Slides - Politecnico di Milano

Transcription

Heart-Pacing Simulation and
Control via Multiagent
Systems
Alessandro Beda1 and Nicola Gatti and Francesco Amigoni2
1
ISVR, U NIVERSITY OF S OUTHAMPTON , S OUTHAMPTON , UK
2
DEI, P OLITECNICO DI M ILANO, M ILANO, I TALY
Beda, Gatti and Amigoni, Heart-Pacing Simulation and Control via Multiagent Systems – p. 1/17
Outline
• We introduce some problems related to the modeling of
physiological processes
Outline
• We present a cooperative negotiation protocol to combine partial
models of physiological processes embedded in agents
Outline
• We present a cooperative negotiation protocol to combine partial
models of physiological processes embedded in agents
• We applied and evaluated the proposed protocol in heart-pacing
modeling
The Global Approach
• Physiological processes are complex to study and model
[Goldberger, West, 1987]
◦ Each process emerges from the interaction of several
elements belonging to an intricate network of relationships
◦ Each element is involved in more processes
The Global Approach
• Physiological processes are complex to study and model
[Goldberger, West, 1987]
◦ Each process emerges from the interaction of several
elements belonging to an intricate network of relationships
◦ Each element is involved in more processes
• Physiological processes are currently described using a set of
partial models [Amigoni, Gatti, 2003]
◦ Open problem: how combine the partial models?
◦ Current solutions: weighted average, overriding, etc.
Our Case Study: Heart-Pacing (1)
• Permanent cardiac pacing is used as effective and reliable
therapy for alterations of cardiac rhythm [Glikson, Hayes, 2001]
• Cardiac pacemakers partially or totally take over the function of
the Sinoatrial Node
• Permanent cardiac pacing is used as effective and reliable
therapy for alterations of cardiac rhythm [Glikson, Hayes, 2001]
• Cardiac pacemakers partially or totally take over the function of
the Sinoatrial Node
• Kinds of pacemakers [Harvey, 1995]:
◦ Asynchronous (fixed pacing frequency)
◦ Synchronous (fixed pacing frequency, activated just when
needed)
◦ Adaptive (frequency is a function of physiological parameters)
• The adaption aims at mimicking adequately the heart regulatory
system of healthy subjects
• Currently there is no answer to the question: what is the optimal
model of heart-pacing?
• Currently there is no answer to the question: what is the optimal
model of heart-pacing?
• The adopted technique is to combine different physiological
models
◦ The model combination is based on:
• Overdrive
• Cross-checking
• Weighted average
Modeling Complex Systems
• Complex systems are systems that exhibit intricate
interconnections, high dimensionality, multiresolution, etc. [Astrom
et al., 2001]
• It is commonplace in literature the idea to face complexity by
using different models according to scale, operating contexts, etc.
et al., 2001]
• From a modeling point of view, a physiological process is similar
to a complex system
et al., 2001]
• From a modeling point of view, a physiological process is similar
to a complex system
• An emerging technique is decentralized optimization where the
single models are embedded in decisional makers with objective
function Ji

min / max Ji (u1 (t), . . . , un (t), x0 ) ∀i
u
s.t. f (u) ≤ 0
i
Anthropic Agency
A multiagent system for physiological processes [Amigoni et al.,
2003] able to accomplish several tasks:
• Signal Processing
• Decision Making
• etc.
Anthropic Agency
A multiagent system for physiological processes [Amigoni et al.,
2003] able to accomplish several tasks:
• Signal Processing
• Decision Making
• etc.
Modeling with Anthropic Agency
• Each agent embeds a model
• Each agent repeatedly performs an optimization with respect to
the model it embeds (agent optimization)
• The global model is the result of a distributed decision making
process performed via a cooperative negotiation among the
agents (agency optimization)
Modeling with Anthropic Agency
• Each agent embeds a model
• Each agent repeatedly performs an optimization with respect to
the model it embeds (agent optimization)
• The global model is the result of a distributed decision making
process performed via a cooperative negotiation among the
agents (agency optimization)
• Requirements [Amigoni, Gatti, 2004]:
◦ High formal degree of the protocol
• To allow an analytical study of the protocol properties:
stability, optimality, etc.
◦ High parameterization degree of the protocol
• To allow a fine tailoring the combination phase to the
specific human being
• A novel protocol is needed
Assumptions
• n contracting agents and a mediator
• Each contracting agent i embeds a partial model referring to a
space of variables Ai ∈ RNi
• Different Ai can overlap and the global space of variables is
Sn
A = i=1 Ai
• Each contracting agent i is associated with a potential function
Ui : Ai → [0, +∞) that represents the utility of the agent i
◦ It expresses the “distance” of a state from the optimal curve of
the model embedded by the agent
• pti→e is the proposal of the agent i at time t to the mediator e
• pte→i is the counter-proposal of the mediator e at time t to the
agent i
Examples of Potential Functions
„
1930.4 − QT
HR = −8.2/ log
1734.7
[Sarma et al.; 1984]
«
HR = 26.98 ·
arctan (0.0995 · RR − 2.5947) + 95.02
[Voukydis et al.; 1967]
„
1930.4 − QT
HR = −8.2/ log
1734.7
«
HR = 26.98 ·
arctan (0.0995 · RR − 2.5947) + 95.02
8
d(p)2
>
>
<
if d(p)2 < 20
10
„„
«
«
Definition of potential U :
2
d(p)
>
>
− 20 + 1
if d(p)2 > 20
:20 + 10 ∗ log
10
„
1930.4 − QT
HR = −8.2/ log
1734.7
«
HR = 26.98 ·
arctan (0.0995 · RR − 2.5947) + 95.02
8
d(p)2
>
>
<
if d(p)2 < 20
10
„„
«
«
Definition of potential U :
2
d(p)
>
>
− 20 + 1
if d(p)2 > 20
:20 + 10 ∗ log
10
The Negotiation Protocol (1)
1.
WHILE
true
2. R EAD CurrentState pi
3. Each agent operates a local search:
p0i→e ← LocalSearch (pi , Ui (·))
4.
WHILE
Agreement has not been reached
5. Each agent sends to the mediator: hpti→e , Ui (pti→e )i
6. The mediator computes the agreement mt
7. The mediator sends the agreement mt to each agent
8. The agents computes their new proposal pt+1
i→e
9. t = t + 1
10.
END WHILE
11.
END WHILE
• Succession of proposals: p0i→e p0e→i p1i→e · · · pτe→i
Pn
t
t
p
·
N
·
[1
+
U
(p
i
i
i→e
i→e )]
i=1
t
t
t
• Agreement: m =
Pn
,
p
=
m
e→i
t
i=1 Ni · [1 + Ui (pi→e )]
Pn
t
t
p
·
N
·
[1
+
U
(p
i
i
i→e
i→e )]
i=1
t
t
t
• Agreement: m =
Pn
,
p
=
m
e→i
t
i=1 Ni · [1 + Ui (pi→e )]
• New proposal:
t+1
t+1
t
t
t
=
p
+
kp
−
p
k(α
(p
)u
+
β
(p
)w
)
pt+1
i
i
i
i
i→e
e→i
i→e
i→e
i
i
◦
ut+1
i
◦ vit+1
pte→i − pti→e
=
kpte→i − pti→e k
(accommodate the tendency of society
with weight αi )
∇Ui (pti→e )
=
k∇Ui (pti→e )k
◦ wit+1 =
ut+1
i
kut+1
i
−
−
vit+1
vit+1
·
·
t+1
ut+1
v
i
i
t+1
ut+1
k
v
i
i
(keep close to optimal
curve with weight βi )
A Negotiation Example
Two agents negotiate on the HR value
410
405
QT
Negotiation
LocalSearch
400
395
390
60
70
80
90
100
110
120
130
140
150
120
130
140
150
HR
30
25
RR
Negotiation
LocalSearch
20
15
10
60
70
80
90
100
110
HR
Experimental Setup in Heart-Pacing
• 5 sequences 24-hours long ECGs taken from PhysioNet
(http://www.physionet.org/ )
• Signal processing of ECG to extract temporal series: QT, RR, HR
Neg. Prot. Evaluation in Heart-Pacing
Indexes
• e: absolute value of the difference between the esteemed value of
HR and the real value of HR
• E[e]: the average of e over time (24 hours)
• var[e]: the variance of e
Neg. Prot. Evaluation in Heart-Pacing
Indexes
• e: absolute value of the difference between the esteemed value of
HR and the real value of HR
• E[e]: the average of e over time (24 hours)
• var[e]: the variance of e
Results
• Averaging HR values of two partial models:
E[e] = 4.6 ± 1.3, var[e] = 8.6 ± 3.0
• Negotiating HR values of two partial models:
E[e] = 3.9 ± 1.3, var[e] = 6.8 ± 1.2
Negotiation Protocol Analysis
• Our negotiation protocol generalizes other techniques for model
combination in heart-pacing (by using particular values for
parameters):
◦ Weighted average
◦ Overdrive
◦ Cross-checking
parameters):
◦ Overdrive
◦ Cross-checking
• Advantages:
◦ Improvement of E[e] and var[e] over other techniques
◦ Adoption of βi improves results
◦ Less sensitivity to weights with respect to weighted average
parameters):
◦ Overdrive
◦ Cross-checking
• Advantages:
◦ Improvement of E[e] and var[e] over other techniques
◦ Adoption of βi improves results
◦ Less sensitivity to weights with respect to weighted average
• Drawbacks:
◦ Increased complexity of tailoring the model on a particular
patient
Conclusions and Future Works
• Cooperative negotiation is an interesting paradigm to combine
physiological partial models
• The proposed protocol improve effectively the current
heart-pacing model combination techniques
• Future works:
◦ Enrich heart-rate modeling
◦ Apply our approach to model other physiological processes
◦ Study analytical properties of the protocol
◦ Develop learning techniques for automatically tailoring
parameters

Slides - Politecnico di Milano

Transcription

Similar documents

iSIM iSIM

Institutional Community Involvement Center Quarterly Reports

Power devices - Crosslight Software

ALL FOR ONE HURRICANE RELIEF CONCERT ALL

Gizmos and Gadgets in Emergency Medicine

SIMPro3 Backhoe Loader

VISUAL SIMULATION As viewed from Orono Fairgrounds South

When Colette Foisy-Doll arrived in Qatar last year

ASE2000 Version 2 - Applied Systems Engineering Inc.

Venerabile Voices Issue 4 - Venerable English College