Dynamic Behavior Of Heterogeneous Cell Populations Growing Under Mass Transport Limitations

Abstract

Tissue growth in biomimetic scaffolds is strongly influenced by the dynamics and heterogeneity of cell populations. A significant source of heterogeneity is nutrient (or growth factor) depletion. Cells slow down, stop dividing or die when the concentrations of key nutrients or growth factors drop below critical levels in the scaffold interior. As a result, we still cannot grow in vitro tissue samples thicker than a few millimeters for metabolically active cells.To provide theoretical guidance for the in vitro cultivation of bioartificial tissues, we have developed a multi-scale model that can describe how the complex interplay among key intracellular processes, cell population dynamics and nutrient depletion regulates the growth of tissues in 3D scaffolds. We use a discrete, stochastic algorithm to describe the population dynamics of migrating, interacting and proliferating cells. Diffusion and consumption of a limiting nutrient is modeled by a partial differential equation subject to boundary conditions appropriate for common bioreactors. This PDE is solved numerically and the computed concentration profiles are used to modulate cell proliferation rates and migration speeds. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how mass transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors.Simulation results show that the severity of mass transport limitations can be estimated by the magnitude of two dimensionless groups. Critical system parameters like cell population heterogeneity, the initial spatial distribution of seed cells, the distribution of cell migration speeds, and the hydrodynamic environment are shown to affect not only the overall rate, but also the pattern of tissue growth. More specifically, the interplay of cell population heterogeneity and cell death due to nutrient depletion can lead to dynamic self-assembly of cells and the formation of stratified structures.