# Proliferation-invasion (reaction-diffusion) models of glioma

Source: https://onco.cc/technologies/reaction-diffusion-glioma-model/  
OnCo record `reaction-diffusion-glioma-model` (Technology). Data CC BY-NC 4.0, attribute "Data from OnCo (onco.cc)"; commercial use needs a licence.

## TL;DR

Gliomas grow by both dividing and migrating through the brain, and a two-parameter equation fitted to a patient's MRI scans estimates how far invisible cells have spread, which can guide how much brain to irradiate and how fast the tumour will grow.

## Summary

Kristin Swanson, James Murray and colleagues modelled glioblastoma as a reaction-diffusion process: cells proliferate at rate rho and diffuse at rate D, faster along white matter. Fitting the two parameters to serial MRI gives a patient-specific 'velocity' of growth and an estimate of tumour cell density beyond the visible edge, which has been used to individualise radiotherapy margins, to define 'days gained' as a response measure, and to predict survival. The model is the most clinically tested biophysical tumour model but requires two pretreatment scans and simplifies the biology of invasion.

## Fields

- Kind: Technology
- Status: emerging
- Last checked: 2026-09-17
- Tags: mathematical-model
- Principle: Partial differential equation dc/dt = grad(D grad c) + rho·c(1 - c/K): net growth from proliferation and spatial spread from diffusion, with D higher in white matter.
- Since: 2000
- Strengths: Patient-specific from routine MRI; Predicts invisible spread beyond the scan; Tested in radiotherapy planning and response assessment
- Limitations: Needs two scans before treatment; Ignores immune and vascular effects; Not yet in routine planning systems

## Sources

- Swanson, Alvord and Murray 2000, Cell Proliferation: https://doi.org/10.1046/j.1365-2184.2000.00177.x

## Connected records

- cancers: [Brain and spinal cord tumours (all types)](https://onco.cc/cancers/brain-tumours/), [Glioma & glioblastoma](https://onco.cc/cancers/glioblastoma/)
- fronts: [AI & Computation](https://onco.cc/fronts/ai-computation/), [Drug Discovery Platforms](https://onco.cc/fronts/drug-discovery/)
- technologies: [Adaptive radiotherapy (online replanning)](https://onco.cc/technologies/adaptive-radiotherapy/), [Dose painting and biologically guided radiotherapy](https://onco.cc/technologies/dose-painting/), [MRI](https://onco.cc/technologies/mri/), [Patient digital twins](https://onco.cc/technologies/digital-twin-patient-models/)

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