Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.Author summary: The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of model agents as well as diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this surrogate to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis by a factor of 562 times compared to single-core CPM code execution on CPU. For up to three recursive evaluations, or 300MCS, our model captures the emergent behaviors demonstrated by the original mechanistic Cellular-Potts model of vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. Our approach demonstrates a step towards the development of surrogate models for CPM simulations using deep neural networks, enabling faster evaluation of computationally expensive CPM simulations of biological processes.