A computer program for calculating distribution parameters for drugs behaving nonlinearly that is based on disposition decomposition analysis

A comparison of nonlinear pharmacokinetics of erythropoietin in sheep and humans

The primary mechanism of erythropoietin's (EPO) in vivo elimination and the tissue, or tissues, responsible are unknown. Previous studies indicating that EPO pharmacokinetic (PK) behaviour is nonlinear suggest that EPO elimination takes place by a saturable mechanism. A versatile PK system analysis, the Disposition Decomposition Analysis (DDA), capable of quantification of the Michaelis-Menten parameters, V(m) and k(m) was used to analyze and compare EPO's PK behaviour in newborn sheep and preterm infants. Lambs and infants both demonstrated nonlinear PK behaviour appropriately analyzed with DDA. Compared to preterm infants, lambs had significantly greater (p<0.05) elimination capacity as determined by the V(m) (2789+/-525 versus 1767+/-250 mU/mL per h (mean+/-S.E.), respectively), and larger extrapolated linear clearances (116+/-19.1 versus 21.3+/-1.75 mL/kg per h, respectively) (p<0.01). Lambs also demonstrated significantly larger (p<0.01) degrees of nonlinearity as judged by smaller mean k(m) values (2142+/-258 versus 6796+/-1.007 mU/mL, respectively). Of note, although the DDA does not distinguish what the mechanism of EPO elimination is, enzymatic degradation and receptor-mediated cellular internalization are two possibilities. The in vivo DDA-derived k(m) values were similar to reported in vitro binding affinity k(d) data for erythroid progenitors and cell lines having EPO-R's, i.e. 240-2400 mU/mL. The present study's demonstration that EPO's nonlinear PK behaviour in both sheep and humans can be analyzed by the DDA methodology indicates that the sheep model may be used in invasive studies needed to further characterize the mechanism of EPO elimination.

Add-in macros for rapid and versatile calculation of non-compartmental pharmacokinetic parameters on Microsoft Excel spreadsheets

We developed a package of macro programs (named PK_MOMENT) to automatically calculate non-compartmental pharmacokinetic parameters on Microsoft Excel spreadsheets. These macros include rigorous algorithms to execute moment calculations in a comprehensive manner. An optimum number of terminal data points for infinite-time extrapolation can be calculated with one of these macros so that automatic calculation of infinite moment parameters is possible. The moment calculation with PK_MOMENT provided satisfactory results using the hybrid (mixed linear-logarithmic) trapezoidal method rather than the conventional linear trapezoidal method. The macro-aided pharmacokinetic analyses turned out to be useful in that the macro-containing cells can be easily copied and pasted to analyze other data sets and that powerful tools of Excel can be utilized. The use of our macros will be significantly time-saving for routine pharmacokinetic analyses, considering that pharmacokinetic data are usually stored in a spreadsheet format, typically with Excel.

Kinetic evaluation of nonlinear drug elimination by a disposition decomposition analysis. Application to the analysis of the nonlinear elimination kinetics of erythropoietin in adult humans

The disposition-decomposition analysis (DDA) methodology enables isolation of the overall elimination and distribution effects in pharmacokinetics and facilitates analysis which focuses on drug elimination kinetics and does not require a specific structured modeling of drug distribution processes. A computer algorithm enables a curve fitting and a kinetic estimation by integration of the convolution type integrodifferential equation in the DDA. The approach is demonstrated in an analysis of the nonlinear disposition kinetics of erythropoietin (Epo) in 10 healthy, adult human subjects who each received 10, 100, and 500 U/kg i.v. bolus doses of Epo. The nonlinearity is analyzed according to a Michaelis-Menten type nonlinear elimination function, considering simultaneous fitting to the data from all three doses in each subject. The simultaneous fittings produced estimates of the Michaelis-Menten parameters (mean, % cv) Vm (901 mU/mL/h, 19.4%) and km (4814 mU/mL, 24.6%). A linear clearance parameter is defined as the asymptotic clearance value approached when the drug level decreases toward zero. The degree of nonlinearity reached from various dosings was quantified in terms of a clearance ratio which is defined as the ratio between the linear clearance and the clearance estimated for the maximum drug concentration encountered at the given dose level. The subjects showed very little nonlinearity at the 10 U/kg dosing with a mean clearance ratio of 1.07 (2.1% CV) A statistically significant increase in the degree of nonlinearity was observed in the Epo elimination kinetics as the dosing level was increased to 100 and 500 U/kg, reaching clearance ratios of 1.66 (14% CV) and 4.33 (27% CV), respectively. A zero value for the global elimination rate parameter in all 30 dosings indicates that Epo's elimination is entirely accounted for by nonlinear pathway(s).

Mean residence time of drugs administered non-instantaneously and undergoing linear tissue distribution and reversible metabolism and linear or non-linear elimination from the central compartment

Based on disposition decomposition analysis (DDA), equations for the mean residence times (MRT) in the body are derived for a drug and its interconversion metabolite that undergo linear tissue distribution and linear or non-linear elimination from the central compartment after non-instantaneous administration of the drug. The MRT of the drug after non-instantaneous input can be related to the MRT of the drug after intravenous administration, the ratio of the total area under the plasma concentration-time curve of the drug after non-instantaneous administration to that after intravenous administration, the bioavailability of the drug, and the mean input time of the drug. Similar relationships also exist for the MRT of the interconversion metabolite after non-instantaneous input of the drug. The application of these equations to a non-linear reversible metabolic system is illustrated with computer simulations.