A better understanding of the complex interplay between cell population dynamics and mass transport is necessary for overcoming the barriers that have slowed down the development of bioartificial tissues. In a recent publication , we presented the development of a multi-scale computational model that describes the dynamic behavior of homogeneous cell populations growing under mass transfer limitations in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient or growth factor; a cellular automaton describing cell migration, proliferation and collisions in a cubic lattice; and equations that quantify how the varying nutrient or growth factor concentration modulates cell division and migration. The hybrid (discrete-continuous) model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results revealed that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. The initial spatial distribution of seed cells, their migration speed and the hydrodynamics of the bioreactor also influenced the overall rate and the pattern of tissue growth. This study presents a significant extension of this model to heterogeneous cell populations growing in three-dimensional scaffolds with “artificial” vessels. To account for different cell phenotypes, the new model considers cell populations exhibiting bimodal distributions of migration speeds, persistence and division times. The model also allows for scaffold heterogeneities, cell differentiation, natural cell death (apoptosis) and cell death caused by nutrient or growth factor depletion (necrosis). Simulation of three-dimensional tissue growth is a computationally challenging problem requiring large grids to capture the growth of tissues of practically significant size. To meet this challenge, our algorithm has been parallelized to run on a Cray XD1 computer cluster. The computational domain is partitioned into subdomains along one dimension (slab decomposition) and each subdomain is assigned to a different processor. Our simulation results reveal that cell differentiation or necrosis can lead to the formation of complex tissue architectures when heterogeneous cell populations grow under conditions leading to severe transport limitations. These tissue patterns can also be affected by the initial spatial distribution of seed cells, time-dependent addition of the critical nutrient or growth factor to the media and the hydrodynamics of the bioreactor that modulate the boundary conditions of the diffusion-reaction problem. Finally, we explore the effect of vascularization on the growth rates and structure of regenerated tissues. “Artificial” vessels with cylindrical or other shapes are placed in the 3D scaffolds to enhance the transport of nutrients to the interior of developing tissues. We will present simulation results that show how tissue development is affected by (a) the geometry of the artificial vessels, and (b) temporal variations in the flow rates of culture media or the concentrations of limiting nutrients. These results provide us with guidelines for a rational design of in vitro cell culture experiments that will lead to the formation of bioartificial tissues with desired architecture. Reference:  G. Cheng, P. Markenscoff and K. Zygourakis, “A 3D Hybrid Model for Tissue Growth: The Interplay Between Cell Population and Mass Transport Dynamics”, Biophysical Journal, 97, 401-414 (2009).
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