AI 中文总结
本文针对基于PCA的心脏瓣膜统计形状模型存在的缺陷，提出贝叶斯后验采样框架，该框架在低数据 regime 下表现优于PCA方法，可高效生成生理合理的瓣膜形状，适用于各类瓣膜的下游应用。
AI 中文摘要
心脏瓣膜的统计形状模型（SSM）通常依赖主成分分析（PCA），用于支持计算机模拟建模、形态学分析和介入规划等下游任务。但基于PCA的SSM缺乏条件形状生成机制，会产生非物理形状，且在低数据 regime（<20个形状）下表现不佳。为解决这些问题，本文提出贝叶斯后验采样框架，用于从后验估计生成瓣膜形状。该框架的先验基于具有数据驱动混合模式的高斯混合模型，似然估计通过训练分类器获得，该分类器用于区分紧凑正交分解（POD）系数空间中的有效与无效区域。本文在模型问题上验证该框架，并在参数构建的主动脉瓣膜数据集上进行验证，结果表明该方法能捕捉多种模式、遵守形状空间中的决策边界，且在低数据 regime 下优于基于PCA的SSM。本文还根据数据集大小表征框架性能，确定所提出的生成形状模型出现收益递减的情况。最后，本文将该框架应用于10例成人三尖瓣三维经食管超声心动图图像队列，先对图像进行分割以提取形状，再生成一组符合生理的新形状，展示了该方法在瓣膜的下游应用，包括瓣膜力学的计算机模拟建模和合成图像-掩码创建以扩充有限数据集，所提方法比基于PCA的SSM更高效地构建图像-掩码数据集，尽管仅在主动脉瓣和三尖瓣上验证，但该方法可广泛应用于所有瓣膜。
英文摘要
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.
