ECGi Workshop @ Bad Herrenalb (Germany)

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

[email protected] @FelipeURJC

ECGi-Workshop, Bad Herrenalb, 26th march 2015

Felipe Alonso-Atienza

26th March 2015 2ECGi Workshop

Motivationo  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.



First steps: model of sphereso  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)



First steps: model of sphereso  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



RMSE analysis



CC analysis



Tikhonov performance

15 Hz10 Hz

original SNR = 10 dB SNR = 100 dB



Model of spheres: conclusionso  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)



3D realistic modelso  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)



First trial in 3D realistic modelsRALA

50 mV-100 mV

SNR = 100 dBRMSE = 0.92CC = 0.40

SNR = 30 dBRMSE = 0.96CC = 0.26

SNR = 20 dBRMSE = 0.97CC = 0.22

SNR = 10 dBRMSE = 0.98CC = 0.18



DF maps

RALA

12 Hz5 Hz

SNR = 100 SNR = 30

SNR = 20 SNR = 10

8 Hz



3D realistic models: conclusionso  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



Clinical data: current situationo  BSPMs: 54 electrodes, and simultaneouslyo  Endocardial mapping

o  Up to now, since October 2014§  13 patients: 7W, 6M.

²  7 AFs²  4 persistent AF²  4 Atrial Flutter

o  Building the patient-specific geometrical model of atria and torso.



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 .

ECGi Workshop @ Bad Herrenalb (Germany)

Engineering

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