Analysis of transport/reaction processes in biological systems using volume and area averaging methods: Applications in tissue engineering and transdermal drug delivery

Mathematical models are derived to describe the regeneration of cartilage in vitro for tissue engineering applications and iontophoretic drug delivery through the skin utilizing volume and area averaging methods. These multi-phase biological systems were chosen due to their complex geometry, where averaging methods prove most useful in simplifying the modeling process, and to their relevance to current medical applications.; The regeneration of cartilage is a dynamic process where chondrocytes (cartilage cells) are seeded and grown in a polymer scaffold. Four mathematical models have been developed to determine if chondrocyte growth is diffusion-limited by nutrient and product concentrations in the polymer scaffold. All of the models were compared directly or qualitatively to experimental results of cartilage regeneration in variously thick polymers (Freed et al., 1994a). The volume averaging method provided a means of coupling the cell growth equation to the transport equations through effective diffusion and metabolic rate coefficients. The results of this analysis concluded that diffusional limitations on cell growth alone could not account for the cell growth trends shown in the experimental data (Freed et al., 1994a).; Modeling of iontophoretic transport of hydrophilic uncharged molecules through the skin was performed to analyze the relative flow rates through the various pathways of the skin. The system consisted of four compartments: (1) a donor cell, (2) dermal tissue, (3) shunts of the skin, and (4) stratum corneum. The area averaging method was used in simplifying the modeling process for the shunts of the skin. The effects of applied electric field, number of shunts in a skin sample, shunt surface potential, and blood flow rate on the relative flow rates were analyzed. It was concluded that application of an electric field, which increased the electroosmotic, flow in the shunts, increased the variety of hydrophilic uncharged molecules that can pass through the shunts.; The averaging methods used in this dissertation provided a very useful and unique way to analyze transport and reaction in complex biological systems. Both mathematical approaches are not only versatile but also allow for the derivation of effective transport parameters, which can be compared to obtainable experimental data.