Page 193 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 5 Machine learning methods for robust parameter estimation 165

coefficients β i,j . During testing, i.e. when one wants to estimate
the diffusivity coefficients from ECG data on an unseen case, the
ECG parameters are first normalized and then the function g is
applied.

5.2.2 Experiments and results

5.2.2.1 Setup and uncertainty analysis
The method presented in this section was comprehensively
evaluated in [220]. We report in the following the main high-
lights. The evaluation was performed on a dataset of 19 patients
with dilated cardiomyopathy (DCM) and a QRS duration higher
than 120 ms. Patients were eligible for CRT according to the cur-
rent guidelines of the European Society of Cardiology and re-
ceived treatment at University Hospital Heidelberg. The work-
flow described in chapter 2 (Fig. 2.1) was followed to create the
anatomical model from magnetic resonance images (MRI). For
each case, 500 different EP simulations were performed, making
a total of 9500 different simulations. Cardiac EP was calculated
using the Lattice-Boltzmann solver for the monodomain prob-
lem (section 2.2.1) using the Michell-Schaeffer cellular model [71],
with an isotropic grid resolution of 1.5 mm. The diffusivity coeffi-
cients were randomly sampled according to a uniform distribu-
2
2
tion between 50 mm /s and 5000 mm /s, with c Myo ≤ c LV ,c RV .
Leveraging the large number of simulations, the uncertainty of
the inverse problem could be estimated. In other words, one could
assess the spread of diffusivity values for which the forward model
would produce very similar values of QRS duration and electrical
axis. To factor out the effect of the heart geometry and position,
the analysis was done on the normalized ECG parameters. The
pairs (x,y) were clustered in 20 × 20 bins along the QRSd and α
axes respectively. The bin-wise standard deviations of c Myo , c LV
and c RV were calculated. The uncertainty of the diffusivity co-
efficients was then defined as the ratio between the average of
all bin-wise standard deviations over the total standard deviation
(Table 5.2). Fig. 5.2 illustrates the bin-wise standard deviations.
As one can see, the largest uncertainty happened in the healthy
ranges for both QRS duration and electrical axis (up to 180%), con-
firming the ill-posed nature of the EP inverse problem.

5.2.2.2 Verification on synthetic data
A first evaluation consists in verifying whether the learned re-
gression model is able to recover the true diffusivity coefficients
on the simulated database, using a leave-one-patient-out strat-
egy. A case was selected randomly for evaluation, while the re-