Tracer kinetic theory

The determination of cerebral perfusion using CTP is based on examining the relationships between the arterial, tissue, and the venous enhancement. More specifically, tracer kinetic theory states that if one knows the input and the output of a tracer from a voxel, one can determine the volume of distribution (i.e., fractional vascular volume) and the clearance rate (i.e., flow per unit tissue volume) [20, 114, 115]. The fractional vascular volume,/, is defined by the following equation ... 

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

For the interested reader, there are several reviews of the theory and applications to pharmacokinetics and pharmacodynamics (Steimer et aL, 19 5 Sheiner and Ludden, 1992), but so far, the methods have not been applied to tracer kinetic problems in metabolism and nutrition. The goal of this paper is to provide an introductory review of the theory, applications, and available software, with particular attention to how they relate to problems in metabolism and nutrition. 

The mathematics of pharmacokinetics strongly resembles, and arises from, the mathematics of chemical kinetics, enzyme kinetics, and radioisotope (tracer) kinetics. Table 2.1 shows how, over the years, the mathematical theory of pharmacokinetics and that of its older siblings has been substantiated by experimental work. In fact, substantiation of a particular kinetic theory often... 

Compartmental modehng was first formalized in the context of isotopic tracer kinetics. Over the years it has evolved and grown as a formal body of theory [Carson et al. 1983 Godfrey, 1983 Jacquez 1996 Cobelli et al., 2000]. 

A. Fick, Ann. Phys. (Leipzig) 170, 50 (1855). He actually set up his two laws for the temporal spreading of the concentration of a tracer substance, not for the probability. The first evolution equation for a probability was the Boltzmann equation [L. Boltzmann Vorlesungen tiber Gastheorie I (J. A. Barth, Leipzig, 1896)], following Maxwell s theory of gas kinetics. 

The contribution of MS to identification of compounds and quantification of their concentration is complementary to other detection techniques and, despite being very practical and versatile, it remains fundamentally replaceable. However, knowledge of molecular weight is a prerequisite for techniques that rely on the synergies with stable isotopic tracers. In fact, powerful analytical methods exist to obtain important insights on cell dynamics from the ratiometric measurement of marked and not-marked species (or atoms). We cite, for example, (1) relative abundances of virtually all metabolites or proteins in two separate cultures are quantified based on the isotope dilution theory [43 5] (2) information on the mechanisms and kinetics of nonlinear chemical processes can be extracted from response tracer experiments [46 7] and (3) the labeling patterns in metabolic intermediates are used to resolve the relative rate in convergent reactions in vivo [48,49]. 

In the following we analyze the influence of errors on our approach and its accuracy and compare the results with those obtained by using linearized kinetics. We consider a nonlinear kinetic example for which a detailed analytical study is possible. We compare that exact solution with the first-order response theory based on appropriate tracer measurements, and also compare it with the response of the linearized kinetic example. An important interest here is in the effects of error propagations in the analysis due to the application to measurements of poor precision. 

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