Tissue as a Maze: Why FLASH Radiation Acts Unevenly express

Original: "Fractal geometry-governed oxygen diffusion: Tumors vs. Normal Tissues"
arXiv:2604.15478 · 2026-04-16 · CC BY 4.0 · 2 min
A new model explains why ultra-fast irradiation affects healthy and diseased tissues differently.

Imagine a city where streets are not straight but winding, with dead ends and hidden passages. A bike courier will take much longer to deliver a package than in a city with a regular grid of roads. Similarly, molecules inside living tissue: their path depends on how "tangled" the tissue structure is.

Scientists built a model that describes the movement of molecules in such a "tangled" environment. They used the concept of a fractal — an object that looks the same at different scales, like a tree branch or a coastline. Tissue is characterized by a fractal dimension D: the larger it is, the more "spacious" the medium is for molecules. But there is another parameter — θ (theta)—which accounts for the "memory" of the medium: how much a molecule's past movement influences its future. When θ is greater than zero, molecules move slower than usual and get stuck in traps.

When θ > 0, transport becomes subdiffusive: molecules spread slower than in normal diffusion, and even in steady state, the concentration does not become uniform.

The model was applied to FLASH therapy — a radiation method where the dose is delivered in milliseconds. It turned out that in tissues with high structural complexity (large θ), reactive molecules produced by radiation do not have time to distribute evenly. Instead, they remain in isolated "pockets" where reactions last longer. This changes the damage pattern: healthy tissues with a certain structure may be protected, while tumors with a different structure may receive more damage.

This approach helps understand why the FLASH effect is not always observed and depends on tissue type. The model provides a tool to predict how a specific tissue will respond and could help develop safer radiotherapy protocols.

The fractal dimension of a human lung is about 2.97—almost like three-dimensional space, even though the lung occupies only part of the chest cavity. This allows a huge surface area for gas exchange to be packed into a small volume.

In Greg Egan's novel "Permutation City," people live in a simulation with changeable geometry of space — an idea that resonates with controlling molecular transport through altering fractal structure.

Scientists
Albert EinsteinAndrey Markov
Concepts
fractal dimension fractal diffusion mri diffusion multifractal detrended fluctuation analysis Gauss's theorem chemotaxis symplectic geometry density functional theory differential form detrended fluctuation analysis tumor segmentation quantum geometry fluid dynamics in porous media chemotherapy healthy tissue neural network memory architecture horizontal gene transfer heat transport phylogenetic network