Three compartmental plasma-ISF-parenchymal cell exchange
model with flow through plasma only. All three compartments
instantaneously well mixed.
Fp (flow through plasma compartment), PSc (exchange
coefficient between plasma and ISF), and PSpc (exchange
coefficient between ISF and parenchymal cell) have same
units, ml/(g*min) in physiological terminology to relate
them to fluxes per gram of tissue.
Figure 1: Concentrations: Default parameter set
The concentrations in the plasma (Cp), ISF (Cisf), and
parenchymal cell (Cpc) are plotted as functions of
time in seconds. The inflowing concentration, Cin, divided
by 2 is also plotted.
Figure 2: Residual content in tissue: Default parameter set
The residual content in the tissue is calculated in two ways:
Q is computed from the sum of the concentration volume productions,
Q = Vp*Cp + Visf*Cisf + Vpc*Cpc
and Qint is computed as the integral of the product of the flow
times the difference of the inflowing and outflowing concentrations.
/ t
Qint(t) = | Fp*( Cin(t')-Cp(t') ) dt' .
/ t.min
/*MODEL NUMBER: 0267
MODEL NAME: Comp3FlowExch
SHORT DESCRIPTION: Three compartment model for plasma (p),
interstitial fluid (ISF) and parenchymal cell (pc)
*/
import nsrunit; unit conversion on;
math Comp3FlowExch {
// INDEPENDENT VARIABLE
realDomain t sec; t.min=0; t.max=30; t.delta=0.10;
// PARAMETERS
real Fp = 2 ml/(g*min), // Plasma compartment flow
Vp = 0.07 ml/g, // Plasma volume
Visf = 0.15 ml/g, // ISF volume
Vpc = 0.6 ml/g, // Parenchymal cell volume
PSc = 3.0 ml/(g*min), // Exchange Coefficient between capillary and
// ISF, (Permeability-Surface Area product for
// cleft.
PSpc = 3.0 ml/(g*min), // Exchange coefficient between ISF and
// parenchymal cell
Cp0 = 0 mM, // Initial plasma concentration
Cisf0 = 0 mM, // Initial ISF contration
Cpc0 = 0 mM; // Initial parenchymal cell concentration
extern real Cin(t) mM; // Inflowing concentration
// VARIABLES
real Cp(t) mM, // Plasma concentration
Cisf(t) mM, // ISF concentration
Cpc(t) mM, // Parenchymal cell concentration
Q(t) nmol/g, // Quantity of material in system,
// by direct calculation
Qint(t) nmol/g; // Quantity of material by integration
// INITIAL CONDITIONS:
when(t=t.min) {Cp = Cp0; Cisf = Cisf0; Cpc = Cpc0;
Qint = Vp*Cp0 + Visf*Cisf0 + Vpc*Cpc0;}
// ORDINARY DIFFERENTIAL EQUATIONS
Cp:t = Fp*(Cin-Cp)/Vp + PSc*(Cisf-Cp)/Vp;
Cisf:t = PSpc*(Cpc-Cisf)/Visf + PSc*(Cp-Cisf)/Visf;
Cpc:t = PSpc*(Cisf-Cpc)/Vpc;
// ADDITIONAL CALCULATIONS
Q = Vp*Cp + Visf*Cisf + Vpc*Cpc;
Qint:t = Fp*(Cin-Cp);
} // End of Model
/*
DIAGRAM:
__________________
| Cp(t) |
Fp* Cin(t)---> ---> Fp*Cp(t)
| Vp |
| ^ |
----PSc-|--------|
| v Cisf(t)|
| Visfp |
| ^ |
---PSpc-|--------|
| v Cpc(t)|
| Vpcp |
| |
------------------
DETAILED DESCRIPTION:
Three Compartment model for exchange between plasma, ISF and
parenchymal cell with flow in the plasma compartment. The flow
transports an inflowing concentration, Cin, into the plasma
compartment and transports the outflowing concentration, Cp, out of
the plasma compartment.
KEY WORDS:
compartment, compartmental, flow, exchange, mixing chamber, permeability,
PS/F, washout, inflow-outflow operator, plasma, ISF, parenchymal cell,
Tutorial
REFERENCES: None.
REVISION HISTORY:
Original Author : GaryR Date: 17/Dec/09
Revised by : BEJ Date: 10/May/10
Revision: 1) Update comment format, fix comment typo
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2010 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Academic use is unrestricted. Software may be copied so long as this copyright notice is included.
This software was developed with support from NIH grant HL073598.
Please cite this grant in any publication for which this software is used and send an email
with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
*/