Cell-based modeling of tissue development in a scaffold affected by shear stresses

Abstract

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We derived the explicit expression for shear stresses in the fluid flow through a wavy channel and use it to simulate the tissue development. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows for obtaining complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. FSNM-2023-0003).

Speaker

Dmitry Bratsun
Perm National Research Polytechnic University
Russia

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