Numerical modeling of static cell culture growth during growth factor desorption in bioreactor pores

The growth of cell culture in porous scaffolds depends on the pore architecture and the dis-tribution of growth factors, including their desorption from the porous matrix. Mathematical mod-eling allows for the quantitative assessment of the influence of channel geometry and boundary conditions on the morphological and mechanical characteristics of a cell culture. This paper pre-sents a mathematical model of cell tissue growth in scaffold pores of various geometries, taking into account the desorption of growth factors from the walls of the porous matrix. Three channel configurations are considered: straight, sinusoidal, and gradient-periodic. The model is based on a vertex model, which enables tracking of the morphometric, mechanical, and energy character-istics of each cell over time. A comparative analysis of key indicators was conducted: tissue growth rates, average cell shape factor, normalized average cell area, potential energy, and the distribution of maximum shear stresses. It is shown that the channel shape significantly affects the extreme values of mechanical characteristics despite similar average values. Sinusoidal channel geometry leads to increased peak energy values and a more elongated cell morphology. Straight channels provide higher growth rates in the early stages. The gradient-periodic channel shape demonstrates intermediate values in terms of growth rates and key indicators. The ob-tained conclusions can serve as a basis for optimizing the architecture of porous carriers in tis-sue engineering to control mechanical load and cell morphology. The developed mathematical model allows for predicting the morphological and mechanical responses of a cell culture to changes in pore geometry, which expands the possibilities for the targeted design of scaffolds.