  Mathematical modeling and simulation is a promising approach to personalized
cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of
cancer pose significant computational challenges. Coupling discrete cell-based
models with continuous models using hybrid cellular automata is a powerful
approach for mimicking biological complexity and describing the dynamical
exchange of information across different scales. However, when clinically
relevant cancer portions are taken into account, such models become
computationally very expensive. While efficient parallelization techniques for
continuous models exist, their coupling with discrete models, particularly
cellular automata, necessitates more elaborate solutions. Building upon FEniCS,
a popular and powerful scientific computing platform for solving partial
differential equations, we developed parallel algorithms to link stochastic
cellular automata with differential equations (
https://bitbucket.org/HTasken/cansim ). The algorithms minimize the
communication between processes that share cellular automata neighborhood
values while also allowing for reproducibility during stochastic updates. We
demonstrated the potential of our solution on a complex hybrid cellular
automaton model of breast cancer treated with combination chemotherapy. On a
single-core processor, we obtained nearly linear scaling with an increasing
problem size, whereas weak parallel scaling showed moderate growth in solving
time relative to increase in problem size. Finally we applied the algorithm to
a problem that is 500 times larger than previous work, allowing us to run
personalized therapy simulations based on heterogeneous cell density and tumor
perfusion conditions estimated from magnetic resonance imaging data on an
unprecedented scale.
