Full-field surrogate modeling of cardiac function encoding geometric variability
Journal:
arXiv
Published Date:
Apr 29, 2025
Abstract
Combining physics-based modeling with data-driven methods is critical to
enabling the translation of computational methods to clinical use in
cardiology. The use of rigorous differential equations combined with machine
learning tools allows for model personalization with uncertainty quantification
in time frames compatible with clinical practice. However, accurate and
efficient surrogate models of cardiac function, built from physics-based
numerical simulation, are still mostly geometry-specific and require retraining
for different patients and pathological conditions. We propose a novel
computational pipeline to embed cardiac anatomies into full-field surrogate
models. We generate a dataset of electrophysiology simulations using a complex
multi-scale mathematical model coupling partial and ordinary differential
equations. We adopt Branched Latent Neural Maps (BLNMs) as an effective
scientific machine learning method to encode activation maps extracted from
physics-based numerical simulations into a neural network. Leveraging large
deformation diffeomorphic metric mappings, we build a biventricular anatomical
atlas and parametrize the anatomical variability of a small and challenging
cohort of 13 pediatric patients affected by Tetralogy of Fallot. We propose a
novel statistical shape modeling based z-score sampling approach to generate a
new synthetic cohort of 52 biventricular geometries that are compatible with
the original geometrical variability. This synthetic cohort acts as the
training set for BLNMs. Our surrogate model demonstrates robustness and great
generalization across the complex original patient cohort, achieving an average
adimensional mean squared error of 0.0034. The Python implementation of our
BLNM model is publicly available under MIT License at
https://github.com/StanfordCBCL/BLNM.
