Large-Scale Parallel Simulations of 3D Cell Colony Dynamics: The Cellular Environment

The authors present a large-scale, hybrid 3D model for simulating dynamics of cell colonies growing in and interacting with a variable environment. For this purpose, they extended an earlier mathematical and computational formulation of a cell colony model to incorporate the cellular environment modeled in a continuous manner. A mathematical description based on partial differential equations is formulated for selected important components of the environment. Such extension is necessary to deal with complex biological processes such as cancer growth, where a number of scales need to be considered (subcellular, cellular, and tissue). The authors show how a continuous model can be efficiently solved on a massively parallel processing system. They also present computational methods that couple discrete and continuous descriptions while maintaining high scalability of the resulting application.

[1]  S. McDougall,et al.  Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. , 2006, Journal of theoretical biology.

[2]  Robert D. Falgout,et al.  Scaling Hypre's Multigrid Solvers to 100, 000 Cores , 2011, High-Performance Scientific Computing.

[3]  Mark A J Chaplain,et al.  Computational modeling of single-cell migration: the leading role of extracellular matrix fibers. , 2012, Biophysical journal.

[4]  S. McDougall,et al.  Multiscale modelling and nonlinear simulation of vascular tumour growth , 2009, Journal of mathematical biology.

[5]  H. Othmer,et al.  A HYBRID MODEL FOR TUMOR SPHEROID GROWTH IN VITRO I: THEORETICAL DEVELOPMENT AND EARLY RESULTS , 2007 .

[6]  J. Folkman,et al.  SELF-REGULATION OF GROWTH IN THREE DIMENSIONS , 1973, The Journal of experimental medicine.

[7]  M. Chaplain,et al.  Continuous and discrete mathematical models of tumor-induced angiogenesis , 1998, Bulletin of mathematical biology.

[8]  Maciej Cytowski,et al.  Large-Scale Parallel Simulations of 3D Cell Colony Dynamics , 2014, Computing in Science & Engineering.

[9]  S. McDougall,et al.  Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies , 2002, Bulletin of mathematical biology.

[10]  A. Anderson,et al.  A Hybrid Multiscale Model of Solid Tumour Growth and Invasion: Evolution and the Microenvironment , 2007 .

[11]  B Ribba,et al.  A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. , 2006, Journal of theoretical biology.

[12]  A. Anderson,et al.  A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype. , 2008, Journal of theoretical biology.

[13]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. , 2005, Mathematical medicine and biology : a journal of the IMA.

[14]  Alexander R. A. Anderson,et al.  Mathematical modelling of cancer cell invasion of tissue , 2008, Math. Comput. Model..

[15]  Ignacio Ramis-Conde,et al.  Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis , 2009, Physical biology.

[16]  M. Chaplain,et al.  Free boundary value problems associated with the growth and development of multicellular spheroids , 1997, European Journal of Applied Mathematics.

[17]  H. Frieboes,et al.  Nonlinear modelling of cancer: bridging the gap between cells and tumours , 2010, Nonlinearity.