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Preliminary investigation of the inhibitory effects of mechanical stress in tumor growth

In the past years different models have been formulated to explain the growth of gliomas in the brain. The most accepted model is based on a reaction-diffusion equation that describes the growth of the tumor as two separate components- a proliferative component and an invasive component. While many improvements have been made to this basic model, the work exploring the factors that naturally inhibit growth is insufficient. It is known that stress fields affect the growth of normal tissue. Due to the rigid skull surrounding the brain, mechanical stress might be an important factor in inhibiting the growth of gliomas. A realistic model of glioma growth would have to take that inhibitory effect into account. In this work a mathematical model based on the reaction-diffusion equation was used to describe tumor growth, and the affect of mechanical stresses caused by the mass effect of tumor cells was studied. An initial tumor cell concentration with a Gaussian distribution was assumed and tumor growth was simulated for two cases- one where growth was solely governed by the reaction-diffusion equation and second where mechanical stress inhibits growth by affecting the diffusivity. All the simulations were performed using the finite difference method. The results of simulations show that the proposed mechanism of inhibition could have a significant affect on tumor growth predictions. This could have implications for varied applications in the imaging field that use growth models, such as registration and model updated surgery.