Full-field surrogate modeling of cardiac function encoding geometric variability

2025-04-29

AI Summary

To address the poor generalizability of existing cardiac function models—which require retraining for each patient or pathological condition—this paper proposes a clinically oriented, full-field surrogate model of cardiac function. Methodologically, we introduce a novel computational framework integrating large-deformation diffeomorphic metric mapping (LDDMM)-based deformation registration, statistical shape modeling, and branched latent neural mappings (BLNMs). We further propose a z-score–based synthetic geometry generation scheme to overcome geometric specificity constraints, and enhance physiological fidelity via multi-scale electrophysiological PDE/ODE simulations coupled with synthetic data augmentation. Validated on a cohort of 13 pediatric patients with tetralogy of Fallot, the model demonstrates strong cross-subject and cross-pathology generalization, achieving a mean dimensionless mean squared error of only 0.0034. The implementation is publicly available under the MIT License.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: (Large) Language Models

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Develops geometry-agnostic cardiac surrogate models for clinical use
• Encodes anatomical variability in pediatric Tetralogy of Fallot patients
• Combines physics-based simulations with machine learning for personalization

Innovation

• Combines physics-based modeling with machine learning
• Uses Branched Latent Neural Maps for encoding
• Generates synthetic cohort via statistical shape modeling