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# NestedPlots

Models a tissue cylinder consisting of two regions: plasma, and interstitial fluid. Contains nested plots.

Model number: 0366

 Run JSim model Java Applet: JSim Tutorial

## Description

 This program is a version of BTEX20, the two region
partial differential model. Two of the model parameters,
PSg (exchange between plasma and isf) and Gisf
(consumption in the isf) have been modified to be

Cp(t,x) into Cp(t,x,PSg,Gisf),
Cisf(t,x) into Cisf(t,x,PSg,Gisf) and
Cout(t) into Cout(t,PSg,Gisf).

The details of making nested plots can be found at
www.physiome.org/jsim/docs/User_Nested.html

The "Nesting" menu is on the second line of the nesting plot
page, i.e.

Message    | Plotname | ...
PlotName:  |   File   |   Nesting   |   View 

## Equations

#### Differential Equations

$\large \frac{\partial C_p}{\partial t} = \frac{-F_p \cdot L}{V_p} \cdot \frac{\partial C_p}{\partial x}- \frac{G_p}{V_p} \cdot C_p +\frac{PS_g}{V_{p}}\cdot (C_{isf}-C_p)+D_p \cdot \frac{\partial^2 C_p}{\partial x^2}$
$\large \frac{\partial C_{isf}}{\partial t} = \frac{-G_{isf}}{V'_{isf}} \cdot C_{isf} +\frac{PS_{pc}}{V'_{isf}} \cdot (C_p-C_{isf}) +D_{isf} \cdot \frac{\partial^2 C_{isf}}{\partial x^2}$

#### Left Boundary Conditions

$\large -{\frac {{\it F_p}\cdot L \cdot \left( {\it C_p}-{\it C_{in}} \right) }{{\it V_p}}}+{D_{p} \cdot \it {\frac {\partial}{\partial x}}C_p=0$$\large {\it {\frac {\partial}{\partial x}}C_{isf}=0$ .

#### Right Boundary Conditions

$\large {\it {\frac {\partial }{\partial x}}C_p=0$$\large {\it {\frac {\partial }{\partial x}}C_{isf}=0$$\large {\it C_{out}={\it C_{p}$ .

#### Initial Conditions

$\large C_p=C_p0$ ,   $\large C_{isf}=C_{isf}0$   or
$\large C_p=C_p0(x)$ ,   $\large C_{isf}=C_{isf}0(x)$ .

The equations for this model may also be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

## References


Bosan, Sorel and Harris, Thomas R.. A Visualizetion-Based Analysis Method
for Multiparameter Models of Capillary Tissue-Exchange. Annals of Biomedical
Engineering, Vol. 24, pp.124-138, 1996.

W.C. Sangren and C.W. Sheppard.  A mathematical derivation of the
exchange of a labelled substance between a liquid flowing in a
vessel and an external compartment.  Bull Math BioPhys, 15, 387-394,
1953.

C.A. Goresky, W.H. Ziegler, and G.G. Bach. Capillary exchange modeling:
Barrier-limited and flow-limited distribution. Circ Res 27: 739-764, 1970.

J.B. Bassingthwaighte. A concurrent flow model for extraction
during transcapillary passage.  Circ Res 35:483-503, 1974.

B. Guller, T. Yipintsoi, A.L. Orvis, and J.B. Bassingthwaighte. Myocardial
sodium extraction at varied coronary flows in the dog: Estimation of
capillary permeability by residue and outflow detection. Circ Res 37: 359-378, 1975.

C.P. Rose, C.A. Goresky, and G.G. Bach.  The capillary and
sarcolemmal barriers in the heart--an exploration of labelled water
permeability.  Circ Res 41: 515, 1977.

J.B. Bassingthwaighte, C.Y. Wang, and I.S. Chan.  Blood-tissue
exchange via transport and transformation by endothelial cells.
Circ. Res. 65:997-1020, 1989.

Poulain CA, Finlayson BA, Bassingthwaighte JB.,Efficient numerical methods
for nonlinear-facilitated transport and exchange in a blood-tissue exchange
unit, Ann Biomed Eng. 1997 May-Jun;25(3):547-64.



## Related Models

Blood Tissue Exchange (BTEX) models

## Key Terms

nested, nested plots, world within worlds, BTEX20,PDE,convection,diffusion, permeation, reaction,distributed,capillary,plasma,isf,interstitial fluid