A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy

Abstract

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 (CA) 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 CA, 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 CA with differential equations (https:// bitbucket.org/HTasken/cansim). The algorithms minimize the communication between processes that share CA 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.

ABC of the future

“…Personalised cancer treatment is an application area where simulator‐based inference has a lot of potential, given the constantly improving biological generative models for the evolution of the disease under treatment (Sottoriva & Tavaré, 2010; Kozłowska et al , 2018; Lai et al , 2019; Lai et al , 2021). Realistic biological generative tumor models that are built up from the molecular and cellular processes result typically in a level of complexity that renders analytical solutions infeasible.…”

Fractional mathematical oncology: cancer-related dynamics under an interdisciplinary viewpoint

“…For instance, a finite-state automata model can be used to represent different cell states whereas a continuous dynamics system describes cell behavior according to such state (PHILLIPS et al, 2020). On a different note, those models can also be used to predict the outcome from different medical care strategies or to identify potential targets for cancer treatment -e.g., breast cancer therapy (LAI et al, 2022).…”