Volume 3, Issue 5, October 2015, Page: 27-37
A Hybrid Continuous-Discrete Model of Tumour-Induced Angiogenesis is Solved Numerically in Parallel and Performance Improvements Analysed
Paul M. Darbyshire, Department of Computational Biophysics, Algenet Cancer Research, Nottingham, UK
Received: Aug. 30, 2015;       Accepted: Sep. 22, 2015;       Published: Oct. 13, 2015
DOI: 10.11648/j.ejb.20150305.11      View  4171      Downloads  110
The main aim of this paper is to investigate the potential performance improvements gained from a serial versus parallel implementation of the numerical solution to a system of coupled nonlinear PDEs describing tumour-induced angiogenesis. After applying a suitable finite difference scheme, the resulting hybrid continuous discreet model is solved based on a set of cellular rules defining endothelial cell movement towards a tumour. In addition, the model explicitly incorporates the processes of branching, anastomosis and cell proliferation. Parallel implementations are based on the CUDA programming model with a detailed look at efficient thread deployment and memory management. Results show substantial speedups for the CUDA C language against that of conventional high performance languages, such as C++. Such increased performance highlights the potential for simulating more complex mathematical models of tumour dynamics, such as vascularisation networks, tumour invasion and metastasis, leading to the potential for more rapid experimental results for a range of complex cancer models.
Cancer Modelling, Tumour Angiogenic Factors (TAF), Tumour-Induced Angiogenesis, Anastomoses, Parallel Programming, Compute Unified Device Architecture (CUDA), Graphical Processing Unit (GPU), High Performance Computing (HPC)
To cite this article
Paul M. Darbyshire, A Hybrid Continuous-Discrete Model of Tumour-Induced Angiogenesis is Solved Numerically in Parallel and Performance Improvements Analysed, European Journal of Biophysics. Vol. 3, No. 5, 2015, pp. 27-37. doi: 10.11648/j.ejb.20150305.11
Arnaoutova, I. and Kleinman, H. K. In vitro angiogenesis: Endothelial cell tube formation on gelled basement membrane extract. Nature Protocols, 5, 628–635. 2010.
Gimbrone MA, Cotran RS, Leapman SB, Folkman J: Tumor growth and neovascularization: An experimental model using the rabbit cornea. Journal of the National Cancer Institute. 52, 413–427. 1974.
Folkman, J. and Haudenschild, C. Angiogenesis in vitro. Nature, 288, 551–556. 1980.
Muthukkaruppan, V. R., Kubai, L., Auerbach, R. Tumorinduced neovascularization in the mouse eye. Journal of the National Cancer Institute, 69, 699–705. 1982.
Jain RK, Schlenger K, Hӧckel M. and Yuan F: Quantitative angiogenesis assays: Progress and problems. Nature Medicine 3: 1203–1208.1997.
Hanahan, D and Folkman, J. Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis. Cell, 86, 353–364. 1996.
Albini, A., Tosetti, A. F., Li, W. V., Noonan, D. M. and Li, W. W. Cancer prevention by targeting angiogenesis Nature Reviews Clinical Oncology 9, 498-509. 2012.
Ferrara, N. and Kerbel, R. S. Angiogenesis as a therapeutic target. Nature, 438 967–974. 2005.
Carmeliet, P. Angiogenesis in life, disease and medicine. Nature, 438: 932–936. 2005.
Bouard S. de, Herlin, P. and Christensen, J. G. Antiangio-genic and anti-invasive effects of sunitinib on experimental human glioblastoma. Neuro-Oncology, Vol. 9, No. 4, 412– 423. 2007.
Norden, A. D, Drappatz, J. and Wen P. Y. Novel antiangiogenic therapies for malignant gliomas. The Lancet Neurology, Vol. 7, No. 12, 1152–1160. 2008.
Peirce, S. M. Computational and mathematical modeling of angiogenesis. Microcirculation, 15(8), 739–751. 2008.
M. Scianna, M., Bell. C. and Preziosi L. A review of mathematical models for the formation of vascular networks. Oxford Centre for Collaborative Applied Mathematics. 2012.
Darbyshire, P. M. Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Computational Biology and Bioinformatics. Vol. 3, No. 5, 65-73. 2015.
Rejniak A. K. and Anderson A.R.A. Hybrid models of tumor growth. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 3(1), 115–125. 2011.
Paweletz, N. and M. Knierim M. Tumor-related angiogenesis. Critical Reviews in Oncology and Hematology, 9, 197–242. 1989.
Paku, S. and N. Paweletz. First steps of tumor-related angiogenesis. Laboratory Investigation, 65, 334–346. 1991.
Schor S. L., Schor A. M., Brazill G. W. The effects of fibronectin on the migration of human foreskin fibroblasts and Syrian hamster melanoma cells into three-dimensional gels of lattice collagen fibres. Journal of Cell Science, 48, 301–314, 1981.
Bowersox J. C. and Sorgente N. Chemotaxis of aortic endothelial cells in response to fibronectin. Cancer Research 42, 2547–2551. 1982.
Quigley J. P., Lacovara J., and Cramer E. B. The directed migration of B-16 melanoma-cells in response to a haptotactic chemotactic gradient of fibronectin. Journal of Cell Biology 97, A450–451. 1983.
Stokes C. L., Lauffenburger D. A., and Williams S. K. Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. Journal of Cell Science, 99: 419–430. 1991.
Stokes C. L., Rupnick M. A., Williams S. K., and Lauffenburger D. A. Chemotaxis of human microvessel endothelial cells in response to acidic fibroblast growth factor. Laboratory Investigation, 63, 657–668, 1991.
Stokes C. L. and Lauffenburger D. A. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. Journal of Theoretical Biology, 152, 377–403. 1991.
Anderson, A. R. A. and Chaplain, M. Continuous and discrete mathematical models of tumour-induced angiogenesis, Bulletin of Mathematical Biology, 60, 857-900. 1998.
Anderson, A., B. D. S. Sleeman, I. M. Young and B. S. Griffiths. Nematode movement along a chemical gradient in a structurally heterogeneous environment: II. Theory. Fundamental and Applied Nematology, 20, 165–172. 1997.
Nvidia Corporation. CUDA C programming guide. Version 6.0. 2014.
Cheng, J., Grossman, M and McKercher, Ty. Professional CUDA C Programming. Wrox. 2014.
Venkatasubramanian, S. and Vuduc, R. W. Tuned and wildly asynchronous stencil kernels for hybrid CPU/GPU systems. In Proceedings of the Association of Computing Machinery International Conference on Supercomputing, New York. 2009.
Amorim, R., Haase, G., Liebmann, M. and Weber dos Santos, R. Comparing CUDA and OpenGL implementations for a Jacobi iteration. In Proceedings of High Performance Computing and Simulation Conference, Berlin. 2009.
Cecilia, J. M., Garcıa, J. M. and Ujaldon, M. CUDA 2D stencil computations for the Jacobi method. Springer, 173-183. 2012.
Browse journals by subject