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Since August Krogh's original work in 1919, organ perfusion has been modelled extensively after what is known as "single capillary" model. In these models, the perfused organ is conceptualized as composed of identical building blocks, each consisting of either a circular or a hexagonal tissue cylinder supplied by a single capillary. A vast literature has grown up on such models, the most noteworthy of which are listed in references. Krogh's original model, shown in Fig. 1, consists of identical parallel capillaries each supplying it's own circular tissue cylinder. A variant of Krogh cylinder model for a well-perfused organ with parallel capillaries with equal flow and supplying hexagonal axisymmetric tissue columns of equal lengths is that of Bassingthwaighte and is shown in Fig. 2. Another approach to perfusion modelling is that of compartmental analysis where the perfused organ is divided into a blood and a tissue compartment. Various assumptions are then made regarding the nature of these two compartments. The tissue compartment is usually considered to be well stirred and for the blood compartment, a linearly distributed capillary bed is assumed. This is equivalent to a single capillary with an axial variation of concentration down its length. Usually the mixing in the radial direction is assumed to take place infinitely rapidly. Most important of these models are those of Renkinll , Johnson and Wilson, and Levitt. The model presented here is shown in Fig. 3, and assumes that the blood compartment, where the microcirculation takes place, is a random network of interconnected microchannels, the network being in contact with the tissue compartment. Blood from the arterial side enters this capillary network in which microcirculation takes place with or without exchange with the tissue compartment, and finally the perfused blood exits at the venus end. This clearly departs from the single capillary models since no assumption is made as to the orientation, distribution and identity in structure of the microcirculatory capillaries. For the same reason, this also differs from the linearly or any other deterministically distributed capillary bed of the compartmental analysis. Moreover, the concentration distribution in such a network is not inferred or prescribed, but is calculated from the basic hydrodynamics of the medium. This leads to a concentration distribution in both parallel and perpendicular (to mean flow) directions in terms of the dispersion of statistical hydrodynamics.
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