Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization

TL;DR

A novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks, is introduced, which proposes a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations.

Abstract

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient's anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

Figures (6)

• Figure 1: Method overview: (a) 3D MRI and PET scans of a glioblastoma patient (b) Preprocessed input includes brain tissue maps, tumor segmentation, and a metabolic map from FET-PET. (c) Tumor cell distribution and brain anatomy inferred using a loss function based on assumptions about physical processes, initial conditions. (d) Outcomes: initial healthy anatomy, spatial tumor cell distribution, and system identification parameters.
• Figure 2: Learning process overview: optimization of spatiotemporal distributions of tumor cells and tissues. (a) Initial condition penalties enforce symmetric healthy anatomy, with the initial tumor distribution at $t=0$ as a small Gaussian blob. (b) Physics penalties regularize dynamics between the initial and the final time. The first row shows gray matter contours with particle positions; the second row shows white matter contours with learned tumor concentrations. (c) Agreement of tumor distribution with anatomical tissues, visible tumor segmentations, and metabolic map after transforming the final tumor distribution through the imaging function.
• Figure 3: Inference overview: (a) Patient's MRI 3D scans. (b) Estimated tissues through non-rigid registration of the average brain, showing white matter and visible tumor segmentations. (c) Learned tumor cell distribution, regularized by the physics residual and aligned with patient data. (d) Learned initial condition of the tissues representing healthy anatomy. (e) Average brain template for reference, rigidly registered to the MRI scan. Notable anatomical differences include the lack of matter passage between the hemispheres next to the tumor, which could affect tumor cell inference results.
• Figure 4: Radiotherapy planning: a) Pre-operative segmentations with white matter concentration as background. b) Distance map from the tumor core segmentation with a 1.5 cm contour and within diffusive tissue, constituting the Standard Plan. c) Our learned tumor cell distribution with the isosurface contour where the enclosed volume equals the total volume of the Standard Plan.
• Figure 5: Direct patient-by-patient comparisons to the Standard Plan of radiotherapy plans with equal total volumes: "Greater," "Equal," and "Less" refer to the direct numerical comparison of Recurrence Coverage. a) Recurrence is defined as the union of edema, enhancing core, and necrotic core on the follow-up MRI segmentation. b) Recurrence is defined as the enhancing core on the follow-up MRI segmentation.