The development and testing of a discrete model describing the dynamic process of tissue growth in three-dimensional scaffolds is presented. The model considers populations of cells that execute persistent random walks on the computational grid, collide, and proliferate until they reach confluence. To isolate the effect of population dynamics on tissue growth, the model assumes that nutrient and growth factor concentrations remain constant in space and time. Simulations start either by distributing the seed cells uniformly and randomly throughout the scaffold, or from an initial condition designed to simulate the migration and cell proliferation phase of wound healing. Simulations with uniform seeding show that cell migration enhances tissue growth by counterbalancing the adverse effects of contact inhibition. This beneficial effect, however, diminishes and disappears completely for large migration speeds. By contrast, simulations with the "wound" seeding mode show a continual enhancement of tissue regeneration rates with increasing cell migration speeds. We conclude that cell locomotory parameters and the spatial distribution of seed cells can have profound effects on the dynamics of the process and, consequently, on the pattern and rates of tissue growth. These results can guide the design of experiments for testing the effectiveness of biomimetic modifications for stimulating tissue growth.

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We report the development of new class of discrete models that can accurately describe the contact-inhibited proliferation of anchorage-dependent cells. The models are based on cellular automata, and they quantitatively account for contact inhibition phenomena occurring during all stages of the proliferation process: (a) the initial stage of "exponential" growth of cells without contact inhibition; (b) the second stage where cell colonies form and grow with few colony mergings; and (c) the final stage where proliferation rates are dominated by colony merging events. Model prediction are presented and analyzed to study the complicated dynamics of large cell populations and determine how the initial spatial cell distribution, the seeding density, and the geometry of the growth surface affect the observed proliferation rates. Finally, we present a model variant that can simulate contact-inhibited proliferation of asynchronous cell populations with arbitrary cell cycle-time distribution. The latter model can also compute the percentage of cells that are in a specific phase of their division cycle at a given time.

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient 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 show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.

This study establishes that the cellular automata models developed in an earlier article capture the essential features of the proliferation process for anchorage-dependent contact-inhibited cells. Model predictions are in excellent agreement with experimental data obtained with bovine pulmonary artery endothelial cells. The models are particularly suitable for predictive purposes since they have no adjustable parameters. All model parameters can be easily obtained from a priori measurements. Our studies also show that proliferation rates are very sensitive to the spatial distributions of seed cells. The adverse effects of seeding heterogeneities become more pronounced as a cell population approaches confluency and they should be accounted for in experimental studies attempting to assess the response of cells to external stimuli.