Schematic representation of the ring-shaped tube model

Based on the above, an elementary pharmacokinetic model considering the entire circulatory system was constructed. Thus, apart from the arterial and venular trees, a second set of arterial and venular trees, corresponding to the pulmonary vasculature, must be considered as well. These trees follow the same principles of (8.10) and (8.13), i.e., tubes of radius p0 are considered with appropriate length to accommodate the correct blood volume in each tree. 

We assign the first portion of the tube length from z = 0 to z = z to the arterial tree, the next portion from z = z to z = z to the venular, and the rest from z = z to z = L to the two symmetrical trees of the lungs. We consider that the venular tree is a structure similar to the arterial tree, only of greater, but fixed, capacity. Also, the two ends of the tube are connected, to allow recirculation of the fluid. This is implemented by introducing a boundary condition, namely c (0, t) = c(L,t), which makes the tube ring-shaped. The 

Two separate values were used for the dispersion coefficient Da for the arterial segment and Dp for the pulmonary segment. For the venular segment we consider that the dispersion coefficient has the value Da (z z ) /z, mean- 

Boundary and initial conditions are considered as discussed above. 

The model was used to identify indocyanine green profile in man after qo = 10 mg intravenous bolus injection. Both injection and sampling sites (zq and z, respectively) were closely located on the ring-shaped tube. The model of drug administration was a thin Gaussian function  

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