Numerical Simulation of the Vascular Solid Tumour Growth Model and Therapy – Parallel Implementation
The main interest of the authors 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 influence of different types of therapies. A system of partial differential equations was introduced in order to simulate growth of tumour and normal cells as well as the dynamics of the diffusing nutrient and anti-angiogenic or chemotherapeutic factors within the tissue. Numerical simulations of our model were executed toward finding a suboptimal therapy protocol using stable FDTD (finite difference time-domain) method implementation. Combined therapy protocols has been selected by means of meta-heuristic algorithms. In this work we have selected genetics algorithms, ant colony algorithms and simulated annealing method. For those algorithms convergence to suboptimal solution was examined and compared, as well as average tumour size, average iteration count and average execution time.
Keywordstumour growth model parallel implementation therapy optimisation heuristic methods
Unable to display preview. Download preview PDF.
- 2.Dormann, S., Deutsch, A.: Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. Silico Biology 2, 393–406 (2002)Google Scholar
- 5.Lowengrub, J.S., Frieboes, H.B., Jin, F., Chuang, Y.-L., Li, X., Macklin, P., Wise, S.M., Cristini, V.: Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity 23, R1–R9 (2010)Google Scholar
- 9.Chaplain, M.A., Anderson, A.R.: Mathematical modelling, simulation and prediction of tumour-induced angiogenesis. Invasion Metastasis 16, 222–234 (1996)Google Scholar
- 10.Sherratt, J.A.: Predictive mathematical modeling in metastasis. Methods Mol. Med. 57, 309–315 (2001)Google Scholar
- 11.Evans, G., Blackledge, J., Yardley, P.: Numerical Methods for Partial Differential Equations. Springer, London (1999)Google Scholar
- 12.The Message Passing Interface (MPI) standard, http://www.mcs.anl.gov/research/projects/mpi/
- 13.Nvidia CUDA Toolkit, https://developer.nvidia.com/cuda-toolkit
- 14.Larsson, S., Thomee, V.: Finite Difference Methods for Hyperbolic Equations. Springer, Heidelberg (2003)Google Scholar