Journal of Pharmacokinetics and Biopharmaceutics

A numerical calculation method for dispersion models was developed to analyze nonlinear and nonsteady hepatic elimination of substances. The finite difference method (FDM), a standard numerical calculation technique, was utilized to solve nonlinear partial differential equations of the dispersion model. Using this method, flexible application of the dispersion model becomes possible, because (i) nonlinear kinetics can be incorporated anywhere, (ii) the input function can be altered arbitrarily, and (iii) the number of compartments can be increased as needed. This method was implemented in a multipurpose nonlinear least-squares fitting computer program, Napp (Numeric Analysis Program for Pharmacokinetics). We simulated dilution curves for several nonlinear two-compartment hepatic models in which the saturable process is assumed in transport or metabolism, and investigated whether they could definitely be discriminated from each other. Preliminary analysis of the rat liver perfusion data of a cyclic pentapeptide, BQ-123, was performed by this method to demonstrate its applicability.

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters have been estimated either by fitting all individuals' data together as though there were no individual kinetic differences, the naive pooled data (NPD) approach, or by fitting each individuals' data separately and then combining the individual parameter estimates, the two stage (TS) approach. A third approach, NONMEM, takes a middle course between these. This study provides further evidence of NONMEM's validity by comparing, using simulation, the three approaches on three types of data sets corresponding to three typical types of pharmacokinetic studies. The estimates of population parameters provided by the NPD method are poorer than those provided by either of the other methods. The estimates provided by the TS method are adequate for mean values and for residual variability, but not for interindividual kinetic variability. NONMEM's estimates are as good as those of the TS method for mean parameters and for residual variability, and considerably better for interindividual variability. The latter estimates are still not acceptable in an absolute sense. This is probably due, not to an intrinsic fault of the method (as it is in the case of the TS approach), but to an insufficient number of individuals being studied.

The pharmacokinetic behavior of diminazene in plasma after administration of 2 mg/kg i.v. and 3.5 mg/kg i.m. was studied in four healthy Dala × Ryggja rams. Following i.v. injection, the data were satisfactorily described by a triexponential equation; the apparent volume of distribution at the steady-state was 0.56±0.04 L/Kg (X±sd; n=4); total body clearance averaged 1.1±0.09 ml/kg/min and elimination half-life was 9.30±1.40 hr. After intramuscular administration peak plasma levels of 6.30–7.57 μg/ml were reached in 20 to 45 min and the mean absorption time averaged 5.83±1.61 hr. Systemic availability relative to the intravenous dose was 95.10±23.21% and mean residence time averaged 14.16±1.55hr. The partition of diminazene between erythrocytes and plasma averaged 0.64±0.10; plasma protein binding was high (65–85%) and concentration-dependent. Based on the experimental data obtained, an initial i.m. dose of 2.5 mg/kg followed by 2 mg/kg 24 hr later should be safe and effective in cases of babesiosis and trypanosomiasis sensitive to diminazene. A preslaughter withdrawal period of 14–26 days was estimated.

The serum and urinary concentrations of 5-FU after continuous portal and jugular infusion have been followed by means of a highly sensitive microbiological assay method. Our data indicate that more than 90% of 5-FU was eliminated in the liver after continuous portal infusion of 0.625 mg × kg −1 × hr −1 ,corresponding to a dose of 15 mg × kg −1 ×24 hr −1 .Negligible amounts of intact 5-FU were excreted into the bile, and the urinary excretion was only a few percent of the amount infused. The arterial concentration was on average tenfold higher during the continuous jugular infusion than after the continuous portal infusion, indicating that the route of administration has a pronounced effect on the disposition of 5-FU. Twenty-three percent of the jugular dose reached the liver; 77% was degraded by extrahepatic metabolism. Of these, degradation in the prehepatic splanchnic area accounted for 15%.

A simulation study was carried out to determine the impact of various design factors on the accuracy and precision with which population pharmacokinetic parameters are estimated in preclinical pharmacokinetic studies. A drug given by intravenous bolus injection and having monoexponential disposition characteristics was assumed. The factors investigated were (i) number of animals sampled at specified times with one observation taken per animal, (ii) error in observed concentration measurements, and (iii) doubling the number of observations per animal while varying the number of animals. Data were analyzed with the NONMEM program, and the least number of animals per time point (where each animal supplied one concentration-time point) required for accurate and precise parameter estimation was determined. The one observation per animal design yielded biased and imprecise estimates of variability, and residual variability could not be estimated. Increasing the error in the concentration measurement led to a significant deterioration in the accuracy and precision with which variability was estimated. Obtaining a second sample from each animal practically eliminated bias and facilitated the partitioning of interanimal variability and residual intraanimal variability, by introducing information about the latter. Doubling the total number of observations per animal required using half (i.e., 50) the total number of animals required for accurate and precise parameter estimation with the one sample per animal design.

Myocardial contractility of normotensive and spontaneously hypertensive rabbits was determined following an iv bolus injection of propranolol HCl. Left ventricular pressure and dimension were used to calculate the contractility parameters of (dP/dt) max ,maximum fiber shortening velocity V cf , and the slope of the end systolic pressure-end systolic volume line (ESP-ESV line). Hypertension was induced by a methoxamine HCl iv infusion which mimicked the cardiac effects seen in essential hypertension. Propanolol caused a significant decrease in all contractility parameters (p<0.05)within 15min after administration, with a peak effect occurring after 30–35 mins. The pharmacokinetics and pharmacodynamics of propranolol were fit using Hill's equation in conjunction with the concentration of drug in the theoretical effect compartment. The normotensive group of rabbits had a calculated EC (50) of 12.7 ng/ml, while the hypertensive group had an EC 50 of 6.9 ng/ml,indicating that the hypertensive rabbits were much more sensitive to the propranolol than the normotensive group. In addition, the normotensive group of rabbits demonstrated a much different pharmacokinetic-pharmacodynamic relationship than that of the hypertensive group, indicating that the hypertensive state of the animal has a significant effect upon the concentration-effect relationship.

We investigated the influence of bias in the estimates of the population pharmacokinetic parameters on the performance of Bayesian feedback in achieving a desired drug serum concentration. Three specific cases were considered (i) steady-state case, (ii) lidocaine example, and (iii) mexiletine example. Whereas in the first case both the feedback and the desired concentration represented steady-state values, in the lidocaine and mexiletine examples the feedback concentration was assumed to be sampled shortly after starting therapy. RMSE was used as a measure of predictive performance. For the simple steady-state case the relationship between RMSE and bias in the parameter estimates describing the prior distribution could be derived analytically. Monte Carlo simulations were used to explore the two non-steady-state situations. In general, the performance of Bayesian feedback to predict serum concentrations was relatively insensitive to bad population parameter estimates. However, large changes in RMSE could be observed with small changes in the true variance component parameters in particular in the intraindividual residual variance, σ ɛ 2 , indicating that the prediction interval, in contrast to point prediction, is sensitive to bias in the estimates of the population parameters.

An arterial and venous blood (or plasma) concentration difference of drugs across the lung of rats was evaluated based on the recirculatory concept. The recirculatory system is given by the combination of the transfer functions for the pulmonary and the systemic circulations and is described by a Laplace-transformed equation, i.e., an image equation. For the manipulation of the image equations, the fast inverse Laplace transform (FILT) was adopted and MULTI(FILT) was used for the simultaneous curve fitting to estimate the pharmacokinetic parameters in the recirculatory model. Metoprolol as a test drug and cephalexin as a control drag were infused, respectively into the femoral vein for 30 min, and arterial and venous blood samples were collected simultaneously through the cannula at the femoral artery and at right atrium during and after the infusion. Exponential functions were assumed for the weight functions through both the pulmonary and systemic circulations. Results of the curve fitting showed that the single-pass extraction ratio through the pulmonary circulation (Ep)of meloprolol was about 0.2, whereas that of cephalexin was negligible. The mean transit times through the pulmonary circulation (¯tp of metoprolol and cephalexin were both about 0.5 min, which is small. The singlepass extraction ratios through the systemic circulation (Es)of metoprolol and cephalexin were both about 0.1. and the mean transit times through the systemic circulation (¯ts were 11.5 min and 8.2 min, respectively.

Bupivacaine is used as a racemate. In previous studies the mean total body clearance ofR(+)-bupivacaine was found to be greater thanS(−)-bupivacaine by 65% after iv bolus dose of separate enantiomers and by 20% after iv infusion to steady state of racemate. The present studies were performed to determine whether different study designs using different iv dosage regimens could influence the pharmacokinetic parameters determined for either bupivacaine enantiomer. rac-Bupivacaine·HCl was administered iv to 6 adult Merino ewes by bolus, brief infusion, and prolonged infusion. Arterial blood concentrations ofR(+)- andS(−)-bupivacaine were measured by enantioselective HPLC. These regimens consistently produced lower arterial blood concentrations ofR(+)-bupivacaine thanS(−)-bupivacaine due toR(+)-bupivacaine having a greater initial dilution volume by 16 (95%CI=3–29)%, volume of distribution at steady state equilibrium by 32 (95%CI=17–32)% and mean total body clearance by 28 (95%CI=21–35)%. The slow half-life ofR(+)-bupivacaine, however, was found to be 15 (95%CI=0–31)% longer than that ofS(−)-bupivacaine. The difference between enantiomers in mean total body clearance thus was similar to the previous study based upon infusion to steady state of rac-bupivacaine. Differences in pharmacokinetics attributable to the dosage regimen consisted of a greater mean total body clearance forR(+)-bupivacaine along with a smaller terminal half life with the bolus regimen and a longer half-life ofS(−)-bupivacaine after prolonged infusion. Differences in pharmacokinetics between the bupivacaine enantiomers occurred consistently in both distribution and clearance but the magnitude of the effect was less than 50% in each case. Systematic differences in pharmacokinetics associated with the dosage regimen were found mainly in terminal half-life. Dosage regimen, thus, was found to influence the pharmacokinetic results found experimentally and is therefore a significant variable in its own right.

Since the pioneering work of Haggard and Teorell in the first half of the 20th century, and of Bischoff and Dedrick in the late 1960s, physiologically based pharmacokinetic (PBPK) modeling has gone through cycles of general acceptance, and of healthy skepticism. Recently, however, the trend in the pharmaceuticals industry has been away from PBPK models. This is understandable when one considers the time and effort necessary to develop, test, and implement a typical PBPK model, and the fact that in the present-day environment for drug development, efficacy and safety must be demonstrated and drugs brought to market more rapidly. Although there are many modeling tools available to the pharmacokineticist today, many of which are preferable to PBPK modeling in most circumstances, there are several situations in which PBPK modeling provides distinct benefits that outweigh the drawbacks of increased time and effort for implementation. In this Commentary, we draw on our experience with this modeling technique in an industry setting to provide guidelines on when PBPK modeling techniques could be applied in an industrial setting to satisfy the needs of regulatory customers. We hope these guidelines will assist researchers in deciding when to apply PBPK modeling techniques. It is our contention that PBPK modeling should be viewed as one of many modeling tools for drug development.