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

TL;DR

Anatomy-DT tackles the challenge of predicting patient-specific evolution of tumor and surrounding anatomy by unifying cross-diffusion reaction-diffusion PDEs with differentiable deep learning. Anatomy is represented as a multi-class probability field on the simplex $p(x,t) \in \Delta^{K-1}$ and evolved through a cross-diffusion PDE, solved with a differentiable IMEX scheme that enforces simplex conservation. A topology-preserving regularizer (ATL) combining centerline skeleton preservation and no-overlap constraints ensures global anatomical plausibility during evolution. The approach yields state-of-the-art or superior performance on synthetic benchmarks and clinically relevant brain glioma data, demonstrating improved boundary fidelity and topological consistency, and offering a principled path toward clinically viable anatomy-to-anatomy digital twins.

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.

Figures (8)

• Figure 1: Existing baselines model only tumor growth and do not consider adjacent anatomy changes. Our proposed method, Anatomy-DT, models both anatomy and tumor growth conditioned on different treatment paradigms.
• Figure 2: Anatomy-DT architecture. Our proposed method has three primary components: a) A Growth CNN that learns the residual patterns of anatomy growth, b) the cross-diffusion PDE which models multi-anatomy evolution and c) a topology loss function preserving the anatomical structures.
• Figure 3: Datasets. We use two synthetic datasets and a real clinical dataset.
• Figure 4: Qualitative results. A. We compare the tumor segmentation masks from our generated method with different baselines. We report the DSC scores for each cases. B. We show the ground-truth (in red) and predicted (in green) tumor, white matter tracts, cortical gray matter, and lateral ventricle segmentation contours. We report the DSC score for each structure.
• Figure 5: Results on different structures. We show box plots for DSC and cl-Dice scores of different structures (WMT and CGM).

Theorems & Definitions (11)

• Definition 1: Anatomical State
• Remark 1
• Definition 2: Cross-Diffusion PDE model
• Remark 2
• Definition 3: Anatomy Structure Regularizer
• Definition 4: Anatomy Overlap Regularizer
• Theorem 1: Existence and Uniqueness
• Theorem 2: Stability of IMEX Scheme
• Lemma 1: Feasibility and Conservation
• Theorem 3: Topology Preservation via ATL