On the equivalence between Agent-Based and Continuum models for cell population modeling. Application to glioblastoma evolution in microfluidic devices

Abstract

Mathematical models are invaluable tools for understanding the mechanisms and interactions that control the behavior of complex systems. Modeling a problem as cancer evolution includes many coupled phenomena being therefore impossible to obtain sufficient experimental results to fully evaluate all possible conditions. In this work, we focus on Agent-Based Models (ABMs), as these models allow to obtain more complete and interpretable information at the individual level than other types of in silico models. However, ABMs, need many parameters, requiring more information at the cellular and environmental levels to be calibrated. To overcome this problem we propose a complementary approach to traditional calibration methods. We used existent continuum models able to reproduce experimental data, validated and with fitted parameters, to establish relationships between parameters of both, continuum and agent-based models, to simplify and improve the process of adjusting the parameters of the ABM. With this approach, it is possible to bridge the gap between both kinds of models, allowing to work with them simultaneously and take advantage of the benefits of each of them. To illustrate this methodology, the evolution of glioblastoma (GB) is modeled as an example of application. The resulting ABM obtains very similar results to those previously obtained with the continuum model, replicating the main histopathological features (the formation of necrotic cores and pseudopalisades) appearing in several different in vitro experiments in microfluidic devices, as we previously obtained with continuum models. However, ABMs have additional advantages: since they also incorporates the inherent random effects present in Biology, providing a more natural explanation and a deeper understanding of biological processes. Moreover, additional relevant phenomena can be easily incorporated, such as the mechanical interaction between cells or with the environment, angiogenic processes and cell concentrations far from the continuum requirement as happens, for intance, with immune cells.