Understanding the Role of Physics-Informed Inductive Biases in Brain Tumor Segmentation: A Theoretical and Methodological Perspective

Abstract

Physics-informed deep learning models have received increasing attention in medical image segmentation and particularly in brain tumor analysis, owing to their ability to incorporate mechanistic prior knowledge into data-driven architectures. Although numerous studies have presented empirical observations using physics-informed constraints, considerably less attention has been paid to why, when, and under what conditions such prior knowledge meaningfully contributes to segmentation behavior. This study presents a theoretical and methodological analysis of physics-informed segmentation frameworks from an inductive bias perspective. Rather than proposing new models or numerical benchmarks, we examine how reaction-diffusion-based priors influence model behavior across different spatial scales, tumor growth assumptions, and imaging scenarios. We argue that physics-informed constraints function not as universal improvers but as context-dependent regularization mechanisms whose effectiveness depends on the alignment between biological assumptions and imaging characteristics. By reframing physics-informed segmentation as a problem of inductive bias compatibility rather than numerical optimization, this study clarifies the conceptual role of mechanistic priors and provides guidance for their principled use in future segmentation studies. To operationalize this perspective, we introduce two central constructs: a dimensionless scale ratio R that delimits the spatial regime in which reaction-diffusion priors remain valid, and an alignment function A that captures the compatibility between encoded biological assumptions and the underlying data-generating process. We formalize the conditions under which physics-informed regularization is expected to be beneficial, neutral, or potentially harmful, and propose a reporting framework for the transparent evaluation of physics-informed approaches.