Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. I. Log-convex drug disposition curves

Introducing the phenomenoiogical concept of a time-varying fractional rate of elimination k_D(t)and applying the theory of lifetime distributions, implications of the log-convexity of drug disposition curves are examined and some important applications are described. Linear pharmacokinetic systems exhibiting a log-convex impulse response and satisfying the basic conditions underlying the noncompartmental approach have the following properties: (1) The time-varying volume of distribution V(t)increases, and consequently the fractional rate of elimination k_D(t)=CL/V(t)decreases monotonically. (2) The concentration-time curve and the time course of total amount of drug in the body, respectively, have an exponential tail [where V(t)approaches the equilibrium value V_Z].The relative dispersion of residence times (CV _D ² =VDRT/MDRT²)and the ratio V_ss/V_Z (V _ss is the volume of distribution at steady state) act as measures of departure from pure monoexponential decay (one-compartment behaviour). The role of the latter parameters as shape parameters of the curve that characterize the distributional properties of drugs is discussed. Upper and lower bounds of the time course of drug amount in the body are derived using the parameters MDRTand CV _D ² or _z (terminal exponential coefficient), respectively. This approach is also employed to construct upper bounds on the fractional error in AUCdetermination by numerical integration that is due to curve truncation. The significance of the fractional elimination rate concept as a unifying approach in interspecies pharmacokinetic scaling is pointed out. Some applications of the results are demonstrated, using digoxin data from the literature.     

Dynamics of drug distribution. I. Role of the second and third curve moments

Conventionally, the dynamics of distribution in the body is evaluated by the so-called distribution half-life (e.g., t _1/2, but then the mean time of the distribution process is underestimated due tothe influence of elimination. By contrast, information about the dynamics of distribution contained in drug disposition curves can be extracted by the second and third curve moments, parameters that are related to the variance (VDRT)and skewness (SDRT)of residence time distributions; whereas the equilibrium state characterized by the volume of distribution (V_ss), isdetermined by the mean residence time (MDRT)or the first curve moment. The approach represents a general noncompartmental analysis that is independent of a detailed structural model or a particular disposition function. Two parameters are introduced to characterize the dynamics of drug distribution: (i)the degree of departure of the system from well-mixed behavior of instantaneous distribution equilibrium (related to VDRT)and (ii)the mean time until equilibration is achieved (mean equilibration time, MEQT),which additionally depends on SDRT.Both parameters are quantitative measures of the dynamics of distribution and display explicit physical significance in terms of distribution within the corresponding noneliminating system. It is further shown that the so-called distribution phase in biexponential disposition curves is related to a monoexponential mixing curve of its corresponding noneliminating system with an equilibration or mixing half-time, t _1/2,M =t _1/2, (V/V _ss ^* ), where V _ss ^* denotes the distribution volume of the noneliminating system. The results are applied to mixing and disposition curves measured for acetaminophen in liver-ligated and intact rats, respectively.This work was supported by the Medical Research Council of Canada. M. Weiss was a Visiting Rosenstadt Professor at the University of Toronto. K. S. Pang is a recipient of the Faculty Development Award, Medical Research Council of Canada.     

Determination of mean input time,mean residence time,and steady-state volume of distribution with multiple drug inputs

A general treatment for determination of mean residence time (MRTV)and steady-state volume of distribution (V _ss )after multiple drug inputs via any mode of administration is presented. For multiple inputs, either simultaneous or consecutive, the mean input time (MIT)can be readily calculated using the general equations presented here. Sample calculations for (MIT, MRT),and V _ss following different combinations of multiple drug inputs are presented. Errors inherent in noncompartmental area determinations are discussed.This work was supported in part by NIH grants GM26691 and HL32243.     

A new method for assessment of drug disposition in muscle: Application of statistical moment theory to local perfusion systems

A new experimental system is used to determine exact information concerning local drug disposition. Rabbit hind leg is perfused in situusing a single-pass technique, and outflow curves of drugs are analyzed using statistical moment theory. By the introduction of Chromatographic concepts and the application of the well-stirred model to the local perfusion system, physiologically and/or physicochemically meaningful parameters are derived from the first three moments. Moreover, in the assessment, drug disposition is divided into elimination and distribution. The elimination process is also evaluated with respect to rate and extent. This system is used to elucidate the disposition characteristics of mitomycin C and its lipophilic derivative nonyloxycarbonyl mitomycin C.     

Moment analysis of drug disposition in kidney. V:In Vivo transepithelial transport ofp-aminohippurate in rat kidney

A new method that can assess the kinetics of in vivotransepithelial transport in rat kidney has been established. The method is based upon a multiple-indicator dilution experiment and the moment analysis theory. After simultaneous bolus injections of p-aminohippurate (PAH) and inulin into the right renal artery, blood samples were taken from the carotid artery and urine was separately collected from right and left ureters. The characteristic response for the first passage of drugs through the right kidney was evaluated by taking blood circulation into consideration. To determine the mean artery-tovein transit time and the extraction ratio in the kidney, an intravenous injection was also performed as a reference experiment for deconvolution. The urinary excretion curve corresponding to the first passage was obtained as the difference between both kidneys. The mean artery-tolumen transit time (mean transepithelial transit time, ¯T _cell )was computed by subtracting the mean urinary transit time of inulin from that of secreted PAH. Sinc transport across the luminal membrane into the lumen from tubular epithelial cells can influence the cellular residence time of drugs, ¯ T_cell and the single-pass mean residence time in epithelial cells (¯T _cell.sp )can be thought of describing luminal membrane transport. The value of ¯T _{cell obtained for 0. t mM PAH was 22 sec and it was prolonged to 61 sec in the presence of probenecid, suggesting an inhibitory effect on transport across the luminal membrane. On the other hand, antiluminal membrane transport into cells from blood is characterized by the volume of distribution in the kidney} (Vd _PAH ). Vd _{PAH was remarkably decreased by treatment with probenecid, indicating an inhibitory effect on antiluminal membrane transport. The effects of probenecid on both sides of epithelial cell membrane transport were first demonstrated} in vivo.The present method is useful for the analysis of in vivotransepithelial transport including antiluminal and luminal membrane transport for drugs excreted via tubular secretion.     

The determination of mean residence time using statistical moments: Is it correct?

The estimation of mean residence time using statistical moment theory is shown to lead to the true mean residence time only in the case of a concentration-time curve which is a single exponential. In other cases, including the commonly encountered double exponential, there is a systematic error present which can lead to the result being incorrect by as much as a factor of 2. For the case of instantaneous input, an alternative estimation procedure is suggested which gives an estimate much closer to the true mean residence time.     

A theoretical consideration of percutaneous drug absorption

The percutaneous drug absorption process and its clinical significance are not fully known. In this article we propose a theoretical method to obtain two parameters (k _d and k_c) of percutaneous drug absorption from in vivodata. These parameters are related to diffusion of a drug through the skin and removal process at the skin-capillary boundary, respectively, characterizing several pharmacokinetic aspects of the drug applied to the skin. Moreover, by employing these two kinetic constants, a simulation of percutaneous drug absorption can be theoretically generated. On the basis of our theoretical considerations on the percutaneous drug absorption process described herein, we conclude that the percutaneous drug absorption process is better understood by employing two kinetic constants in a mathematical model and that its clinical application would be highly possible.     

Effect of plasma protein binding on drug disposition in muscle tissue: Application of statistical moment analysis and network theory toin situ local single-pass perfusion system

The local disposition characteristics of mitomycin C (MMC) and five lipophilic prodrugs in rabbit hind leg muscle were examined using an in situ single-pass perfusion experiment. Test compounds inputted into a perfusion line as a rectangular function (unit pulse) were perfused with or without albumin and their outflow patterns were analyzed by statistical moment analysis. In interpretation of statistical moment parameters, the well-stirred model was applied to the local perfusion system based on the plate theory of a chromatographic system and some general pharmacokinetic parameters (the disposition parameters) were derived from the moments. A new theory which elucidates the relationships among the moments for plasma protein binding, unbound (free), and total drug fraction was established based on network theory. Using this system, the following conclusions were made for mitomycin C and its five lipophilic derivatives: (i) In the absence of albumin, an increase in lipophilicity led to an increase in organ clearance and distribution volume; (ii) drug bound to albumin did not transfer to the extravascular space; (iii) in the presence of albumin, an increase in lipophilicity results in a decrease in clearance.     

On the accuracy of calculation of the mean residence time of drug in the body and its volumes of distribution based on the assumption of central elimination

1.?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 (Cp(t)) following intravenous (iv bolus or constant rate infusion) drug administration.

2.?These traditional calculations are valid for the linear pharmacokinetic system with central elimination (i.e. elimination rate being proportional to drug concentration in plasma). The assumption of central elimination is not valid in general, so that the accuracy of the traditional calculation of these parameters is uncertain.

3.?The comparison of V_ss, V_β, and MRT calculated by the derived exact equations and by the commonly used ones was made considering a physiological model. It turned out that the difference between the exact and simplified calculations does not exceed 2%.

4.?Thus the calculations of V_ss, V_β, and MRT, which are based on the assumption of central elimination, may be considered as quite accurate. Consequently it can be used as the standard for comparisons with kinetic and in silico models.     

Effect of sinapic acid on aripiprazole pharmacokinetics in rats: Possible food drug interaction

Dietary supplements and foods can interact with various drugs, leading to possible clinical concerns. This study aimed to investigate the effect of orally administered sinapic acid (SA) on the pharmacokinetics of aripiprazole (APZ) in rats and its possible modulatory effects on hepatic cytochrome P450 (CYP3A2 and CYP2D6) expression in the liver tissues. Single dose and multiple dose parallel groups of wistar rats were categorized into six groups (n = 6 each) which abstained from food for 12 h prior to the experiment, while water was allowed ad libitum. The investigation was carried out for single dose: Group I was treated with normal saline orally for 15 days (normal control). Group II was administered normal saline orally for 15 days and received APZ (3 mg/kg p.o.) on day 15. Group III received SA (20 mg/kg p.o.) for 15 days and received APZ (3 mg/kg p.o.) on day 15. Group IV was treated with SA (20 mg/kg p.o.) for 15 days. For the multiple dose study, Group I was treated with normal saline orally for 15 days (normal control); Group II received APZ (3 mg/kg p.o.) daily for 15 days; Group III was administered with SA (20 mg/kg p.o.) and APZ (3 mg/kg p.o.) for 15 days and Group IV received SA (20 mg/kg p.o.) for 15 days. The group I and IV were kept common in single and multiple dose groups. After last APZ dose, plasma samples were collected and APZ concentrations were determined using an UPLC-MS/MS technique. The pharmacokinetic parameters were calculated using a non-compartmental analysis. The concomitant administration of APZ with SA (as single or multiple dose) resulted in an increase in APZ absorption and a decrease on its systemic clearance. This was associated with a reduction in CYP3A2 and CYP2D6 protein expressions by 33–43% and -71–68% after the single and multiple co-administration, which are two enzymes responsible of the metabolism of APZ. Therefore, a reduction in the metabolic clearance appears to be the mechanism underlying the drug interaction of dietary supplement containing SA with APZ. Therefore, the concomitant administration of SA and APZ should be carefully viewed. Further investigations are required to assess the clinical significance of such observations in humans.     

Blends of hydrophobic and swelling agents in the swelling layer in the preparation of delayed-release pellets of a hydrophilic drug with low MW: Physicochemical characterizations and in-vivo evaluations

In this study, a hydrophobic material, ethylcellulose, which was used as its aqueous suspension Surelease^®, was combined with a swelling agent as the swelling layer to prepare delayed-release pellets for Danshensu, which is a hydrophilic drug with low MW. A rupturable, delayed-release pellet consists of a drug core, a swelling layer containing a swelling agent (cross-linked sodium carboxymethyl cellulose) with a hydrophobic agent (Surelease^®), and a controlled layer composed by an insoluble, water-permeable polymeric coating (aqueous ethylcellulose dispersions) was developed in a fluidised bed. Results showed that blending Surelease^® into the swelling layer could effectively extend the release of Danshensu from the pellets, which may be attributed to the slowed swelling rate by reduction of water penetration and improvement of mechanical integrity of the swelling layer. Drug in the delayed pellets showed sustained release in beagle dogs after oral administration with comparable in-vivo exposure to the uncoated drug pellets. In conclusion, blends of hydrophobic and swelling agents in the swelling layer in double-membrane pellets could achieve a delayed drug-release profile in vitro, as well as delayed and sustained absorption in vivo for highly soluble, low-MW drug. The present study highlighted the potential use of a delayed-release system for other hydrophilic, low-MW drugs to meet the formulation requirements for chronopharmacological diseases.     

Evaluation of the impact of the exposure route on the human kinetic adjustment factor

The objective of this study was to assess the impact of the exposure route on the human kinetic adjustment factor (HKAF), for which a default value of 3.16 is used in non-cancer risk assessment. A multi-route PBPK model was modified from the literature and used for computing the internal dose metrics in adults, neonates, children, elderly and pregnant women following three route-specific scenarios to chloroform, bromoform, tri- or per-chloroethylene (TCE or PERC). These include 24-h inhalation exposure, body-weight adjusted oral exposure and 30 min dermal exposure to contaminated drinking water. Distributions for body weight (BW), height (BH) and hepatic cytochrome P450 2E1 (CYP2E1) content were obtained from the literature, whereas model parameters (flows, volumes) were calculated from BW and BH. Monte Carlo simulations were performed and the HKAF was calculated as the ratio of the 95th percentile value of internal dose metrics in subpopulation to the 50th percentile value in adults. On the basis of the area under the parent compound's arterial blood concentration vs time curve (AUC(pc)), highest HKAFs were obtained in neonates for every scenario considered, and were the highest for bromoform (range: 3.6-7.4). Exceedance of the default value based on AUC(PC) was also observed for an oral exposure to chloroform in neonates (4.9). In all other cases, HKAFs remained below the default value. Overall, this study has pointed out the dependency of the HKAF on the exposure route, dose metrics and subpopulation considered, as well as characteristics of the chemicals investigated.     

Characterization of organic anion transporting polypeptide 1b2 knockout rats generated by CRISPR/Cas9: a novel model for drug transport and hyperbilirubinemia disease

Organic anion transporting polypeptide 1B1 and 1B3 (OATP1B1/3) as important uptake transporters play a fundamental role in the transportation of exogenous drugs and endogenous substances into cells. Rat OATP1B2, encoded by the Slco1b2 gene, is homologous to human OATP1B1/3. Although OATP1B1/3 is very important, few animal models can be used to study its properties. In this report, we successfully constructed the Slco1b2 knockout (KO) rat model via using the CRISPR/Cas9 technology for the first time. The novel rat model showed the absence of OATP1B2 protein expression, with no off-target effects as well as compensatory regulation of other transporters. Further pharmacokinetic study of pitavastatin, a typical substrate of OATP1B2, confirmed the OATP1B2 function was absent. Since bilirubin and bile acids are the substrates of OATP1B2, the contents of total bilirubin, direct bilirubin, indirect bilirubin, and total bile acids in serum are significantly higher in Slco1b2 KO rats than the data of wild-type rats. These results are consistent with the symptoms caused by the absence of OATP1B1/3 in Rotor syndrome. Therefore, this rat model is not only a powerful tool for the study of OATP1B2-mediated drug transportation, but also a good disease model to study hyperbilirubinemia-related diseases.