A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup

Abstract

The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.