Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation

TL;DR

A two-step framework that decouples geometric representation from learning the physics response, to enable shape-informed surrogate modeling under data-scarce conditions and allows for accurate predictions and generalization to unseen geometries, and robustness to noisy or sparsely sampled inputs.

Abstract

High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging, particularly in data-scarce settings. We propose a two-step framework that decouples geometric representation from learning the physics response, to enable shape-informed surrogate modeling under data-scarce conditions. First, a shape model learns a compact latent representation of left ventricular geometries. The learned latent space effectively encodes anatomies and enables synthetic geometries generation for data augmentation. Second, a neural field-based surrogate model, conditioned on this geometric encoding, is trained to predict ventricular displacement under external loading. The proposed architecture performs positional encoding by using universal ventricular coordinates, which improves generalization across diverse anatomies. Geometric variability is encoded using two alternative strategies, which are systematically compared: a PCA-based approach suitable for working with point cloud representations of geometries, and a DeepSDF-based implicit neural representation learned directly from point clouds. Overall, our results, obtained on idealized and patient-specific datasets, show that the proposed approaches allow for accurate predictions and generalization to unseen geometries, and robustness to noisy or sparsely sampled inputs.

Figures (19)

• Figure 1: Data processing, modeling, and training pipelines. Solid black lines/boxes show the pipeline of patient-specific left ventricular (LV) models; dashed gray lines/boxes that of the idealized LV models. They differ in that the idealized model cohort is not augmented by synthetically generated geometries. a) LV geometry extraction from 4-chamber patient-specific heart geometries, retrieving 44 LV geometries. b) Idealized LV models generated from varying long axis, diameter, and wall thickness $\ell$, $d$, and $w$, respectively, retrieving 512 models. c) $\text{SDF-SM}$ training: learning of signed-distance function to represent the geometry boundary. d) Geometry generation by $\text{SDF-SM}$. e) Mechanical forward problem setup. Left: Reference geometry $\mathit{\Omega}_0$, with Robin (spring) boundaries on the base ($\mathit{\Gamma}_0^{R,\mathrm{b}}$) and the epicardium ($\mathit{\Gamma}_0^{R,\mathrm{e}}$) as well as a Neumann boundary at the endocardium ($\mathit{\Gamma}_0^{N}$). Right: Fiber field $\boldsymbol{f}_0$; color indicates the fiber angle $\alpha$ with respect to the circumference. f) $\text{SDF-SM}$ encoding. g) $\text{PCA-SM}$ encoding. h) Computation of universal ventricular coordinates (UVCs). i) Simulation of the forward model to generate displacement training data. Left: undeformed geometry. Right: deformed model with displacement field $\boldsymbol{u}$, color indicating its magnitude. j) Surrogate model, informed by cartesian coordinates $\mathbf{x}$, UVCs $\boldsymbol{\upxi}$, a shape code $\boldsymbol{\mu}_{g}$ (either from $\text{PCA-SM}$, $\text{SDF-SM}$, or an analytic descriptor of shape features, e.g. features from the idealized geometries), and possibly some parameters $\boldsymbol{\mu}_{p}$.
• Figure 2: Visualizations of the learned latent space for the idealized geometries dataset. a) Comparison between reconstructed latent codes and original geometric features for the idealized geometries. Each column corresponds to an individual geometry, with colors representing the z-normalized value of the associated original feature to ensure homogeneous color scaling across dimensions. b) Pairwise Pearson correlation matrices between the learned latent codes and the original geometric features for the idealized geometries. c) Three-dimensional visualization of the learned latent space for the idealized geometries. Points represent individual samples in the space of the first three latent codes and are colored according to the z-normalized values of the original geometric features, illustrating how variations in physical parameters are embedded in the latent representation.
• Figure 3: Performance metrics for $\text{SDF-SM}$ reconstructed geometries.
• Figure 4: a) Reconstructed meshes colored according to the distance [mm] to the closest point on the target mesh. First row: heart failure patients, second row: healthy patients. b) Reconstructed meshes (in purple) and original ones (in white). First row: heart failure patients; second row: healthy patients.
• Figure 5: a) Correlation matrices computed after inference. Matrix on the left describes correlation among different components of the latent space. Matrix on the right describes correlation between codes of different geometries. Colored line at the bottom distinguishes the two cohorts of patients, while the color of the index indicates wether the geometry belongs to training or test set. b) Empirical distributions of pairwise correlations respectively between codes and geometries. Histograms show the density of the upper triangular elements of the corresponding correlation matrices (excluding the diagonal), so that each variable pair is counted once. Vertical dashed lines indicate correlation thresholds of $\pm 0.5$.