Fractal geometry-governed oxygen diffusion: Tumors vs. Normal Tissues

TL;DR

This study introduces a fractal geometry-based diffusion model to explain how structural heterogeneity affects oxygen transport in tissues, with implications for understanding tumor versus normal tissue responses under high-dose irradiation.

Contribution

The paper develops an analytical generalized diffusion-reaction model on fractal substrates that captures anomalous transport and heterogeneity effects in biological tissues.

Findings

Increased tissue complexity suppresses long-range transport and enhances localization.

Fractional dynamics induce subdiffusive behavior and non-Gaussian concentration profiles.

Geometric and fractional effects can lead to distinct regimes of tissue transport behavior.

Abstract

{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport in biological tissues. {\bf Methods}: We formulate a generalized diffusion--reaction model on fractal substrates to describe molecular transport in heterogeneous media. Tissue architecture is characterized by a fractal (Hausdorff) dimension \(D\), while scale-dependent transport inefficiency and memory effects are captured by a fractional parameter \(\theta\). Analytical solutions for radially symmetric geometries are derived and compared with classical normal (Euclidean) diffusion and a Gaussian reference model under identical physical conditions. Transport behavior is quantified through transient probability distributions and steady-state spatial profiles. {\bf Results}: The model reveals systematic suppression of long-range transport and enhanced localization as tissue structural complexity increases. Increasing \(\theta\) leads to subdiffusive dynamics, reduced effective diffusion lengths, and persistent non-Gaussian concentration profiles, even in the steady state. While increasing \(D\) alone enhances spatial accessibility, fractional dynamics dominate transport behavior when \(\theta>0\), counteracting geometric connectivity. These effects produce a separation between regimes characterized by efficient inter-track overlap and rapid homogenization, and regimes marked by isolated, long-lived reactive domains.