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

2025-09-29

AI Summary

Modeling the spatiotemporal evolution of tumors and adjacent anatomical structures in medical imaging remains challenging due to complex interdependencies and anatomical constraints. Method: We propose a digital twin framework based on a cross-diffusion–reaction system incorporating inter-class competition and exclusivity mechanisms, augmented with topological regularization to ensure anatomical plausibility and centerline consistency. An implicit–explicit differentiable PDE solver integrates partial differential equations with differentiable deep learning, constraining solutions to the probability simplex. Contribution/Results: This work presents the first method enabling coupled simulation of tumor growth and concurrent dynamic changes in surrounding tissues—simultaneously preserving morphological fidelity, anatomical exclusivity, and topological consistency. Evaluated on synthetic and multi-center clinical datasets, our approach significantly outperforms existing models in accuracy and robustness. It delivers a high-fidelity, clinically interpretable computational tool for disease progression prediction and treatment response assessment.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Multimodal Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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.

Problem

• Modeling spatiotemporal evolution of tumor morphology from baseline imaging
• Addressing alterations in adjacent anatomical structures during tumor growth
• Creating anatomically exclusive and topologically consistent digital twins

Innovation

• Cross-diffusion system models tumor-anatomy interactions
• Differentiable solver combines implicit-explicit numerical scheme
• Topology regularizer preserves anatomical structure and exclusivity