Page 191 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 5 Machine learning methods for robust parameter estimation 163

a reinforcement learning method to train an agent that estimates
model parameters using a learned strategy. Both methods reach
either similar or superior performance compared to highly en-
gineered inverse problem techniques, while being more efficient
and precise.

5.2 A regression approach to model

parameter estimation
A first data driven approach consists in learning a regression
model to estimate parameters of a physiological model directly
from clinical measurements, as previously described in [220].
Without loss of generality, the method is presented in the context
of cardiac electrophysiology (EP), but it could be applied to mod-
els describing other aspects of cardiac function or other organs.
Furthermore, we will also illustrate how uncertainty estimates can
be calculated by leveraging the large database used to train the
regression model.

5.2.1 Data-driven estimation of myocardial electrical
diffusivity
The monodomain model introduced in section 1.2.2 is used
without loss of generality as any other EP model could be also
employed. The EP model y = f(x) takes as input the diffusivity
coefficients x = (c Myo ,c LV ,c RV ), among other parameters that are
fixed in this example, and returns the ECG features y = (QRS ,α),
d
where QRSd is the QRS complex duration measured on 12-lead
ECG traces, and α is the electrical axis of the QRS complex. The
goal is to learn a function g that approximates the inverse problem
x = g(z) ≈ f −1 (z), namely that takes as input measured 12-lead
ECG parameters (z), and returns an estimate of the model param-
eters x.
In this setting, though, ground truth data, namely pairs of clin-
ical measurements (z) and diffusivity values (x), is not available.
We therefore leverage the computational model to create a large
database of pairs (y,x), assuming the model is accurate enough
to provide realistic ECG features. The database is created by uni-
formly sampling the space of parameters x, feeding the model
with the sampled parameters and collecting the respective out-
puts y. Once the database is ready, one could directly learn a
regression model x = g(y). Unfortunately this task can be made
difficult by the lack of observability of the parameters. Two sets
of parameters x 1 and x 2 could give very similar observed ECG