Tracers in physiological systems modelingAuthors: Anderson JC and Bassingthwaighte JB, 2007
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: Tracers in physiological systems modeling (pdf format):
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.
- 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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