Parallel Implementations of Numerical Simulation of the Vascular Solid Tumour Growth Model under the Action of Therapeutic Agents (Chemo- and

Abstract—The authors ’ main interest was to develop vascular solid tumour growth model, implement efficient numerical methods for simulations towards finding a solution of the model and trying to optimise the influence of different types of therapies. A system of partial differential equations was introduced in order to simulate the growth of tumour and normal cells as well as the dynamics of the diffusing nutrient and anti-angiogenic or chemotherapeutic factors within the tissue. We have implemented finite difference time-domain (FDTD) method, which was formerly shown to produce numerical stable solutions. In order to make calculations in larger space, which includes a complex three-dimensional structure of capillaries, a single processing unit is not sufficient. Hence, there is the need for using high computing power in order to obtain the results at reasonable time. Furthermore, over some computing space limit, the amount of memory required to compute the solution extends the capacity of single computing machine, making computer cluster is the only choice. We are comparing the implementation of the numerical method for multi-computer system (cluster) using the message passing programming (MPI) paradigm with massively parallel computing implementation using graphic computing accelerators. The code was written in C++ and compared with Matlab implementation with appropriate toolboxes (Parallel Computing Toolbox and Distributed Computing Server). In all cases, the use of parallel implementation speedups the simulation time in comparison to the standard implementation on a single processor computer. Our results showed that we can reduce the simulation time significantly, when we use parallel computing written in C++. The speedup depends on the size of the computation domain, available memory size, the type of processors used and realization accuracy. Parallelisation of the code allows to perform optimisation of therapeutic protocols included in the model