Fast Parameter Estimation for Cancer Cell Progression and Response to Therapy

We investigate a mathematical model describing the development of cancer cells in the mammalian cell division cycle under therapy and present an efficient strategy for fast numerical simulations and effective treatment programs in parallel computing environments. We perform a series of computations implemented on a cluster of computers with multicore processors for which the model equations are algorithmically split and solved over independent processors working in parallel and examine the speedup gained. In our implementation, the time interval is split into a number of subintervals corresponding to the number of available processors and the parallelization is invoked across time so that the number of processors to be used is unrestricted. We also extend our implementation to a generalized model of human tumor growth in vivo and demonstrate the computational efficiency of the algorithm and the associated decrease in computational time as the number of utilized processors increases by means of a series of numerical experiments performed in a parallel computing environment.

[1]  Rohit Chandra,et al.  Parallel programming in openMP , 2000 .

[2]  Nicola Bellomo,et al.  MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION , 2004 .

[3]  Nicola Bellomo,et al.  On the foundations of cancer modelling: Selected topics, speculations, and perspectives , 2008 .

[4]  Barbara Zubik-Kowal,et al.  Clinical study and numerical simulation of brain cancer dynamics under radiotherapy , 2015, Commun. Nonlinear Sci. Numer. Simul..

[5]  Barbara Zubik-Kowal.  Numerical algorithm for the growth of human tumor cells and their responses to therapy , 2014, Appl. Math. Comput..

[6]  Barbara Zubik-Kowal,et al.  Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment , 2013, Commun. Nonlinear Sci. Numer. Simul..

[7]  Barbara Zubik-Kowal,et al.  Numerical solution of a model for brain cancer progression after therapy , 2009 .

[8]  Abdelghani Bellouquid,et al.  Global optimization approaches to parameters identification in immune competition model , 2014 .

[9]  Barbara Zubik-Kowal.  A Fast Parallel Algorithm for Delay Partial Differential Equations Modeling the Cell Cycle in Cell Lines Derived from Human Tumors , 2014 .

[10]  Abdelghani Bellouquid,et al.  Asymptotic analysis of a nonlinear integro-differential system modeling the immune response , 2014, Comput. Math. Appl..

[11]  Z. Jackiewicz,et al.  Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. , 2009, Mathematical biosciences and engineering : MBE.

[12]  M. I. Saunders,et al.  Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry. , 1988, British Journal of Cancer.

[13]  Barbara Zubik-Kowal,et al.  Experimental versus numerical data for breast cancer progression , 2012 .

[14]  Peter S. Pacheco.  Parallel programming with MPI , 1996 .

[15]  Barbara Zubik-Kowal,et al.  Nonlinear Modeling with Mammographic Evidence of Carcinoma , 2010 .

[16]  Graeme Wake,et al.  A mathematical model for analysis of the cell cycle in cell lines derived from human tumors , 2003, Journal of mathematical biology.