Mathematical Modeling of Transport and Reaction in Cellular and Tissue Engineering

Tissue engineering is a rapidly developing field seeking to solve biomedical problems with wide-range of clinical applications. Major obstacles to the generation of functional tissue constructs in bioreactor culture devices for these applications is the limited understanding of the regulatory role of specific physicochemical culture parameters on tissue development. In this context, computational methods can serve as a valuable tool to facilitate better understanding of the underlying mechanisms governing physical, chemical, and biological processes in a 3-dimensional culture environment by correlating the cell and tissue behavior to changes in global biochemical bioreactor inputs. These concepts are illustrated in three distinct tissue engineering applications – hematopoietic cell expansion in perfusion bioreactor, human mesenchymal stem cell expansion in perfusion and static culture units, and cartilage tissue formation in hollow fiber bioreactors. Material balances describing mass transport and chemical reaction of nutrients, products are coupled with cell growth, differentiation and extracellular matrix formation in 3-dimensional constructs to determine the effects of transport limitations on cell behavior. Method of volume averaging is used for the determination of the effective diffusion and reaction terms in the species continuity equations in terms of local geometry and spatial restrictions. The volume averaged equations are solved over the macroscopic dimensions of the reactor to assess system performance. This study has the potential to improve tissue engineered functional constructs. The tissue engineering model development applications consider cellular processes in terms of net kinetic expressions linked to changes in macroscopic environmental parameters. In order to develop complete model framework, understanding of processes at the cellular level is essential. To do so, in the second part of this project, muscle cell is chosen for study of metabolic processes in terms of production, transport, conversion and utilization of metabolite species. A reaction-diffusion model of phosphorous metabolites is shown to provide a suitable framework for study of diffusion, reaction, and metabolic organization in muscle cell. This study is intended to understand the interactions between metabolism and cell structure. The current work is a first step towards an overall goal of setting up a rationale for cellular design for attaining a desired cell function.