Polyexponential equation

Taking the inverse Laplace transform will result in the polyexponential equation... 

Studies interested in the determination of macro pharmacokinetic parameters, such as total body clearance or the apparent volume of distribution, can be readily calculated from polyexponential equations such as Eq. (9) without assignment of a specific model structure. Parameters (i.e., Ah Xt) associated with such an equation are initially estimated by the method of residuals followed by nonlinear least squares regression analyses [30],... 

Wagner, J.G. 1976. Linear pharmacokinetic equations allowing direct calculation of many needed pharmacokinetic parameters from the coefficients and exponents of polyexponential equations which have been fitted to the data. 

Suppose one does a study wherein a single dose of the drug is given both orally and intravenously on two separate occasions and finds that the oral concentrationtime data were best fit using a four-term polyexponential equation, whereas after intravenous administration the concentration-time profile was best fit with a two-term polyexponential equation. In this case there are 27 possible compartmental models to choose from. Whereas most books on pharmacokinetics present the 1- and 2-compartment model, the situation is clearly not that simple (see Wagner s (1993) text for examples). 

The Nph monomer form decay has a polyexponential run both in the zeolite and on aerosil. The fluorescence lifetime computed in the two-exponent approximation according to equation... 

Figure 1.2 Scatter plots of simulated concentration-time data ( ) and fitted models (solid lines). Data were simulated using a 2-term polyexponential model and were fit with inverse order polynomials up to degree four and to a 2-term exponential equation. The residual sum of squares for each model is shown in Table 2.

A computer model has been constructed simulating the kinetics of the reaction sequence of Fig. 7. The isotopic enrichment of glycine is represented by the equation for the polyexponential die-away curve of hippurate shown in Fig. 3. That of the amide-N of glutamine is represented by a first order product curve derived from the enrichment of phenylacetylglutamine, which starts at zero, reaches a maximum at 3 hours, and thereafter closely approximates the die-away curve of Fig. 4. The model also includes an arbitrary convention which accelerates a late reaction of the sequence (IMP -> hypoxanthine) as a higher power function of [PP-ribose-P], in order to achieve a ratio of >1 in the expression (increase in rate of synthesis of 3-phosphoribosylamine)/(increase... 

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