Authors: Anderson JC and Bassingthwaighte JB, 2007
Metabolic events within cells are intimately linked with the external influences of substrate delivery and metabolite removal. These influences include the level of cellular activity, the local blood flow, transmembrane transport rates, and humoral and neural regulation of receptors and reaction rates. The question "What are the basic principles that the developers of tracer models should use?" evokes discussion on the scope of the modeling: an extremes is "minimal modeling", wherein one considers only the observations of the injected tracer-labelled solute itself (as in pharmacokinetics), its reaction products, or extend to its effects on the physiology (as in pharmacodynamics).
Minimal modeling can work for classification or diagnosis but, unless the model has the depth to encompass mechanisms of tracer handling, doesn't often provide an explanation. Here we advocate adherence to a broad set of principles for the design and application of models to the understanding of physiological systems: (1) consider the anatomy (a biological constraint) as an essential part of the data, (2) take into account the background physiological state of the subject (biochemical, thermodynamic constraints), (3) consider the processes that the tracer labelled solutes undergo (mechanisms of transport and reaction), (4) be obedient to the laws of physics and chemistry (conservation principles for mass, energy, charge, momentum, etc.), and (5) adhere to a set of modeling standards allowing reproducibility and dissemination of the model. A two compartment model with a binding site illustrates that recognition of the anatomic constraints would foster a better understanding of the system kinetics. Another example is to abandon the lumped compartmental representation of spatially extended capillary-tissue exchange in favor of using anatomic-based equations, thereby obtaining physically meaningful esxtimates of parameter values.
For more detailed information, see:
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.
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.
Three region serial tank and axial dispersion model discussion:
- 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.
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tracer, tracee, metabolic physiologic modeling, lumped compartmental versus spatially distributed systems, capillary-tissue exchange, membrane transporters, enzyme reactions, steady state versus transient states.
Please cite https://www.imagwiki.nibib.nih.gov/physiome 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 https://www.imagwiki.nibib.nih.gov/physiome 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.