Applying Adomian Decomposition Method to Solve Burgess Equation with a Non-linear Source

TL;DR

This paper applies the Adomian Decomposition Method to solve a nonlinear PDE modeling brain tumor growth under combined radiotherapy and chemotherapy, demonstrating its effectiveness in capturing treatment effects and aiding dose calculation.

Contribution

It introduces a novel application of ADM to a nonlinear tumor growth model incorporating treatment effects, enabling better dose planning.

Findings

The ADM effectively solves the nonlinear PDE model.

The model captures the impact of combined therapies.

Potential for optimizing radiotherapy and chemotherapy doses.

Abstract

In the present work we consider the mathematical model that describes brain tumour growth (glioblastomas) under medical treatment. Based on the medical study presented by R. Stupp et al. (New Engl Journal of Med 352: 987-996, 2005) which evidence that, combined therapies such as, radiotherapy and chemotherapy, produces negative tumour-growth, and using the mathematical model of P. K. Burgess et al. (J Neuropath and Exp Neur 56: 704-713, 1997) as an starting point, we present a model for tumour growth under medical treatment represented by a non-linear partial differential equation that is solved using the Adomian Decomposition Method (ADM). It is also shown that the non-linear term efficiently models the effects of the combined therapies. By means of a proper use of parameters, this model could be used for calculating doses in radiotherapy and chemotherapy.