Bayesian Posterior Sampling for Synthetic Shape Generation of Heart Valves

2026-07-30

AI Summary

This work addresses the limitations of conventional PCA-based statistical shape models for heart valves, which struggle with conditional generation and often produce non-physical shapes under small-sample conditions. The authors propose a Bayesian posterior sampling framework that operates in the Proper Orthogonal Decomposition (POD) coefficient space, integrating a Gaussian mixture prior with a classifier-guided likelihood function. This approach enables multimodal, physiologically plausible shape synthesis by combining data-driven multimodal priors with a decision-boundary-aware likelihood mechanism. Evaluated on both aortic and tricuspid valve datasets, the method significantly outperforms standard PCA models, efficiently generating anatomically realistic 3D geometries suitable for biomechanical simulation and synthetic image mask creation, thereby enhancing dataset generation efficiency in data-scarce scenarios.

Abstract

Statistical shape models (SSMs) for heart valves commonly rely on principal component analysis (PCA). They are used to support downstream tasks, including \textit{in silico} modeling, morphological analysis, and interventional planning. However, PCA-based SSMs lack a mechanism for conditional shape generation, i.e., they can create non-physical shapes and perform poorly in low-data regimes (<20 shapes). To overcome these problems, we propose instead a Bayesian posterior sampling framework to generate valve shapes from a posterior estimate. The prior relies on a Gaussian mixture model with data-driven mixture modes. The likelihood estimate is obtained through a classifier trained to distinguish valid from invalid regions in the compact proper orthogonal decomposition (POD) coefficient space. We verify the framework on a model problem and validate it on parametrically constructed aortic valve datasets. Thereby, we demonstrate that our method captures multiple modes, respects decision boundaries in shape space, and outperforms PCA-based SSMs in low-data regimes. We also characterize the framework's performance as a function of dataset size, identifying where diminishing returns arise for the proposed generative shape model. Finally, we apply the framework to a cohort of ten three-dimensional transesophageal echocardiography images of adult human tricuspid valves. We first segment images to extract shapes, then generate a set of physiologically plausible new shapes. We demonstrate downstream applications for both valves, including \textit{in silico} modeling of valve mechanics and synthetic image-mask creation to augment limited datasets. The proposed approach bootstraps building image-mask datasets more efficiently than PCA-based SSMs. Although demonstrated only for the aortic and tricuspid valves, the methodology is broadly applicable to all valves.

Problem

• statistical shape models
• conditional shape generation
• low-data regimes
• non-physical shapes
• heart valves

Innovation

• Bayesian posterior sampling
• Gaussian mixture model
• conditional shape generation
• proper orthogonal decomposition
• statistical shape modeling