Discrete modelling of liver cell aggregation using partial differential equations

Abstract

Since the main purpose of generation of organ-on-chips is to reduce and, at some point, replace experiments on the animals, several different organs were point of interest in developing on-chip technology. The paper will therefore focus on creating mathematical model of liver cell aggregation, generating a basis for creation of artificial organs in that way. Some studies have shown that in the case of hepatocytes (liver cells), improved cell viability and functionality is connected to the formation of spheroidal multicellular aggregates in comparison to the traditional monolayer culture techniques. We present one-dimensional mathematical model of liver cell aggregation, meaning how the liver cell clusters are formed on an extracellular matrix (ECM) layer. Model is based on partial differential equations in the function of space and time, which are solved numerically using finite difference method. Results show that velocity of the cells at the beginning is slow, only to increase later on during the formation of the aggregates. Material properties and initial cell seeding have great effects on the formation of the aggregates. With this model, we aim to achieve a prediction of number of cell clusters, velocity during and before/after clustering etc., which is important in experiments to examine how different parameters, such as initial cell seeding or material characteristics affect cell aggregation and viability of liver cells.