Computational Modeling of Cell Growth Heterogeneity in a Perfused 3D Scaffold

Abstract

Our goal was to develop a computational model describing the spatiotemporal evolution of cell heterogeneity within a three-dimensional porous scaffold during cell growth in a perfusion bioreactor. The scaffold was assumed formed by an ensemble of independent parallel cylindrical channels with a defined diameter distribution. The total flow rate partitioning in each channel depends on the effective diameter, which is reduced by the cell growth on the channel wall. The mass balance for one metabolite and the cell volume balance were solved. For each channel diameter, the model simulation provide the spatiotemporal evolution of velocity, shear stress, metabolite concentration, and cell volume growth. In particular, all of these outcomes can be analyzed as a function of channel diameter providing an evaluation of cell property heterogeneity. The model describes that the cell growth can be substantially different in each channel diameter. For instance, in the small diameter channel, cell growth is limited by metabolite mass transport, whereas in the larger diameter channel, shear stress inhibits cell growth. This mathematical model could be an important tool for a priori estimation of the time variation of the cell volume fraction and its degree of heterogeneity as a function of operational parameters and scaffold pore size distribution.

Current state and perspectives in modeling and control of human pluripotent stem cell expansion processes in stirred‐tank bioreactors

“…Moreover, heterogeneous expression of Stella has been observed within a single colony of mESCs 46 and Nanog expression within individual mESCs has been shown to undergo significant temporal fluctuations. 47 To describe such heterogeneity within a single cell aggregate or colony of stem cells, mathematical or computational models capable of describing the spatial distribution of cells are required, such as partial differential equation (PDE), 48,49 cellular automaton, 50,51 and individual-based models (IBMs). 52,53 Mathematical modeling studies of biofilms and microbial granules (bacterial aggregates), which have a history spanning several decades, may be applicable for developing models of stem cell aggregates.…”

Application of computational fluid dynamics in tissue engineering

“…Simulating cell growth in gas sparged or agitated vessels that do not contain porous structures has been reported (28). Typically, rate constants are defined on unit volume basis rather than unit cell basis by adapting the methodology used in evaluating cellular activity in bioreactors used for protein production (74). Some models have used the cell population dynamics and oxygen consumption within porous matrices.…”

A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor

“…Moreover, mitosis was considered to be proportional to the volume fraction of nutrients, cells and water; whereas apoptosis was considered to be proportional to the volume fraction of cells – thereby disregarding the dependence of such behavior on cellular and spatial heterogeneity. Similarly, Flaibani et al (2010) [34] modeled the spatiotemporal evolution of cell heterogeneity in a porous scaffold by solving the relevant PDEs, (discretised using the finite volume approach). The model considered perfusion conditions.…”