magos tibor

MEASUREMENT 2011, 8th International Conference
Recent Topics in Non-Invasive Cardiac
Electroimaging
Prof. György KOZMANN
Head, R & D Center of Medical Informatics,
Faculty of Information Technology, University of Pannonia,
Veszprém, Hungary
27-30 April 2011, Smolenice Castle, Slovakia
Co-workers, 2011
Prof. Kozmann György
Prof. Nagy Zoltán
Prof. Maros István
Dr. Starkné Werner
Ágnes
Butsi Zoltán
Dr. Juhász Zoltán
Dr. Kósa István
Dr. Magos Tibor
Dr. Vassányi István
Dr. Gaál Balázs
Dulai Tibor
Tarjányi Zsolt
Végső Balázs
Cserti Péter
Fülöp Kornél
Pintér Balázs
Takács István
Tuboly Gergely
Dr. Dombovári Magdolna
Nemes Márta
Essential motivation
• “Cardiac arrhythmias are a major cause of death and
disability. Despite the clinical need and the importance of
studying arrhythmia mechanisms in humans, a
noninvasive
imaging
modality
for
cardiac
electrophysiology is not yet available for routine
application” (Rudy Y. Ann N Y Acad Sci. 2010 Feb;1188:214-21. )
Levels of cardiac electroimaging
Body surface level
• need for reproducible, high-density measurements
• need for biophysically meaningful features
• need for improved inverse computations
Epicardial level
• understanding the cellular level prerequisites of arrhythmia
• need for achiving compatibility with experimental findings
First generation of data acquisition and data
presentation
Improvements in measurement technology
Electrode-vest under development at the Innomed Inc., Budapest
Prerequisites of arrhythmia
According to our current understanding the biophysical substrate of
leathal arrhythmia is the fragmented propagation and the repolarization
heterogeneity
Fragmented propagation is due to
static and dynamic obstacles
Determinants of dynamic obstacles:
• determinants of Um membran
potentials like APD, AP restitution, CV
restitution, cardiac memory, and
• the properties of the Cai (intracellular)
transport between the sarcoplasmic
reticulum and the cytoplasm
Body surface characterization of
repolarization heterogeneity
QRST integrál vs repolarization heterogeneity:
  ( P, t )dt  k  z( P, r) (r)dV
QRST
s
Vs

 m (r, t )  mr (r)dt
QRST
Geselowitz DB.: The ventricular gradient revisited: relation to the area under the
action potential. IEEE Trans Biomed Eng. 1983 Jan;30(1):76-7.
Hubley-Kozey CL et al.: Spatial features in body-surface potential maps can identify
patients with a history of sustained ventricular tachycardia. Circulation. 1995 Oct
1;92(7):1825-38.
8
Extension of depolarization and repolarization
characterization
QRS integrál vs activation sequence
  ( P, t )dt  c  z( P, r)
m
QRS
QRST integrál vs repolarization
heterogeneity
dVs
Vs
  ( P, t )dt  k  z( P, r) (r)dV
QRST
s
Vs

 m (r, t )  mr (r)dt
QRST
Relationship of QRS of QRST
integrals (in KL-domain)
KL(QRST )  T  KL(QRS )  b  e
 a1,1
a
2 ,1
T
 

a12,1
a1, 2
a 2, 2

a12, 2
 a1,12 
 a 2,12 

 

 a12,12 
Kozmann G et al: Beat-to-beat interplay of heart rate, ventricular depolarization, and
repolarization. J Electrocardiol. 2010 Jan-Feb;43(1):15-24.
9
Definition of NDI
12
Definition of the index of non-dipolarity (NDI)
in terms of Karhunen-Loeve (KL) coefficients
NDI 
c
2
i
c
2
i
i 4
12
i 1
Dipolar ei
„eigenmaps”
(KL1-KL3):
ant
BSPM approximation
by the weighted sum
of KL coefficients
F(t) ≈ S ei ci
post
+

PND
PD  PND
Non-dipolar ei „eigenmaps” (KL4-KL12):
ant
post
ant
post
ant
post
QRST integral SD/M ratio in NOR vs ICD
groups
Bubble Scatterplot
16000
ICD
14000
12000
SD
10000
8000
NOR
6000
4000
2000
0
-50000
0
50000
1E5
1,5E5
2E5
2,5E5
3E5
3,5E5
M(KL_N)
Bubble diagram of M and SD values of NOR (small circles) and ICD group
(large circles) QRST integral map KL components
Experimental evidence #1: Effect of cell-tocell coupling modulation
• Single ventricular myocites paced at
constant rate (and held at a constant
temperature) exhibit beat-to-beat
variations in action potential duration
(APD) and in intQRST as well.
• On the body surface the variability is
manifested in beat-to-beat changes of
QRST integral map patterns.
• The increase of cell-to-cell coupling
resistance increase action potential
heterogeneity. Consequently, there is a
need for beat-to-beat evaluation of
repolarization variability.
Zaniboni M, Pollard AE, Yang L, Spitzer KW. Beat-to-beat repolarization variability in
ventricular myocytes and its suppression by electrical coupling. Am J Physiol Heart
Circ Physiol. 278(3):H677-87, 2000.
NDI spikes in the QRST integral of ICD
patients
# of cycles
QRS
dQRS
QRST
dQRST
I_T (series)
1100
40
i-2
35
i=198
30
900
RR[MS]:
25
800
20
700
15
600
NDI(intQRST) [%]:
1000
i-1
i
10
szívciklusok
500
400
150
200
RR[MS] (L)
(a)
250
300
NDI(intQRST) [%] (R)
5
i+1
0
350
i+2
(b)
NDI(intQRST) spikes and RR intervals in a sequence of 200 consequtive cardiac
cycles of an ICD patient (a).
QRS and QRST integral maps and their difference maps around the cycle i=198 (b)
13
Modelling the possible mechanisms of NDI
spikes
NDI(QRS)
Study in progress:
By the use of the slovakian numerical heart and
thoracic models the QRS and QRST integral
responses as well as the NDI responses of wave
initiation point modulations and AP alterations are
studied.
NDI(QRST)
normal
0,0646
0,322
lah2ap-40
0,009
0,0132
lph4ap-40
0,076
0,0162
Experimental evidence #2: concordant and
discordant T-wave alternans
Cellular properties of the
cardiac action potential and
Cai cycling dynamically may
generate wave instability and
wavebreak, even in tissue that
is initially completelly
homogeneous.
There is a need for the spatiotemporal analysis of the
QRST integrals.
Weiss JN et al.: : The dynamics of cardiac fibrillation., Circulation. 2005 Aug
23;112(8):1232-40. Review.
Qu Z, Xie Y, Garfinkel A, Weiss JN.:T-wave Alternans and Arrhythmogenesis in
Cardiac Diseases., Front Physiol. 2010 Nov 1;1(154):1-15.
Alternating intQRST KL components in the
heart cycles of an ICD patient
ant
Spectral analysis: KL9(intQRST)
No. of cases: 348
Hamming weights:,0357 ,2411 ,4464 ,2411 ,0357
post
Spectral Density
+
KL9
+
5E8
5E8
4E8
4E8
3E8
3E8
2E8
2E8
1E8
1E8
0
0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50
Frequency
Spectral peaks of alternation
ant
KL12
Spectral analysis: KL12(intQRST)
No. of cases: 348
Hamming weights:,0357 ,2411 ,4464 ,2411 ,0357
post
+
+
-
-
Spectral Density
+
1E8
1E8
8E7
8E7
6E7
6E7
4E7
4E7
2E7
2E7
0
0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50
Frequency
Green’s theorem, forms of inverse solutions
  



n

 Hi
Epicardial sources:
  


 n  Hi
 Bj
 Hi
 Hi
i = 1, …,N
dFHi
Body surface
sources:
 Bj
j = 1, …,M
dFB
Equation of cardiac electroimaging
Relationship of body surface and epicardial potentials (for
homogeneous thorax model)
 B1
B2
z11
z 21
.  z31
.
.
z n1
 Bn
z12
z 22
.
.
zn 2
z13
.
.
.
zn3
.
.
.
zij
.
.
.
.
.
.
.
.
.
.
.
H1
H 2
H 3
z1m
z2m
z3 m
.
.
.
z nm  H ,m 1
 Hm
Usually: m>>n
In forward direction the equation is solvable, in
inverse direction: ill-posed
Conventional and some recent approaches
Tikhonov regularizition attempts to control the oscillation of the solution. To
this end introduces a single parameter ( γ ) and minimizes the expression:
~
R  F B  TBO F O
2
  FO
2
By this approach the correlation of the real epicardial potential vectors and the
estimated vectors is in the range of 0.7-0.8, which provides qualitatively correct
potential patterns though the numerical values are often quite different.
In some recent solutions:
• truncated singular-value decomposition (TSVD) methods, or
• least-squares QR (LSQR) method, based on Lanczos bidiagonalization and QR
factorization was used.
• Results show that the inverse solutions recovered by the LSQR method were more
accurate than those recovered by the Tikhonov and TSVD methods.
• By combing the LSQR with genetic algorithms (GA), the performance can be
improved further.
Approaches in progress
• In our approach we wish elaborate optimization techniques for
making the problem “well-posed”.
• In this respect we plan to further develop ideas of (Maros). This
approach will open up considerable flexibility that can be utilized to
take into account a priori knowledge (if available).
• The other aim is to utilize the idea of “important points” for making
the problem well-posed.
Maros, I., Thielemans, K., PET Image reconstruction by vector norm optimization, in
Guang-Zhong Yang (ed.) Proceedings of MIAR 2001, Medical Imaging and Augmented
Reality, IEEE Computer Society, 2001, 152-156.
Maros I: Computational Techniques of the Simplex Method. Kluwer Academic Publishers,
Boston, 2003.
Thank you for your attention!