Mathematical Models of Transport Phenomena in Normal and Neoplastic Tissue

In this chapter, the author reviews several aspects of transport phenomena in the microcirculation with special reference to tumor tissue when it is appropriate. Different mathematical models of indicator transport in the tissue have been developed to facilitate the analysis of such experimental data. Most mathematical models of capillary tissue transport are based on a concept pro-posed by August Krogh in 1919. His model considers an elementary microvascular unit composed of a cylindrical blood vessel surrounded by a co-axial cylindrical tissue volume. The models aimed at providing the information on the regional blood flow from indicator-dilution method are based on the integral relationships of conservation of mass and do not consider details of the microscopic transport in tissue. Therefore, it is apparent that the mathematical models described are relevant as well to the transport of drugs in microcirculation. The majority of studies of drug transport in the cardiovascular system are concerned with distribution of drugs.