Learning surrogate equations for the analysis of an agent-based cancer model
This work provides a method to simplify and analyze complex agent-based cancer models, which is incremental but useful for researchers in computational biology and oncology.
The authors tackled the complexity of analyzing an agent-based cancer model by developing a unified surrogate population-based reaction model with three coupled ordinary differential equations, enabling easier analysis and estimation of parameters to reduce cancer concentration without costly simulations.
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species -- namely immune cells. We run six different scenarios to explore the competition between cancer and immune cells and the initial concentration of the immune cells on cancer dynamics. We then use coupled equation learning to construct a population-based reaction model for each scenario. We show how they can be unified into a single surrogate population-based reaction model, whose underlying three coupled ordinary differential equations are much easier to analyse than the original agent-based model. As an example, by finding the single steady state of the cancer concentration, we are able to find a linear relationship between this concentration and the initial concentration of the immune cells. This then enables us to estimate suitable values for the competition and initial concentration to reduce the cancer substantially without performing additional complex and expensive simulations from an agent-based stochastic model.