A CutFEM Method for a spatial resolved energy metabolism model in complex cellular geometries

Computational techniques have been widely used to tackle problems in the biological sciences. A com- promise between high quality simulations and simple but accurate models can help to understand un- known aspects of this field.
In this work, we will show how the Cut Finite Element Method (CutFEM) [1] can be a powerful tool to solve a reaction diffusion PDE system that models the energy metabolism of a cell. The main difficulty to approach this problem is dealing with the morphology of the cell that can have sharp edges and evolves over time. While classical FEM requires the mesh conform to the domain boundary, CutFEM allows a non-conforming discretisation of the domain, and thus is especially suited for modeling complex and evolving cellular geometries.
First, we introduce our simplified model for metabolic pathways taking place in a region small enough to consider the material property as homogeneous. The results obtained with FEM (FENICS Project [2][3]) and CutFEM suggest that the two methods are equivalent. This allows us to use CutFEM to increase the complexity of the domain, from a spherical shaped cell to an irregular astrocyte.
We conclude that CutFEM is a robust method for tackling biological problems with complex geometries, opening the possibility to extend the complexity of our mathematical model including more features and to consider real cellular shapes that evolve in time in future work.