Page 202 - Artificial Intelligence for Computational Modeling of the Heart

174 Chapter 5 Machine learning methods for robust parameter estimation

sonalization is re-initialized at the second-most-likely x 0 ∈{x 0 },
etc. The process terminates once the designated success state ˆ is
s
reached (success), or after a pre-defined maximum number of it-
erations (failure).

5.3.3 Application to cardiac electrophysiology

We tested the approach on cardiac electrophysiology for 83
dilated cardiomyopathy patients who received treatment at Uni-
versity Hospital Heidelberg. For each patient, the end-diastolic bi-
ventricular anatomy was segmented from short-axis cine MRI, a
tetrahedral anatomical model including myofibers was estimated
and a torso atlas registered to the patient. Please refer to sec-
tion 2.1 for more details.
We consider a graph-based model of EP (see section 2.2.3),
which is controlled by conduction velocities (in mm/s) of myocar-

dial tissue and left and right Purkinje network: x = (c Myo ,c LV ,c RV ) .
In the following experiments, the admissible parameter space Ω
was set to [200;1000] for c Myo and [500;5000] for both c LV and c RV .
Reference increment values to build the action set A were set to

δ = (5,5,5) mm/s for the three model parameters. The goal of
personalization was to estimate x from the measured QRS dura-
tion and electrical axis (EA). Personalization was considered suc-
cessful if the misfits in QRSd and EA were below ψ = (5ms,10 ),
◦
respectively.
Number of representative states Quantization of the state space
relies on a single hyper-parameter n S , the number of represen-
tative states (see section 5.3.1.3). We used eight scouting patients
to find a good value for n S using exhaustive search for n S ∈
{10,20,...,490,500} representative states. The configuration qual-
ity was evaluated based on average number of required forward
model runs and personalization success rate on the scouting pa-
tients. Good quality was observed between 50 to 300 representa-
tive states, with a peak at 120, where success rate was 97%,and
where 101 forwards model runs were required on average. There-
fore, n S = 120 was selected for further experimentation. The eight
scouting datasets were discarded for the following experiments to
avoid bias in the analysis.
Reference methods We compared the results of the RL-based
method against two optimization approaches, both based on an
advanced, gradient-free optimization technique called BOBYQA
[187]:
• SIMPLEGEP mimicks the most basic estimation setup, where
only the minimum level of model and problem knowledge were
assumed. To this end, the sum of absolute QRSd and EA errors