arXiv subjects

Collin E. Haese

Publications and source records attributed to Collin E. Haese.

3 recordsLinked to original sources

arXiv2026

Bayesian Posterior Sampling for Synthetic Shape Generation of Heart Valves

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.

cs.CE↗

arXiv2026

Fully Differentiable Ultrasound Simulation Utilizing Ray-Tracing

Ultrasound imaging tasks such as calibration, inverse parameter estimation, and acquisition design require models that are physically grounded, efficient, and differentiable with respect to meaningful material and system parameters. While full-wave solvers offer high fidelity, they are often too expensive for iterative optimization, and existing ray-based methods have mostly been limited to forward simulation. In this work, we present a fully differentiable end-to-end ultrasound simulation framework based on full-path Monte Carlo ray tracing. Building on UltraRay, the method propagates gradients from image-space losses back through acoustic transport, beamforming, and post-processing, enabling gradient-based optimization over scene and acquisition parameters. The framework combines differentiable ray transport in Mitsuba 3/Dr.Jit with a custom differentiable bridge through the ultrasound image-formation pipeline. Forward examples reproduce expected geometric image features and capture more complex anatomical structures. In inverse problems, the method recovers known parameters in a simulated-reference setting and identifies effective parameters that improve agreement between simulated and experimental B-mode images in a simulation-to-real setting. Finite-difference comparisons further support the consistency of the computed gradients. Overall, this work provides a practical foundation for differentiable, physics-based ultrasound simulation and optimization.

cs.CE↗

arXiv2025

Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection

Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable bodies, especially in the context of varying geometries, is still an open issue. In particular, existing methods are confined to rigid body contact or, at best, contact between rigid and soft objects with well-defined contact planes. Furthermore, they employ contact or collision detection filters that serve as a rapid test but use only the necessary and not sufficient conditions for detection. In this work, we present a graph neural network architecture that utilizes continuous collision detection and, for the first time, incorporates sufficient conditions designed for contact between soft deformable bodies. We test its performance on two benchmarks, including a problem in soft tissue mechanics of predicting the closed state of a bioprosthetic aortic valve. We find a regularizing effect on adding additional contact terms to the loss function, leading to better generalization of the network. These benefits hold for simple contact at similar planes and element normal angles, and complex contact at differing planes and element normal angles. We also demonstrate that the framework can handle varying reference geometries. However, such benefits come with high computational costs during training, resulting in a trade-off that may not always be favorable. We quantify the training cost and the resulting inference speedups on various hardware architectures. Importantly, our graph neural network implementation results in up to a thousand-fold speedup for our benchmark problems at inference.

cs.CE↗