Diffusion-limited tumour growth: simulations and analysis

TY - JOUR

T1 - Diffusion-limited tumour growth

T2 - simulations and analysis

AU - Gerlee, Philip David Marcus

AU - Anderson, A.R.A.

PY - 2010/4/1

Y1 - 2010/4/1

N2 - The morphology of solid tumours is known to be affected by the background oxygen concentration of the tissue in which the tumour grows, and both computational and experimental studies have suggested that branched tumour morphology in low oxygen concentration is caused by diffusion-limited growth. In this paper we present a simple hybrid cellular automaton model of solid tumour growth aimed at investigating this phenomenon. Simulation results show that for high consumption rates (or equivalently low oxygen concentrations) the tumours exhibit branched morphologies, but more importantly the simplicity of the model allows for an analytic approach to the problem. By applying a steady-state assumption we derive an approximate solution of the oxygen equation, which closely matches the simulation results. Further, we derive a dispersion relation which reveals that the average branch width in the tumour depends on the width of the active rim, and that a smaller active rim gives rise to thinner branches. Comparison between the prediction of the stability analysis and the results from the simulations shows good agreement between theory and simulation.

AB - The morphology of solid tumours is known to be affected by the background oxygen concentration of the tissue in which the tumour grows, and both computational and experimental studies have suggested that branched tumour morphology in low oxygen concentration is caused by diffusion-limited growth. In this paper we present a simple hybrid cellular automaton model of solid tumour growth aimed at investigating this phenomenon. Simulation results show that for high consumption rates (or equivalently low oxygen concentrations) the tumours exhibit branched morphologies, but more importantly the simplicity of the model allows for an analytic approach to the problem. By applying a steady-state assumption we derive an approximate solution of the oxygen equation, which closely matches the simulation results. Further, we derive a dispersion relation which reveals that the average branch width in the tumour depends on the width of the active rim, and that a smaller active rim gives rise to thinner branches. Comparison between the prediction of the stability analysis and the results from the simulations shows good agreement between theory and simulation.

U2 - 10.3934/mbe.2010.7.385

DO - 10.3934/mbe.2010.7.385

M3 - Journal article

SN - 1547-1063

VL - 7

SP - 385

EP - 400

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

IS - 2

ER -