Schematic representation of the dichotomous branching network

The disposition of a solute in the fluid as it flows through the system is governed by convection and dispersion. The convection takes place with velocity 

These forms relate the dependence on the system characteristics. Equation (8.13) describes the concentration c(z, t) of a solute in a tree-like structure that corresponds to the arterial tree of a mammal. Considering also the corresponding venular tree situated next to the arterial tree and appropriate inflow and outflow boundary conditions, we are able to derive an expression for the spatiotemporal distribution of a tracer inside a tree-like transport network. We also make the assumption that the arterial and venular trees are symmetric, that is, have the same volume V then, the total length is L = V/Ag The initial condition is c(z, 0) = 0 and the boundary conditions are  

The outflow concentration c(L,t) of the above model describes tracer washout curves from organs that have a tree-like network structure, and it is given by an analytic form reported in [328]. 

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Figure 8.5 (A) Schematic representation of the dichotomous branching network. (B) Cross sections at each level. (C) Single tube with continuously increasing radius. (D) Volume-preserving transformation of the varying radius tube to a fixed radius tube. Reprinted from [328] with permission from Springer.

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