The role of Allee effect in modelling post resection recurrence of glioblastoma.

Zoltan Neufeld,Dora Lakatos,Andras Czirok,William Von Witt,Balazs Hegedus,Jiaming Wang,Leah Edelstein-Keshet

doi:10.1371/journal.pcbi.1005818

Abstract

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence.

Highlights

The growth of a malignant tumour is driven by the uncontrolled proliferation of cancer cells, and their invasion into healthy tissue
Mathematical models of propagating fronts have been used to represent a wide variety of biological phenomena from action potentials in neural cells to invasive species in ecology and epidemic spreading
We show that when such models are used to predict the effects of external perturbations the results can be very sensitive to certain details of the local dynamics

Summary

Introduction

The growth of a malignant tumour is driven by the uncontrolled proliferation of cancer cells, and their invasion into healthy tissue. While the primary therapy often involves the surgical removal of the tumour, the surgery often leaves a small population of cancer cells infiltrated into the surrounding tissue. After a remission period of variable duration, the surviving cancer cells can initiate the recurrence of the disease. This is a serious concern for glioblastoma brain tumours characterised by a diffuse tumour boundary within a complex, heterogeneous and relatively soft brain tissue [1, 2]. The median relapse time was 8 month for local relapses, and progressively longer for distant relapses. The median time for contralateral relapses increased almost two-fold, to 15 months

Objectives

Methods

Results

Discussion

Conclusion