Noninvasive estimation of the cardiac electrical activity by convex optimization

1. Noninvasive estimation of the cardiac
electrical activity by convex optimization
V. Suárez-Gutiérrez, C. Figuera-Pozuelo, D. Álvarez, C.E. Chávez,
J. Requena-Carrión, M. S. Guillem, A.M. Climent, F. Alonso-Atienza
felipe.alonso@urjc.es
@FelipeURJC
ECGi-Workshop, Bad Herrenalb, 26th march 2015

2. Felipe Alonso-Atienza
26th March 2015 2ECGi Workshop
Motivation
o INVERSA, 3 years research grant project 2015-2017
o Objective: to develop a mathematical formulation in the context of the
convex optimization framework that incorporates spatio-temporal
regularization (priors)
o Methodology:
§ 3D simple models: model of spheres
§ 3D realistic models
§ Real data from the EP lab
o Approaches:
§ Estimation of the epicardial potentials
§ Estimation of parameters of clinical interest: ischemic regions,
fundamental frequency and/or activation times.

3. Felipe Alonso-Atienza
26th March 2015 3ECGi Workshop
First steps: model of spheres
o Inner sphere (atrial surface). Radius 5 cm (2562 nodes)
o Outer sphere (torso). Radius 15 cm (642 nodes)
o Countermanche model.
o Boundary Element Method (BEM)

4. Felipe Alonso-Atienza
26th March 2015 4ECGi Workshop
First steps: model of spheres
o Objective
§ To assess different inverse solutions: Tikhonov, TSVD, TTLS, and others (not shown)
[Milanic M et al. Journal of Electrocardiology 2014]
§ To analyze inverse methods free parameters.
o Data
§ Torso potentials (outer sphere signals) corrupted with different noise levels (SNRs)
o Scenarios:
10 mV- 80 mV
Plane wavefront 50 LA + 50 fibrotic 80 RA + 20 fibrotic

5. Felipe Alonso-Atienza
26th March 2015 5ECGi Workshop
RMSE analysis

6. Felipe Alonso-Atienza
26th March 2015 6ECGi Workshop
CC analysis

7. Felipe Alonso-Atienza
26th March 2015 7ECGi Workshop
Tikhonov performance
15 Hz10 Hz
original SNR = 10 dB SNR = 100 dB

8. Felipe Alonso-Atienza
26th March 2015 8ECGi Workshop
Model of spheres: conclusions
o For the algorithms under analysis, Tikhonov (order 0) slightly
outperforms others.
§ Good choice as benchmark.
§ GMRES has been also analyzed with poor results, but not deeply tested.
§ Caution should be paid when selecting Tikhonov free regularization
parameter
o The solution depends on the underlying cardiac activity.
§ It would be nice to try the bayesian approach in different scenarios.
o Dominant frequency maps, calculated from estimated epicardial
potential, seem more stable, even in noisy conditions.
o Tikhonov solution is independent of the simulating platform (tested on
SCIRun)

9. Felipe Alonso-Atienza
26th March 2015 9ECGi Workshop
3D realistic models
o Atria and torso geometrical models
§ Atrial surface: 6114 nodes (6114 epicardial potentials)
§ Torso surface: 771 nodes (771 BSPMs)
o BSPM are corrupted by AWGN (different SNRs) and then preprocessed (band-
pass filtered at 3-30 Hz)

10. Felipe Alonso-Atienza
26th March 2015 10ECGi Workshop
First trial in 3D realistic models
RA
LA
50 mV-100 mV
SNR = 100 dB
RMSE = 0.92
CC = 0.40
SNR = 30 dB
RMSE = 0.96
CC = 0.26
SNR = 20 dB
RMSE = 0.97
CC = 0.22
SNR = 10 dB
RMSE = 0.98
CC = 0.18

11. Felipe Alonso-Atienza
26th March 2015 11ECGi Workshop
DF maps
RA
LA
12 Hz5 Hz
SNR = 100 SNR = 30
SNR = 20 SNR = 10
8 Hz

12. Felipe Alonso-Atienza
26th March 2015 12ECGi Workshop
3D realistic models: conclusions
o Estimation of epicardial potentials does not provide accurate solutions in
realistic conditions (SNRs 5-30 dB)
o Also in this scenario, dominant frequency maps seem more stable, even in
noisy conditions.
o The utilized 3D model has several limitations,
§ No bones, lungs.
§ Atrial tissue as a 3D surface.
o Thus, less accurate results are expected with real clinical data.
o It would be nice to understand how forward problem limitations affect the
inverse solution through errors in the transition matrix

13. Felipe Alonso-Atienza
26th March 2015 13ECGi Workshop
Clinical data: current situation
o BSPMs: 54 electrodes, and simultaneously
o Endocardial mapping
o Up to now, since October 2014
§ 13 patients: 7W, 6M.
² 7 AFs
² 4 persistent AF
² 4 Atrial Flutter
o Building the patient-specific geometrical model of atria and torso.

14. Felipe Alonso-Atienza
26th March 2015 14ECGi Workshop
Final conclusions
❌ In general, tested algorithms do not provide accurate results for estimating
epicardial potentials in realistic situations (SNRs < 30).
q Future work: to implement other approaches accounting for spatio-temporal
regularization techniques (i.e. Kalman Filter), and novel approaches (in the context of
convex optimization framework).
ü Tikhonov outperforms other methods, might be used for benchmarking
ü Spectral features of inverse solutions might provide more robust solutions
q Future work: to implement and to analyze inverse algorithms based on the frequency
content of the cardiac signals
o A common testbed would be of interest for comparing both old and novel
approaches: electrophysiological model, geometrical models, simulation
parameters, and common performance metrics .