Anderson_JC_2007_fig7
Two compartment model. Optimization to fit 2-Eq model to 3-Eq model solution assuming the absence of ligand binding in V1 or V2. Figure 2 of "Tracers in Physiological Systems Modeling".
Model number: 0044
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Description
Two compartment model with constant volumes, V1 and V2,
B is an uncomplexed binding site which reacts, first order, with C1 to form CB
The reverse dissociation reaction converts CB to C1 and B.
The dissociation const Kd = koff/kon and at equilibrium = C1*B/CB
The program test the addition of tracers "tr" and "T" both in pM,
but either or both of which can be added to mM levels and thus are not "tracers",
but are competing chemical species, displacing C1 from the C1B complex.
Tracer "C1tr" has the same equations for binding as does C1.
Tracer "C1T" hsa equation based on assuming instantaneous binding to C to B in V1.
thus C1T is an approximation which becomes correct when kon is very fast.
Function generator, Qintr and QinT, provide delayed step inputs to inject after SS
is reached for C1
For more detailed information, see:
Tracers in physiological systems modeling (pdf format).
"Return to Tracers in physiological systems modeling" Home page..
Equations
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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References
Anderson JC and Bassingthwaighte JB: "Tracers in physiological systems modeling". In: "Mathematical Modeling in Nutrition and Agriculture". Proc 9th International Conf on Mathematical Modeling in Nutrition, Roanoke, VA, August 14-17, 2006, edited by Mark D. Hanigan JN and Casey L Marsteller. Virginia Polytechnic Institute and State University, Blacksburg, VA 2007, pp 125-159.
Related Models
Models used to produce figures in Anderson JC 2007 paper.
Two compartment model discussion:
- Figure 2: Equilibrium conc for increasing kon for two compartment model.
- Figure 3: Volume of Distribution of equilibrium binding and unsteady state.
- Figure 4: Tracer added after tracee and binding site have equilibrated.
- Figure 5: Tracer transients Slow versus fast binding.
- Figure 6: Optimization tracer fit of pseudo two equation fit to three equation fit.
- Figure 7: Optimization to fit 2-Eq model to 3-Eq model solution assuming the absence of ligand binding in V1 or V2.
- Figure 11: Pulse responses in axially-distributed three region model.
- Figure 12: Pulse responses of Nth order Poisson operator with N tanks varied from 2 to 109 tanks in series.
- Figure 13: MID curve data fitted to three region PDE and serial compartment models.
- Figure 14: Fitting Intravascular reference curve to serial stirred tank model.
- Figure 15: MID data curves fit to stirred tank model - compare 1 tank versus 15 serial tanks.
Key Terms
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Model History
Get Model history in CVS.Acknowledgements
Please cite www.physiome.org 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.
[This page was last modified 04Feb10, 10:50 am.]
Model development and archiving support at physiome.org provided by the following grants: 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.
