/*MODEL NUMBER: 0265
MODEL NAME: Comp2FlowMRIContrast
SHORT DESCRIPTION: Model for analysis of NMR contrast agents from MRI signal
from an organ region of interest (ROI)
*/
import nsrunit; unit conversion on;
math Comp2FlowMRIContrast {
// INDEPENDENT VARIABLE
realDomain t sec; t.min=0; t.max=1000; t.delta=0.1; // time t
// PARAMETERS
real Flow = 0.02 ml/sec, // Flow rate
scalar = 1, // Multiplier for inflow of GdDPTA
V1 = 0.05 ml, // Volume of compartment 1 (flow compartment)
V2 = 0.10 ml, // Volume of compartment 2
G = 0.80 mM^(-1)/sec, // Conversion of W to WS dependent of [GdDPTA]
PS = 0.002 ml/sec, // Permeability Surface area product for GdDTPA
PSw = 0.10 ml/sec, // Permeability Surface area product for W and WS
Tr = 1 sec; // Water spin relaxation time constant 0.6 to 1 sec
extern real GdDPTAin(t); // Input function for GdDTPA
extern real Win(t); // Input function for water
// VARIABLES
real GdDPTA1(t) mM, GdDPTA2(t) mM, // Concentrations of gdDPTA
W1(t) mM, W2(t) mM, // Concentration of water
WS1(t) mM, WS2(t); // Concentration of water spin
// INITIAL CONDITIONS
when(t=t.min) {GdDPTA1=0; GdDPTA2=0;
W1=1; W2=1;
WS1=0; WS2 =0;}
// ORDINARY DIFFERENTIAL EQUATIONS
GdDPTA1:t = Flow*(scalar*GdDPTAin-GdDPTA1)/V1 + (PS/V1)*(GdDPTA2-GdDPTA1);
GdDPTA2:t = (PS/V2)*(GdDPTA1-GdDPTA2);
WS1:t= Flow*(0-WS1)/V1 + G*GdDPTA1*W1 - WS1/Tr + (PSw/V1)*(WS2-WS1);
WS2:t= G*GdDPTA2*W2 - WS2/Tr - (PSw/V2)*(WS2-WS1);
W1:t = Flow*(Win-W1)/V1 - G*GdDPTA1*W1 + WS1/Tr + (PSw/V1)*(W2-W1);
W2:t = - G*GdDPTA2*W2 + WS2/Tr - (PSw/V2)*(W2-W1);
}
/*
DIAGRAM
+-----------------------------------------+
Flow*GdDPTAin*Scalar----> G -->Flow*GdDPTA1
Flow*Win----------------> GdDPTA1+W1--->WS1 -->Flow*W1
| (conversion) -->Flow*WS1
| |
| TR |
| WS1--->W1 |
| (spin relaxation) |
| |
| GdDPTA1 W1 WS1 |
| ^ ^ ^ V1 |
+-----|PS---------|PSw----|PSw------------+
| v v v |
| GdDPTA2 W2 WS2 |
| |
| G |
| GdDPTA2+W2--->WS2 |
| (conversion) |
| |
| TR |
| WS2--->W2 V2 |
+-----------------------------------------+
DETAILED DESCRIPTION:
Two compartment model for MRI contrast using GdDTPA (gadolinium chelated
with diethylenetriamine penta-acetic acid to convert water (W) to water
spin (WS). The permeability-surface are product for GdDPTA is PS and for
W and WS is PSw. The spin relaxation which converts WS back to W is given
by Tr. V1 is the volume of the flowing region and V2 is the volume of
the exchange region. The conversion rate is governed by G.
Kroll et al. 1996 uses an axially-distributed 1-regional BTEX to analyze data
from polylysine-bound GdDTPA, and intravascular indicator. Kroll did not
account for WS outside of the vascular space. The WS-Gd relationship was
taken to be a saturation curve (Langmuir isotherm). There was no non-exchanging
vascular space distinguished from the capillary plasma. Hematocrit was not accounted for.
KEY WORDS:
Transport physiology, Flow, Compartmental, NMR contrast agent, functional MRI,
Gadolinium, flow estimation from residue curves, permeating GdTPA, GdDpta polylysine,
myocardial blood flow hetergeneity, regional tissue blood flows,
capillary-tissue exchange, CTEX, interstitial fluid space, Tutorial
REFERENCES:
Kroll K, Wilke N, Jerosch-Herold M, Wang Y, Zhang Y, Bache RJ, and
Bassingthwaighte JB. Modeling regional myocardial flows from residue functions of
an intravascular indicator. Am J Physiol: 271:H1643-55, 1996.
REVISION HISTORY:
Dec 2009: GR Revision of variable and parameter names.
JSim SOFTWARE COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
JSim software was developed with support from NIH grants HL088516,
and HL073598. Please cite these grants in any publication for which
this software is used and send one reprint of published abstracts or
articles to the address given below. Academic use is unrestricted.
Software may be copied so long as this copyright notice is included.
Copyright (C) 1999-2009 University of Washington.
Contact Information:
The National Simulation Resource,
Director J. B. Bassingthwaighte,
Department of Bioengineering,
University of Washington, Seattle, WA
98195-5061
*/