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 an accurate multi-scale mathematical model coupling partial and ordinary differential equations. We adopt Branched Latent Neural Maps (BLNMs) as a computationally efficient 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 z-score sampling approach based on statistical shape modeling 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.

Cardiac deformation is a crucial biomarker for the evaluation of cardiac function. Current methods for estimating cardiac strain might underestimate local deformation due to through-plane motion and segmental averaging. Mesh-based mapping methods are gaining interest for localized analysis of cardiac motion and strain, yet they often do not consider important properties of cardiac tissue. In this work, we propose an extension of the large deformation diffeomorphic metric mapping framework to incorporate near incompressibility into the loss function that guides the mapping. As such, our mechanically regularized mLDDMM allows for accurate and mechanically coherent estimation of volume displacement and strain tensors from time-resolved three-dimensional meshes. We benchmark our method against the results of a finite element simulation of cardiac contraction and find a very good agreement between our estimation and the simulated ground truth. Our method forms a promising technique to extract volume displacement and strain tensors from time-resolved meshes while accounting for the incompressibility of cardiac tissue.

Abstract: Sex-based differences in cardiovascular disease are well documented, yet the precise nature and extent of these discrepancies in cardiac anatomy remain incompletely understood. Traditional scaling models often fail to capture the interplay of age, blood pressure and body size, prompting a more nuanced investigation. Here we use statistical shape modelling in a healthy subset (n = 456) of the UK Biobank to explore sex-specific variations in biventricular anatomy. We reconstruct 3D meshes and perform multivariate analyses of shape coefficients, controlling for age, blood pressure and various body size metrics. Our findings reveal that sex alone explains at least 25% of morphological variability, with strong discrimination between men and women (AUC = 0.96–0.71) persisting even after correction for confounders. Notably, the most discriminative modes highlight pronounced differences in cardiac chamber volumes, the anterior–posterior width of the right ventricle and the relative positioning of the cardiac chambers. These results underscore that sex has a fundamental influence on cardiac morphology, which may have important clinical implications for differing cardiac structural assessments in men and women. Future work should investigate how these anatomical differences manifest in various cardiovascular conditions, ultimately paving the way for more precise risk stratification and personalised therapeutic strategies for both men and women. (Figure presented.). Key points: Men's and women's hearts differ significantly in overall shape and size, but an in-depth quantification of these sex differences in healthy cardiac anatomy is lacking. We used a three-dimensional statistical shape modelling approach that goes beyond standard clinical measurements to capture subtle anatomical features. Our findings show that sex alone accounts for at least 25% of the natural variation in heart structure, even after correcting for age, blood pressure and various body size metric confounders. Female hearts consistently present smaller chambers and different inter-chamber positioning compared with male hearts. Our findings highlight the importance of sex-specific anatomical insights for better diagnosis, treatment and research on heart disease.