The field of tissue engineering has emerged from the idea of mimicking nature by stimulating autologous cells to differentiate and synthesize tissue-specific extracellular materials. This rapidly evolving, multi-disciplinary field represents a logical progression of current practice in tissue/wound repair. Numerous Tissue engineering strategies involve events, which occur simultaneously over multiple length scales with changing boundary conditions. Together, these multi-scale effects govern the interactions between living cells and their environment. Above the 10-4 to 10-2 m length scale, micro-architecture of the environment influence nutrient transport, which govern cell metabolism and cycle, and fluid mechanics, which affects cellular mechano-signal transduction. Continued tissues growth on this length scale is impacted by the changing boundary conditions for nutrient transport. At the other extreme, processes such as protein adsorption onto biomaterial surfaces, and cell receptor-protein binding, are influenced by processes at the 10-9 to 10-7 m scale. Processes at both ends of the length scale spectrum affect the intermediate length scale 10-7 to 10-3 m, and influence cytokine diffusion, cell adhesion, cell mobility, cell morphology, cell differentiation, and cell function. Tissue engineering, therefore, present a set of highly complex problems involving multiple length-scales, multiple interfaces, and changing boundary conditions.
Modeling of these problems can yield useful hypotheses and provide simulations for interpretation of experimental results at different length scales. This is a critical next step for this emerging field, and can only be achieved with focused collaboration between engineers, cell biologists, and mathematicians. In many situations the modeling involves a moving interface. This results in a multiphase transport process, which resembles Stefan and related problems, which arise in physics and materials science. Recent developments in numerical simulation of such problems have resulted in accurate predictions of problems in e.g. epitaxial growth. Additional areas of interest include multiscale analysis, multiphase interface problems, microfluidics and structural analysis.
Mathematicians, physicists, and computationally oriented engineers working in these areas are encouraged to attend and interact with tissue engineers. The goal is to increase the scale of collaboration in this area, as was suggested by the program content thrust of recent NIH programs.
Michael Longaker (Stanford University)
Ichiro Nishimura (UCLA)
Stanley Osher (IPAM)
Bill Tawil (Baxter Biosciences)
Howard Winet (UCLA /Orthopaedic Hospital)
Ben Wu (UCLA)