Trace compartmental modeling

Pharmacokinetics emerged as a discipline in the 1960s with its foundation in compartmental modeling, although earlier origins of pharmacokinetics can be traced [1], Mammillary compartmental models provided the framework for phar-... 

The experiment consists of applying an intravenous bolus of sulphate traced by a radioactive isotope and measuring the activity of blood samples. The compartmental model in Fig. 5.7. leads to the differential equations... 

From the above it can be concluded that in many instances the introduction of an artificial radionuclide into the environment provides us with a natural tracer experiment. Indeed, this is the basis for the application of deterministic compartmental models, based on tracer kinetics, to radioecology (Whicker and Schultz, 1982). This approach is largely based on the assumption that radionuclide movements will exhibit first order kinetics although the existence of naturally-occurring tracees (stable isotopes) at relatively high abundance may result in more complex concentration-dependent kinetics. Furthermore, nutrient analogues may exert even more complex effects on processes such as radioion absorption across root plasma membranes this will become evident later in the chapter. 

The origins of PB/PK models may be traced to Teorell, - Bellman, Bischoff and Brown, and Dedrick and Bischoff. The combined investigations of these individuals established the idea of characterizing drug distribution to speciQc organs in terms of relevant anatomical and physiological variables. In contrast to classical compartmental modeling, tissue compartments represent speciQc... 

We began modeling under the assumption that the introduction of the tracer (mass) into the system did not affect the mechanisms present for metabolism of the tracee. The compartmental model was compatible with the assumption that non-steady-state mechanisms for metabolism of /3-carotene were not induced by the tracer because the model prediction of the tracer state, the tracee state, and the steady state could be achieved using the same set of fractional transfer coefficients (FTCs). The appropriateness of this assumption is discussed again under Statistical Considerations. FTC is the fraction of analyte in a donor compartment that is transferred to a recipient compartment per unit of time, in this case per day. 

Element losses together with element bioavailability determine how much of an element has to be provided through the diet to remain in element balance. For assessment of losses, a label needs to be administered once either orally or intravenously. Compartmental modeling techniques permit to calculate when the label has equilibrated with the natural element in all body compartments. When isotopic labeling has been achieved, continuous replacement of lost isotopic label with the natural element from the diet results in a continuous decline of the body s isotopic enrichment. The change in tracer to tracee ratio in blood corresponds directly to the fraction of the body s element inventory that has been lost and replaced. 

The appropriate interfacing of chemical with biologic and hydrologic models is a rather difficult problem. For example, the prediction of trace-element bioaccumulation by phytoplankton may require in some instances that the uptake rates and the compartmentalized loss rates for various solute species of the element present in the system be known. The effect, if any, on compartmentalized loss rates of the particular solute species taken up (e.g. HgCH3" " vs Hg " ") also needs to be known. The interaction effect of the concentration of one element upon the uptake and loss rates of another element, such as Hg on Se (33, 34, 35), also need to be known. In many instances, hydrodynamic models may have to be linked with,or otherwise incorporated, into the biologic and chemical models to permit predictions of, for example, increased trace-element levels in oysters resulting from increased anthropogenic inputs to an estuary. 

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