesetu(k—1)=3.7ml/h,whichwouldresultintoasteady-stateconcentrationofC=200ng/ml.Onthex-andy-axisy\trefan(i2/2,re/arerepresented,respectively.Intheupperandlowerplot,regionsforr=150andr=103arerepresented.
Figure
220
[ng/ml]
102
100
120
140
160
180
200
220
240
260
Analgesia
280
300
a
H
P2
'
70
100
180
200
Vi.ref
Figure
3.8: For
detailed
a
description
caption of Fig. 3.7. In the
10~3 are represented.
r
220
[ng/ml]
of the content of the
upper and lower
plot,
plot, regions
for
r
refer to the
150 and
=
=
An
©
is represented in Fig.
3.7, where the partition of the space
M8 of the explicit MPC algorithm for two different sets of output
example
C
weights
is
depicted.
In both
the output constraints and
defined
according
to
Eq.
plots,
input
(3.16)
In order to be able to draw the
the
same
increments
is
set of
was
represented
regions
in
a
weights
for the
input,
Every region
different gray-scale.
considered.
with
a
2-dimensional space,
the first six elements of 9 to constant values. On the
x-
and
we
fixed
y-axis, different
values for the output references yi,re/ and y2,ref inside the output ranges are
considered, respectively. In the upper plot, we chose output weights such
r
=
wV2/wVl
=150 whereas in the lower
different choices of the output
Eq. (3.16)
as
well
as
the
plot
we
set
r
=
3000.
weights affect both the affine control
topology of the regions partition in the state
The
action in
space.Asanexample,letusconsiderthepointPidepictedinFig.3.7suchthatVi,ref=120ng/mlandy2,ref=80mmHg.Sincej/ire/<Vi,thecontroller
that
would decrease the inlusion rate to track
input
rate
actions
Eq. (3.10)
consider the
are
have Am
=
computed
are
Am
inlusion rate. As
a
[18.24
=
with
[—3.04
In this case, both control
significantly higher
15.36
Eq. (3.16),
—
result ol the
0.69
=
errors
12.77]T
0]T.
point P2, lor which yiêf
higher
which
ol the output
That
for the second set ol
against Am
=
[9.52
4.08]T,whichwerecomputedforthefirstsetolregions.Moreover,letusnoticethatinthelowerplotPiandP2belongtothesameactiveregion,unlikefortheupperplot.Thisisgenerallytruefortheregionsdepictedinthelowerplot.Thatis,oncethecontrolerror2/2,re/—Viisfixed,thereisjustoneaffinecontrollawwhichcoversthestatespaceregardlessolthevaluesfor2/1,re/—Vi-Thisisaconsequenceolthehigherrinthelowerplot.ThisbehaviourcanalsobejustifiedbyconsideringthatforhighrvaluestheSingleInputMultipleOutput(SIMO)controllerbecomesaSISOcontrollerfortheoutputvariablewiththedominantweight.Asaresult,theactivelinearcontrollerisuniquelydeterminedbysuchoutputvariable.Figure3.8depictsregionscorrespondingtoahighweightforfirstoutputandsupportsthisconjecture.Inthelowerplot,theregionscomputedforr=10~3andthesamesetolotheroptimizationweightsasforFig.3.7arerepresented.Intheupperplot,thesamesetolregionsdepictedintheupperplotolFig.3.7aredepictedforeaseolcomparison.Again,asaresultolahigherweightforthefirstoutput,theregionsareessentiallydefinedbythevaluesofVi,ref-V\ratherthany2,ref-V2-Wemayconcludethatthetopologyofpartitioninthestatespaceisalsoaffectedbyotherfactorssuchasthecomplexityoftheoptimizationproblem,theconstraintsontheoutputvariablesandtheparticularsectionofthestatespaceconsideredinthisexample.However,Figures3.7and3.8leadustoconsidertheratioofthetwooutputweightsrasarelevantfactordeterminingthetopologyoftheexplicitMPCcontroller.
3.3 Control
design
103
However,
since 2/2,re/ < 2/2, the controller would also increase the inlusion
150. The final
rate to lower MAP. Let us consider first the regions lor r
predicted plasma
concentrations.
optimal in the sense ol
is, lor this particular choice
are
=
weights, the control error yi,re/
Vi dominates 2/2,re/
V2
in determining the luture input actions at the point P\. Not surprisingly,
lor r
3000 we would obtain Am
[14.88 12.29 9.98]T. That is, MAP
deviations from the reference value dominate in this case.
Also, let us
—
—
=
240 ng/ml and y2,ref
80 mmHg.
would lead the controller to increase the
=
=
ratio r, the increments ol the inlusion
regions.
6.58
Precisely,
we
104
-20
-10
0
10
20
30
Analgesia
40
A j/2 [mmHg]
Figure
3.9:
Steady-state
MPC controller behaviour.
steady-state behaviour of the controller as a function
weights r. On the x-axis, MAP deviations from the
target values Aj/2
2/2—2/2,re/ are represented, whereas on the y-axis plasma
concentration deviations Aj/i
yi
2/i,re/ are represented. We obtained
the curves depicted in Fig. 3.9 by computer simulation. The plot shows that
if
during the closed-loop drug administration the patient's MAP stays
permanently away from the reference value by Aj/2, then the controller will
infuse to maintain plasma concentration such that Aj/i
aAj/2, where
Figure
3.9
depicts
the
of the ratio of the output
=
=
—
-
-
=
straight line corresponding to the particular set of
100
surprisingly, a increases with r. We chose 2/i,re/
400 ng/ml 2/i,mm
0 ng/ml and y2,re/
80 mmHg to
ng/ml, 2/i.maa;
simulate the steady-state controller's behaviour
is the
slope
in
use.
of the
Not
=
=
=
=
depictedinFig.3.9.Asaresultofthisparticularchoice,allthestraightlinesreachalowerandanupperasymptoteatAyiimax=—100ng/mlandAyiimax=300ng/ml,respectively.However,thesametypeoflinearbehaviourappliesregardlessofthespécifievaluesfor2/1,re/and2/2,re/-
a
weights
3.3 Control
3.3.3
design
105
Artifact tolerant controllers
Because measurement artifacts deteriorate the controller's
performance
and
Masuzawa, 1989),
patient (Fukui
appropriate
algorithm to detect and remove artifacts was designed. Unlike other ap¬
plications where artifacts occur in exceptional cases, in anesthesia they are
caused by routine manipulation of both the measuring devices and the pa¬
tient (Reid and Kenny, 1987; Ruiz et al., 1993). In our application, where the
blood pressure signal is acquired through the invasive method depicted in
Fig. 3.10 there are several sources of artifacts. Firstly, they occur when the
catheter line is flushed to prevent blood clots or whenever blood samples are
taken. Secondly, they may result from calibration of the measuring device
Our
or involuntary movement of the catheter (Van Egmond et al., 1985).
theoretical
framework
for
artifacts
observerin
a
handling
group proposed
based control schemes (Frei, Bullinger, Gentilini, Glattfelder, Sieber and
Zbinden, 2000; Frei, Kraus and Blanke, 1999; Frei, 2000). This approach
was extended here to the case of MPC and complemented with an approach
based on signal analysis techniques. Both approaches run in parallel during
closed-loop drug administration. That is, MAP measurements are consid¬
ered corrupted by artifacts when the first or the second method detects
can
be harmful for the
and
an
them.
Thiee-way
Blood
Catheter
Figure 3.10:
functioning,
valve
sampling
To
Flush
Invasive blood pressure
pigtail
signal
catheter inserted into the radial artery. To take
pigtail
bepulled.Inbothcasesthetransducerreceivestheinputsignalfromthepressurizedsolutioninsteadofthecatheter.Inordertodescribetheobserver-basedapproach,letusconsiderthe
the
mustfol ow-
by
Transducer
solution
To monitor
During normal
acquired through the
blood sample, the three-
measuring system.
the continuous blood pressure
way valve must be rotated
pressmized
a
is
90° counterclockwise.
To flush the system,
ing discrete-time
xc(kn(k
-
described
discrete-time
Ac
0
y(k)
where the states
=
are
C
by Eqs (3.1,3.2,3.9)
equivalent
xc(k)
n{k)
-
xc(k- -1)
1)
n(k
and
to cope with MAP disturbances.
an
together with a disturbance model represented by
The dynamics of n(k) are described by a pure (3.24)
integrator,whichwassuffi¬cienttocapturealltheMAPdisturbancestriggeredbyclinicalintervention.AcandBcarethediscrete-timeequivalentsofEqs(3.1,3.2,3.9).Theout¬putsy(k)inEq.(3.19)areplasmaconcentrationsandMAP,respectively.WeassumedthatMAPcanberegardedasthesuperpositionoftheeffectsitecontributionandtheadditionalstaten(k).Summarizing,wehave:C=10000000A;1(3.20)wherekassumesthevaluereportedinTab.3.1.w(k)andv(k)inEqs(3.18,3.19)weremodeledaswhitenoisesequenceswithcovariances:E(w(k)wT(k))E{v{k)vT{k))Pc00Pnoc00On(3.21)(3.22)WechosePc=0.1,Pn=1,Oc=0.1,On=1.Adiscrete-timeobserverwasdesignedfromEqs(3.18,3.19)andEqs(3.21,3.22)usingtheKaimanfilterdesignmethods.ArtifactsinMAPleadtounreasonableestimatesoftheobserverstates.Asaconsequence,thecontroller'sperformancewoulddeteriorateandthepatient'ssafetywouldbeputatrisk.Thereforeartifactsarerejectedintheupdateequationoftheobserverstates:x(k+l\k)==Ax{k\k-1)+Bu{k)+Le{k)i>{e{k))(3.23)y(k+l\k)==Cx(k+l\k)+Du(k)
106
Bc
0
Eqs (3.18,3.19)
u{k)
additional state
of the PK model introduced with
can
+
n(k)
be
which
Analgesia
state space model:
w(k)
(3.18)
-v(k)
(3.19)
the concentrations in the different compartments
was
added
xc(k)
regarded as the
Eqs (3.1,3.2,3.9)
the additional state
n(k).
3.3 Control
where
e(k)
=
design
y(k)
107
y(k),
—
it (l-w
mk))
=
L is the innovation matrix and
J
\y2{k)-h{k)\<b
M*)-fc(*)l>>
l
\^MtjFW
(3-25)
Eqs (3.23,3.24) and Eq. (3.25) is to reject MAP mea¬
to outlying values of the residuals e(k). The nonlinear
mapping tp(e(k)) is represented in Fig. 3.11. We can interpret Eq. (3.23)
The idea behind
surements
leading
40
-30
-20
-10
0
10
20
30
40
e(fc)[mmHg]
3.11:
artifact
follows:
as
Non-linear filter function
rejection
at every
with the MAP value
sampling time,
given by:
y*(k)=y(k)
If
no
(-0
<
artifact occurs,
1),
tp(e(k))
defined in
Eq.
(3.25)
for
purposes.
^
—>
1 and
the observer states
+
the states of the observer
^(e(k)) (y(k)-y(k)).
y*(k)
are
—>
y(k).
updated
When
with
an
averageofthemeasurementy(k)andtheobserverpredictiony(k).Inthissensetp(k)
Figure
a
weighted=
are
updated
(3.26)
artifact is detected
are
from
t
=
min
capturedbytheobserverdynamics.Notethattheeffectofartifactsatt=74minontheclosed-loopinfusionrateisminimizedbutnotcompletelysuppressed,sincethemeasuresy(k)stilldocontributetoy*(k),accordingtoEq.(3.26).Thisisnecessarytoguaranteethaty(k)—>y(k)whentheperiodofartifactisover.Theobserver-basedapproachhingesupontheassumptionthatallMAPtransientsresultingfromoccurrenceofartifactsleadtochangesinthedy¬namicsoftheresidualse(k)whicharemarkedlyfasterthanthetransientsresultingfromsurgicalmanipulationorphysiologicaldisturbances.Thisas¬sumptionmaybeviolatedduringperiodswhereintensesurgicalstimulationoccurs,suchasduringtheintubationphase.Figure3.13reportsanexamplefromaclinicalstudywhereMAPincreasedby25mmHgatt=113.3mininonesamplingtimeasareactiontointubation.Theartifactdetectionalgo¬rithmconsistedexclusivelyoftheobserver-basedmethoddescribedbefore.Asdepictedinthefigure,MAPmeasurementswereconsideredcorruptedbyartifactswhentheyweren't.Consequently,thecontrollerdidnotincreasetheinfusionratesignificantly.Thebénéficiaieffectsofhigherconcentrationsofanalgesicsduringtheintubationphasecouldnotbeobserved.AcomplementaryapproachbasedonsimultaneousanalysisofSystolic(SBP)andDiastolic(DBP)BloodPressurewasaddedtocompensateforthe
108
ip(e(k))
MAP measurement at that
looser,
a
during
in
flushing
Moreover,
was
Eq.
By choosing
such
device and
a
5
of the
(3.25)
considered to be
=
the artifact detection
Eq. (3.25) as thresholds for
one can suppress successfully artifacts resulting from
catheter and blood sampling. We did perform an off-line
7
68 min and the t
flushing
appropriatelyshort-
can
=
be regarded as a
particular sample
does not consider the presence of artifacts
most artifacts may lead to
mmHg
the MAP increase
and
a
validation. It is worth
74 min
=
particular surgical procedure.
noticing
time. The
measure
as
Figure
a
the artifact detection criterion is made
sharper (i.e. small MAP
artifacts) important MAP transients due
improper controller
that the artifacts
3.12 shows the
Analgesia
of confidence of the
dichotomous indicator.
proposed approach
deviations
to
of the catheter
resulting
measuring
respectively, were correctly detected.
due to increased surgical stimulation at t
50
from calibration of the
occurring
=
If
stimulus may be missed. On the contrary, if the artifact detection is made
painful
reaction.
20 in
simulation of the artifact detection scheme with real MAP data obtained
performance
at
3.3 Control
design
109
50
55
60
50
55
60
65
70
75
65
70
75
5
1
45
time
Figure
3.12:
80
[mm]
Off-line observer validation with clinical MAP data.
In the
plot, predicted and reference alfentanil concentrations are depicted.
In the second plot measured MAP (
) is plotted together with the ref¬
erence value, upper and lower constraints. The dotted line (•
•) represents
the values y*(k) which are fed back to the MPC controller. In the last plot,
the closed-loop infusion rate is depicted. MAP artifacts at t
68 min and
74 min were correctly captured.
at t
upper
•
=
=
comings of the observer-based approach. The method derives from observ¬
ing that during blood sampling
device
no
heart
pulse
or
is detected.
transients the transducer of the
not
flushing
or
calibration of the measurement
This is due to the fact that
measuring system depicted
receiving the input signal from the catheter placed
absence of
in
in the
during such
Fig. 3.10 is
artery. In the
pulse, SBP and DBP delivered by the monitor converge
Consequently, the Pressure Peak (PP) defined as PP=SBP-DBP
outlying values.
A
moving
average
approach
was
to MAP.
tends to
used to detect MAP artifacts with the
110
o
112
1125
113
114
Analgesia
1145
120-
fcf
Intubation
100-
60
-
.
112
^40
1=
3
_
_
2U
1
2
J
L
1125
113
1135
time
Figure 3.13: Example of an
description of the contents of
PP method.
At every
114
1145
incorrect artifact detection.
each
sampling
plot,
time
the average of the past N valid PPs.
11
[mm]
refer to the
k,
For
a
caption of Fig.
the actual PP is
detailed
3.12.
compared
with
If the actual value deviates from
mean at most by ±APP, the corresponding MAP value is
accepted and fed back to the MPC algorithm. Moreover, the actual PP
updates the vector of adequate PP values. If not, the MAP predicted by the
observer is fed back both to the controller and to the observer. The moving
average of PP values was adopted to accommodate for higher PP at higher
SBP. In any case, no PP values higher than 100 mmHg and lower than 20
mmHg are accepted. If artifacts persist, the infusion rate of the controller
would be determined by the MAP predicted by the model of the patient
included in the MPC algorithm and not by the MAP value itself. Using the
mere model prediction when artifacts occurs guarantees safe administration
for two reasons. First, MAP predicted by the PK-PD model embedded in
the MPC algorithm will always be decreased by alfentanil, since we assume
k < 0. Second, the model considered describes MAP profiles of a sensitive
the calculated
3.3 Control
design
111
subject without painlul stimulus. One may venture to say that under
considerations, the inlusion rate will always start to decrease as long
artilact
Figure
occurs
these
as
an
when yi > 2/2,re/on-line validation ol the
proposed algorithm during
15 mmHg. At t
256 min and
N=5, APP
blood
taken
and
the
PP
values
291
min
t
two
samples were
during those
transients lall outside the allowable range. In spite ol the large MAP values
displayed by the monitor, there is no harmlul increase ol the inlusion rate
by the controller.
a
3.14
clinical
reports
study.
an
We chose
=
=
=
samples
Blood
op
60
and
flushings.
—
50^
40302010-
0^
240
270
time
Figure
on
3.14:
[mm]
On-line validation ol the artilact
the PP values.
In the first
In the second
represented.
plot
and lower acceptable value. In
the controller is represented.
the
rejection procedure based
SBP, MAP and DBP are
plotted together with the upper
(• •)
last plot, the infusion rate computed by
plot
PPs
from above
•
are
controlwasstartedwithyi,re/=100ng/mlandy2,ref=70mmHg.TheupperandlowerlimitforpredictedplasmaconcentrationweresettoVi,max=400ng/mlandy\min=0ng/ml,respectively.ConcerningMAP,wesety2,max=120mmHgand2/2,mm=60mmHg,respectively.Wesetr=500,whichresultsinasteady-stateslopea=10[ng/ml/mmHg],asdepictedinFig.3.9.Inthefirstclinicalvalidationexamined,a37yearsoldwomanwhowasscheduledforlumbarherniaremovalwasenrolledforthestudy.Thesurgerylastedapproximately1hr.Figure3.15showstheclosed-loopcontrolper¬formanceafterthepatientwasintubated.Att=130minthepatientwasmovedintoasupinepositionbeforeenteringtheoperatingroom.Thisstim¬ulationincreasedMAPvaluesby30mmHgin2.5minapproximately.Thecontrollerincreasedtheinfusionrateuntilapredictedplasmaconcentrationof300ng/mlwasreached.Att=132minthetransducerdidnotreceivethesignalfromthearterialline.Thethree-wayvalvedepictedinFig.3.10wasinfactaccidentallyturnedwhilerepositioningthepatient.Thisre¬sultedinMAPartifacts,whichwerecorrectlydetected.Consequently,thecontrollerdidnotreactbyincreasingtheinfusionrate.Whenartifact-freeMAPmeasurementswereagainavailableatt=134min,theywereclosetothereferencevalue.Atthesametime,predictedconcentrationswere
112
were
3.4
In this section
controller.
coronary
installed
doses of
In all
cases
at
matichigher
we
perfusion abnormalities, hypertension or
study. Written informed
consent was obtained shortly before the premedication visit. The patients
received a 7.5 mg tablet of midazolam orally 30 min prior to anesthesia
as a premedication.
ECG, Pulsoxymetry, BIS-electrodes, intravenous line
artery disease
prior
dominant hand of the
propofol
thesiologist
provide the patient
u
=
120
were
arterial pressure measurement
to induction.
muscle relaxant mivacurium
presented here,
with
ml/h
a
was
patient.
was
for
Unconsciousness
and maintained with isofiurane
the infusion rate
was
approximately
was
right
maintained
sufficient initial amount of
analgesic.
Analgesia
Test of the Controller
Patients with cerebral
discuss the results of the clinical validation of the MAP
excluded from the
A 22 gauge Teflon catheter for invasive
inserted in the radial artery of the
induced with bolus
by
the
non
administered before intubation.
after intubation. The
1 min before intubation to
anes¬
Then auto¬
3.4 Test of the Controller
than their reference value.
rate to 0
113
Therefore the controller reduced the infusion
ml/h.
'
300
'
'
1
1
'
'
/
r—.
%
200
X
\
^100
^
j
n
j
j
120
125
i
Patient
reposition!!
i
L
L
120
Artifact
100
130
time
135
[mm]
Closed-loop control performance after intubation. In the upper
plots, predicted plasma concentrations y\ and MAP values yi are
represented together with the output constraints and the reference values,
respectively. In the lower plot, the infusion rate u is depicted.
Figure
3.15:
and middle
Figure
3.16
surgery.
60
depicts closed-loop performance during
At t
=
170 min and t
ng/ml, respectively.
control
same
adequate
rate.
The controller
the central
phase
of the
187 min yiêf was decreased to 80 and
The anesthesiologist wanted to test whether the
=
performance could be achieved with a lower infusion
able to perform adequately with respect to MAP
was
plasma concentration lower than 100 ng/ml from t =170 min
203 min, MAP
During skin closure, which started at t
The controller's reaction brought plasma concentration
was rising again.
up again, since MAP has a higher output weight in the controller design.
regulation
with
to t =200 min.
In the second
case
=
considered
we
examine
a
49 years old
woman
who
un-
114
Analgesia
200
Alternative titrations
150
1
/
100
^
50
0
L
1
J
1
L
J
1
1
1
J
160
165
170
175
180
185
190
195
200
205
210
90
Skin closure^
L
1
J
1
L
J
1
1
1
J
160
165
170
175
180
185
190
195
200
205
160
165
170
175
..AA^.
180
time
Figure
Ai
IW.W
jM.
lAl.
185
190
195
210
200
205
210
[mm]
Closed-loop control performance during a clinical study. For a
description of the contents of each plot, refer to the caption of Fig.
3.16:
detailed
3.15.
derwent hernia removal.
As it
can
be noticed from
revealed to be very sensitive both to
surgical
Intense and short
Fig. 3.17,
the
patient
stimulation and to alfentanil.
lasting stimulations at t
100,109,120,137,150,169 min
respectively triggered quick controller reactions which can be compared to
manually administered bolus doses. MAP decreased sharply after each raise
in the predicted concentrations. The most evident of these MAP drops oc¬
curred at t
=
100
=
min, when MAP decreased from the
minimum allowed level
MAP
signal resulting
during
anesthesia. At t
from the
flushing
of the
=
maximum to the
162 min
sampling
an
line
artifact in the
was
correctly
identified.
Fig.
3.18 the
uled for hernia
perioperative
removalisdepicted.Automaticcontrolwasactiveduringthewholeperiodconsideredinthefigure.Att=190minanarteriawasaccidentallycutbythesurgeon,creatingaconsiderablebloodlossan
In
a
course
of
a
49 years old
man
who
was
sched¬
115
1
1
1
1
1
400
Ï
3°°
-
-
!
0Û
£,
200
>-•
100
\
-
V
yX
v
-
0
90
L
L
L
l
1
l
J
J
100
110
120
130
140
150
160
170
M
20
S
Strong stimuli
/
00
-
80
60
90
/
'
j
/
^
!
«K
'
~~
-1
,
100
110
120
130
50
0
90
160
170
18
N
\
100
110
130
time
Figure
150
Repetitive bolusçs
5
•g
140
140
150
[mm]
3.17:
detailed
3.15.
slow decrease in MAP. As it
can be noticed from the figure, the automatic
190 min as a result of the hy¬
stopped the infusion rate at t
artifacts
period.
Furthermore,
potensive
occurring at t
210,227 and 252
min were correctly detected. The blood loss was not harmful for the patient
considered his relatively high BML
controller
=
=
In
Fig. 3.19 the initial phase of the closed-loop drug administration is de¬
picted for a 60 years old female patient. The surgery consisted in removing
a spinal tumor located in the proximity of the neck. Automatic control was
started at approximately t
8 min. We initially set yi,re/
50 ng/ml
because bolus doses of fentanyl were given before the controller was started.
The stimulations occurring at t
8.5 min and t
17.5 min respectively
triggered a controller reaction which led to peaks in the predicted concen¬
trations of approximately y\
=
=
=300ng/ml.Letusnowconsiderthestimula¬tionsoccurringaftert=55min,whereMAPreachedthesamelevelsasin
=
=
116
250
Analgesia
r
200150100-
0
100
200
220
240
260
-
-
S
a/
*S
i
**'*
"
'
'-|
**
¥f
f*
l^\J'l
*
rf
Blood
100
50
loss^^^
120
140
160
180
120
140
160
180
^
M^w*
200
220
240
260
280
200
220
240
260
280
r
40
30
20
10
100
time
Figure
[mm]
3.18:
detailed
3.15.
the
period
100
ng/ml,
between t
=
8 min and t
=
20 min. Since yi,re/
was
increased to
the controller reacts to
predicted concentrations,
In
as we
surgical stimulation by targeting higher
expected from Fig. 3.9.
Fig. 3.20 the performance of the closed-loop controller is depicted for the
patient considered before during occurrence of drift artifacts. These
artifacts can not be detected by the PP-approach but they can with the
observer-based approach. Drifts in the MAP signal are caused by a vertical,
accidental displacement of the three-way valve depicted in Fig. 3.10, with
which the MAP signal is calibrated. MAP drifts were artificially generated
by the anesthesiologistsbeatt=159.5minandt=161.5min,respectively.Inthefirstcase,thesensorwasmoveddownwards,leadingtolowMAPvalues.Inthesecondcase,thesensorwasmovedupwards,leadingtohighMAPvalues.AsdepictedinthemiddleplotofFig.3.20,thePPvaluesremainintheboundariesfortheartifactdetectioninbothsituations,
same
117
400
\
Alternative titration
f
300
I
200
\
\
\
-
\
>r
100
1
0
1
L
L
10
20
1
1
J
J
1
L
120
3
100
80
>-.
60
5
g
50
40
50
time
Figure
60
[mm]
description ol the contents ol each plot, refer to the caption ol Fig.
3.19:
detailed
3.15.
perturbation in the waveform ol the blood pressure signal.
approach was able to detect the sudden change
in MAP values, as depicted in the upper plot ol Fig. 3.20. Consequently,
the controller did not react to such artilacts episodes.
cause
there is
Figure
avoided
no
the artilact-based
However,
3.21
shows
clinical validation where the controller
a
overdosing. At
t
=
140 min
approximately,
a
successlully
strong surgical stim¬
ulation occurred. The controller increased the inlusion rate until the upper
Even though MAP remained at 110 mmHg for
was hit.
min, the controller decreased the inlusion rate during that pe¬
constraint y\tmax
roughly
2
riod to maintain
t
=
predicted
160 min and t
reference value. As
=
a
result,
in the range between 200
tion
Aj/2
=
y2
—
concentration at the upper constraint. Between
190 min MAP remained
constantly higher than the
targeted predicted concentrations
ng/ml. Despite the constant devia¬
was not constantly increasing until
the controller
ng/ml
and 300
2/2,re/, the inlusion rate
118
Analgesia
Drift artifacts
60-
40
J-
20-
159
501—
40-
^5
30-
g
"203
10-
159
160
161
162
time
163
164
165
[nun]
Figure 3.20: Controller's performance during drift artifacts. In the upper
plot the continuous line represents MAP measurements corrupted by arti¬
facts whereas
y*(k) (•
MPC controller.
•
•) represents
In the second
the upper and lower
acceptable
the values which
plot
PPs
(•
•
•)
are
fed back to the
plotted together with
plot, the infusion rate is
are
value. In the last
depicted.
the upper constraint y\tmax
Fig. 3.9.
was
hit,
thus
realizing
the trade-off
depicted
in
119
400
Dynamic trade-off
300
No
200
overdosing
o
120
120
Strong
100
stimulus
'
K
\
-
80
60
120
100
5
1
o1—
120
150
160
time
Figure
3.15.
3.21:
detailed
170
[nun]
120
Analgesia
Chapter
Modeling
of Anesthetic
4
Drug
Interactions
121
122
4
Modeling
of Anesthetic
Drug
Interactions
Se Esau vende la primogenitura per un piatto di lenticchie,
bisogna dire che il loro uso, come alimento, è antichissimo,
e che egli o n'era ghiotto all'ecesso o soffriva di bulimia.
Artusi,
La
sctenza
in
cucina
e
I'arte rh mangiare bene.
Foreword
In the
introductory section of chapter 1 we rephrased the practice of clinical
as a complex Multiple Input Multiple Output (MIMO) problem.
In chapters 2 and 3 we extracted two essentially decoupled Single Input Sin¬
gle Output (SISO) systems for the closed-loop administration of hypnotics
and analgesics, respectively.
anesthesia
The main
simplifying assumptions emerged from
analysis
study conducted on vol¬
The study protocol was described in detail in chapter 2.
The
unteers.
of
subsets
of
the
data
in
two
was
analysis
particular
performed
chapters 2
and 3. Loosely speaking, there was no evidence in the data that the anal¬
gesic alfentanil does systematically affect Bispectral Index (BIS). Similarly,
there was no evidence that the volatile hypnotic isofiurane does blunt Mean
Arterial Pressure (MAP) reactions to surgical stimulation.
reasons
the
for
adopting
such
of the data collected from the clinical
However, nothing
excludes that interactions between
notics may
In
was
decreased
chapter
as a
2
we
result of
documented the
a
and hyp¬
patient whose
analgesics
case
bolus dose of alfentanil.identifying
Suchanepisodeleadstoanintriguingquestion:howcanwebenefitfromsuspectedinterac¬tionamonganestheticdrugsinanautomaticcontrolsetting?Twosituationsmaybedistinguished.Inthefirstcase,likeitseemstobehappeningforanesthesiamaintainedwithisofiuraneandalfentanil,interactionsareweakandnotsystematic.InthiscasesporadicepisodesofdrugsynergiesmaybecompensatedwithoutdifficultybylettingthetwoSISOcontrollersproposedinchapters2and3runinparallel.Inthecasewheresynergiesarepresent,theywouldbebestexploitedbyautomaticcontrolstrategiesifamodeltoquantifythemwouldexist.Asamatteroffact,thepossibilityof
BIS
occur.
of
a
123
an
interaction model may be the
cases
discriminating
criterion between the two
envisioned above.
The need for
a modeling framework to quantify anesthetic drug interactions
triggering factor of the analysis presented in the the following chap¬
was
the
ter.
We will show that
existing approaches such
as
isobolographic
suffer from
methods
On the
multiple logistic regression
significant
the
model
the
surface
method¬
we propose hinges upon
hand,
response
ology, which emerges as a better solution for the special case of anesthetic
drugs. The interaction model we propose offers several advantages:
or
limitations.
other
•
it is suitable to describe different
between
types of interactions such
agonists, partial agonists, competitive antagonists
as
those
and inverse
agonists;
•
its
be
measured
complexity, as
identified, can
by
the number of parameters which must
be tailored to the size of the data set.
data sets of limited size the interaction
can
be described
Precisely,
by
one
for
single
parameter;
•
it
provides
accurate
description
concentration-response
•
of the interactions
over
the whole
range;
compatible with single drug models when interactions between
pairs of anesthetic drugs are considered. In the case of interactions
it is
among three
tween
drugs, it is also compatible with interaction models be¬
pairs of drugs. Particularly, pharmacodynamic (PD) parame¬
ters of both
single drug
embedded in the three
and combination of two
drug
drugs
can
be
directly
interaction model without the need of
re-estimating them;
the
was performed in collaboration with several institutions:
Department of Anesthesia and Pain Management at the Royal North Shore
Hospital in Sydney, Australia, the Stanford University School of Medicine,
California, the Department of Anesthesiology at the University Hospital in
Bern, Switzerland and Pharsight Corporation, Mountain View, California.
Our contribution at the Automatic Control Laboratory of the Swiss Federal
Institute of Technology
wastodevelopthemodelingframeworkforthethreedruginteractioncase.Wearepreciouslyindebtedtotheabovementionedinstitutionsforhavinginvolvedusinsuchachallengingproject.
This work
124
The
4
chapter
actions with
among
and
a
Modeling
of Anesthetic
Drug
Interactions
covers the mathematical part of the model for the drug inter¬
great detail. A clinical study was conducted to assess synergies
propofol,
midazolam and alfentanil. The result of the clinical
shorter mathematical
lowing chapter appeared
description
than the
one
presented
study
in the fol¬
as:
Minto, CF., Schnider, T.W., Short, T.G., Gregg, K.M., Gentilini, A. and
Shafer, S.L.: 2000, Response surface model for anesthetic drug interactions,
Anesthesiology 92, 1603-1616.
A
computational
and
tion of the models
a
visualization tool which support the identifica¬
presented
here
http://www.anesthesiology.org
can
be downloaded from the web site:
4.1 Introduction
125
Introduction
4.1
Combinations of anesthetic
in the clinical
drugs instead of a single agent are widely used
practice, both during the induction and the maintenance
of anesthesia.
Before the patient is intubated for instance, already three
drugs may have been already administered: a sedative during pre¬
medication, a hypnotic to induce unconsciousness and an analgesic to blunt
the hemodynamic reaction to intubation. Maintenance of anesthesia may
include continuous administration of a hypnotic and an analgesic, accord¬
ing to the principles that we embedded into the automatic control systems
described in chapters 2 and 3.
different
Several clinical benefits
sia
(Vuyk, 1997).
were
reported when performing multi-drug anesthe¬
advantages may result from drug synergies.
Most of these
Loosely speaking, synergy occurs
is capable of achieving the same
than the if
single drugs
were
when
a
clinical
side effects
end-point
used alone. In the
bination is less effective than the
interaction.
combination of two
opposite
the clinical
nificant
insight
we
case, when
a com¬
about
may provide sig¬
general anesthesia (Meyer, 1899;
recently discovered experimental ev¬
mechanism has been aban¬
Anesthesia must rather be
regarded as a series of
pharmacological actions. It may be conjectured for
that drug mixtures exhibiting synergies or antagonism are a clear
that drug effect is mainly modulated
concomitant
byligand-recpto¬s.Mfuwhvmx,(G195)TqB8;:
evidence
agents
amounts
practice, understanding drug synergies
(Kissin, 1993).
instance
drug
into the mechanisms of
Overton, 1901). In fact, in the light of
idences, the concept of anesthesia as a unitary
different,
or more
single agents,
speak
antagonistic
Synergy represents a favorable situation clinically, since most
are generally a consequence of drug overdosing.
Beyond
doned
with less
126
4
Modeling
of Anesthetic
Drug
Interactions
thetic
drugs: logistic regression is not mathematically consistent with the
single drug case, whereas isobolographic methods often provide descriptions
which
are
In this
limited to
range of concentrations.
framework to describe anesthetic
drug
First, we review the ap¬
proaches adopted in the literature, with particular emphasis on logistic
regression and isobolograhics methods. Precisely, the mathematical defi¬
Then we will introduce our
ciencies of such approaches are highlighted.
three
modeling approach to quantify two or
drug interactions.
we
interactions based
case
locus of
clinical
on
a
new
response surface methods.
Isobolographic
4.2
In the
propose
of two
pairs of
methods
drug interactions, isobolographic methods represent the
drug concentrations (Ca, Cb) achieving a determined
two
end-point
E.
In the
case
of additive
interaction, the isobole
isde¬scribedbythefollowingexpression(LoeweandMuischnek,1926):ECa,eECb,ewhereCaandCbrepresentthedrugconcentrationsofspeciesAandBattheeffectsite,respectively.ECa,ean(iECbêarethetheeffectsiteconcentrationsofspeciesAandBwhicharenecessarytoachievetheend-pointEifusedassingleagents.Thefollowingremarkscanbemade.1.Eq.(4.1)issatisfiedbychoosingCa=otECa,eandCb=(1—a)ECb,eVa<1.Thatis,inthecaseofadditiveinteraction,agivenend-pointEcanbereachedbychoosing(Ca,Cb)ascomplementaryfractionsoftheirrespectivepotencies(ECa,e,ECb,e)-2.IfCB=0(CA=0)Eq.(4.1)reducestoECa,e=CA(ECb,e=CB),whichisnothingbutthedéfinitionofECa,e(ECb,e)-Inotherwords,Eq.(4.1)iscompatiblewithsingledrugmodels.3.IfaHill(Hill,1910)modelischosentodescribethesingledrugeffect
chapter
a narrow
then
where
(4.2)
Em ax
ing
we
—
provides
oftheadditiveinterac¬tionexpressedbyEq.(4.3)foraspécifiesetofparameters.Figure4.2depictsthecorrespondingisobolesintheplaneofthedrugunitsUt=Ct/ECS0,ti=A,B.Inthecaseofsynergisticinteraction,weexpectthatthedrugconcentrationsinEq.(4.1)achievingadeterminedeffectEaresuchthatCt<ECtiE-ThefollowingmodelwassuggestedtobalanceanewtheleftsideofEq.(4.1):Ca,Cb,CaCbEGa,eECb,eECa,eEC^b,e1(4.4)wherea>0isasynergyparameterwhichcanbeidentifiedfromthedata.Themodeliscapableofdescribingantagonistictypeofinteractionifa<0.Figure4.3represents50%isoboles(r=1/2)forseveralvaluesofa.Thehigherthesynergyparametera,themoresignificantthebowingtowardstheorigin.TheratioS=om/on,whereomandonarethesegmentsdepictedinFig.4.3forthe50%isobole,isoftenusedasageometricindicatorofdrugsynergy(Grecoetal.,1995).IfEq.(4.4)holds,itcanbeshownthat:S=.,a:r-.(4.5)Thereisaspecialreasonwhythe50%isoboleisconsideredtodefinethegeometricindicatorinEq.(4.5).Infact,justinthisparticularcase,themostsynergisticdrugcombinationoccurswhenUa=
4.2
Isobolographic
Eq. (4.1)
we
set
may be
value AE
E
Eq instead of E. Consequently, also AEmax
Eq would have to be used instead of Em ax In the follow¬
a
=
will
r
methods
E
keep
=
can
=
EMAX
be
the
127
relationship
C?
CA
E/Emax-
simpler
^
+
rearranged
EC50it
alternatively expressed
t
as a
notation
three dimensional representationUb
=
expressed
A,B
Note that the clinical
the results which will be derived hold for both notations.
in
Eq.
(4.2)
as:
,
C
(4.3)
deviation from the baseline
end-point
(4.2),
in
—
Figure
Eq.
=
since
4.1
128
4
Modeling
of Anesthetic
Drug
Interactions
Figure 4.1: Response surface for additive interaction described by Eq. (4.1).
Both drugs are assumed to follow a Hill model with parameters: 7^4
4,
=
lB
=
2, EC50,A
=
20
EC50,B
=
10.
Eqs (4.1) and (4.4) hinge upon two assumption which severely limit their
application to anesthetic drugs. First, it is assumed that both drugs can
cause an effect E if used alone, which if not necessarily true, especially if
drugs A and B are administered to achieve different clinical end-points.
This may be the case for instance if A is a hypnotic, B an analgesic and E
is a clinical end-point for hypnosis such as BIS. In this case, we may have
00 and Eq.
Ca- Further,
(4.4) trivially reduces to ECa,e
ECb,e
provided the first assumption is satisfied, both drugs must achieve the same
end-effect, as represented for instance by the Em ax parameter in Eq. (4.2).
—>
Further, Eq. (4.4)
in
=
is also not
greater maximum effect
or
of describing interactions which result
asymmetric behaviour.
capable
4.3
Logistic regression
Figure
4.2: Isoboles
curves
corresponding
Logistic models
crete by nature,
scores.
measure,
For
are
often used to describe clinical
such
as
probability
depicted
in
Fig.
instance, if the considered clinical end-point
denoted
as
P, then
we
4.1.
probability
of
a
certain
concentration C such that
f(C)
=
are
dis¬
pain and seda¬
is
a
probability
have:
l +
P is the
which
end-point
of movement response,
P
drug
to surface
Logistic regression
4.3
tion
129
event,
f(C)
(4.6)
f(C)
f(C)
> 0.
e«o+alog(C)
If
_
is
a
generic function of the
we assume
ea0 Qot
(4.7)
130
4
of Anesthetic
Modeling
Drug
Figure 4.3: Isoboles at 50% for a
0,10,100,1000 in Eq.
drug model parameters were specified in the caption of Fig.
Interactions
(4.4). Single
=
where
a
>
0, then Eqs (4.7) and (4.6)
Hill model in
can
V
—
Em ax
ECso,2
equivalence
C
=
0
holds
provided
0.
implies P
The extension of
drugs
can
that:
a
EG'so,?
=
7 and «o
=
—"fôg(ECso)-
With
=
(4.7)
Eq.
be formulated
logit
One
to the
(4.8)
(^k.
\
Eq. (4.7)
equivalent
Eq. (4.2):
E
The
be considered
4.1
P
=
as
log
to describe additive interactions between two
follows:
P
=
1-P
positive aspect of Eq. (4.9)
a0 +
olaCa
+
(4.9)
aBCi
is that the 50 % isobole
(P
=
0.5)
is the
4.4 The two
straight
drugs
interaction model
line
CB
=
-«L
aB
as we
-
^CA
(4.10)
cv-B
expect for symmetry with additive models described in the previous
section.
major flaw of Eq. (4.9) is that, in the absence of both drugs,
end-point has the non-zero probability P
ea°/(l + ea°).
One
the clinical
A
131
=
straightforward
correction to such
deficiency
would be to
use
the
following
additive model:
logit
P
=
a0 +
aA\og(CA)
log(CB)
+ aB
(4.11)
Eq. (4.9). In this case however, the 50 % isobole is bowed towards
origin, independently from the choice of the parameters. Precisely, we
instead of
the
have:
CB
=
C-^.
(4.12)
CT
Eq. (4.12)
also
to reach 50
The
implies
following
Lang:
modification of
constantaddedinsidethelogarithmofeachdrugconcentrationwaspresumablyintroducedtohavelog(1+C^)=0ifCA=0.However,thebowingtowardstheoriginremains,sinceEq.(4.13)canbemerelyregardedasashiftofEq.(4.11)intheplaneofthedrugconcentrations(Ca,Cb).4.4ThetwodrugsinteractionmodelBeforeintroducingthenewmodel,letintroducethedefinitionofunitsofdrugsAandB:Ua=W^~Ub=w^~(414)
logit
The additive
that either
drug
must have
an
infinite concentration
% of the maximum effect if used alone.
P
=
a0 + aA
Eq.
(4.11)
log(l
+
CA)
was
proposed by
+ aB
log(l
+
McEwan and
CB).
(4.13)
132
Then,
let
us
define
a
of Anesthetic
Modeling
4
fixed combination of
drugs A
Drug
Interactions
and B with the fractional
unit:
»
The model
we
propose
hinges
=
Ä-
upon two main
(4-1B»
assumptions. First,
a
fixed
drugs (9
regarded
drug. Second,
const.)
drug follows a Hill model when the total concentration is increased
while maintaining a fixed drug fraction 9. Extending the Hill model in Eq.
(4.2) to describe this two drug interaction we have:
combination of
be
can
as a new
new
(Ua + Ub
E
=
yU;{8)\l{e)
EMAX{9)
i
1
where
7(6*)
and
Em ax (6)
are
7(s)
,
+
V
Ua±Ub}
ly
'
(4.16)
u50(e)
the steepness and the maximum effect parame¬
tersofhdugcmbina.C/50(6)pylvzI,w9=1Eq4H2TU-SLxF+kVG[]<'>^¬:ß7
this
=
1.
2.
plane(Ua,Ub)occursfor1/a=Ub-Figs4.4and4.5representthesurfaceresponseandtheisobolesforaparticularchoiceofthesetofparameters.Forthe50%isobolewehave:S=,4N.(4.18)(4-/3){'FromEq.(4.18)wealsoderiveß<4.3.ThesynergyparameterßinEq.(4.17)canbeestimateddirectlyfromthe50%isobole.Infact,onthiscurve,accordingtoEq.(4.16)itmustbeUA+UB=1/50(6)Precisely:U\+U%+U\(WB-1)+Ul(WA-1)=(ß+2)UAUB.(4.19)ßbeestimatedwithstandardlinearregressionalgorithmfromthepreviousexpression.IfEq.(4.17)istoorestrictive,inthelightofthediscussionabove,higherorderpolynomialcanbeused.However,if1/50(6)GPn,n—1parametersmustbeidentified.Thismaybedifficult,consideredtheextremeinterindi-vidualvariabilityandthecostofeverydatapoint.InEq.(4.17),testingsynergyislimitedtothetestofasingleparameter.Analogousargumentsholdforthedéfinitionof7(0)andEmax(Q)-Simi¬larlytoEq.(4.17),wemaydefine7(0)=7A+(IB-1A-ß)0+ß62(4.20)Emax(ö)=Emax,a+(Emax,b-EMax,a-ß)0+ß62.(4.21)
4.4 The two
at 6
1/50(6)
Let
that
the
=
drugs
=
drug
combination of
that
1/a
=
a
us assume
EMax,a
interaction model
and
=
In this case, the
Ub
equal
=
b
or
that there is
EMax,b
point of
units.
=
Ua
=
b and
133
in the
Synergy in Eq. (4.17) occurs if ß > 0. Let us assume that this is the case
following discussion. Two properties of Eq. (4.17) are worth to be
mentioned.
C/5o(l 6). That is, the maximum synergy occurs necessarily
1/2 and there is a symmetric behaviour with respect to the
—
In other
Ub
words,
=
a
are
combinations such
equivalent.
no
interaction at the Em ax parameter and
EMax- That is, EMax(0)
EMax V 6.
maximum curvature of the 50% isobole in
=
134
Figure
(4.16)
Response
4.4:
and
(4.17).
parameters:
EMax,a
4.5
Modeling
4
=
7^4
surface for
Both
4,
=
Emax,b
=
75
drugs
=
100 and
The three
For the three
drugs
synegistic
are
Drug
Interactions
interaction described
assumed to follow
2, ECso,a
1.5.
ß
=
20
a
ECso,b
by Eqs
Hill model with
=
10.
Further,
=
interaction model
drugs
interaction
of Anesthetic
model, the same concepts and assumptions
apply. For any fixed ratio of the drugs
described in the
previous
A,B,CrA simple
ship. That is:
Hill model describes the concentration
section
vs.
effect relation¬
(Ua+Ub + Uc^1^
E
—
1
In this case,
however,
a
(750(e)
\
Emax{6)
Ua + Ub + Uc
combination is
fractions of two among the three
drugs
(4.22)
7(s)
U50(9)
uniquely
defined when the
in the mixture
are
specified.
drug
We
4.5 The three
Figure
interaction model
drugs
4.5: Isoboles
curves
135
to surface
corresponding
depicted
in
Fig.
4.4.
may choose:
Ur
Up
UA
Obviously
priate
6a
1
=
functions
—
Ob
+
—
UB+ Uc
For
®c
a
UA
fixed
+
(4.23)
UB+ Uc
drug combination,
Emax(Qb,Qc), 7(#b,#c)
and
Uso(6b,6c)
we
seek appro¬
which meet the
following specifications.
1.
If
6a
ically
=
0, the three drugs
arguments
2.
If there is
Consider
same
must hold il
an
a
sham
drug,
should
yield
A and C.
6b
=
0
or
6c
=
drugs
B and C.
a
experiment in
drug that shows
the
which
Analogous
0.
additive interaction among the three
experiment, the
or
interaction model should resolve mathemat¬
to the interaction model between
drugs
drugs,
B and C
synergy with
then U;50
are
drug A.
actually
1.
the
In this sham
interaction of A with any combination of B and C
same
interaction
as
the interaction between A and B
4.
and
Few
4
other
The model should be
words, it should
which drug is assigned
We propose
by a parabola. Even though higher
order polynomials would give more flexibility, it may be hard to identify
all the parameters from experimental data with sufficient accuracy. Every
interaction parameter can be described by the following polynomial:
Uso(6b,0c)
a
P
are
=
+
q0 +
qBc0B0c
properties of Eq. (4.24)
canbehighlighted.1.Themodelispolynomial,thereforesmoothandinfinitelydifferen-tiable.2.Themodelisafunctionof0Band6c,because9a=1—9B—9c-9aisexpressedinthelasttermforclarity.Thetermçabccanberegardedasthe'threedruginteractionterm',sinceitvanishesoneachaxisofthetriangleofcompositions,thatiswhenpairsofdrugsareconsidered.3.ThelasttermqABC'9A9B9cinEq.(4.24)canbesubstitutedwiththemoregeneralexpression9a9b9c/(9),wheref(9)isageneralfunctionofthecompositionvector9.Thistermsatisfiesthesamepropertyofvanishingontheaxesandenablesmoreflexibilitywiththechoiceof1(0).SinceforthethreedrugsinteractioncaseofEq.(4.22)theeffectisafunc¬tionofthreeindependentvariables,theeffectsurfaceresponsecannotberepresentedgraphically.However,sincetheinteractionparameterswereas¬sumedtodependonthecompositionofthemixture,athreedimensionalrepresentationispossible.Figure4.6depictsthecompositiontrianglewhichisusedforthreedimensionalrepresentations.Everypointinsidethetrian¬gledefinesadrugcompositionsuchthat9a+9B+9c=1.Figure4.7representstheinteractionparameterP=Emaxforaparticulardrugcom¬binationexhibitingantagonism.Figure4.8representstheinteractionpa¬rameterP=Usoforaparticulardrugcombinationexhibitingsynergy.
136
Modeling
as
qBeB
+
A,
+
qc9c
of Anesthetic
symmetrical
meet the above
model where interaction parameters
+
qBB92B
qABc0A0B0c
+
Drug
with
<lcc9c
Interactions
regards to A, B and C.
specified criteria regardless
In
B and C.
of
described at most
Emax(9b, 6c), l(9B, #c)
+
(4.24)
4.5 The three
Figure
4.6:
parameters
triangle
drugs
Three
by projecting
verified that 6 a +
(4.24)
was
137
drugs composition triangle
Emax(Qb,Qc), i(0b,0c)
is assumed to have
be obtained
Eq.
interaction model
Ob
+
®c
and
to
represent the interaction
Uso(6b,Oc)- Every
side of the
unitary length. The fraction of each drug
the
=
point
1
p
along
the three axis. It
can
be
can
easily
•
developed by assuming
that for every
pair of drugs the
interaction model is known and has the form:
Pab =Pa
+
(Pb -Pa- ßAB)0B
+
ßAB 02B
(4.25)
Pac
Pa
+
(Pc -Pa- ßAc)Oc
+
ßAc0c
(4-26)
Pb
+
(Pc -Pb- ßBc)0c
+
ßBc02c
(4.27)
Pbc
=
=
where
Pa, Pb and Pc are the parameters of the single drugs when given
ßAB, ßAC and ßßc are the coefficients for the three paired inter¬
actions. By imposing the surface in Eq. (4.24) to become Eqs (4.25,4.26,4.27)
when 6c
0 and 6a
0 respectively, we obtain the following set
0, Ob
alone,
and
=
=
=
4
138
4
Modeling
of Anesthetic
Drug
Interactions
—
35-
3
—
25-
2-
1 5-
1-
05-
01 2
Figure
4.7:
such that:
ßßC
=
Interaction parameter
EMax,a
2, /?ABC
=
=
3, EMax,b
=
Emax(Qb,®c)
3.5, EMax,c
f°r
=
drug combination
4, /?ab
3, /?ac
3.5,
a
=
=
5.
of constraints:
Pa
--=
<7o
(4.28)
Pb
--=
qo + qB + çbb
(4.29)
Pc
--=
qo + qc + qcc
(4.30)
ßAB
==
qBB
(4.31)
ßAC
--=
qcc
ßBc
--=
qcc + qBB
(4.32)
-
cqsc-
(4.33)
Eqs (4.28,4.33) represent a linear system of order 6. This was expected, since
the parameters we imposed equivalence with are single drug parameters
(Pa, Pb,Pc) and the paired interaction parameters (ßAB, ßßc, ßAc)- Since
the interaction models for the three different pairs of drugs are known by
4.5 The three
Figure 4.8:
that: ßAB
interaction model
drugs
Interaction parameter
=
0, ßAC
=
2, ßBC
assumption, Eqs (4.28,4.33)
=
can
139
Uso(9B, 6c)
1, ßABC
=
for
a
drug
combination such
-2.
be inverted to
give:
<7o
==
Pa
(4.34)
<1B
==
pB-PA-ßAB
(4.35)
qc
==
Pc-Pa-ßAc
(4.36)
qBB
==
ßAB
(4.37)
qcc
--=
ßAC
qBc
--=
ßAB
(4.38)
+
ßAC
-
ßl
(4.39)
specified in Eq. (4.24), the three
Testing of synergy resolves to testing significance
of one single parameter, in analogy with the two drugs interaction case. If
experimental data justify the use of more involved types of expressions in
Eq. (4.24), then the term /(#) may be used instead. It can be verified
that Eq. (4.24) satisfies both the symmetry condition and the condition
There is
just
one
left parameter to be
term interaction çabc-
140
4
expressed by
just
a
the sham
matter of
brevity.
Modeling
of Anesthetic
Drug
Interactions
experiment. Since verification of such statements is
simple algebraic manipulations, the details are omitted for
Chapter
5
Conclusions
5 Conclusions
142
Slugs
and snails
are
after me, DDT
keeps
me
Now I guess I'll have to tell 'em that I got
Gonna get my Ph.D. I'm
The
a
-
This thesis described the recent
Rocket to Russia. Side
developments
cation in the realm of anesthesia.
first
cerebellum.
B,
I.
Main achievements
5.1
and
happy
teenage lobotomy.
Ramones, Teenage Lobotomy
were
no
of automatic control
appli¬
Two model-based feedback controllers
thoroughly discussed for the closed-loop administration
analgesic drugs. To the best of the author's knowledge,
model-based controllers ever applied on humans for the
of
hypnotics
both
are
scribed in the thesis. We discussed the above mentioned controllers not
presenting their technical aspects, but
feasibility
we
patients undergoing general
on
the
purposes de¬
only
also demonstrated their clinical
surgery.
This thesis also discussed
an important contribution to the study of anes¬
drug interactions. We introduced an adequate modeling framework
quantify pharmacodynamic (PD) interactions among two and three drugs
thetic
to
combinations.
In this final
chapter
we
summarize the main results achieved.
section is associated to every
the
as the chapter title.
approaches proposed in
same
of the
some
chapter
In every section
the
approaches presented
practice.
may have
we
on
We also focus
other research
A separate
The section title is
discuss the limitations
corresponding chapters
directions for future research.
clinical
of the thesis.
on
the
while suggesting
impacts that the
applications
and
on
the
5.2 Automatic control in anesthesia
Automatic control in anesthesia
5.2
Main achievements
5.2.1
In
143
chapter
1 the
steps towards the development of
system taken at
an
described. As
autonomous anesthesia
result of a solid coop¬
laboratory
evaluate the clinical
in
we
can
University Hospital
Bern,
benefits of closed-loop controllers which regulate seven different patient's
outputs. To date, more than 200 patients were treated with closed-loop
controllers during general anesthesia. These controllers regulate O2, CO2,
inspired and expired anesthetic gas concentrations in the breathing sys¬
tem, Bispectral Index (BIS) and Mean Arterial Pressure (MAP) with both
our
were
a
eration with the
volatile and intravenous anesthetic agents.
Two controllers which
this
chapter.
use
Both aim at
isoffurane
drug were described in
depth of hypnosis using MAP and
controllers adopt particular schemes to
regulating
BIS
as
anesthetic
the
The
as surrogate measures.
prevent overdosing in the clinical practice and guarantee safe operation in
the presence of measurement artifacts.
different
The controllers also adapt to the
operating regimes of the breathing system, guaranteeing adequate
performance.
practice
were
was
The successful application of both controllers in the clinical
shown, indicating a higher quality anesthesia for subjects who
treated with automatic control.
5.2.2
Outlook
Chapter 1 raises the question whether there will be a time when closedloop drug administration will be routinely adopted in the operating room.
Assuming technical perfection and guaranteed safety of the proposed ad¬
On
one
schemes,
two obstacles must be overtaken.
hand, anesthesiologists
must be
persuaded
that automationsrelotnc
inthsfeldoamrvgpu.R,bykcAB:"9%1N
ministration
5 Conclusions
144
cannot take
the
over during emergency situations. However, they
working quality for the 99% of the time.
On the other
hand, patients
must be convinced that
with automatic controllers represents
a
clear
advantage
can
undergoing
both for
improve
surgery
her/his
rioperative and postoperative period. We found that convincing
a
pe¬
patient
about the
advantages of closed-loop drug delivery is quite straightforward,
provided
anesthesiologist is convinced first. We feel that most of the
persuasive power lies in the enthusiasm and in the confidence of physicians.
the
To obtain informed consent from
controllers,
that you would
would you
patients for the clinical evaluation of
our
it often sufficed to face them with the
never
travel
across
the
ocean
or
an automatic controller aboard?".
prefer
fly
the
the
between
the flight and the dive into uncon¬
Having grasped
analogy
most
sciousness,
patients accepted favorably the automatic controller.
5.3
5.3.1
In
to
with
following dilemma: "Given
without a pilot in the cockpit,
without
Feedback control of
hypnosis
Main achievements
closed-loop controller to regulate hypnosis as¬
Volatile agents
was thoroughly discussed.
such as isofiurane have slower onset and require more cumbersome actua¬
tors than intravenous drugs such as propofol. However, concentrations in
the central compartment can be measured on-line. This advantage was ex¬
ploited by the proposed cascaded Internal Model Control (IMC) structure:
the control system has an internal closed-loop controller for endtidal concen¬
trations which dominates if BIS measurements are corrupted by artifacts.
chapter
2 the cascaded
sessed with BIS with isofiurane
We showed that for
particular application, both the cascade arrange¬
approach to control offer several advantages over
other techniques. First, it permits useful off-line model validation and anal¬
ysis. Second, it allows to adapt the controller to the different respiratory
our
inastraightforwardmanner.Third,italsoprovidedaneasyframeworktodesignartifact-tolerantcontrollers.Fourth,thecontrolleriscapableoflimitingendtidalconcentrationsbetweenalowerandanupper
ment and the model-based
conditions
5.3 Feedback control of
hypnosis
145
limit to prevent the
patient from awareness and to avoid overdosing, re¬
spectively. Fifth, anti-windup measures protect the control scheme against
performance degradation in the event of saturation of the input signal.
Summarizing, we were able to show satisfactory performance of the BIS
controller during general anesthesia. We believe that the clinical validation
of the controller will also confirm the usefulness of BIS monitors as a guide
for the closed-loop administration of hypnotic agents.
Outlook
5.3.2
Not
withstanding
their
increasing popularity
monitors may not be the ultimate
depth
(AEP)
of
hypnosis.
may reveal
advantages
situations. As recent studies
the
practice, BIS
as
Auditory
Evoked Potentials
with respect to BIS monitors in
seem
region of light sedation and
to
react
suggest, they
more
may be
promptly
in
more
detecting
particular
reliable in
an
arousal
al., 1999).
design closed-loop controllers which deliver hypnotics on
a basis of a degree of hypnosis estimated from multiple sensors. If designed
properly, those controllers may not only provide a better patient care, but
they may give important insight into the nature of drug induced uncon¬
reaction
case
(Gajraj
chapter
Other indicators such
in the clinical
in the seek of monitors for the
et
A natural research direction to pursue in this
would be to
sciousness.
It
can
be
that on-line identification of the patient's spécifie charac¬
improve the controller's performance. For instance, identifying
argued
teristics may
whether
a subject is particularly sensitive to the drug may suggest the need
detuning the controller to prevent overdosing. These ideas are currently
being explored in our research project and will be published in future works.
The
proposed
control structure is not limited to isofiurane. In
factthesameapproachcouldbeadoptedforanyvolatileanestheticaslongastheappro¬priatepharmacokinetic-pharmacodynamic(PK-PD)modelisused.Thismakesitanidealdesignforotherclinicalsituationssuchaspediatricanes¬thesiawhereothervolatileagentsareused.AfeasibleextensionoftheproposedapproachwouldconsistinincludingotherphysiologicalvariablessuchasMAPinthedecisionalgorithmfordrugadministration.Ingeneral,wecannotallowexcessivelylowMAP
for
5 Conclusions
146
while the
drug is administered
closed-loop control of
to maintain
a
desired level of BIS. A simul¬
BIS and MAP may be
designed to address
equivalently to the
one presented for control of MAP and endtidal concentrations in chapter
2 may serve the desired purposes. Alternatively, vasoactive drugs may be
infused to compensate for the hypotensive or hypertensive periods.
taneous
the above mentioned issues.
Feedback control of
5.4
5.4.1
In
An override arrangement,
analgesia
Main achievements
closed-loop administra¬
regulating both
MAP and predicted plasma concentration, realizing an adjustable trade-off
between open- and closed-loop administration schemes. An MPC control
algorithm was adopted, which is capable of handling complex control ob¬
jectives such as input/output constraints and drug minimization. Anesthe¬
siologists are able to adjust output constraints to the intensity of surgical
stimulation or to the patient's characteristics.
chapter
tion of
The
3
we
introduced
opiates during
explicit
a new
surgery.
paradigm
for the
The control system aims at
formulation of the MPC
algorithm
problem
considered for the
imple¬
platform, which gives
more insight about controller behaviour for a particular choice of the ob¬
server's states, output and references values, respectively. Also, it allows
mentation of the control
was
in the real-time
to show the
relationship between the optimization weights in the MPC al¬
gorithm and the control action in a more transparent way. Among the
advantages of the proposed control strategy, we want to stress that this
approach may be adopted for any other analgesic drugs by simply using a
different PK-PD model in the MPC algorithm.
An observer- and
a signal-based artifact detection algorithm were imple¬
closed-loop system. The controller is therefore capable of
handling MAP artifacts during surgery and consequently to protect the pa¬
mented in the
contrle'sbhaviu.Tfpmwdx¬
tient from hazardous
5.4 Feedback control of
5.4.2
As
analgesia
147
Outlook
pointed
out in the
more
in this
indicator of the
There have been
tient from
chapter,
and much
than for
hyp¬
optimal
analgesic drug
major lack
Even though analgesic drugs are primarily adminis¬
to be compensated.
tered to obtund hemodynamic reaction to surgical stimulations, MAP may
not be the optimal clinical end-point for opiate infusion. In this respect,
an approach using several hemodynamic variables such as HR, cardiac out¬
put and blood pressure signal simultaneously may reveal advantages with
respect to the scheme presented here.
notics,
the
numerous
attempts
variables.
to rate the
analgesic
None of them
state of the pa¬
to have
emerged
closed-loop delivery, probably because cardio¬
vascular signals like MAP are modulated by numerous other factors beyond
insufficient analgesia such as biological feedback regulation and vasoactive
drugs.
as a
hemodynamic
case
effect is the
seems
stand-alone indicator for
Alternatively, one may use Somatosensory Evoked Potentials (SEP) for the
closed-loop infusion of analgesic drugs, which may also provide insight both
into the nature of perception of noxious stimulation during unconscious¬
ness and into the influence of opiates on the autonomic system reaction
(Thorpe, 1984). A considerable benefit may result from performing such in¬
vestigations in a future research. Also, one may ascertain whether the costs
of an additional monitoring technique are outweighed by a better infusion
regime of intravenous analgesics.
The infusion
policy we presented for analgesic drugs could be extended to
therapies for insulin-dependent diabetes subjects. As we de¬
scribed in the chapter, the control strategy realizes an adjustable trade-off
between an open- and a closed-loop infusion policy. The open-loop policy
is determined by a drug distribution infusion
new
modelwhichishighlyuncertain.Theclosed-looppolicyisdeterminedbyameasurementofdifficultinterpreta¬tionsuchasMAP.Thesamepremisesholdforstate-of-artinsulintherapies.Theopen-loopinfusionregimenisdeterminedbyanexperiencedphysicianwhoprescribesinsulininjectionsonthebasisofthepatient'slifestyle.Thedosesofthesingleinjectionsareadjustedonthebasisofsparsebloodglucoseconcentrationmeasurementstakenbythepatient.Thisconstitutesaclosed-loopadjustmenttotheopen-looppolicy.Thecontrolsystemfor
define
5 Conclusions
148
of
analgesics can be rephrased with the terminology of insulin therapy by
substituting MAP with blood glucose measurements. Also, predicted con¬
centrations of analgesics must be substituted by concentrations of glucose
predicted by a dynamic model of the glucose-insulin system. If used in the
insulin therapy context, the Model Predictive Controller (MPC) presented
in the chapter would allow to handle constraints both for predicted and mea¬
sured variables. This makes it ideal for insulin therapy, since hypoglicemic
or hyperglicemic episodes may be ruled out in the same way underdosing
or overdosing of analgesic drugs were in the closed-loop strategy presented
in the chapter.
Another
interesting research opportunity unearthed by the closed-loop vali¬
dation of the controller lies in
some
aspects of the artifact
detection/prediction
were not covered by this and pre¬
physiological signals,
vious works (Frei, 2000). In fact, even though model-based approaches for
artifact handling can be easily implemented as extensions of model-based
control strategies, they are still inherently coupled with the particular con¬
trol strategy for which they were designed.
Further, for observer-based
their
is
correct
methods,
guaranteed if and only if artifacts lead
operation
to transients in the residual dynamics which are faster than those triggered
by surgical stimulation or other physiological events. As we showed with
a clinical example, this assumption may not always be true. We did intro¬
duce a signal-based algorithm, which compensates for such limitation. We
believe that an artifact detection approach which is solely based on the beat
to beat blood pressure signal sampled at high frequencies (> 50 Hz) may
represent
on
a
which
feasible solution for control purposes.
frequency
and time
several purposes.
A
have
Several methods based
been
techniques
already
successfully applied
major advantage of such approach would be that
least for the detection part
-
the method would be entirelyproject.
decoupledfromtheparticularcontrolapplicationconsidered.Thisissuemaybeaddressedinthefutureoftheresearch
problem
for
-
for
at
5.5
Modeling
drug
interactions
of anesthetic
Modeling
5.5
149
drug
interactions
Main achievements
5.5.1
In
of anesthetic
a new modeling framework to quantify anesthetic drugs inter¬
proposed. The approach we described overcomes the limitations
of other methods which were applied in other biomedical disciplines such
The
as isobolographic methods or multiple logistic regression techniques.
framework we proposed stems from the response surface methodology which
emerges as a better solution for the special case of anesthetic drugs. It is
chapter
actions
4
was
suitable to describe different types of interactions such
onists, partial agonists, competitive antagonists and
as
those between ag¬
agonists. The
complexity, as measured by the number of parameters which must be
identified, can be tailored to the size of the data set. Precisely, for data set
of limited size interaction can be described by one single parameter. Finally,
it is compatible with previously identified model parameters for single and
inverse
model
pairs of anesthetic drugs.
5.5.2
Outlook
Even
though
notic
synergies
the
presented models have already been used to explore hyp¬
midazolam, propofol and alfentanil, several other in¬
need
be
carried out before automatic controllers can exploit
to
vestigations
these synergies. Just when this stage is attained, it will be possible to ex¬
ploit the benefits of multi-drug anesthesia in automatic control algorithms.
As an example, opiates often potentiate the hypotensive effects of isoflurane (Vuyk, 1997). In a control scheme where hypotension is regulated by
volatile hypnotic agents, closed-loop administration of small doses of opiates
may lead to the same therapeutic effect with less drug consumption.
5.6
The
among
advantages
isnaturaltoaskwhethersuchcontrolstrategies
All the control schemes
based
approaches.
It have
presented
in this thesis
were
designed
with model-
5 Conclusions
150
real
a
of
advantage over more classical control techniques such as simple PID
fuzzy controllers. The author of this thesis is inclined to believe they do.
A first
represented by the ease
though model-based control schemes require a more in¬
volved implementation, they are easier to tune than other techniques and
easier to adapt to changes in the operating regimes. An example was pro¬
vided by the cascaded IMC controller described in chapter 2, where anes¬
thesiologists can tune the controller to match their expected performance
without the help of the system engineer and where on-line model adaptation
is able to compensate for changes in the actuator dynamics. Second, modelbased control techniques provide an elegant and easy framework to design
artifact and fault tolerant control schemes. Third, model-based control tech¬
niques provide a straightforward framework to implement complex control
objectives such as multiple output regulation, drug minimization, handling
of input and output constraints. We demonstrated the multitasked features
of the MPC controller with the clinical experiments discussed in chapter 3.
of
advantage
tuning.
of model-based control strategy is
Even
The fact that model-based
techniques need a dynamic model is a pleonasmus
spell out. As we showed in chapter 2, identification
of accurate models for the drug distribution and effect is made difficult by
the cost of experimental studies, the lack of measurements which reduces the
which may be worth to
number of parameters which
variability.
can
be identified and the extreme interindivid-
It is naive to say if not erroneous,
though,
Infact,beforetestingourcontrollersonhumans,extensivesimulationoftheclosed-loopperfor¬manceisnecessary.Forthispurpose,amodeloramodelclassforthedrugdistributionandeffectmustbepostulatedalsowhennonmodel-basedtechniquesareadopted.Model-basedcontroltechniquesmakeuseofdynamicmodelstopredictthefuturebehaviourofthepatient'sphysiologicaloutputs.Thesemodelsmir¬rormoreorlessaccuratelytheanesthesiologist'sclinicalexperienceandtheiruseimprovesthephysicians'confidenceinautomaticcontrolstrate¬gies.However,thecontrolalgorithm'perse'islesstransparentwithsuchapproacheswhencomparedtononmodel-basedtechniques.Forinstance,evenfortheexpertsystemengineeritisdifficulttoestimate,onthebasisoftheactualoutputmeasurementswhatwilltheIMCcontrollerdescribedinchapter2chooseasthenextinputaction.Ontheotherhand,thecontrol
ual
non
model-based
strategies do
not
require
a
model.
that alternative
5.6 The
advantages
151
actions computed by a fuzzy controller may be easier to predict. Anesthe¬
siologists tend to prefer control schemes where they are able to predict, in
parallel with the controller, the future input moves. These strategies may
include fuzzy or rule-based controllers. This attitude is understandable if
one considers that the control algorithm will substitute the physician in the
decision process.
However,
a
this does represent
research and
Let
a
clinical
a
limitation
perspective.
more
There
consider
are
than
an
advantage
at least two
both from
reasons
for that.
controller for
us
as an example using a fuzzy
closed-loop drug
delivery during anesthesia. First, tuning a fuzzy controller boils down to
reproducing the anesthesiologists' set of rules to administer drugs. These
set of rules are not only hardly countable but also based on intuition, which
is not translatable into any fuzzy rule. Moreover, every physician develops
her/his set of rules according to the clinical experience, the drugs commonly
used in the operating room and the equipment provided by the hospital. In
the end, the tuning process can be virtually endless. Second, a fuzzy con¬
troller is tuned to match a predetermined infusion policy. On the contrary,
model based-controllers are tuned on the basis of the desired closed-loop
performance. This makes them capable or revealing new administration
strategies which could not be unearthed by a fuzzy controller.
Another limitation shared
their
by
both
systematic approach
in
fuzzy
and classical PID controllers lies in
to handle
example, let us consider the regulation
chapter 1. Constraints for endtidalcontrol.
gasconcentrationswerehandledbytwoadditionalcontrollersconnectedtothemaincontrollerinanoverridescheme.Thesameproblemwassolvedintheclosed-loopcontrolofBISpresentedinchapters1and2byusingasaturationelementforendtidalconcentrationreferencesinthecascadescheme.IntheMPCcontrollerpresentedinchapter3,themultipleconstraintsfortheinputandbothoutputsignalswerehandledinacoherentway.Also,itwaspossibletointroduceaprioritizationintheoutputconstraintsaccordingtotheclinicalseverityoftheconstraintviolation.Everycontrolapplicationmustdealwithconstraintsefficientlyinordertoguaranteereliability.Thisisparticularlytrueforcontrolschemesappliedtobiologicalsystems,wherehighersafetystandardsarerequired.Forthosepurposes,asweshowedinthisthesis,MPCemergesasthenaturalstrategyfor
an
non
input and output
constraints.
As
of MAP with isofiurane described
152
5 Conclusions
Bibliography
J., Stanski, D. and Burm, A.: 1986, Plasma concen¬
required to supplement nitrous oxide anesthesia
general surgery, Anesthesiology 65(4), 362-373.
Ausems, M., Hug,
C.
tration of alfentanil
for
Ausems, M., Vuyk, J., Hug, C. and Stanski, D.: 1988, Comparison of
computer-assisted infusion versus bolus administration of alfentanil as
a supplement to nitrous oxide for lower abdominal surgery, Anesthesi¬
ology 68(6), 851-861.
Bailey, J. and Shafer, S.: 1991, A simple analytical solution to the
three-compartement phamacokinetic model suitable for computercontrolled infusion pumps, IEEE Transactions on Biomedical Engi¬
neering
Bar-Shalom,
38(6),
522-524.
Y. and
Academic
Press,
Fortmann, T.: 1988, Tracking
San Diego.
and Data
Association,
Bemporad, A., Morari, M., Dua, V. and Pistikopoulos, E.: 2000, The ex¬
plicit linear quadratic regulator for constrained systems, Proceedings
of the American Control Conference, Chicago, Illinois, pp. 872-876.
Berenbaum, M.: 1985, The expected effect of a combination
general solution, Journal of Theoretical Biology 114(3),
Berenbaum,
41(2),
M.:
1989,
What
is
synergy
?,
of agents: the
413-431.
Pharmacological
Reviews
93-141.
Bischoff, K. B.: 1975, Some fundamental considerations of the applications
of pharmacokinetics to cancer chemotherapy, Cancer Chemotherapy
Reports 59, 777-793.
153
Bibliography
154
Bryson, A.
and
Ho,
Estimation and
Y.: 1975, Applied Optimal
Control, Taylor & Francis.
Carregal, A., Lorenzo, A., Taboada,
erative control ol
tanil with
47(3),
mean
luzzy logic,
J. and
Control
Barreiro,
Optimization,
-
J.:
2000, Intraop¬
arterial pressure and heart rate with allen-
Revista
espanola
de
Anestesiologia
y
reanimacion
108-113.
Chapman, F., Neweil, J. and Roy, R.: 1985, A feedback controller lor
tilatory therapy, Annals of Biomedical Engineering 13, 359-372.
ven¬
actions
1980, A review ol the control ol depth ol anaesthesia, Trans¬
of the Institute of Measurement and Control 2(1), 38-45.
V.:
1996, Physiologic and Pharmacologic Bases of Anesthesia,
Chilcoat,
Collins,
R.:
Williams & Wilkins.
Cullen, D., Eger, E., Stevens, W., Smith, N., Cromwell, T., Cullen, B.,
Gregory, G., Bahlman, S., Dolan, W., Stoelting, R. and Fourcade, H.:
1972, Clinical signs ol anesthesia, Anesthesiology 36(1), 21-36.
Derighetti,
M.:
1999, Feedback Control
Federal Institute ol
contrololmechanicalventilationduringanesthesia,ProceedingsoftheFourthEuropeanCongressonIntelligentTechniquesandSoftComput¬ing,Aachen,Germany,pp.2046-2049.Doi,M.,Gajraj,R.,Mantzaridis,H.andKenny,G.:1997,Relationshipbetweencalculatedbloodconcentrationolpropololandelectrophysi¬ologicalvariablesduringemergencefromanaesthesia:comparisonolbispectralindex,spectraledgefrequency,medianfrequencyandaudi¬toryevokedpotential,BritishJournalofAnaesthesia78(2),180-184.EgerII,E.I.:1981,Isorlurane:areview,Anesthesiology55(5),559-576.EgerII,E.I.:1984,Thepharmacologyolisorlurane,BritishJournalofAnaesthesia56,71-99.Frei,C:2000,FaultTolerantControlConceptsAppliedtoAnesthesia,PhDthesis,SwissFederalInstituteolTechnology(ETH),Zürich,Switzer¬
Derighetti, M., Frei, C, Glattfelder, A.
land.
in
Anaesthesia,
Technology (ETH), Zürich,
and
PhD
thesis,
Swiss
Switzerland.
Zbinden, A.: 1996, Fuzzy logic
Bibliography
155
Frei, C., Bullinger, E., Gentilini, A., Glattfelder, A., Sieber, T. and Zbinden,
A.: 2000, Artifact tolerant controllers for automatic drug delivery in
anesthesia, Critical Reviews in Biomedical Engineering 28, 187-192.
Frei, C., Derighetti, M., Morari, M., Glattfelder, A. and Zbinden, A.:
2000, Improving regualtion of mean arterial pressure during anesthesia
through estimates of surgery effects, IEEE Transactions on Biomedical
Engineering 47, 1456-1464.
Frei, C., Gentilini, A., Derighetti, M., Glattfelder, A., Morari, M., Schnider,
T. W. and Zbinden, A.: 1999, Automation in anesthesia, Proceedings
of the American Control Conference, San Diego, California, pp. 12581263.
Frei, C., Kraus, F. and Blanke, M.: 1999, Recoverability viewed as a system
property, Proceedings of the European Control Conference, Karlsruhe,
Germany.
Fukui,
Y. and
Masuzawa,
T.:
1989, Knowledge-based approaches
gent alarms, Journal of Clinical Monitoring
5(10),
to intelli¬
211-216.
Gajraj, R.,
Doi,
M.,Mantzaridis,H.andKenny,G.:1999,Comparisonofbispectralindex(EEG)analysisandauditoryevokedpotentialsformonitoringdepthofanesthesiaduringpropofolanaesthesia,BritishJournalofAnaesthesia82(5),672-678.Garcia,C.E.,Prett,D.M.andMorari,M.:1989,Modelpredictivecontrol:Theoryandpractice-asurvey,Automatica25(3),335-348.Gelman,S.,Fowler,K.C.andSmith,L.R.:1984,Regionalbloodflowduringisofluraneandhalothaneanesthesia,AnesthesiaandAnalgesia63,557-565.Gentilini,A.,Frei,C,Glattfelder,A.,Morari,M.andSchnider,T.W.:2000,Identificationandtargetingpoliciesforcomputercontrolledin¬fusionpumps,CriticalReviewsinBiomedicalEngineering28,179-185.
Furutani, E., Araki, M., Sakamoto, T. and Maetani, S.: 1995, Blood pres¬
sure control during surgical operations, IEEE Transactions on Biomed¬
ical Engineering 42(10), 999-1006.
Bibliography
156
Gentilini, A., Rossoni-Gerosa, M., Frei, C., Wymann, R., Morari, M.,
Zbinden, A. and Schnider, T. W.: In press, 2001., Modeling and closed
loop control of hypnosis by means of bispectral index (BIS) with isofiurane, IEEE Transaction on Biomedical Engineering
.
Ghouri, A. F., Monk, T. G. and White, P. F.: 1993, Electroencephalogram
spectral edge frequency, lower esophageal contractility and autonomic
responsiveness during general anesthesia, Journal of Clinical Monitor¬
9,
ing
Glass,
P.
P.:
176-185.
S., Bloom, M., Kearse, L., Rosow, C., Sebel,
1997, Bispectral analysis
propofol, midazolam,
Anesthesiology 86(4),
Glattfelder, A.
and
measures
P. and
Manberg,
sedation and memory effects of
isofiurane and alfentanil in
healthy volunteers,
836-847.
Schaufelberger, W.: 1988, Stability of discrete override
single-loop control systems, IEEE Transaction on
and cascade-limiter
Automatic Control
33(6),
Glattfelder, A., Schaufelberger,
ride control systems,
532-540.
W. and
Fässler,
H.:
International Journal
1983, Stability of
of
Control
37(5),
over¬
1023-
1037.
Goldmann,
review,
C.
Graves,
ofisofiuraneinsurgicalpatients,Anesthesiology41(5),486-489.Greco,W.,Bravo,G.andParsons,J.:1995,Thesearchforsynergy:acriticalreviewfromaresponsesurfaceperspective,PharmacologicalReviews47(2),331-385.Habibi,S.andCoursin,D.:1996,Assessmentofsedation,analgesia,andneuromuscularblockadeinperioperativeperiod,InternationalAnes¬thesiologyClinics34(3),215-241.Hill,A.:1910,Thepossibleeffectsoftheaggregationofthemoleculesofhemoglobinonitsdissociationcurves,JournalofPhysiology40.Hudson,R.,Thomson,I.andBurgess,P.:1991,Alfentanilpharmacokinet¬icsinpatientsundergoingabdominalaorticsurgery,CanadianJournalofAnaesthesia38(1),
effects61-67.
L.:
1988, Information-processing under general anesthesia:
Journal
of
the
L., McDermott,
Royal Society of
R. W. and
Medicine
Bidwai, A.:
81,
a
224-227.
1974, Cardiovascular
Bibliography
157
Hynynen, M., Takkunen, O. and Salmempera, M.: 1986, Continuous infusion ol lentanyl or allentanil for coronary artery surgery. Plasma opi¬
ate concentrations, haemodynamics and postoperative course, British
Journal of Anaesthesia 58(11), 1252-1259.
Isaka, S. and Sebald, A.: 1993, Control strategies for arterial blood pressure
regulation, IEEE Transactions on Biomedical Engineering 40(4), 353363.
Jacobs,
1988, Analytical solution
J. R.:
macokinetic
35(9),
Jacquez,
The
Jacquez,
model,
IEEE
to the
Transaction
on
three-compartment phar¬
Biomedical Engineering
763-765.
1985, Compartmental Analysis
University ol Michigan Press.
J.:
J. A. and
Simon,
C. P.:
in
Biology
and
Medicine,
2
edn,
1993, Qualitative theory ol compartmental
systems, SIAM Review 35, 43-79.
Johnson,
T.
and
Luscombe,
assessment ol machine
F.:
1992,
feedback to
Patient
patients,
controlled
Anaesthesia
analgesia47,
899
-
901.
Kaplan,
J. A.:
1993, Cardiac Anesthesia, Saunders.
L. A., Manberg, P., Chamoun, N., deBros, F. and Zaslavsky, A.:
1994, Bispectral analysis ol the electroencephalogram correlates with
Kearse,
movement to skin incision
thesia, Anesthesiology
81(6),1365-1370.Kissin,I.:1993,Generalanestheticaction:anobsoletenotion?,AnesthesiaandAnalgesia76(2).Kochs,E.,Bischoff,P.,Pichlmeier,U.andSchulteamEsch,J.:1994,Surgicalstimulationinduceschangesinbrainelectricalactivityduringisorlurane/nitrousoxideanesthesia,Anesthesiology80(5),1026-1034.Kothare,M.,Campo,P.,Morari,M.andNett,C:1994,Aunifiedframe¬workforthestudyofanti-windupdesigns,Automatica30(12),1869-1883.Kotrly,K.,Ebert,T.,Vucins,E.,Igler,F.,Barney,J.andKampine,J.:1984,Baroreceptorreflexcontrolofheartrateduringisofluraneanes¬thesiainhumans,Anesthesiology60(4),173-179.
patient
during propofol/nitrous
oxide
anes¬
Bibliography
158
Kottmann, M., Qiu, X. and Schaufelberger, W.: 2000, Simulation
Computer Aided Control Systems Design using Object-Orientation,
Hochshulverlag AG an der ETH Zürich.
Kwakernaak,
H. and
Sivan,
R.:
and
Vdf
1972, Linear optimal control systems, Wiley-
Interscience. New York.
Kwok, K., Shah, S., Finegan, B. and Kwong, G.: 1997, An observational
trial of a computerized drug delivery system on two patients, IEEE
Transactions On Control Systems Technology 5(4), 385-393.
Lee, J., Morari, M. and Garcia, C.: 1994, State-space interpretation
model predictive control, Automatica 30(4), 707-717.
of
D. A. and Hacisalihzade, S. S.: 1990, Computer control systems
pharmacological drug administration: a survey, Journal of Medical
Engineering & Technology 14(2), 41-51.
Linkens,
and
Liu,
Northrop, R.: 1990, A new approach
postoperative pain, IEEE Transaction
F. and
of
37,
to the
on
modeling
Biomedical
and control
Engineering
1147-1158.
Muischnek, H.: 1926, Effect of combinations: mathemat¬
problem, Naunyn-Schmiedehergs Archiv fur experimentelle
Pathologie und Pharmakologie 114, 313-326.
Loewe,
S. and
1986,Differentialdepressionofmyocardialcontractilitybyhalothaneandisofluraneinvitro,Anesthesiology64(5),620-631.Mahfouf,M.andLinkens,D.:1997,Acomparativestudyolflow-limitedanddiffusionlimitedphysiologicalmodelsforfentanyl,ModellingandControlinBiomedicalSystems,TheThirdIFACSymposium,Univer¬sityofWarwick,TheInstituteofMeasurementandControl.Mahfouf,M.andLinkens,D.:1998,Non-lineargeneralizedpredictivecon¬trol(NLGPC)appliedtomusclerelaxantanaesthesia,InternationalJournalofControl71(2),239-257.Maitre,P.O.,Vozeh,S.,Heykants,J.,Thomson,D.A.andStanski,D.R.:1987,Populationpharmacokineticsofalfentanil:theaveragedose-plasmaconcentrationrelationshipandinterindividualvariabilityinpa¬tients,Anesthesiology66(1),
ical basis
Lynch,
C.:
3-12.
Bibliography
159
Martin, J.: 1994, Fuzzy
10, 77-80.
control in
anesthesia,
Martin, J., Schneider, A., Quinn, M.
and efficacy in adaptive control
use
of
39(4),
a
and
Journal
Smith,
N.:
of
Clinical
1992, Improved safety
of arterial blood pressure
supervisor, IEEE Transactions
on
Monitoring
Biomedical
through the
Engineering
381-388.
McEwen, J., Anderson, G., Low, M. and Jenkins, L.: 1975, Monitoring the
level of anesthesia by automatic analysis of spontaneous EEG activity,
IEEE Transactions on Biomedical Engineering 22(4), 299-305.
H. H.:
1899, Zur Theorie der Alkoholnarlose.
i. Mitt. Welche Eigen¬
bedingt ihre narkotische Wirkung ?, NaunynSchmiedebergs Archiv fur experimentelle Pathologie und Pharmakologie
Meyer,
shaft der Anesthetika
42(108).
Miliard, R., Monk, C. and Prys-Roberts, C.: 1988, Self-tuning control of
hypotension during ENT surgery using a volatile anaesthetic, IEE Pro¬
ceedings 135(2), 95-105.
F., Schnider, T. W., Short, T. G., Gregg, K. M., Gentilini, A.
Shafer, S. L.: 2000, Response surface model for anesthetic drug
interactions, Anesthesiology 92(6), 1603-1616.
Minto,
C.
and
C. R.:
1988, Isofiurane and induced
hypotensi,CurOAalg18-93.MdZfE:RbPcHwNJSDmTVLG¬5()74FB2vkI6
Monk,
Bibliography
160
O'Hara,
D.
ers
lor
A., Bogen,
controlling
Noordergral, A.: 1992, The use olcomput¬
delivery ol anesthesia, Anesthesiology 77(3), 563-
D. K. and
the
581.
Ololsen,
E. and
Dahan, A.: 1999,
The
dynamic relationship between endbispectral index and
electroencephalogram, Anesthesiology
tidal sevollurane and isollurane concentrations and
spectral edge frequency
90(5),
Overton,
ol the
1345-1353.
E.:
meinen
1901, Studien über die Narkose zugleich
Pharmakologie, G. Fischer, Jena.
em
Betrag
zur
allge¬
Petersen-Felix, S., Arendt-Nielsen, L., Bak, P., Fischer, M. and Zbinden,
A. M.: 1996, Phsychophysical and electrophysiological responses to
experimental pain may be influenced by sedation: comparison ol the
effects ol a hypnotic (propolol) and an analgesic (allentanil), British
Journal of Anaesthesia 77(2), 165-171.
Petersen-Felix, S., Arendt-Nielsen, L. and Zbinden, A. M.: 1998, Do results
from experimental nociceptive models reflect pain perception during
general anesthesia?, Pain Forum 7, 43-45.
Phibin, D., Rosow, C, Schneider, R., Koski, G. and D'Ambra, M.: 1990,
Fentanyl and sufentanil anesthesia revisited: how much is enough?,
Anesthesiology 73(1), 5-11.
Prys-Roberts,C.:1987,Anaesthesia:apracticalorimpossibleconstruct?,BritishJournalofAnaesthesia59,1341-1345.Prys-Roberts,C.,Lloyd,J.W.,Fisher,A.,Kerr,J.H.andPatterson,T.J.S.:1974,Deliberateprofoundhypotensioninducedwithhalothane:studiesolhaemodynamiesandpulmonarygasexchange,BritishJour¬nalofAnaesthesia46(2),105-116.Prys-Roberts,C.andMillard,R.K.:1990,Sell-tuningadaptivecontrololinducedhypotensioninhumans:acomparisonolisolluraneandSodiumNitroprusside,JournalofClinicalMonitoring6(3),236-240.Rampil,I.J.:1998,AprimerforEEGsignalprocessinganalysis,Anesthe¬siology89(4),980-1002.
Pinsker, M. C.: 1986, Anesthesia:
Analgesia 65(7), 819-820.
a
pragmatic construct, Anesthesia and
Bibliography
Rampil,
161
I.
J. and Laster, M. J.:
1992, No correlation between quantielectroencephalographic measurements and movement response
noxious stimuli during isofiurane anesthesia in rats, Anesthesiology
tive
to
77,
920-925.
Kenny, G.: 1987, Evaluation of closed-loop control of arterial
pressure after cardiopulmonary bypass, British Journal of Anaesthesia
Reid,
J. and
59,
247-255.
Ritchie, G., Ebert,
1985,
ing
A
J.
P., Jannett,
microcomputer
surgery, Annals
of
T.
C., Kissin,
I. and
Sheppard,
L. C.:
based controller for neuromuscular block dur¬
Biomedical
Engineering 13,
3-15.
Ross, J., Mason, D., Linkens, D. and Edwards, N.: 1997, Self-learning fuzzy
logic control of neuromuscular block, British Journal of Anaesthesia
78,
412-415.
Ruiz, R., Borches, D., Gonzalez, A.
nitroprusside-infusion controller
pressure, Biomedical
Scherpereel,
P.:
Corral, J.: 1993, A new sodium
regulation of arterial blood
Instrumentation & Technology 3, 244-251.
T.
for the
1991, Patient-controlled analgesia.,
d'anesthesie et de réanimation
Schnider,
and
W., Minto,
C. F. and
10,
269
Stanski,
Annales
françaises
83.
-
D. R.:
1994, The effect
com¬
partment concept in pharmacodynamic modelling, Anaesthetic Phar¬
Review
2,
Schwilden, H., Schüttler,
204-213.
J. and
Stoeckel,
H.:
1987, Closed-loop feedback .692-0
contrlfmehxiasbyquvEG,A¬g67(3)41-.SwdHk:9CpBJ085ü2
macology
Bibliography
162
Scott, J. C. and Stanski, D. R.: 1987, Decreased fentanyl and alfentanil re¬
quirements with age: a simultaneous pharmacokinetic and pharmaco¬
dynamic evaluation, Journal of Pharmacology and Expérimental Ther¬
apeutics
240(1),
159-166.
Seagard, J., Elegbe, E., Hopp, F., Bosnjak, Z., von Colditz, J., Kalbfleisch,
J. and Kampine, J.: 1983, Effects of isoffurane on the baroreceptor
reflex, Anesthesiology 59(6), 511-520.
Sebel, P., Bowles, S. M., Saini, V. and Chamoun, N.: 1995, EEG bispectrum
predicts movement during thiopental/isoffurane anesthesia, Journal of
Clinical Monitoring 11, 83-91.
Shafer,
S. L. and
and rational
Varvel, J. R.: 1991, Pharmacokinetics, pharmacodynamics
opioid selection, Anesthesiology 74, 53-63.
Shimosato, S., Carter, J., Kemmotsu, O. and Takahashi, T.: 1982, Cardiocirculatory effects of prolonged administration of isoffurane in normocarbicarbic human volunteers, Acta Anaesthesiologica Scandmavica
26,
27-30.
Schwilden, H.: 1995, Feedback control of intravenous anes¬
by quantitative EEG, Control and Automation in Anesthesia,
Springer.
Shüttler,
J. and
thetics
D.andZbie,A:20utomcfkrlvshgwBJ85(6)1-SNH97TpyM&ERYCL4O¬3VI
Sieber, T., Frei, C, Derighetti, M., P., F., Leibundgut,
Bibliography
163
Varvel, J., Donoho, D. L. and Shafer, S. L.: 1992, Measuring
tive performance of computer-controlled infusion pumps,
Pharmacokinetics and Biopharmaceutics 20(1), 63-94.
the
predic¬
of
Journal
Viby-Mogensen, J., Ostergaard, D., Donati, F., D., F., Hunter, J., Kampmann, J., Kopman, A., Proost, J., Rasmussen, S., Skovgaard, L., F.,
V. and Wright, P.: 2000, Pharmacokinetic studies of neuromuscular
blocking agents: good clinical research practice (GCRP), Acta Anaesthesiologica Scandmavica 10(44), 1169-1190.
Vuyk, J.: 1997, Drug interactions
thesiology 10, 267-270.
anaesthesia,
in
Stoelting, R.: 1986,
Drugs Used in Anesthesia,
land., pp. 3-50.
Warren,
T. and
and
Current
/
E. A.:
in
Anaes-
Cardiovascular Actions
Basic
of Anesthetics
Aspects, Karger. Basel, Switzer¬
Wirth, N. and Gutknecht, J.: 1993, Project Oberon:
Operating System and Compiler, ACM Press, New
Woodruff,
Opinion
The
Design of
an
York.
1995, The Biomedical Engineering Handbook, CRC Press
Press, chapter 162, Clinical
Drug Delivery Systems, pp. 24 7-2457.2 8-238.
Wynands,J.,Wong,P.andTownsend,G.:1984,Narcoticrequirementsforintravenousanesthesia,AnesthesiaandAnalgesia63,101-105.Yasuda,N.,Lockhart,S.,Eger,E.,Weiskopf,R.,Johnson,B.,Freire,B.andFaussolaki,A.:1991,Kineticsofdesfiurane,isofiurane,andhalothaneinhumans,Anesthesiology74,489-498.Yasuda,N.,Lockhart,S.H.,EgerII,E.L,Weiskopf,R.B.,Liu,J.,Laster,M.,Taheri,S.andPeterson,N.A.:1991,Comparisonofkinet¬icsofsevofluraneandisofiuraneinhumans,AnesthesiaandAnalgesia72,316-324.Yasuda,N.,Targ,A.andEger,E.:1989,Solubilityof1-653,sevoflurane,isofiurane,andhalothaneinhumantissues,AnesthesiaandAnalgesia69,370-373.Zwart,A.,Smith,N.andBeneken,E.:1972,Multiplemodelapproachtouptakeanddistributionofhalothane:Theuseofananalogcomputer,ComputersandBiomedicalResearch5,
IEEE
Care of Patients with
Closed-Loop
Gubelstrasse 19
8050 Zürich
Switzerland
email:
home page:
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www.control.ethz.ch/~gentilin
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:
+41-1-311 52 02
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Highlights
Chemical
engineering :
in modeling and design of chemical processes, thermodynamics, industrial chem¬
istry, transport phenomena and numerical methods for partial differential equations.
research experience in chromatography, particularly in the separation of pharmaceutical
-
expertise
-
enantiomers.
Electrical
engineering :
knowledge of control systems technology.
expertise in the design of linear, robust, Multivariable, Model Predictive (MPC), Internal
Model (IMC), H infinity (Hoc) and frequency domain based controllers.
demonstrated ability in implementing finite state machines, I/O drivers and fault tolerant
control structures for real time applications.
proven ability in performing experimental studies on humans.
strong background in signal process analysis, with experience in physiological signals.
-
extensive
-
-
-
-
Biomedical
engineering :
depth knowledge of mathematical statistics, with expertise in identification methods,
regression analysis and multivariate observations.
strong background in Pharmacokinetic-Pharmacodynamic modeling, with special emphasis
on anesthetic drugs.
expertise in modeling and operation of drug administration devices.
-
in
-
-
Education
Apr. 2001: Ph.D. in Electrical Engineering
Department of Electrical Engineering.
Swiss Federal Institute of Technology (ETH), Switzerland.
Thesis:
"Feedback Control of Hypnosis and Analgesia in
Results:
realization of a platform for computer-aided1
1997
-
-
anesthi.-modlgfrbucvpwkyx'
Apr.
Humans".
Sep.
Sep.
Sep. 1999: Postgraduate degree in Statistics
Department of Mathematics.
Thesis:
"Time Frequency Representation of EEG during
1997
-
Painful Electrical Stimulation".
Sep. 2000: Postgraduate degree in Information Technology
Department of Electrical Engineering.
Thesis:
"Modeling and Closed-loop Control of Hypnosis by Means of Bispectral
1998
-
Index with Isofiurane".
Sep.
1991
Feb.
-
Department
degree in Chemical Engineering
Engineering.
Milano, Italy.
"Continuous Chromatography of Binary Mixtures
Design of the Operating Conditions".
1997:
Politecnico di
Thesis:
100/100
Final mark:
Sep.
1986
Jun.
-
M.S.
of Chemical
1991:
"summa
Diploma
cum
Work
Apr.
laude".
di Maturità Scientifica
Liceo Scientifico Vittorio Veneto in
Final mark:
with Variable
Milano, Italy.
60/60.
experience
Teaching Assistant
Laboratory, Department of Electrical Engineering.
Tasks:
preparation and oral presentation of lectures and exercises
on linear Algebra, linear and non-linear control systems.
1997
-
Dec.
2000:
Automatic Control
-
-
-
Apr.
1997
-
organization, preparation and evaluation of
supervision
Dec.
2000:
of students
Research assistant
Laboratory, Department of Electrical Engineering.
Technology (ETH), Switzerland.
candidate under the supervision of Prof Dr. Manfred Morari.
1999
Dipl.
-
Jun.
1999:
Scientific consultant
Volkswirt Chrisitian
Task:
ofthesalaryinequalitiesintheE.U.basedontheEurostatdatabase.Dec.1998-Jan.1999:ScientificconsultantGWMS.p.A.,Italy.Tasks:-developmentofE.U.qualitycertificationforautomaticspindlemachines.-developmentoftechnicalsolutionstoimprovetheoperationalsafety.-authorofbothtechnicalandoperatingmanuals.2
May.
Ph.D.
assessment
exams.
during laboratory experiments.
Automatic Control
Task:
written
Schnidler, B.G.A., Germany.
Selectivity:
Grants, Patents and Awards
May
2001:
U.S. patent File No. 70025.
"Arrangement
Title:
and process for
controlling
a
numerical value for
patient
respiration".
Submitted to the U.S. patent office.
Apr.
E.U. patent No.
2000:
Title:
"Layout
of
an
100-15-026.8.
automatic controller for the
numerical value with autonomous
regulation of
respiratory systems".
a
patient's
Submitted to the E.U. patent office.
Dec.
"Pastonesi Award"
1997:
Award:
recipient.
Engineering presented
best thesis in Chemical
in the Academic Year
1996/97.
of the Swiss National Science Foundation 32-51028.97 grant.
Sep.
1997:
Co-recipient
Jun.
1996:
Dow Chemical
Award:
at the Politecnico di Milano
scholarship.
distinguished undergraduate
academic record.
Computer Skills
Operating systems:
extensive
Programming languages:
Text
I/O
formatting: L^T^X,
in
experience with Unix, Windows and XOberon.
depth knowledge
of
Matlab, S-Plus, Oberon, Fortran,
Microsoft Office and Adobe Acrobat
interfaces: demonstrated
ability
in
implementing
C.
packages.
data communication
through
RS-232 and
TCP/IP protocols.
Real-time systems: strong
machines for real-time
experience in the design of closed-loop
applications. Implementation in Oberon.
Networking technology: expertise
Web
publishing: expertise
in
FTP, TFTP,
in Web pages
design
controllers and finite state
telnet.
with HTML.
Languages
and
English: writing
French:
writing
Sep. 1977
Jan.
1996:
speaking fluently.
and
-
speaking fluently
July 1980:
primary
school at the "Licée
andspeakingfluentlyItalian:mothertongue.
from the "Centre culturel
German:
writing3
Français" in Lisbon, Portugal.
Langue Française" (CELF)
français" in Milano, Italy.
obtained "Certificat d'études de la
Personal
sketch
Biographical
Dec.
1972
Sep.
1977
Jul.
1980
Jul.
1984
Apr.
Skills
Born in
-
-
-
1997
Objective :
Looking
for
-
a
Jun.
1980
Jun.
1984
Mar.
1997
present
dynamic
experience
Able to find out
tions which
environment where fast
am
learning
and interaction with
people
is must.
communicating with medical doctors, researchers and support staff.
opportunities
in the medical field and
improve both the patient
known for
care
and
provided new engineering solu¬
anesthesiologists' working environment.
getting things done.
:
thriatlete, a marathon runner,
people, reading and sports.
am a
with
in
new
Recreational activities
I
Livorno, Italy.
Lisbon, Portugal.
Rosignano Solvay, Italy.
Milano, Italy.
Zürich, Switzerland.
:
Extensive
I
:
a
certificate diver and
4
a
skier.
Also,
I
enjoy interacting
List of Publications
Journal
Papers
Chemical
Engineering
Publications
A.
Gentilini, C. Migliorini, M. Mazzotti and M. Morbidelli.
"Optimal Operation of Simulated Moving-Bed Units for Non-linear Chromatographic Sep¬
arations II. Bi-Langmuir Isotherm".
Journal of Chromatography A., Vol. 805, pp. 37-44, 1998.
C.
Migliorini, A. Gentilini, M. Mazzotti and M. Morbidelli.
"Design of Simulated Moving Bed Units under Non-ideal Conditions".
Industrial & Engineering Chemistry Research, Vol. 38, pp. 2400-2410,
Anesthesia and Electrical
A.
Engineering
1999.
Publications
Frei, A.H. Glattfelder, M. Morari and T.W. Schnider.
Targeting Policies for Computer-Controlled Infusion Pumps".
Biomedical Engineering, Vol. 28, pp. 179-85, 2000.
C.W.
Gentilini,
"Identification and
Reviews in
C.W.
Frei,
Critical
Bullinger, A. Gentilini, A.H. Glattfelder, T. Sieber and A.M. Zbinden.
Drug Delivery in Anesthesia."
Reviews in Biomedical Engineering, Vol. 28, pp. 187-92, 2000.
E.
"Artifact-Tolerant Controllers for Automatic
Critical
C.
Minto, T. Schnider, T. Short, K. Gregg, A. Gentilini and S. Shafer.
"Response Surface Models for Anesthetic Drug Interactions".
Anesthesiology, Vol. 92, pp. 1603-1616, 2000.
A.
Gentilini,
C.W.
Frei,
M.
Derighetti, A.H. Glattfelder,
T.W.
Schnider,
T. Sieber and A.M.
Zbinden.
Closed-Loop Control in Anesthesia".
Engineering in Medicine and Biology Magazine,
"Multitasked
A.
Gentilini, M. Rossoni-Gerosa,
"Modeling and Closed-Loop
C.
Frei,
R.
Control of
Vol.
20,
pp.
Wymann, M. Morari, A.
Hypnosis by5
MeansofBispectralIndex(BIS)withIsofiurane".IEEETransactionsonBiomedicalEngineering.Inpress.A.Gentilini,C.Schaniel,M.Morari,C.Bieniok,R.WymannandT.Schnider."ANewParadigmfortheClosed-LoopIntraoperativeAdministrationofAnalgesicsinHu¬mans".IEEETransactionsonBiomedicalEngineering.Submittedforpublication.A.GentiliniandM.Morari."ChallengesandOpportunitiesinControlofBiomedicalSystems".AIChEJournal.Inpress
IEEE
39-53,
2001.
Zbinden and T. Schnider.
Conference
C.
Papers
Frei, A. Gentilini,
M.
Derighetti, A.H. Glattfelder,
M.
Morari,
Schnider and A.M.
T.W.
Zbinden.
"Automation in Anesthesia".
Proceedings
of the American Control
Conference,
San
Diego CA,
pp.
1258-1263,
1999.
A.
Gentilini, S. Alemdar, C. Frei, M. Morari.
"Time Frequency Representation of Electro Encephalogram (EEG) during experimental
painful stimulations correlate with movement response under general anesthesia".
Proceedings of the World Congress on Medical Physics and Biomedical Engineering, Chicago
IL, 2000.
A.
Gentilini,
M. Gerosa
Frei, T. Schnider, M. Morari.
Pharmacodynamic (PK-PD) modeling of Bispectral Index (BIS) with
Isofiurane for closed loop control of depth of anesthesia".
Proceedings of the World Congress on Medical Physics and Biomedical Engineering, Chicago
IL, 2000.
,
C.
"Pharmacokinetic
C.
P.
Schaniel, A. Gentilini, M. Morari, C. Bieniok, R. Wymann and T. Schnider.
"Perioperative Closed-Loop Control of Analgesia in Humans".
23rd Annual International Conference of the IEEE Engineering in Medicine
Society, Istanbul, Turkey, 2001.
Grieder, A. Gentilini, M. Morari,
"A Patient Adaptive Approach
mans"
C.
Bieniok, R. Wymann and T. Schnider.
Closed-Loop Control of Bispectral Index (BIS)
for
Biology
in Hu¬
.
23rd Annual International Conference of the IEEE
Society, Istanbul, Turkey,
A.
and
Engineering
in Medicine and
2001.
Gentilini, M. Morari, C. Bieniok, R. Wymann and
"Closed-loop Control of Analgesia in Humans".
Invited Session at the Conference in Decision and
T. Schnider.
Control,
Talks
Invited seminar at the Institute of Process
"Feedback control of
2001.InvitedseminaratRoyalVictoriaHospital."AutomationinAnesthesia".Montreal,Canada,March2001.InvitedseminarattheBiomedicalEngineeringDepartmentofMcGillUniversity."AutomationinAnesthesia".Montreal,Canada,March2001.InvitedlectureatDräger'sGmbHHeadquarters."BispectralIndexandMeanArterialPressureControllers.AChallengeforResearchandDevelopment".Lübeck,Germany,January2001.InvitedlectureatPharsightCorporationHeadquarters."FeedbackControlofHypnosisandAnalgesiainHumans".MountainViewCA,January2001.6
hypnosis
Zürich, Switzerland, April
and
Engineering of ETH.
analgesia in humans".
Orlando
FL,
2001.
Biology
Invited lecture at the
École Polytechnique Fédérale de Lausanne.
"Automatic Control in Anestesia".
Lausanne, Switzerland,
Presentation at the World
December 2000.
Congress on Medical Physics and Biomedical Engineering.
Depth of Hypnosis during Anesthesia".
Control of
"Closed-loop
Chicago IL, July
2000.
Presentation at the World
Congress on Medical Physics and Biomedical Engineering.
Frequency Representation of Electro Encephalogram (EEG) Correlate with
ment Response under General Anesthesia".
Chicago IL, July 2000.
"Time
Invited lecture at the Politecnico di Milano.
"Controllori Automatici in Anestesia:
Milano, Italy, May
Invited lecture at
un
Nuovo
Paradigma
nelle Sale
Operatorie".
2000.
Aspect
Medical
Systems,
Inc.
Newton
MA, April
Invited lecture at Roche
2000.
Diagnostics Corporation.
Indianapolis IN, April
2000.
Presentation at the American Control Conference.
S.
Diego CA,
June 1999.
Presentation at the 18th Southern Biomedical
Engineering Conference.
Drug Delivery in Anesthesia".
"Artifact Tolerant Controllers for Automatic
Clemson
University SC,
June 1999.
Presentation at the 18th Southern Biomedical
"Identification and
Policies for
Clemson
1999.
Targeting
University SC, June
Engineering Conference.
Computer Controlled Infusion Pumps".
7
Move¬
References
Prof. Dr. Manfred Morari.
Head of the Automatic Control
Physikstrasse 3,
Laboratory
ETL I 29 CH-8092 Zürich,
email: [email protected].
Phone: +41 1 632 76 26.
Fax: +41 1 632 12 11.
Dr. Milos
Popovic.
Manager of the Functional
University Hostpital Balgrist.
Forchstrasse 340, CH-8008 Zürich.
Leader and
Electrical Stimulation
Phone: +41 1 386 37 36.
Fax: +41 1 386 37 31.
PD. MD. Thomas Schnider.
Department of Anesthesiology,
Inselspital CH-3010, Bern,
Bern
University Hospital.
Tel. ++41
Fax ++41
(0)31
(0)31
632 39 65.
381 62 85
8
Group.
Technology (ETH).

Hypnosis and Analgesia - ETH E-Collection

Transcription

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