Page 178 - Artificial Intelligence for Computational Modeling of the Heart

150 Chapter 4 Data-driven reduction of cardiac models

tional features for a second model f 2 :[θ,f 1 (θ)] → v dr . Further, we
also consider a variant of the second model, in which components
of v dr are iteratively estimated, and used as additional features for
the regression of the remaining ones. This defines a total of four
methods:
M 1 use only θ as model input;
M 2 use [θ,f 1 ] as model input
M 3 use [θ,v dr (1),···v dr (i)] as model input to predict v dr (i + 1)
M 4 use [θ,f 1 ,v dr (1),···v dr (i)] as model input to predict v dr (i +1)
We evaluate the four methods using both MARS and PPR for
pca
model estimatation. The embedding Ω is generated as the span
AP
of 15 PCA components.
We report in Table 4.5 the fitting errors of different quantities
of interest of the action potential profile, when using a model
estimated by PPR using the four different methods. All reported
errors are computed as the difference between the quantity as ex-
tracted from the predicted action potential profile, and the quan-
tity extracted from the ground truth profile; normalized by the
mean value of the same quantity in the training database. Small
errors in MAD and V rest suggest that the profiles estimated by
the model capture correctly the amplitude of the action potential;
small errors in APD suggest that the time pattern is properly re-
constructed; small errors in AUC indicate a global goodness of fit,
with no significant localized discrepancies between the predicted
and ground truth action potential profiles. The results indicate
that using f 1 as additional input parameter for model estimation
reduces the error in APD,butnottheerrorin MAD. Introducing
the iterative estimation of the components of v dr significantly de-
creases the MAD error. Overall, method M 4 produces the most
accurate prediction. An example of the estimated action potential
profiles by PPR with M 4 is shown in Fig. 4.21.
The model estimated with MARS achieved comparable perfor-
mance when using method M 4 , and slightly lower performance
when using the other methods. MARS has a potential advantage
over PPR since it produces faster predictions thanks to a simpler
model structure. This can be relevant for applications requiring
repeated estimation of the action potential profile, such as param-
eter estimation for model personalization.

4.2.2.4 Application in tissue-level EP modeling
We tested the application of the regression cellular model to
the study of the electrical activation of cardiac tissue. Starting from
diagnostic cardiac images, the left atrium and right atrium are au-
tomatically segmented using a machine learning approach [31]