A Spherically Symmetric Model for the Tumor Growth

Saeed M Ali,M Yousuf,F D Zaman,Ashfaque H Bokhari

doi:10.1155/2014/726837

Abstract

The nonlinear tumor equation in spherical coordinates assuming that both the diffusivity and the killing rate are functions of concentration of tumor cell is studied. A complete classification with regard to the diffusivity and net killing rate is obtained using Lie symmetry analysis. The reduction of the nonlinear governing equation is carried out in some interesting cases and exact solutions are obtained.

Highlights

The tumor growth has been usually modeled as a reactiondiffusion process in the literature
A model describing the growth of the tumor in brain taking into account diffusion or motility as well as proliferation of tumor cells has been developed in a series of papers [2, 3]
In continuation of this approach, Tracqui et al [4] suggest a model which takes into account treatment and killing rate of tumor cells along with the above factors

Summary

Introduction

The tumor growth has been usually modeled as a reactiondiffusion process in the literature. A model describing the growth of the tumor in brain taking into account diffusion or motility as well as proliferation of tumor cells has been developed in a series of papers [2, 3]. They have performed Lie symmetry analysis and presented some exact solutions based upon this approach. The present study is based upon the fact that the diffusivity is not necessarily a constant and may depend upon the concentration of tumor cells. The net killing rate K is taken to be u-dependent This introduces nonlinearity in the governing equation. Some recent studies in nonlinear diffusion equations using this approach can be found in [1, 6]

Symmetry Analysis of the Tumor Equation

Classification

Some Reduction