The Connection Between the Steady State (Vss) and Terminal (Vβ) Volumes of Distribution in Linear Pharmacokinetics and The General Proof That Vβ ≥ Vss

Theoretical Examination Seeking Tangible Physical Meanings of Slopes and Intercepts of Plasma Concentration-Time Relationships in Minimal Physiologically Based Pharmacokinetic Models

In minimal physiologically based pharmacokinetic (mPBPK) models, physiological (e.g., cardiac output) and anatomical (e.g., blood/tissue volumes) variables are utilized in the domain of differential equations (DEs) for mechanistic understanding of the plasma concentration-time relationships [Formula: see text]. Although fundamental biopharmaceutical variables in terms of distribution (e.g., [Formula: see text] and [Formula: see text]) and elimination kinetics (e.g., [Formula: see text]) in mPBPK provide greater insights in comparison to classical compartment models, an absence of kinetic elucidation of slopes and intercepts in light of such DE model parameters hinders more intuitive appreciation of [Formula: see text]. Therefore, this study seeks the tangible physical meanings of slopes and intercepts of the plasma concentration-time relationships in one- and two-tissue mPBPK models (i.e., m2CM and m3CM), with respect to time parameters that are readily understandable in PK analyses, i.e., the mean residence ([Formula: see text]) and transit ([Formula: see text]) times. Utilizing the explicit equations (EEs) for the slopes, intercepts, and areas of each exponential phase in the m2CM and m3CM, we theoretically and numerically examined the limiting/boundary conditions of such kinetic properties, based on the ratio of the longest tissue [Formula: see text] to the [Formula: see text] in the body (i.e., [Formula: see text]) that is useful for dissecting complex PBPK systems. The kinetic contribution of the area of each exponential phase to the total drug exposure was assessed to identify the elimination phase between the terminal and non-terminal phases of the [Formula: see text] in the m2CM and m3CM. This assessment provides improved understanding of the complexities inherent in all PBPK profiles and models.

Drug Disposition in Subjects with Obesity: The Research Work of Darrell R. Abernethy

In 1979, the late Dr. Darrell R. Abernethy and colleagues began a series of clinical studies aimed at understanding the pertinent determinants of drug distribution, elimination, and clearance in obesity, and how those variables are interconnected. The studies confirmed that volume of distribution (Vd) and clearance are the principal independent biological variables, which conjointly determine elimination half-life as a dependent variable. For drugs distributed by passive diffusion, their pharmacokinetic Vd - after correcting for plasma protein binding - was increased in obesity, depending in part on the physicochemical lipophilicity of the individual drugs, and the quantitative extent of obesity in overweight individuals. Across all studies, the ratio of mean clearance in obese divided by control groups had an overall median value of 1.21 (range: 0.75 to 3.11), indicating a small and variable effect of obesity on clearance, without clear directionality. Since drug clearance was not clearly related to lipophilicity or degree of obesity, the prolonged half-life of lipophilic drugs in obese patients was largely explained by the increased Vd. Dr. Abernethy further identified delayed attainment of steady-state after initiation of multiple-dose treatment, and delayed washout after termination of dosage, as potential clinical consequences of the extended half-life in obese persons. These consequences for specific drugs have been recently emphasized in contemporary studies of chronic dosage in subjects with obesity. Without data identifying an obesity-related change in clearance for a specific drug, maintenance doses (in milligrams) should be based on ideal weight rather than adjusted upward based on total weight. This article is protected by copyright. All rights reserved.

Optimization of Personalized Amlodipine Dosing Strategies for Children Based on Pharmacokinetic Data from Chinese Male Adults and PBPK Modeling

For children, a special population who are continuously developing, a reasonable dosing strategy is the key to clinical therapy. Accurate dose predictions can help maximize efficacy and minimize pain in pediatrics. Methods: This study collected amlodipine pharmacokinetics (PK) data from 236 Chinese male adults and established a physiological pharmacokinetic (PBPK) model for adults using GastroPlus™. A PBPK model of pediatrics is constructed based on hepatic-to-body size and enzyme metabolism, used similar to the AUC_0-∞ to deduce the optimal dosage of amlodipine for children aged 1–16 years. A curve of continuous administration for 2-, 6-, 12-, 16-, and 25-year-olds and a personalized administration program for 6-year-olds were developed. Results: The results show that children could not establish uniform allometric amplification rules. The optimal doses were 0.10 mg·kg⁻¹ for ages 2–6 years and −0.0028 × Age + 0.1148 (mg/kg) for ages 7–16 years, r = 0.9941. The trend for continuous administration was consistent among different groups. In a 6-year-old child, a maintenance dose of 2.30 mg was used to increase the initial dose by 2.00 mg and the treatment dose by 1.00 mg to maintain stable plasma concentrations. Conclusions: A PBPK model based on enzyme metabolism can accurately predict the changes in the pharmacokinetic parameters of amlodipine in pediatrics. It can be used to support the optimization of clinical treatment plans in pediatrics.

Meta-Assessment of Metformin Absorption and Disposition Pharmacokinetics in Nine Species

The objective of this study was to systematically assess literature datasets and quantitatively analyze metformin PK in plasma and some tissues of nine species. The pharmacokinetic (PK) parameters and profiles of metformin in nine species were collected from the literature. Based on a simple allometric scaling, the systemic clearances (CL) of metformin in these species highly correlate with body weight (BW) (R2 = 0.85) and are comparable to renal plasma flow in most species except for rabbit and cat. Reported volumes of distribution (VSS) varied appreciably (0.32 to 10.1 L/kg) among species. Using the physiological and anatomical variables for each species, a minimal physiologically based pharmacokinetic (mPBPK) model consisting of blood and two tissue compartments (Tissues 1 and 2) was used for modeling metformin PK in the nine species. Permeability-limited distribution (low fd1 and fd2) and a single tissue-to-plasma partition coefficient (Kp) value for Tissues 1 and 2 were applied in the joint mPBPK fitting. Nonlinear regression analysis for common tissue distribution parameters along with species-specific CL values reasonably captured the plasma PK profiles of metformin across most species, except for rat and horse with later time deviations. In separate fittings of the mPBPK model to each species, Tissue 2 was considered as slowly-equilibrating compartment consisting of muscle and skin based on in silico calculations of the mean transit times through tissues. The well-fitted mPBPK model parameters for absorption and disposition PK of metformin for each species were compared with in vitro/in vivo results found in the literature with regard to the physiological details and physicochemical properties of metformin. Bioavailability and absorption rates decreased with the increased BW among the species. Tissues such as muscle dominate metformin distribution with low permeability and partitioning while actual tissue concentrations found in rats and mice show likely transporter-mediated uptake in liver, kidney, and gastrointestinal tissues. Metformin has diverse pharmacologic actions, and this assessment revealed allometric relationships in its absorption and renal clearance but considerable variability in actual and modeled tissue distribution probably caused by transporter differences.

Pharmacokinetics, Safety and Tolerability of JNJ-56136379, a Novel Hepatitis B Virus Capsid Assembly Modulator, in Healthy Subjects

INTRODUCTION

Hepatitis B viral capsid assembly is an attractive target for new antiviral treatments. JNJ-56136379 (JNJ-6379) is a potent capsid assembly modulator in vitro with a dual mode of action. In Part 1 of this first-in-human study in healthy adults, the pharmacokinetics (PK), safety and tolerability of JNJ-6379 were evaluated following single ascending and multiple oral doses.

METHODS

This was a double-blind, randomized, placebo-controlled study in 30 healthy adults. Eighteen subjects were randomized to receive single doses of JNJ-6379 (25 to 600 mg) or placebo. Twelve subjects were randomized to receive 150 mg JNJ-6379 or placebo twice daily for 2 days, followed by 100 mg JNJ-6379 or placebo daily for 10 days.

RESULTS

The maximum observed plasma concentration and the area under the curve increased dose proportionally from 25 to 300 mg JNJ-6379. Following multiple dosing, steady-state conditions were achieved on day 8. Steady-state clearance was similar following single and multiple dosing, suggesting time-linear PK. All adverse events (AEs) reported were mild to moderate in severity. There were no serious AEs or dose-limiting toxicities and no apparent relationship to dose for any AE.

CONCLUSION

JNJ-6379 was well tolerated in this study. Based on the safety profile and plasma exposures of JNJ-6379 in healthy subjects, a dosing regimen was selected for Part 2 of this study in patients with chronic hepatitis B. This is anticipated to achieve trough plasma exposures of JNJ-6379 at steady state of more than three times the 90% effective concentration of viral replication determined in vitro.

TRIAL REGISTRATION

Clinicaltrials.gov identifier, NCT02662712.

FUNDING

Janssen Pharmaceutica.

Time Varying Apparent Volume of Distribution and Drug Half-Lives Following Intravenous Bolus Injections

We present a model that generalizes the apparent volume of distribution and half-life as functions of time following intravenous bolus injection. This generalized model defines a time varying apparent volume of drug distribution. The half-lives of drug remaining in the body vary in time and become longer as time elapses, eventually converging to the terminal half-life. Two example fit models were substituted into the general model: biexponential models from the least relative concentration error, and gamma variate models using adaptive regularization for least relative error of clearance. Using adult population parameters from 41 studies of the renal glomerular filtration marker ¹⁶⁹Yb-DTPA, simulations of extracellular fluid volumes of 5, 10, 15 and 20 litres and plasma clearances of 40 and 100 ml/min were obtained. Of these models, the adaptively obtained gamma variate models had longer times to 95% of terminal volume and longer half-lives.

On the accuracy of a one-compartment approach for determination of drug terminal half-life

The drug terminal half-life (t(1/2)) is commonly predicted by a simplified one-compartment approach (t(1/2) = ln 2V(ss)/CL), where V(ss) and CL are the steady-state volume of distribution and the total body clearance of drug, respectively. The analysis of the accuracy of this approach is provided. It turns out that most often a simplified one-compartment calculation underestimates t(1/2) by no more than 25% for human, 26% for dog, 20% for monkey, 19% for rat, and 23% for mouse. Thus, the application of a one-compartment calculation of t(1/2) is well justifiable, except for the rare cases of very high drug clearance (CL/(rQ) ≳ 0.5), where r is the equilibrium blood-plasma concentration ratio, and Q is the cardiac output.

The Øie-Tozer model of drug distribution and its suitability for drugs with different pharmacokinetic behavior

INTRODUCTION

Drug distribution is a major pharmacokinetic process that affects the time course of drug concentrations in tissues, biological fluids and the resulting pharmacological activities. Drug distribution may follow different pathways and patterns, and is governed by the drug's physicochemical properties and the body's physiology. The classical Øie-Tozer model is frequently used for predicting volume of drug distribution and for pharmacokinetic calculations.

AREAS COVERED

In this review, the suitability of the Øie-Tozer model for drugs that exhibit different distribution patterns is critically analyzed and illustrated. The method used is a pharmacokinetic modeling and simulation approach. It is demonstrated that the major limitation of the Øie-Tozer model stems from its focus on the total drug concentrations and not on the active (unbound) concentrations. Moreover, the Øie-Tozer model may be inappropriate for drugs with nonlinear or complex pharmacokinetic behavior, such as biopharmaceuticals, drug conjugates or for drugs incorporated into drug delivery systems. Distribution mechanisms and alternative distribution models for these drugs are discussed.

EXPERT OPINION

The Øie-Tozer model can serve for predicting unbound volume of drug distribution for 'classical' small molecular mass drugs with linear pharmacokinetics. However, more detailed mechanism-based distribution models should be used in preclinical and clinical settings for drugs that exhibit more complex pharmacokinetic behavior.

Parameters for pyrethroid insecticide QSAR and PBPK/PD models for human risk assessment

In this review we have examined the status of parameters required by pyrethroid QSAR-PBPK/PD models for assessing health risks. In lieu of the chemical,biological, biochemical, and toxicological information developed on the pyrethroids since 1968, the finding of suitable parameters for QSAR and PBPK/PD model development was a monumental task. The most useful information obtained came from rat toxicokinetic studies (i.e., absorption, distribution, and excretion), metabolism studies with 14C-cyclopropane- and alcohol-labeled pyrethroids, the use of known chiral isomers in the metabolism studies and their relation to commercial products. In this review we identify the individual chiralisomers that have been used in published studies and the chiral HPLC columns available for separating them. Chiral HPLC columns are necessary for isomer identification and for developing kinetic values (Vm,, and Kin) for pyrethroid hydroxylation. Early investigators synthesized analytical standards for key pyrethroid metabolites, and these were used to confirm the identity of urinary etabolites, by using TLC. These analytical standards no longer exist, and muste resynthesized if further studies on the kinetics of the metabolism of pyrethroids are to be undertaken.In an attempt to circumvent the availability of analytical standards, several CYP450 studies were carried out using the substrate depletion method. This approach does not provide information on the products formed downstream, and may be of limited use in developing human environmental exposure PBPK/PD models that require extensive urinary metabolite data. Hydrolytic standards (i.e., alcohols and acids) were available to investigators who studied the carboxylesterase-catalyzed hydrolysis of several pyrethroid insecticides. The data generated in these studies are suitable for use in developing human exposure PBPK/PD models.Tissue:blood partition coefficients were developed for the parent pyrethroids and their metabolites, by using a published mechanistic model introduced by Poulin and Thiele (2002a; b) and log DpH 7.4 values. The estimated coefficients, especially those of adipose tissue, were too high and had to be corrected by using a procedure in which the proportion of parent or metabolite residues that are unbound to plasma albumin is considered, as described in the GastroPlus model (Simulations Plus, Inc.,Lancaster, CA). The literature suggested that Km values be adjusted by multiplying Km by the substrate (decimal amount) that is unbound to microsomal or CYPprotein. Mirfazaelian et al. (2006) used flow- and diffusion-limited compartments in their deltamethrin model. The addition of permeability areas (PA) having diffusion limits, such as the fat and slowly perfused compartments, enabled the investigators to bring model predictions in line with in vivo data.There appears to be large differences in the manner and rate of absorption of the pyrethroids from the gastrointestinal tract, implying that GI advanced compartmental transit models (ACAT) need to be included in PBPK models. This is especially true of the absorption of an oral dose of tefluthrin in male rats, in which 3.0-6.9%,41.3-46.3%, and 5.2-15.5% of the dose is eliminated in urine, feces, and bile,respectively (0-48 h after administration). Several percutaneous studies with the pyrethroids strongly support the belief that these insecticides are not readily absorbed, but remain on the surface of the skin until they are washed off. In one articular study (Sidon et al. 1988) the high levels of permethrin absorption through the forehead skin (24-28%) of the monkey was reported over a 7- to 14-days period.Wester et al. (1994) reported an absorption of 1.9% of pyrethrin that had been applied to the forearm of human volunteers over a 7-days period.SAR models capable of predicting the binding of the pyrethroids to plasma and hepatic proteins were developed by Yamazaki and Kanaoka (2004), Saiakhov et al. (2000), Colmenarejo et al. (2001), and Colmenarejo (2003). QikProp(Schrodinger, LLC) was used to obtain Fu values for calculating partition coefficients and for calculating permeation constants (Caco-2, MDCK, and logBBB). ADMET Predictor (Simulations Plus Inc.) provided Vm~,x and Km values for the hydroxylation of drugs/pyrethroids by human liver recombinant cytochrome P450 enzymes making the values available for possible use in PBPK/PD models.The Caco-2 permeability constants and CYP3A4 Vmax and Km values are needed in PBPK/PD models with GI ACAT sub models. Modeling work by Chang et al.(2009) produced rate constants (kcat) for the hydrolysis of pyrethroids by rat serumcarboxylesterases. The skin permeation model of Potts and Guy (1992) was used topredict K, values for the dermal absorption of the 15 pyrethroids.The electrophysiological studies by Narahashi (1971) and others (Breckenridgeet al. 2009; Shafer et al. 2005; Soderlund et al. 2002; Wolansky and Harrill 2008)demonstrated that the mode of action of pyrethroids on nerves is to interfere with the changes in sodium and potassium ion currents. The pyrethroids, being highly lipid soluble, are bound or distributed in lipid bilayers of the nerve cell membrane and exert their action on sodium channel proteins. The rising phase of the action potential is caused by sodium influx (sodium activation), while the falling phase is caused by sodium activation being turned off, and an increase in potassium efflux(potassium activation). The action of allethrin and other pyrethroids is caused by an inhibition or block of the normal currents. An equation by Tatebayashi and Narahashi (1994) that describes the action of pyrethroids on sodium channels was found in the literature. This equation, or some variation of it, may be suitable for use in the PD portion of pyrethroid PBPK models.

Liquid chromatography-tandem mass spectroscopic method for the determination of zerumbone in human plasma and its application to pharmacokinetics

A rapid, sensitive, specific and selective LC-MS/MS method for the determination of zerumbone (ZER) in human plasma using 2,4-diamino-6-(4-methoxyphenyl)-1,3,5-triazine (DMTZ) as an internal standard (IS) has been developed and validated. ZER was chromatographed on C8 column using a mobile phase of acetonitrile/water (80:20, v/v) at a flow rate of 0.25 ml min(-1) . Quantitation was achieved using ESI+ interface, employing multiple reaction monitoring (MRM) mode at m/z 219 > 81 and 218 > 134 for ZER and IS, respectively. The calibration standards were linear over a range of 5-3000 ng ml(-1) (r(2)=0.9994) with an LLOQ of 5 ng ml(-1) (RSD %; 11.4% and bias%; 9.5%). Intra- and inter-day precision of ZER assay ranged from 0.18 to 3.56% with accuracy (bias) that varied between -5.09 and 4.3%, demonstrating good precision and accuracy. Recoveries of ZER and the IS from human plasma were above 85%. The developed method was validated for the determination of ZER in rat plasma. Linearity, stability of ZER and the ME on rat plasma were discussed. The applicability of the developed method was demonstrated by measuring ZER in rat plasma samples following intravenous and intraperitoneal administration of ZER prepared in hydroxypropyl-β-cyclodextrin (HPβCD) and sodium carboxymethyl cellulose (CMC), respectively, in 20 mg kg(-1) and this study indicated a clear significant difference (p<0.05) in pharmacokinetic parameters of ZER in ZER/HPβCD complex compared with ZER in CMC preparation.

On the accuracy of estimation of basic pharmacokinetic parameters by the traditional noncompartmental equations and the prediction of the steady-state volume of distribution in obese patients based upon data derived from normal subjects

The steady-state and terminal volumes of distribution, as well as the mean residence time of drug in the body (V(ss), V(β), and MRT) are the common pharmacokinetic parameters calculated using the drug plasma concentration-time profile C(p) (t) following intravenous (i.v. bolus or constant rate infusion) drug administration. These calculations are valid for the linear pharmacokinetic system with central elimination (i.e., elimination rate being proportional to drug concentration in plasma). Formally, the assumption of central elimination is not normally met because the rate of drug elimination is proportional to the unbound drug concentration at elimination site, although equilibration between systemic circulation and the site of clearance for majority of small molecule drugs is fast. Thus, the assumption of central elimination is practically quite adequate. It appears reasonable to estimate the extent of possible errors in determination of these pharmacokinetic parameters due to the absence of central elimination. The comparison of V(ss), V(β), and MRT calculated by exact equations and the commonly used ones was made considering a simplified physiologically based pharmacokinetic model. It was found that if the drug plasma concentration profile is detected accurately, determination of drug distribution volumes and MRT using the traditional noncompartmental calculations of these parameters from C(p) (t) yields the values very close to that obtained from exact equations. Though in practice, the accurate measurement of C(p) (t), especially its terminal phase, may not always be possible. This is particularly applicable for obtaining the distribution volumes of lipophilic compounds in obese subjects, when the possibility of late terminal phase at low drug concentration is quite likely, specifically for compounds with high clearance. An accurate determination of V(ss) is much needed in clinical practice because it is critical for the proper selection of drug treatment regimen. For that reason, we developed a convenient method for calculation of V(ss) in obese (or underweight) subjects. It is based on using the V(ss) values obtained from pharmacokinetic studies in normal subjects and the physicochemical properties of drug molecule. A simple criterion that determines either the increase or decrease of V(ss) (per unit body weight) due to obesity is obtained. The accurate determination of adipose tissue-plasma partition coefficient is crucial for the practical application of suggested method.

Prediction of the Possibility of the Second Peak of Drug Plasma Concentration Time Curve after iv Bolus Administration from the Standpoint of the Traditional Multi-Compartmental Linear Pharmacokinetics

It is shown that the existence of the second peak on the drug plasma concentration time curve C(p)(t) after iv bolus dosing can be explained by considering the traditional multi-compartmental linear pharmacokinetics. It was found that a direct solution of the general three-compartment model yields the second peak of C(p)(t) for the certain values of the rate constants, and C(p)(t) includes the term with oscillating preexponent, that is, K sin(omegat + phi) exp(-lambdat), in this case. The considered model describes the drug entero-hepatic recirculation in the species which do not have gall bladder (rats). The model fit of the experimental data from rat pharmacokinetic studies where the second peak of C(p)(t) was observed, yields the rate of bile production that is consistent with the physiological value ( approximately 0.7 mL/h).

On the determination of the time delay in reaching the steady state drug concentration in the organ compared to plasma

A problem of substantial delay in reaching the steady state drug concentration in particular organ (compartment) compared to the time of reaching the steady state plasma concentration is considered. It is shown that the ratio of the terminal (V(beta)) and the steady state (V(ss)) volumes of distribution, V(beta)/V(ss), appears to be an indication of possible lag in reaching the steady state in the organ tissue compared to plasma. The estimations of the time of reaching the steady state drug concentration in the organ are suggested. The in vivo based pharmacokinetic model, which uses the experimentally measured drug plasma concentration time course and the appropriate equation for the kinetics of drug distribution into the tissues, is suggested. It is intended to determine the kinetic mechanism of drug distribution into the tissues. The model was applied to interpret the kinetics of drug distribution into the brain. The importance of precise measurement of drug plasma concentration at terminal phase for obtaining accurate values of V(beta) and V(ss) is emphasized: this allows predicting a possible slow plasma-tissue drug transfer and substantial difference in time of reaching the steady state by the body and plasma.