Boundary-Mediated Tumor Growth II: Empirical Scaling Across Transport Regimes

Abstract This work presents a detailed empirical evaluation of the boundary-mediated tumor growth framework introduced in Boundary-Mediated Tumor Growth (Sirotnikov, 2026; https://doi.org/10.5281/zenodo.19342311). Tumor growth is examined across a spectrum of biologically distinct transport regimes, including diffusion-limited spheroids, oxygen-limited systems, vascularized tumors, and perfusion-dominated tumors. A unified dataset is constructed from published studies to enable direct comparison across regimes. Observed tumor growth exponents increase systematically with transport efficiency and closely follow the scaling relation: α = (2 + β)/3 The agreement between predicted and observed values is consistent across heterogeneous systems, supporting the interpretation of tumor growth as a transport-limited, boundary-mediated accumulation process governed by geometric constraints and flux efficiency. This work provides structured empirical support for the framework and establishes a basis for future quantitative estimation of transport parameters in tumor systems. Program Context and Related Works This work is part of the Boundary-Mediated Growth (BMG) Theory research program, which develops a unified scaling framework for growth processes governed by transport across reactive boundaries. The present paper provides empirical validation of tumor growth scaling across transport regimes and builds directly on the foundational theoretical framework established in: - Boundary-Mediated Growth Instability: A Scaling Framework for Solid Tumor Dynamics https://doi.org/10.5281/zenodo.19342311 The broader theoretical structure of the BMG program is developed in: - Boundary-Mediated Growth Theory: A Unified Scaling Framework Across Systems https://doi.org/10.5281/zenodo.19265920 Together, these works establish a consistent relationship between transport efficiency, geometric constraints, and observed growth dynamics across biological and physical systems.