arXiv 2509.252802025-09-29eess.IVcs.CV

Anatomy-DT：用于解剖结构演化的交叉扩散数字孪生

Anatomy-DT: A Cross-Diffusion Digital Twin for Anatomical Evolution

Stony Brook University（斯通布罗克大学）；Columbia University（哥伦比亚大学）

Moinak Bhattacharya, Gagandeep Singh, Prateek Prasanna

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AI总结：

本文提出Anatomy-DT框架，用交叉扩散反应-扩散PDE、可微隐式-显式求解和拓扑正则化联合预测肿瘤及周围解剖演化，在合成与临床数据上取得最优表现。

摘要：

从基线影像准确建模肿瘤形态的时空演化，是开发能够模拟疾病进展和治疗反应的数字孪生框架的先决条件。大多数现有方法主要刻画肿瘤生长，却忽略了相邻解剖结构随之发生的改变。实际上，肿瘤演化具有高度非线性和异质性，不仅受到治疗干预的影响，也由其空间背景以及与邻近组织的相互作用所塑造。因此，将肿瘤进展与周围解剖结构联合建模，对于获得全面且具有临床相关性的疾病动力学理解至关重要。我们提出一个具有数学基础的框架，将机制性偏微分方程与可微深度学习结合起来。解剖结构被表示为单纯形上的多类概率场，并通过一个交叉扩散反应-扩散系统进行演化，该系统强制实现类别间竞争和互斥性。可微的隐式-显式格式对刚性扩散进行隐式处理，同时显式处理非线性反应项和事件项，随后投影回单纯形。为进一步增强全局合理性，我们引入一种拓扑正则化器，同时强制中心线保持并惩罚区域重叠。该方法在合成数据集和一个临床数据集上得到验证。在合成基准上，我们的方法在保持拓扑的同时达到了最先进的精度，并且在临床数据集上也展现出优越性能。通过整合PDE动力学、拓扑感知正则化和可微求解器，本工作为数字孪生的解剖结构到解剖结构生成建立了一条有原则的路径，使其具有视觉真实性、解剖互斥性和拓扑一致性。

英文摘要：

Accurately modeling the spatiotemporal evolution of tumor morphology from baseline imaging is a pre-requisite for developing digital twin frameworks that can simulate disease progression and treatment response. Most existing approaches primarily characterize tumor growth while neglecting the concomitant alterations in adjacent anatomical structures. In reality, tumor evolution is highly non-linear and heterogeneous, shaped not only by therapeutic interventions but also by its spatial context and interaction with neighboring tissues. Therefore, it is critical to model tumor progression in conjunction with surrounding anatomy to obtain a comprehensive and clinically relevant understanding of disease dynamics. We introduce a mathematically grounded framework that unites mechanistic partial differential equations with differentiable deep learning. Anatomy is represented as a multi-class probability field on the simplex and evolved by a cross-diffusion reaction-diffusion system that enforces inter-class competition and exclusivity. A differentiable implicit-explicit scheme treats stiff diffusion implicitly while handling nonlinear reaction and event terms explicitly, followed by projection back to the simplex. To further enhance global plausibility, we introduce a topology regularizer that simultaneously enforces centerline preservation and penalizes region overlaps. The approach is validated on synthetic datasets and a clinical dataset. On synthetic benchmarks, our method achieves state-of-the-art accuracy while preserving topology, and also demonstrates superior performance on the clinical dataset. By integrating PDE dynamics, topology-aware regularization, and differentiable solvers, this work establishes a principled path toward anatomy-to-anatomy generation for digital twins that are visually realistic, anatomically exclusive, and topologically consistent.

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