Axially distributed 2-region capillary-tissue exchange operator and analogous 2 compartment model.

Description

   One-dimensional convection-permeataion-diffusion-
   reaction model consisting of two concentric cylinders separated by a 
   membrane. The advecting plasma region with volume Vp has flow Fp, no 
   consumption, and axial diffusion (disperion) Dp. Units are physiological
   per gram of tissue so that a single unit can model a homogeeously perfused 
   organ. Radial diffusion is assumed instantaneous (short radial distances).
   Exchange into a second surrounding non-flowing region is passive with
   conductance, PS, the Permeability capillary Surface area product. 
   This interstitial fluid region, isf, of volume Visf, like the capillary, 
   is axially distributed, and the gradients axially are dissipated by
   a concentration-independent axial diffusion or dispersion. Radial diffusion 
   within this space is considered instantaneous, and consumption, Gisf, is
   first order. This model is used in multicapillary models as one of a set of 
   units in parallel.Sangren and Sheppard (1954) give the analytical solution
   for D = 0.

 VERIFICATION TEST: Change the input function from the LagNormal cuver to 
   a 1 second pulse input of 1 mM from 3 to 4 seconds. Then set Dp =0. Leave the 
   PSg unchanged, but increase Gisf to 1000 so that everything entering the ISF 
   is consumed and backflux from ISF to plasma goes to zero. These are the
   condtions under which the Crone-Renkin expression for extraction becomes true:
       PSg/Fp = 1 - ln (1 - E), where E is the fractional extraction between
   entrance and exit, and represents a unidirectional flux. Or, restated:
       E = 1 - exp(-Psg/Fp.
   The spatial profile Cp(x) at the peak of the pulse has the envelope:
       Cp(x) = exp((-PSg/Fp)*x/L)..
   For a constant infusion input Cin, the profile is Cp(x) = Cin*exp((-PSg/Fp)*x/L).
   Plot this. It should fit the peaks of the pulses. Check the Text output for the graph
   to see how many digits accuracy are obtained. Test different solvers.

Equations

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