Model number


Model for analysis of NMR contrast agents from MRI signal from an organ region of interest (ROI)


fig 1

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.



     Ordinary Differential Equation







     Initial Condition

e6 , e7 ,e8 , e9 , e10 , and e11 . 

The equations for this model may 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.

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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.
Key terms
Transport physiology
NMR contrast agent
functional MRI
flow estimation from residue curves
permeating GdTPA
GdDpta polylysine
myocardial blood flow hetergeneity
regional tissue blood flows
capillary-tissue exchange
interstitial fluid space

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.