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Stochastic agent-based models can account for millions of cells withspatiotemporal movement that can be a function of different factors. However,these simulations can be computationally expensive. In this work, we develop anovel computational framework to describe and simulate stochastic cellularprocesses that are coupled to the environment. Specifically, through upscaling,we derive a continuum governing equation that considers the cell density as afunction of time, space, and a cumulative variable that is coupled to theenvironmental conditions. For this new governing equation, we consider thestability through an energy analysis, as well as proving uniqueness andwell-posedness. To solve the governing equations in free-space, we propose anumerical method using fundamental solutions. As an application, we study acell moving in an infinite domain that contains a toxic chemical, where acumulative exposure above a critical value results in cell death. We illustratethe validity of this new modeling framework and associated numerical methods bycomparing the density of live cells to results from the correspondingagent-based model.

Computational framework to capture the spatiotemporal density of cells with a cumulative environmental coupling