Showing papers in "Journal of Pharmacokinetics and Biopharmaceutics in 1993"

Comparison of four basic models of indirect pharmacodynamic responses

Abstract: Four basic models for characterizing indirect pharmacodynamic responses after drug administration have been developed and compared. The models are based on drug effects (inhibition or stimulation) on the factors controlling either the input or the dissipation of drug response. Pharmacokinetic parameters of methylprednisolone were used to generate plasma concentration and response-time profiles using computer simulations. It was found that the responses produced showed a slow onset and a slow return to baseline. The time of maximal response was dependent on the model and dose. In each case, hysteresis plots showed that drug concentrations preceded the response. When the responses were fitted with pharmacodynamic models based on distribution to a hypothetical effect compartment, the resulting parameters were dose-dependent and inferred biological implausibility. Indirect response models must be treated as distinct from conventional pharmacodynamic models which assume direct action of drugs. The assumptions, equations, and data patterns for the four basic indirect response models provide a starting point for evaluation of pharmacologic effects where the site of action precedes or follows the measured response variable.

The importance of modeling interoccasion variability in population pharmacokinetic analyses

Abstract: Individual pharmacokinetic parameters may change randomly between study occasions. Analysis of simulated data with NONMEM shows that ignoring such interoccasion variability (IOV) may result in biased population parameter estimates. Particular parameters affected and the extent to which they are biased depend on study design and the magnitude of IOV and interindividual variability. Neglecting IOV also results in a high incidence of statistically significant spurious period effects. Perhaps most important, ignoring IOV can lead to a falsely optimistic impression of the potential value of therapeutic drug monitoring. A model incorporating IOV was developed and its performance in the presence and absence of IOV was evaluated. The IOV model performs well with respect to both model selection and population parameter estimation in all circumstances studied. Analysis of two real data examples using this model reveals significant IOV in all parameters for both drugs and supports the simulation findings for the case that IOV is ignored: predictable biases occur in parameter estimates and previously nonexistent period effects are found.

Pharmacokinetics and pharmacodynamics of furosemide in protein-calorie malnutrition.

Abstract: The influence of dietary protein deficiency on pharmacokinetics and pharmacodynamics of furosemide was investigated after iv bolus (1 mg/100 g) and oral (2 mg/100 g) administration of furosemide to male Sprague-Dawley rats fed on a 23% (control) or a 5% (protein-calorie malnutrition: PCM) protein diet ad lib.for 4 weeks. After iv administration, the mean values of CL R , V ss, and the percentages of dose excreted in 8-hr urine as furosemide were increased 81, 31, and 61%, respectively, in PCM rats when compared with those in control rats, however, CL NR was 54% decreased in PCM rats. The decreased CLNR in PCM rats suggested the significantly decreased nonrenal metabolism of furosemide. The urine volume per g kidney after iv administration was not significantly different between the two groups of rats although the amount of furosemide excreted in 8-hr urine per g kidney increased significantly in PCM rats. The diuretic, natriuretic, kaluretic, and chloruretic efficiencies reduced significantly in PCM rats after iv administration. After oral administration, the extent of bioavailability increased considerably from 27.6% in control rats to 47.0% in PCM rats, probably as a result of decreased gastrointestinal and hepatic first-pass metabolism. This was supported by a tissue homogenate study; the amount of furosemide remaining per g tissue after 30-min incubation of 50 μg of furosemide with the 9000 × gsupernatant fraction of stomach (42.4 vs. 47.9 μg) and liver (41.4 vs. 45.9 μg) homogenates increased significantly in PCM rats. No significant differences in CLR and t1/2 were found between the control and the PCM rats after oral administration. The 24-hr urine volume and the amount of sodium excreted in 24-hr urine per g kidney increased significantly in PCM rats, and this might be due to a significantly increased amount of furosemide reaching the kidney excreted in urine per g kidney.

Dermal and Underlying Tissue Pharmacokinetics of Salicylic-Acid After Topical Application

Abstract: The time course of salicylic acid at a dermal application site and in local underlying tissues below the site in rats was examined using a physiologically based pharmacokinetic model assuming first-order diffusional mass transfer between the dermis and underlying tissues. The concentrations of salicylic acid in tissues below the applied site were measured and compared with plasma concentrations and concentrations in similar tissues on the contralateral side. The direct penetration of salicylic acid was dominant only to a depth of 3–4 mm below the applied site for the first ∼2 hr after application. The time course of salicylic acid in individual rats was modeled using known tissue blood flows and tissue-tissue clearances by (i) numerical integration and nonlinear regression of a series of differential equations representing events in individual tissues, and (ii) numerical integration and nonlinear regression of a single differential equation representation of the concentration-time course in an individual tissue with a polynomial representation of salicylate concentrations in other input tissues and an exponential representation of the input from the solution. Tissue-tissue clearances were deduced by both nonlinear regression and mass balance analysis (only for underlying dennis) using area-under-the-curves from salicylic acid tissue penetration data in anesthetized rats. The relative importance of direct penetration and blood supply in determining the concentrations of salicylic acid in deeper tissues was assessed by simulations in which either no direct penetration occurred or there was zero input from blood. Simulations confirm that direct penetration is only evident in the superficial tissues for ∼2 hr. An attempt was also made to examine the dermal pharmacokinetics of salicylic acid using statistical moments.

Effect of misspecification of the absorption process on subsequent parameter estimation in population analysis.

Abstract: A prospective simulation study has been carried out to evaluate the effect of potential misspecification of the absorption rate constant (ka) in population pharmacokinetic analysis when few to no concentration-time data were available in the absorption phase and estimation of ka was not possible. Data were simulated for 100 subjects using a one-compartment model at steady state with first-order input. Data were generated over a range of ka values: ka was misspecified in the NONMEM analysis by factors of 0.25, 0.5, 1, 2, 3, and 4. In general, clearance (CL) was typically estimated with a small, constant underprediction, regardless of the range of misspecification of ka or whether data were present in the absorption phase. The same was not true for volume of distribution (V), values were biased and sensitive to the degree of misspecification, but only when the data contained even a little information about absorption. If studies are to be designed in which information absorption is either not required or is of no therapeutic use, then blood samples could be concentrated in the postabsorption phase and the absorption input fixed according to the best a priori information available.

Tissue distribution of fentanyl and alfentanil in the rat cannot be described by a blood flow limited model.

Abstract: Traditionally, physiological pharmacokinetic models assume that arterial blood flow to tissue is the rate-limiting step in the transfer of drug into tissue parenchyma. When this assumption is made the tissue can be described as a well-stirred single compartment. This study presents the tissue washout concentration curves of the two opioid analgesics fentanyl and alfentanil after simultaneous 1-min iv infusions in the rat and explores the feasibility of characterizing their tissue pharmacokinetics, modeling each of the 12 tissues separately, by means of either a one-compartment model or a unit disposition function. The tissue and blood concentrations of the two opioids were measured by gas-liquid chromatography. The well-stirred one-compartment tissue model could reasonably predict the concentration-time course of fentanyl in the heart, pancreas, testes, muscle, and fat, and of alfentanil in the brain and heart only. In most other tissues, the initial uptake of the opioids was considerably lower than predicted by this model. The unit disposition functions of the opioids in each tissue could be estimated by nonparametric numerical deconvolution, using the arterial concentration times tissue blood flow as the input and measured tissue concentrations as the response function. The observed zero-time intercepts of the unit disposition functions were below the theoretical value of one, and were invariably lower for alfentanil than for fentanyl. These findings can be explained by the existence of diffusion barriers within the tissues and they also indicate that alfentanil is less efficiently extracted by the tissue parenchyma than the more lipophilic compound fentanyl. The individual unit disposition functions obtained for fentanyl and alfentanil in 12 rat tissues provide a starting point for the development of models of intratissue kinetics of these opioids. These submodels can then be assembled into full physiological models of drug disposition.

Kinetic analysis of AUC-dependent saturable clearance of liposomes: mathematical description of AUC dependency.

Abstract: The objective of this study was to examine the AUCdependency of saturable hepatic clearance (CL h )of liposomes and to postulate a mathematical model to describe the characteristics. The AUCdependency of saturable CL h was examined under intravenous rapid administration at various doses. The CL h increased with increasing blood concentration but decreased with the increase of AUCat each dose. In addition, the relationship between AUCand CL h was consistent with that observed in previously reported infusion studies. These experimental data confirm the AUCdependency of saturable CL h of liposomes. A mathematical model was developed for this AUCdependency. The decrease of CL h was described by the uptake amount (X)as follows: CL h =CL m (1−X/X m ),where CL m and X m represent the maximum uptake clearance and the maximum uptake amount, respectively. The rate equation for uptake was analytically solved as CL h =X/AUC=X m AUC(1-exp(CL m /X m AUC)).Uptake clearance can be described by CL m , X m ,and AUC,and so uptake clearance is constant if AUCis constant. These experimental analyses and theoretical considerations show the validity of the AUC-dependent saturable CL h of liposomes.

Formed and preformed metabolite excretion clearances in liver, a metabolite formation organ: Studies on enalapril and enalaprilat in the single-pass and recirculating perfused rat liver

Abstract: Single-pass and recirculating rat liver perfusion studies were conducted with [14C]enalapril and [3H]enalaprilat, a precursor-product pair, and the data were modeled according to a physiological model to compare the different biliary clearances for the solely formed metabolite, [14C]enalaprilat, with that of preformed [3H]enalaprilat. With single-pass perfusion, the apparent extraction ratio (or biliary clearance) of formed [14C]enalaprilat was 15-fold the extraction ratio of preformed [3H]enalaprilat, an observation attributed to the presence of a barrier for cellular entry of the metabolite. Upon recirculation of bolus doses of [14C]enalapril and [3H]enalaprilat, the biliary clearance, estimated conventionally as metabolite excretion rate/midtime metabolite concentration, for formed [14C]enalaprilat was again 10- to 15-fold higher than the biliary clearance for preformed [3H]enalaprilat, but this decayed with perfusion time and gradually approached values for preformed [3H]enalaprilat. The decreasing biliary clearance of formed enalaprilat with recirculation was explained by the dual contribution of the circulating and intrahepatic metabolite (formed from circulating drug) to excretion. Physiological modeling predicted (i) an influx barrier (from blood to cell) at the sinusoidal membrane as the rate-limiting process in the overall removal of enalaprilat, (ii) a 15-fold greater extraction ratio or biliary clearance for formed [14C]enalaprilat over [3H]enalaprilat during single-pass perfusion, and (iii) the time-dependent and declining behaviour of the biliary clearance for formed [14C]enalaprilat during recirculation of the medium. In the absence of a direct knowledge of eliminating organs in vivo, this variable pattern for excretory clearance of the formed metabolite within the organ is indicative of a metabolite formation organ.

A mathematical model for dynamics of cardiovascular drug action: application to intravenous dihydropyridines in healthy volunteers.

Abstract: A physiologically based mathematical model was built to describe the pharmacodynamic effects in response to the administration of intravenous (iv)dihydropyridine drugs in healthy volunteers. This model incorporates a limited number of hemodynamic variables, namely, mean arterial blood pressure (MAP),cardiac output (CO)or heart rate (HR),stroke volume (SV),and total peripheral resistance (TPR),into a closed-loop system supposed to represent essential features of the cardiovascular regulation. We also defined an additional auxiliary control variable (U)which is thought to represent primarily the role of the baroreceptor reflex. It was assumed that the variable Uwas related to MAPchanges through both deviation- and ratesensitive mechanisms. Other model parameters are the baseline levels for MAP, CO(or HR),and TPR,as well as time constants to account for further temporal aspects of the regulation. Finally, TPRwas assumed to be linked to the plasma concentrations of dihydropyridine drugs via a conventional pharmaco-kinetic/pharmacodynamic (PK/PD) model, relying upon an effect compartment and a linear, hyperbolic, or sigmoidal relationship between the reduction in TPRand the drug concentrations at the effect site. The model characteristics were explored by studying the influence of various parameters, including baseline levels and deviation- and rate-sensitive control parameters, on the hemodynamic responses to a fictive constant rate ivinfusion of a vasodilator drug. Attempts were also made to mimic literature data with nifedipine, following ivadministration under both constant and exponentially decreasing infusion rates. The applicability of the model was demonstrated by fitting hemodynamic data following ivinfusion of nicardipine to healthy volunteers, under experimental conditions similar to those described above for nifedipine. The effect model for the action of nicardipine on TPR,combined with the physiological model including a feedback control loop, allowed an adequate quantitative description of time profiles for both cardiac output and mean arterial pressure. The suggested model is a useful tool for integrated data analysis of hemodynamic responses to vasodilator drugs in healthy volunteers. Computer simulations suggest that a graded variation of a few model parameters-including baseline levels of TPRand MAPand the deviaion-sensitive parameter of the arterial pressure control-would also be able to account for the pattern of hemodynamic response observed in hypertensive patients, which is qualitatively different to that seen in normotensive subjects. Extrapolation of drug response from the healthy volunteer to the hypertensive patient is allowed by our model. Its usefulness for an early evaluation of drug efficacy during drug development is under current investigation.

Stereoselective, Competitive, and Nonlinear Plasma Protein Binding of Ibuprofen Enantiomers as Determined in Vivo in Healthy Subjects

Abstract: The plasma protein binding and competitive inhibition parameters of R(-)- and S(+)-ibuprofen were determined in vivo in 12 healthy subjects. Subjects participated in a 4 x 4 Latin square design in which oral solutions of drug were administered as 300 mg R(-)-ibuprofen, 300 mg S(+)-ibuprofen, 300 mg R(-)- + 300 mg S(+)-ibuprofen, and 300 mg R(-)- + 600 mg S(+)-ibuprofen. Unlabeled ibuprofen enantiomers were quantitated using a stereospecific reversed-phase HPLC assay, and plasma protein binding experiments were performed using radiolabeled 14C-enantiomers and an ultrafiltration method at 37C. At therapeutic drug concentrations, the protein binding of each enantiomer was greater than 99%. Furthermore, the binding of ibuprofen enantiomers was stereoselective and mutually competitive, as well as nonlinear. The bound-free data were fitted to a model in which the non-linearity of plasma protein binding and competition between enantiomers for binding sites could be accommodated. There were substantial differences in the affinity of ibuprofen enantiomers for protein binding sites (RP2 = 0.358 +/- 0.185 vs. SP2 = 0.979 +/- 0.501 micrograms/ml; mean +/- SD) but no differences in their binding capacity (RP1 = 160 +/- 86 vs. SP1 = 161 +/- 63 micrograms/ml). Although statistically significant, the differences in competitive inhibition parameters were more modest (SKI = 0.661 +/- 0.363 vs. RKI = 0.436 +/- 0.210 micrograms/ml). As a result, the intrinsic binding (i.e., P1/P2) of R(-)-ibuprofen was greater than S(+)-ibuprofen, and the unbound fraction was significantly greater for S-enantiomer vs. R-enantiomer after a given dose of R-ibuprofen or racemate.

Two constrained deconvolution methods using spline functions.

Abstract: This paper describes two new methods to solve the following estimation problem. Given n1 noisy measurements (yi1,i,i=1,..., n1)of the response of a system to a knowninput [A1(t) where tindicates time], and n2 noisy measurements yi,2,i=l,..., n2 of the response of a system to an unknowninput [A2(t)], obtain an estimate of A2(t) and K(t) (the unit impulse response function of the system) under the model: $$y_{ij} = \int_0^{t_{ij} } {A_j (s)} K(t_{ij} - s)ds + \varepsilon _{ij} $$ weree i,j are independent identically distributed random variables. Both methods use spline functions to represent the unknown functions, and they automatically select the spline functions representing the unknown input and unit impulse response functions. The first method estimates separately the unit impulse response function and the input, recasting the problem in terms of inequality-constrained linear regression. The second method jointly estimates the unit impulse response function and the input function, recasting the problem in terms of inequality-constrained nonlinear regression. Simulated and real data analysis are reported.

Physiological pharmacokinetics of solutes in the isolated perfused rat hindlimb: characterization of the physiology with changing perfusate flow, protein content, and temperature using statistical moment analysis.

Abstract: Distribution of Evans Blue (EB), sucrose, and water into the isolated perfused rat hindlimb was studied under various conditions using the multiple indicator dilution (MID) technique. Statistical moment analyses of the outflow profiles for the EB, sucrose, and water were used to define the vascular, extravascular, and total water spaces, respectively. The varied perfusion conditions included albumin content (2, 4.7, and 7%), temperature (25, 37, and 42 C), perfusate flow rate (2, 4, 8, and 12 ml/min) and the presence/absence of red blood cells. The range of studies undertaken were chosen to represent the variety of conditions used in the preparation of both isolated animal and human limbs, the latter being particularly important in cytotoxic therapy for recurrent malignant melanoma. The distribution volumes of EB, sucrose, and water were dependent on the flow rate and the albumin content of perfusate. The normalized variances (CV 2 ) of the markers were of the following order: sucrose (2.18) > water (1.58) > EB (0.68), indicating that some disequilibrium occurs during the capillary exchange of water and sucrose. It is suggested that a Krebs-Henseleit buffer containing 2% BSA is a suitable perfusate for most studies of the isolated rat hindlimb perfusion. The effect of albumin concentration manifests itself only at higher flows.

Targeting anticancer drugs to the brain: II. Physiological pharmacokinetic model of oxantrazole following intraarterial administration to rat glioma-2 (RG-2) bearing rats

Abstract: The disposition of the anticancer drug oxantrazole (OX) was characterized in rats bearing the rat glioma-2 (RG-2) brain tumor. Following intraarterial administration of 3 mg/kg of OX, serial sacrifices were completed from 5 min to 5 hr after administration. Blood and tissue samples collected at the time of sacrifice were processed and measured for OX concentrations by HPLC. The kidney had the greatest affinity for OX with the Cmaxbeing 40.6 μg/mlat 15 min after administration. OX concentrations in brain tumor were higher than in normal right and left brain hemispheres, and consistent with enhanced drug blood-tumor barrier (BTB) permeability seen in experimental models for brain tumors. Observed heart, liver, lung, and spleen OX concentrations were similar, ranging from approximately 2 μg/mlto 20 μg/ml. A unique technique was used to develop a global physiological pharmacokinetic model for OX. A hybrid or forcing function method was used to estimate individual tissue compartment biochemical parameters (i.e., partition and mass transfer coefficients). A log likelihood optimization scheme was used to determine the best model structure and parameter sets for each tissue. Most tissues required a 3-subcompartment structure to adequately describe the observed data. The global model was then reconstructed with an arterial blood and rest of body compartments that provided predicted OX concentrations in agreement with the data. The model development strategy provides a systematic approach to physiological pharmacokinetic model development.

Targeting the systemic exposure of teniposide in the population and the individual using a stochastic therapeutic objective

Abstract: A stochastic control approach for dose regimen design is developed and applied to the problem of targeting the systemic exposure, defined as the area under the blood concentrationtime curve (AUC),of the anticancer drug teniposide in both the population and individual patients. The control objective involves maximizing the probability that AUCis within a selected target interval given either the population distribution for the kinetic model parameters (a priori control) or the posterior distribution for an individual patient (feedback control). Results of a detailed simulation study are presented, illustrating the feasibility of applying stochastic control principles to the design of dose regimens. The predictive ability of the calculated distributions of AUCfor the population and for individuals is evaluated in part by determining the percentage coverage of the computed 95% uncertainty intervals using the simulation results. For the a priori control phase, 94% of the simulated subjects had values of systemic exposure within the computed 95% uncertainty interval, while 93.4% of the simulated subjects had feedback control phase systemic exposure values within their computed 95%uncertainty intervals. Similar evaluation of the uncertainty intervals calculated for plasma concentrations further document the ability of the proposed stochastic control method to predict the uncertainty associated with future therapy.

A pharmacokinetic-pharmacodynamic model for quantal responses with thiopental.

Abstract: The pharmacokinetic-pharmacodynamic model developed here characterizes the relationship between simulated plasma concentrations of thiopental and two dichotomous endpoints determined at induction of anesthesia: loss of voluntary motor power (clinical endpoint), and burst suppression of the electroencephalogram (EEG endpoint). The model incorporated data from two separate thiopental patient studies: a pharmacokinetic study with 21 males, and a pharmacodynamic study with 30 males. In the pharmacodynamic study, cumulative quantal dose-response curves for the clinical and EEG endpoints were developed from observations made during a constant-rate infusion of thiopental. Population mean parameters, derived from the bolus pharmacokinetic thiopental study, were used to simulate concentration-time data for the 150 mg·min1 thiopental infusion rate used in the dose-response study. A single biophase model incorporating the two endpoints was generated, combining the pharmacokinetic and pharmacodynamic data from the two groups. Estimates of the mean effective thiopental concentrations affecting 50% of the population (EC50s) for the clinical and EEG endpoints were 11.3 and 33.9μg·ml−1, respectively. The half-time for equilibration between arterial thiopental and the effect compartment was 2.6 min. These results are in reasonable agreement with previously described quantal concentration-response data, and with pharmacodynamic models developed for graded EEG responses. Simulation of bolus doses of thiopental with the new model provided ED50s for the clinical and EEG endpoints of 265 mg and 796 mg, respectively; the dose predicted to produce loss of voluntary motor power in 90% of an adult male population was 403 mg. A model combining population pharmacokinetics with cumulative dose-response relationships could prove useful in predicting dosage regimens for those drugs with responses that are categorical.

Nonlinear protein binding and enzyme heterogeneity: Effects on hepatic drug removal

Abstract: The kinetics of substrate removal by the liver and the resulting nonlinear changes in unbound fraction along the flow path at varying input drug concentrations were examined by a model simulation study. Specifically, we varied the binding association constant, KA, and the Michaelis-Menten constants (Km and Vmax) to examine the steady state drug removal (expressed as hepatic extraction ratio E) and changes in drug binding for (i) unienzyme systems and (ii) simple, parallel metabolic pathways; zonal metabolic heterogeneity was also added as a variable. At low KA, E declined with increasing input drug concentration, due primarily to saturation of enzymes; only small differences in binding were present across the liver. At high KA, a parabolic profile for E with concentration was observed; changes in unbound fraction between the inlet and the outlet of the liver followed in parallel fashion. Protein binding was the rate-determining step at low input drug concentrations, whereas enzyme saturation was the rate-controlling factor at high input drug concentration. Heterogeneous enzymic distribution modulated changes in unbound fraction within the liver and at the outlet. Despite marked changes in unbound fraction occurring within the liver for different enzymic distributions, the overall transhepatic differences were relatively small. We then investigated the logarithmic average unbound concentration and the length averaged concentration as estimates of substrate concentration in liver in the presence of nonlinear drug binding. Fitting of simulated data, with and without assigned random error (10%), to the Michaelis-Menten equation was performed; fitting was repeated for simulated data obtained with presence of a specific inhibitor of the high-affinity, anteriorly distributed pathway. Results were similar for both concentration terms: accurate estimates were obtained for anterior, high affinity pathways; an overestimation of parameters was observed for the lower affinity posteriorly distributed pathways. Improved estimations were found for posteriorly distributed pathways upon inhibition with specific inhibitors; with added random error, however, the improvement was much decreased. We applied the method for fitting of several sets of metabolic data obtained from rat liver perfusion studies performed with salicylamide (SAM) (i) without and (ii) with the presence of 2,6-dichloro-4-nitrophenol (DCNP), a SAM sulfation inhibitor. The fitted results showed that SAM sulfation was a high-affinity high-capacity pathway; SAM glucuronidation was of lower affinity but comparable capacity as the sulfation pathway, whereas SAM hydroxylation was of lower affinity and lower capacity.

Assessing drug exposure in rodent toxicity studies without satellite animals

Abstract: Five major objectives for pharmacokinetic investigations in support of toxicity studies are identified as follows: Assess whether animals exhibited measurable blood concentrations in a dose-dependent manner; estimate average area under the concentration- time curve (AUC)and maximal concentration (Cmax)for each treatment group; elucidate general patterns in the concentration-time (CxT)profile, and summarize relationships between CxTand treatment group; determine CxTdependence on day into study; and judge interanimal variability and identify any animals with unusual concentration response. Such objectives are generally addressed in rodent toxicity studies by including “satellite” animals in the study. Satellite animals are extra animals dosed as per protocol but not subjected to toxicological and pathological observations and tests. Instead, they are used exclusively for the evaluation of pharmacokinetic characteristics of the test compound. In this paper, methods are described for achieving the five listed pharmacokinetic objectives in rodent toxicity studies without the use of satellite animals. A rat toxicity study is presented as an example.

Combined recirculation of the rat liver and kidney: studies with enalapril and enalaprilat.

Abstract: Combined recirculation of the rat liver (L) and kidney (IPK) at 10 ml min−1 per organ (LK) was developed to examine the hepatorenal handling of the precursor-metabolite pair: [14C]-enalapril and [3H]enalaprilat. Loading doses followed by constant infusion of [14C]enalapril and preformed [3H]enalaprilat to the reservoirs of the IPK or the LK preparation was used to achieve steady stale conditions. In both organs, enalapril was mostly metabolized to its dicarboxylic acid metabolite, enalaprilat, which was excreted unchanged. At steady state, the fractional excretion for [14C]enalapril (FE=0.45 to 0.48) and preformed [3H]enalaprilat (FE{pmi}=1.1) were constant and similar for both the IPK and LK. The additivity of clearance was demonstrated in the LK preparation, namely, the total clearance of enalapril was the sum of its hepatic and renal clearances. However, the apparent fractional excretion for fanned [14C]enalaprilat, FE{mi} and the apparent urinary clearance were time-dependent and higher than the corresponding values for preformed [3H]enalaprilat in both the IPK and LK. The FE{mi} and urinary clearance values further differed between the IPK and LK. Biliary clearance of formed vs. preformed enalaprilat displayed the same discrepant trends as observed for FE{mi} vs. FE{pmi} for the LK. These observations on the time-dependent and variable excretory clearance (urinary or biliary) of the formed metabolite vs. the constant, and much reduced, excretory clearance of the preformed metabolite are due to dual contributions to formed metabolite excretion: the nascently formed, intracellular metabolite which immediately underwent excretion and the formed metabolite which reentered the circulation, behaved as a preformed species. When data for the IPK and LK preparations were modeled with a physiological model with parameters previously reported for the L and IPK, all data, including metabolite excretory clearances, were well predicted. Model simulations revealed that the apparent FE{mi} differed between the LK and IPK preparations when the liver was present as an additional metabolite formation organ; the apparent excretory (urinary or

Influence of barrier-crossing limitations on the amount of macromolecular drug taken up by its target.

Abstract: Macromolecules (substitutive enzymes, polymeric prodrugs, immunotoxins, radiolabeled antibodies, or peptide hormones) are of interest in the treatment of several diseases. To reach the tissues, these macromolecular drugs have to cross the capillary wall, which represents an important transfer limitation. While pharmacokinetics usually studies the changes in drug concentration in different body compartments, analyzing the amount of drug gaining access to its target may be more relevant for assessing the efficiency of macromolecules than for low molecular mass drugs. To determine the influence of different parameters on the fraction of the injected dose gaining access to the pharmacologic target, we constructed pharmacokinetic models where two uptakes, both linear or nonlinear, work either in the same compartment (no transport limitation), or in compartments separated by a transport barrier. Numerical applications were carried out with parameters obtained either experimentally or from the literature. We conclude that it is of little use to increase the affinity (Kuptakeof a macromolecular drug for its target when a transport limitation and an undesired elimination from the plasma space are both present. Likewise, an increase of the uptake (rate of uptake or maximal velocity) by the target is not very productive because permeability of the capillary wall is the factor limiting access of macromolecules to tissues. Maximal efficiency of therapeutic macromolecules could be achieved by increasing, where feasible, the transport across the barrier between the plasma and the target, and by preventing the undesired eliminations as much as possible.

Pharmacokinetic modeling of the sinusoidal efflux of anionic ligands from the isolated perfused rat liver: The influence of albumin

Abstract: This study contains a pharmacokinetic analysis on the efflux of organic anions from the liver into the bloodstream (sinusoidal efflux) with specific reference to the influence of albumin. The net sinusoidal efflux rate of dibromosulfophthalein (DBSP) from preloaded livers, being the resultant of sinusoidal efflux and reuptake of ligand by hepatocytes downstream the sinusoid, can be strongly increased by the presence of bovine serum albumin (BSA), a protein having multiple binding sites for DBSP. We previously attributed this effect to a reduction of reuptake through extracellular binding of the organic anion to the protein, rather than to an intrinsic stimulatory effect on the actual membrane transport process from the cells. In the present study we tested this hypothesis using a pharmacokinetic multicompartment liver model. This model resembles the parallel tube model in that the liver is described by several compartments placed in series instead of a single well-stirred compartment and it takes into account rates of dissociation and association in binding to proteins in the sinusoidal space. The model parameters were fitted from the sinusoidal efflux and biliary excretion data from efflux experiments measuring the stimulatory effect of various concentrations of BSA. Equilibrium binding of DBSP to albumin as well as the dissociation rate constant (koff) were determined in vitro with rapid filtration techniques. The experimental data could not be fitted satisfactorily when using the experimentally obtained values of the protein association and dissociation rate constants (kon and koff). However, they could be simulated accurately assuming 16 times higher values for the association and dissociation rate constant compared to those determined in vitro. Time constants of the perfusate flow, liver (re)uptake, and protein association and dissociation indicate that binding equilibrium does not exist within the sinusoids and that, in particular at low protein concentrations, the net sinusoidal efflux rate is association rate-limited: A large fraction of the ligand effluxed from the cell into the median is taken up by the hepatocyte before binding to the proteins occurs. Higher kon and koff values predicted by the model might indicate altered DBSP-albumin binding characteristics upon passage through the liver but alternatively can be explained by an intrinsic effect of albumin on the carrier-mediated efflux process. Efflux experiments showed a marked stimulatory effect of the protein on sinusoidal efflux but only a moderate effect on biliary excretion, despite a strong decrease in liver content. These patterns indicate that sinusoidal efflux and biliary excretion occur from two different intracellular compartments that equilibrate slowly.

Variability in the renal clearance of cephalexin in experimental renal failure

Abstract: This study forms a part of an investigation into the extent to which the type of renal damage influences the renal clearance of drugs. We have already demonstrated an effect of different types of experimental renal failure (ERF) on the renal clearance of two cations: cimetidine, a drug that is filtered and secreted by the nephron, and lithium, which is filtered and reabsorbed by more than one segment of the nephron. In this report the renal clearance of cephalexin (CLCEX) is investigated, a drug that has a different mode of renal elimination, since it is filtered, secreted, and reabsorbed by the proximal tubules. The aim was to extend our earlier studies to an organic anion, and to provide an opportunity to evaluate the feasibility of using the renal clearance of N-1-methylnicotinamide (NMN) to predict the renal clearance of anionic drugs in renal failure. Different models of site-specific ERF have been developed in the rat; proximal tubular necrosis (induced by cisplatin), papillary necrosis (induced by 2-bromoethylamine), and glomerulonephritis (induced by sodium aurothiomalate or by antiglomerular basement membrane antibodies). Glomerular function (GFR) was assessed by the clearance of inulin (CLNULIN), and tubular function was assessed by the clearance of endogenous NMN (CLNMN). OUr results show that even if the models of ERF used were not absolutely site-specific, glomerular function and tubular function did not decrease to the same extent in the different ERF. Therefore, glomerulo-tubular imbalance existed, which is incompatible with the "intact nephron hypothesis," i.e., the site of the damage along the nephron and not only the degree of renal dysfunction, is a potential source of variability in the clearance of certain drugs. The renal clearance of cephalexin was estimated more accurately by CLNMN than GFR (r = 0.90). We conclude that the clearance of the endogenous cation NMN can be used to predict the renal clearance of drugs that are not only filtered by the glomeruli but also secreted and/or reabsorbed by the proximal tubules, and in the limited examples investigated appears to apply to both anionic and cationic compounds. In this respect the GFR alone was not an adequate parameter for the prediction of the renal clearance of such drugs.

A physiological and system analysis hybrid pharmacokinetic model to characterize carbon tetrachloride blood concentrations following administration in different oral vehicles

Abstract: Oral absorption of chemicals can be influenced significantly by the administration vehicle or diluent. It has been observed that the oral absorption of carbon tetrachloride (CCl4)and other volatile organic chemicals is markedly affected by the dosing vehicle, with administration in oils producing erratic blood concentration-time profiles with multiple peaks. Analysis of this type of data by a compartmental modeling approach can be difficult, and requires numerous assumptions about the absorption processes. Alternatively, a system analysis method with few assumptions may provide a more accurate description of the observed data. In the current investigations, a nonlinear system analysis approach was applied to blood CCl4concentration-time data obtained following iv and oral administration. The oral regimens consisted of 25 mg CCl4/kgbody wt given as an aqueous emulsion, in water, as pure chemicals, and in corn oil. The system analysis procedure, based upon a disposition decomposition method, provided an absorption input rate function, F,for each regimen. A physiological pharmacokinetic model, based primarily on parameters available in the literature, and the Finput functions, formed a hybrid model that adequately described the observed blood CCl4concentration-time data. The same physiological pharmacokinetic model, employing conventional first-order absorption input schemes, did not predict the data as well. Overall, the system analysis approach allowed the oral absorption of CCl4to be characterized accurately, regardless of the vehicle. Though system analysis is based on general mathematical properties of a system's behavior rather than on its causal mechanisms, this work demonstrates that it can be a useful adjunct to physiological pharmacokinetic models.

Effect of phenobarbital and p-hydroxyphenobarbital glucuronide on acetaminophen metabolites in isolated rat hepatocytes: Use of a kinetic model to examine the rates of formation and egress

Abstract: Conventional analysis of initial uptake and egress rates in isolated hepatocytes is limited in the ability to distinguish between rates of metabolite formation and egress, and to separate basolateral and canalicular transport processes. The present study examined the applicability of kinetic modeling in describing acetaminophen glucuronide (AG) and acetaminophen sulfate (AS) formation and egress in hepatocytes after acute exposure to phenobarbital or p-hydroxyphenobarbital glucuronide p-OHPBG) in vitro,or in vivophenobarbital pretreatment. A significant pretreatment effect on AG and AS disposition was seen based on initial rates of egress. In vivophenobarbital pretreatment decreased the initial egress rate of AG compared to vehicle pretreatment, and the initial egress rate of AS compared to all other treatments. A pharmacokinetic model incorporating AG and AS formation in hepatocytes as well as egress processes (including diffusional and active transport components) was fit to the data. Parameter estimates derived from model fits to the data showed the expected increase in acetaminophen glucuronidation and decrease in sulfation after phenobarbital pretreatment;in addition, an increase in the AG diffusional rate constant and a decrease in the AS diffusional rate constant was apparent. The excretion Vmax for AG was decreased statistically after acute phenobarbital exposure in vitro,and in vivophenobarbital pretreatment, with a concomitant statistical increase in the KmforAG excretion. In vitroacute p-OHPBG exposure also decreased significantly the excretion Vmax for AG. These data are consistent with the hypothesis that phenobarbitalimpaired biliary excretion of AG is a function of impaired canalicular transport due to the presence of p-OHPBG. They further suggest that the mechanism may not be simple competitive inhibition. This work demonstrates the utility of a kinetic modeling approach to differentiate metabolic and transport processes when analyzing data from isolated hepatocyte studies. Additional information may be gained that would not be apparent by conventional methods of analysis.

Simplified methods for the evaluation of the parameters of the time course of plasma concentration in the one-compartment body model with first-order invasion and first-order drug elimination including methods for ascertaining when such rate constants are equal.

Abstract: The many limitations in determining the pharmacokinetic parameters of firstorder invasion of, and elimination from, the onecompartment body model by the method of residuals or by “feathering” Ct data can be minimized by applying the simplified methods outlined herein. Comparisons of the apparent volumes of distribution, V, calculated on the premises that the Bateman Function represents ka>keor its converse, ke>ka,i.e., flip-flop, can permit a proper choice of the correct version. Estimation of kecan be obtained by regression of (A0/V)/C(oncentration) on AUC1/ Cwhere A0/Vis estimable from knowledge of Cmaxand tmaxsince\(A_0 /V = C_{max} e^{k_e t_{max} }\).The ratio of the magnitude of the rate constant of invasion to that of elimination, m=ka/ke,is related to ketmaxby the expression ketmax=ln m/ (m−1)for all possible values of m.A table for the determination of m from values of ketmaxis given. When bioavailability, γ=A0/Dose,is known or complete, keand Vcan be determined from the respective ordinate and abscissa of the intersection of\(A_0 /C_{max} e^{k_e t_{max} }\)and Cl(clearance)/ke,both plotted against arbitrary kevalues. The two functions may not intersect at low values of mdue to errored C-t values but the kevalue when the two curves are closest (kmin)may approximate ke.The intersections of\(C_{max} e^{k_e t_{max} }\)and keAUCT (AUCtrap)plotted against variable kevalues (Method A) provide estimates of kefrom their abscissa values and A/Vfrom their ordinate values when γis unknown. Method B appears to give more reliable estimates of keat the kminof the difference\(e^{k_e t_{max} } /k_e - AUCT/C_{max}\)plotted against ke.Since kminof this plot is 1/tmaxwhen m=1,the identity of the mas unity underlying the C-t data is indicated when either kmintmaxis approximately unity or kmin ispractically synonymous with 1/tmax.This was clearly shown when 12 constructed m=1,C-t cases with 10% random error were evaluated by Method B. Better estimates were effected by all procedures when the raw C-t data were smoothed.

Pharmacokinetics and pharmacodynamics of nitroglycerin and its dinitrate metabolites in conscious dogs: Intravenous infusion studies

Abstract: Intravenous infusions of nitroglycerin (GTN), 1,2-glyceryl dinitrate (1,2-GDN), and 1,3-glyceryl dinitrate (1,3-GDN) were given to four conscious dogs at 10 micrograms/min, 30 micrograms/min, 50 micrograms/min, and 70 micrograms/min of GTN and 20 micrograms/min and 100 micrograms/min of GDNs. The steady state plasma concentrations (Css) of GTN were reached after about 60 min whereas for 1,2-GDN and 1,3-GDN the Css were reached at about 150 min after the infusion began. Except for one dog, the Css of GTN were not proportional to infusion rate, however, all dogs together showed a good linear relationship between Css of GTN and infusion rates with an average correlation coefficient of 0.917 +/- 0.102. Large variability in GTN clearance after various infusion rates was observed in all dogs. The Css ratios of 1,2-GDN/GTN and 1,3-GDN/GTN yield overall averages of 31.5 +/- 17.2 and 5.47 +/- 3.19, respectively. Average Css ratios of metabolites 1,2-GDN/1,3-GDN were 5.78 +/- 1.23. This ratio is different from those obtained after iv bolus and oral dosing indicating that the biotransformation of GTN to 1,2-GDN and 1,3-GDN differs for each dosing route. The clearances for 1,2-GDN and 1,3-GDN were not changed over the dose range of 20 micrograms/min to 100 micrograms/min. Terminal half-lives of 1,2-GDN and 1,3-GDN postinfusion were similar to those values obtained after a single bolus dose (45 min). It appears that all the GTN dose at steady state can be accounted for by the formation of measurable 1,2-GDN and 1,3-GDN. Large intra- and interdog variations in systolic blood pressure decrease (SPD) following infusions of GTN were observed, however, all dogs showed a clear systolic blood pressure decrease when the highest infusion rate (70 micrograms/min) was given. No significant systolic blood pressure drop was detected following 20 micrograms/min infusions of 1,2-GDN or 1,3-GDN. It was clear that systolic blood pressure in all dogs decreased following 100 microgram/min infusions of 1,2-GDN or 1,3-GDN. When SPD values were plotted vs. log GTN concentrations following the infusion of 70 micrograms/min of GTN in all four dogs, a counterclockwise hysteresis was observed indicating the significant contribution of the active dinitrate metabolites to GTN pharmacodynamics.

Classification of benzodiazepine hypnotics in humans based on receptor occupancy theory

Abstract: Benzodiazepine (BZP) hypnotics are now classified into four groups according to their plasma elimination rates: ultrashort-, short-, intermediate-, and long-acting drugs. Since the specific binding affinities for the BZP receptor vary widely among the BZPs and their active metabolites, it may be more reasonable to correlate their pharmacological activities with the BZP receptor occupancy rather than with their plasma concentrations. The time courses of total plasma concentrations of BZPs and their active metabolites after a single oral administration were obtained from the literature, and their unbound concentrations (Cu) were calculated from the reported values of their plasma unbound fractions. The data of the receptor binding affinities of the BZPs, reported as dissociation constants (Kd) determined by in vitro binding experiments, were also obtained from the literature. Using these values, the time courses of receptor occupancies [Cu/(Kd + Cu) x 100%] were calculated for the various BZPs. A mutual competitive inhibition was considered in the case of the drugs that had active metabolites. Although plasma total and unbound concentration time profiles of the BZPs showed a wide variation, similar patterns were obtained for the time courses of the receptor occupancy among the BZPs in each group, indicating that the BZP hypnotics can be classified more conveniently based on receptor occupancy theory.

Generalized pharmacokinetic modeling for drugs with nonlinear binding: I. Theoretical framework

Abstract: The following integrodifferential equation is proposed as the basis for a generalized treatment of pharmacokinetic systems in which nonlinear binding occurs $$\phi '(c_u )c'_u = - q(c_u ) + g*c_u + f$$ where cu≡unbound plasma drug concentration, f≡drug input rate,'indicates the derivative of a function, and * indicates the convolution operation: (g* cu)(t)=∫0tg(t−u)cudu.Possible physical interpretations of the functions q, g and f are: q (cu)≡ rate at which drug leaves the sampling compartment, g * cu≡ rate at which drug returns to the sampling compartment from the peripheral system (tissues that are kinetically distinct from the sampling compartment), and φ(cu) ≡ amount of drug in the sampling compartment. The approach assumes that drug binding is sufficiently rapid that it may be treated as an equilibrium process. It may be applied to systems in which nonlinear binding occurs within the sampling compartment, i.e., in the systemic circulation or in tissues to which drug is rapidly distributed. The proposed relationship is a generalization of most existing models for drugs with nonlinear binding. It can serve as a general theoretical framework for such models or as the basis for “model-independent” methods for analyzing the pharmacokinetics of drugs with nonlinear binding. Computer programs for the numerical solution of the integrodifferential equation are presented. Methods for pharmacokinetic system characterization, prediction and bioavailability are presented and demonstrated.

Nonlinear mixed effect modeling of the pharmacodynamics of natriuretic peptides in rats

Abstract: Natriuretic peptides have not only natriuretic/diuretic but also hypotensive activities, and the decreased renal perfusion caused by the excessive hypotension is known to attenuate the diuretic actions. The present study was designed to examine the relationship between the dosing (intravenous constant infusion) rates and the diuretic actions of alpha-rat atrial natriuretic peptide (alpha-rANP) and rat brain natriuretic peptide (rBNP) in rats, and population (nonlinear mixed effect model) analysis was applied to these complicated diuretic actions. The intrinsic diuretic activities of alpha-rANP and rBNP could be analyzed, and the effects of blood pressure, heart rate, and also inhibition of degradation enzyme on the diuresis of natriuretic peptides were estimated simultaneously. The population analysis was useful for analyzing such pharmacodynamic data for which the individual analysis could not be applied easily.

Saturable elimination and saturable protein binding account for flavone acetic acid pharmacokinetics

Abstract: Flavone acetic acid (FAA) is an antineoplastic agent that has undergone extensive study in Phase I trials. Concentration-dependent plasma protein binding has been demonstrated in vitroconcentrations of total drug that are achieved in vivo.Moreover, dose-dependent total systemic clearance has been described when FAA has been administered as a short iv infusion. When administered as a prolonged 24-hr infusion, total FAA (bound plus unbound) plasma pharmacokinetics are well described with a first-order two-compartment model. However, measurement of unbound FAA intra- and post-intravenous infusion in eight patients revealed a twofold increase in fraction of FAA unbound in plasma intrainfusion. We attempted to fit pharmacokinetic structural models of varying complexity to the unbound concentrations alone and simultaneously to the unbound and bound FAA plasma concentrations. The data were adequately described only by a model that incorporated simultaneous saturable plasma protein binding and a Michaelis-Menten process for elimination. A comparison among models is presented, as well as pharmacokinetic parameter estimates for FAA in children. These clinical data are consistent with predictions of the clearance model in which both saturable protein binding (resulting in a dynamically increasing unbound fraction) and saturable elimination (resulting in gradually decreasing unbound intrinsic clearance) are operative.

Kinetics of combined drug action

Abstract: For the purpose of obtaining quantitative concentration-effect relationship for combined drugs, rationales of the Hill equation were inferred and five models, i.e., normal distribution (NRD), derivative of R (DRV), vacancy-dependent binding (VDB), equiresponse (EQR), and independence (IND), were proposed to estimate the intensity of the combined drug action. In conclusion, we could not come up to the unique concentration-effect relationship. Among the five models, the EQR, NRD, and VDB models gave almost identical response intensity. Discrimination of these three models is not of great importance. The DRV model gave a characteristic concave isobologram (overadditive), for a given ratio of Hill constants and independent of pharmacologic effect. In contrast, the IND model was able to cope with convex isobolograms (underadditive).