Competing computational approaches to reaction-diffusion equations in clusters of cells

S. Stella, R. Chignola, E. Milotti
Department of Physics, University of Trieste, Italy; Department of Biotechnology, University of Verona, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy
J. Phys.: Conf. Ser. 490 012129


   title={Competing computational approaches to reaction-diffusion equations in clusters of cells},

   author={Stella, Sabrina and Chignola, Roberto and Milotti, Edoardo},

   booktitle={Journal of Physics: Conference Series},





   organization={IOP Publishing}


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We have developed a numerical model that simulates the growth of small avascular solid tumors. At its core lies a set of partial differential equations that describe diffusion processes as well as transport and reaction mechanisms of a selected number of nutrients. Although the model relies on a restricted subset of molecular pathways, it compares well with experiments, and its emergent properties have recently led us to uncover a metabolic scaling law that stresses the common mechanisms that drive tumor growth. Now we plan to expand the biochemical model at the basis of the simulator to extend its reach. However, the introduction of additional molecular pathways requires an extensive revision of the reaction-diffusion part of the C++ code to make it more modular and to boost performance. To this end, we developed a novel computational abstract model where the individual molecular species represent the basic computational building blocks. Using a simple two-dimensional toy model to benchmark the new code, we find that the new implementation produces a more modular code without affecting performance. Preliminary results also show that a factor 2 speedup can be achieved with OpenMP multithreading, and other very preliminary results indicate that at least an order-of-magnitude speedup can be obtained using an NVidia Fermi GPU with CUDA code.
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