A valid equation for the well-stirred perfusion limited physiologically based pharmacokinetic model that consistently accounts for the blood-tissue drug distribution in the organ and the corresponding valid equation for the steady state volume of distribution

A Complete Extension of Classical Hepatic Clearance Models Using Fractional Distribution Parameter fd in Physiologically Based Pharmacokinetics

The classical organ clearance models have been proposed to relate the plasma clearance CLp to probable mechanism(s) of hepatic clearance. However, the classical models assume the intrinsic capability of drug elimination (CLu,int) that is physically segregated from the vascular blood but directly acts upon the unbound drug concentration in the blood (fubCavg), and do not handle the transit-time delay between the inlet/outlet concentrations in their closed-form clearance equations. Therefore, we propose unified model structures that can address the internal blood concentration patterns of clearance organs in a more mechanistic/physiological manner, based on the fractional distribution parameter fd operative in PBPK. The basic partial/ordinary differential equations for four classical models are revisited/modified to yield a more complete set of extended clearance models, i.e., the Rattle, Sieve, Tube, and Jar models, which are the counterparts of the dispersion, series-compartment, parallel-tube, and well-stirred models. We demonstrate the feasibility of applying the resulting extended models to isolated perfused rat liver data for 11 compounds and an example dataset for in vitro-in vivo extrapolation of the intrinsic to the systemic clearances. Based on their feasibilities to handle such real data, these models may serve as an improved basis for applying clearance models in the future.

The Interplay of Permeability, Metabolism, Transporters, and Dosing in Determining the Dynamics of the Tissue/Plasma Partition Coefficient and Volume of Distribution-A Theoretical Investigation Using Permeability-Limited, Physiologically Based Pharmacokinetic Modeling

A permeability-limited physiologically based pharmacokinetic (PBPK) model featuring four subcompartments (corresponding to the intracellular and extracellular water of the tissue, the residual plasma, and blood cells) for each tissue has been developed in MATLAB/SimBiology and applied to various what-if scenario simulations. This model allowed us to explore the complex interplay of passive permeability, metabolism in tissue or residual blood, active uptake or efflux transporters, and different dosing routes (intravenous (IV) or oral (PO)) in determining the dynamics of the tissue/plasma partition coefficient (Kp) and volume of distribution (Vd) within a realistic pseudo-steady state. Based on the modeling exercise, the permeability, metabolism, and transporters demonstrated significant effects on the dynamics of the Kp and Vd for IV bolus administration and PO fast absorption, but these effects were not as pronounced for IV infusion or PO slow absorption. Especially for low-permeability compounds, uptake transporters were found to increase both the Kp and Vd at the pseudo-steady state (Vdss), while efflux transporters had the opposite effect of decreasing the Kp and Vdss. For IV bolus administration and PO fast absorption, increasing tissue metabolism was predicted to elevate the Kp and Vdss, which contrasted with the traditional derivation from the steady-state perfusion-limited PBPK model. Moreover, metabolism in the residual blood had more impact on the Kp and Vdss compared to metabolism in tissue. Due to its ability to offer a more realistic description of tissue dynamics, the permeability-limited PBPK model is expected to gain broader acceptance in describing clinical PK and observed Kp and Vdss, even for certain small molecules like cyclosporine, which are currently treated as perfusion-limited in commercial PBPK platforms.

Predictive Performance of Physiologically Based Pharmacokinetic Modelling of Beta-Lactam Antibiotic Concentrations in Adipose, Bone, and Muscle Tissues

Physiologically based pharmacokinetic (PBPK) models consist of compartments representing different tissues. As most models are only verified based on plasma concentrations, it is unclear how reliable associated tissue profiles are. This study aimed to assess the accuracy of PBPK-predicted beta-lactam antibiotic concentrations in different tissues and assess the impact of using effect site concentrations for evaluation of target attainment. Adipose, bone, and muscle concentrations of five beta-lactams (piperacillin, cefazolin, cefuroxime, ceftazidime, and meropenem) in healthy adults were collected from literature and compared with PBPK predictions. Model performance was evaluated with average fold errors (AFEs) and absolute AFEs (AAFEs) between predicted and observed concentrations. In total, 26 studies were included, 14 of which reported total tissue concentrations and 12 unbound interstitial fluid (uISF) concentrations. Concurrent plasma concentrations, used as baseline verification of the models, were fairly accurate (AFE: 1.14, AAFE: 1.50). Predicted total tissue concentrations were less accurate (AFE: 0.68, AAFE: 1.89). A slight trend for underprediction was observed but none of the studies had AFE or AAFE values outside threefold. Similarly, predictions of microdialysis-derived uISF concentrations were less accurate than plasma concentration predictions (AFE: 1.52, AAFE: 2.32). uISF concentrations tended to be overpredicted and two studies had AFEs and AAFEs outside threefold. Pharmacodynamic simulations in our case showed only a limited impact of using uISF concentrations instead of unbound plasma concentrations on target attainment rates. The results of this study illustrate the limitations of current PBPK models to predict tissue concentrations and the associated need for more accurate models. SIGNIFICANCE STATEMENT: Clinical inaccessibility of local effect site concentrations precipitates a need for predictive methods for the estimation of tissue concentrations. This is the first study in which the accuracy of PBPK-predicted tissue concentrations of beta-lactam antibiotics in humans were assessed. Predicted tissue concentrations were found to be less accurate than concurrent predicted plasma concentrations. When using PBPK models to predict tissue concentrations, this potential relative loss of accuracy should be acknowledged when clinical tissue concentrations are unavailable to verify predictions.

Application of Physiologically Based Pharmacokinetic Modeling to Predict Maternal Pharmacokinetics and Fetal Exposure to Oxcarbazepine

Pregnancy is associated with physiological changes that may affect drug pharmacokinetics (PKs). The aim of this study was to establish a maternal-fetal physiologically based pharmacokinetic (PBPK) model of oxcarbazepine (OXC) and its active metabolite, 10,11-dihydro-10-hydroxy-carbazepine (MHD), to (1) assess differences in pregnancy, (2) predict changes in PK target parameters of these molecules following the current dosing regimen, (3) assess predicted concentrations of these molecules in the umbilical vein at delivery, and (4) compare different methods for estimating drug placental penetration. Predictions using the pregnancy PBPK model of OXC resulted in maternal concentrations within a 2-fold error, and extrapolation of the model to early-stage pregnancies indicated that changes in median PK parameters remained above target thresholds, requiring increased frequency of monitoring. The dosing simulation results suggested dose adjustment in the last two trimesters. We generally recommend that women administer ≥ 1.5× their baseline dose of OXC during their second and third trimesters. Test methods for predicting placental transfer showed varying performance, with the in vitro method showing the highest predictive accuracy. Exposure to MHD in maternal and fetal venous blood was similar. Overall, the above-mentioned models can enhance understanding of the maternal-fetal PK behavior of drugs, ultimately informing drug-treatment decisions for pregnant women and their fetuses.

Prediction of Pharmacokinetics of IDP-73152 in Humans Using Physiologically-Based Pharmacokinetics

IDP-73152, a novel peptide deformylase inhibitor with an antibacterial effect against Gram-positive bacteria, is in phase I development. The objective of this study was to develop a physiologically-based pharmacokinetic model (PBPK) for IDP-73152 in animals, and to extend the model to humans. Biopharmaceutical properties of IDP-73152 are determined using in vitro/in vivo experimentations for the PBPK model. A transit model consisting of gastrointestinal segments is applied for an estimation of the intestinal absorption kinetics. The PBPK model of IDP-73152 in rats is able to appropriately predict the plasma concentration–time profiles after the administration of IDP-73152 at different doses and by different routes (combined absolute average fold error (cAAFE), 1.77). The model is also found to be adequate in predicting the plasma concentration–time profiles of IDP-73152 in mice (cAAFE 1.59) and dogs (cAAFE 1.42). Assuming the oral administration of IDP-73152 to humans at doses of 640 and 1280 mg, the model is able to reproduce the concentration–time profiles obtained in humans (cAAFE 1.38); therefore, these observations indicate that the PBPK model used for IDP-73152 is applicable to animal species and humans. This model may be useful in predicting efficacious doses of IDP-73152 for the management of infectious disease in humans.

Consideration of Fractional Distribution Parameter fd in the Chen and Gross Method for Tissue-to-Plasma Partition Coefficients: Comparison of Several Methods

PURPOSE

The tissue-to-plasma partition coefficient (K_p) describes the extent of tissue distribution in physiologically-based pharmacokinetic (PBPK) models. Constant-rate infusion studies are common for experimental determination of the steady-state K_p,ss, while the tissue-plasma concentration ratio (C_T/C_p) in the terminal phase after intravenous doses is often utilized. The Chen and Gross (C&G) method converts a terminal slope C_T/C_p to K_p,ss based on assumptions of perfusion-limited distribution in tissue-plasma equilibration. However, considering blood flow (Q_T) and apparent tissue permeability (f_upPS_in) in the rate of tissue distribution, this report extends the C&G method by utilizing a fractional distribution parameter (f_d).

METHODS

Relevant PBPK equations for non-eliminating and eliminating organs along with lung and liver were derived for the conversion of C_T/C_p values to K_p,ss. The relationships were demonstrated in rats with measured C_T/C_p and K_p,ss values and the model-dependent f_d for 8 compounds with a range of permeability coefficients. Several methods of assessing K_p were compared.

RESULTS

Utilizing f_d in an extended C&G method, our estimations of K_p,ss from C_T/C_p were improved, particularly for lower permeability compounds. However, four in silico methods for estimating K_p performed poorly across tissues in comparison with measured K_p values. Mathematical relationships between K_p and K_p,ss that are generally applicable for eliminating organs with tissue permeability limitations necessitates inclusion of an extraction ratio (ER) and f_d.

CONCLUSION

Since many different types/sources of K_p are present in the literature and used in PBPK models, these perspectives and equations should provide better insights in measuring and interpreting K_p values in PBPK.

Effects of 1α,25-Dihydroxyvitamin D3 on the Pharmacokinetics of Procainamide and Its Metabolite N-Acetylprocainamide, Organic Cation Transporter Substrates, in Rats with PBPK Modeling Approach

In this study, possible changes in the expression of rat organic cationic transporters (rOCTs) and rat multidrug and toxin extrusion proteins (rMATEs) following treatment with 1α,25-dihydroxyvitamin D₃ (1,25(OH)₂D₃) were investigated. Rats received intraperitoneal administrations of 1,25(OH)₂D₃ for four consecutive days, and the tissues of interest were collected. The mRNA expression of rOCT1 in the kidneys was significantly increased in 1,25(OH)₂D₃-treated rats compared with the control rats, while the mRNA expressions of rOCT2 and rMATE1 in the kidneys, rOCT1 and N-acetyltransferase-II (NAT-II) in the liver, and rOCT3 in the heart were significantly decreased. Changes in the protein expression of hepatic rOCT1 and renal rOCT2 and rMATE1 were confirmed by western blot analysis. We further evaluated the pharmacokinetics of procainamide (PA) hydrochloride and its major metabolite N-acetyl procainamide (NAPA) in the presence of 1,25(OH)₂D₃. When PA hydrochloride was administered intravenously at a dose 10 mg/kg to 1,25(OH)₂D₃-treated rats, a significant decrease in renal and/or non-renal clearance of PA and NAPA was observed. A physiological model for the pharmacokinetics of PA and NAPA in rats was useful for linking changes in the transcriptional and translational expressions of rOCTs and rMATE1 transporters to the altered pharmacokinetics of the drugs.

Development of Physiologically Based Pharmacokinetic Model for Orally Administered Fexuprazan in Humans

Fexuprazan is a new drug candidate in the potassium-competitive acid blocker (P-CAB) family. As proton pump inhibitors (PPIs), P-CABs inhibit gastric acid secretion and can be used to treat gastric acid-related disorders such as gastroesophageal reflux disease (GERD). Physiologically based pharmacokinetic (PBPK) models predict drug interactions as pharmacokinetic profiles in biological matrices can be mechanistically simulated. Here, we propose an optimized and validated PBPK model for fexuprazan by integrating in vitro, in vivo, and in silico data. The extent of fexuprazan tissue distribution in humans was predicted using tissue-to-plasma partition coefficients in rats and the allometric relationships of fexuprazan distribution volumes (V_SS) among preclinical species. Urinary fexuprazan excretion was minimal (0.29-2.02%), and this drug was eliminated primarily by the liver and metabolite formation. The fraction absorbed (Fa) of 0.761, estimated from the PBPK modeling, was consistent with the physicochemical properties of fexuprazan, including its in vitro solubility and permeability. The predicted oral bioavailability of fexuprazan (38.4-38.6%) was within the range of the preclinical datasets. The C_max, AUC_last, and time-concentration profiles predicted by the PBPK model established by the learning set were accurately predicted for the validation sets.

A hybrid modeling approach for assessing mechanistic models of small molecule partitioning in vivo using a machine learning-integrated modeling platform

Prediction of the first-in-human dosing regimens is a critical step in drug development and requires accurate quantitation of drug distribution. Traditional in vivo studies used to characterize clinical candidate’s volume of distribution are error-prone, time- and cost-intensive and lack reproducibility in clinical settings. The paper demonstrates how a computational platform integrating machine learning optimization with mechanistic modeling can be used to simulate compound plasma concentration profile and predict tissue-plasma partition coefficients with high accuracy by varying the lipophilicity descriptor logP. The approach applied to chemically diverse small molecules resulted in comparable geometric mean fold-errors of 1.50 and 1.63 in pharmacokinetic outputs for direct tissue:plasma partition and hybrid logP optimization, with the latter enabling prediction of tissue permeation that can be used to guide toxicity and efficacy dosing in human subjects. The optimization simulations required to achieve these results were parallelized on the AWS cloud and generated outputs in under 5 h. Accuracy, speed, and scalability of the framework indicate that it can be used to assess the relevance of other mechanistic relationships implicated in pharmacokinetic-pharmacodynamic phenomena with a lower risk of overfitting datasets and generate large database of physiologically-relevant drug disposition for further integration with machine learning models.

A latent variable approach to account for correlated inputs in global sensitivity analysis

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed.

Physiologically-Based Pharmacokinetic Modeling for Drug-Drug Interactions of Procainamide and N-Acetylprocainamide with Cimetidine, an Inhibitor of rOCT2 and rMATE1, in Rats

Previous observations demonstrated that cimetidine decreased the clearance of procainamide (PA) and/or N-acetylprocainamide (NAPA; the primary metabolite of PA) resulting in the increased systemic exposure and the decrease of urinary excretion. Despite an abundance of in vitro and in vivo data regarding pharmacokinetic interactions between PA/NAPA and cimetidine, however, a mechanistic approach to elucidate these interactions has not been reported yet. The primary objective of this study was to construct a physiological model that describes pharmacokinetic interactions between PA/NAPA and cimetidine, an inhibitor of rat organic cation transporter 2 (rOCT2) and rat multidrug and toxin extrusion proteins (rMATE1), by performing extensive in vivo and in vitro pharmacokinetic studies for PA and NAPA performed in the absence or presence of cimetidine in rats. When a single intravenous injection of PA HCl (10 mg/kg) was administered to rats, co-administration of cimetidine (100 mg/kg) significantly increased systemic exposure and decreased the systemic (CL) and renal (CL_R) clearance of PA, and reduced its tissue distribution. Similarly, cimetidine significantly decreased the CL_R of NAPA formed by the metabolism of PA and increased the AUC of NAPA. Considering that these drugs could share similar renal secretory pathways (e.g., via rOCT2 and rMATE1), a physiologically-based pharmacokinetic (PBPK) model incorporating semi-mechanistic kidney compartments was devised to predict drug-drug interactions (DDIs). Using our proposed PBPK model, DDIs between PA/NAPA and cimetidine were successfully predicted for the plasma concentrations and urinary excretion profiles of PA and NAPA observed in rats. Moreover, sensitivity analyses of the pharmacokinetics of PA and NAPA showed the inhibitory effects of cimetidine via rMATE1 were probably important for the renal elimination of PA and NAPA in rats. The proposed PBPK model may be useful for understanding the mechanisms of interactions between PA/NAPA and cimetidine in vivo.

Exploration of PBPK Model-Calculation of Drug Time Course in Tissue Using IV Bolus Drug Plasma Concentration-Time Profile and the Physiological Parameters of the Organ

An uncommon innovative consideration of the well-stirred linear physiologically based pharmacokinetic model and the drug plasma concentration-time profile, which is measured in routine intravenous bolus pharmacokinetic study, was applied for the calculation of the drug time course in human tissues. This cannot be obtained in the in vivo pharmacokinetic study. The physiological parameters of the organ such as organ tissue volume, organ blood flow rate, and its vascular volume were used in the calculation. The considered method was applied to calculate the time course of midazolam, alprazolam, quinidine, and diclofenac in human organs or tissues. The suggested method might be applied for the prediction of drug concentration-time profile in tissues and consequently the drug concentration level in the targeted tissue, as well as the possible undesirable toxic levels in other tissues.

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 (Vss, Vβ, 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 Vss, Vβ, 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 Vss, Vβ, 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.

A mechanistic framework for in vitro-in vivo extrapolation of liver membrane transporters: prediction of drug-drug interaction between rosuvastatin and cyclosporine

Background and Objectives

The interplay between liver metabolising enzymes and transporters is a complex process involving system-related parameters such as liver blood perfusion as well as drug attributes including protein and lipid binding, ionisation, relative magnitude of passive and active permeation. Metabolism- and/or transporter-mediated drug–drug interactions (mDDIs and tDDIs) add to the complexity of this interplay. Thus, gaining meaningful insight into the impact of each element on the disposition of a drug and accurately predicting drug–drug interactions becomes very challenging. To address this, an in vitro–in vivo extrapolation (IVIVE)-linked mechanistic physiologically based pharmacokinetic (PBPK) framework for modelling liver transporters and their interplay with liver metabolising enzymes has been developed and implemented within the Simcyp Simulator^®.

Methods

In this article an IVIVE technique for liver transporters is described and a full-body PBPK model is developed. Passive and active (saturable) transport at both liver sinusoidal and canalicular membranes are accounted for and the impact of binding and ionisation processes is considered. The model also accommodates tDDIs involving inhibition of multiple transporters. Integrating prior in vitro information on the metabolism and transporter kinetics of rosuvastatin (organic-anion transporting polypeptides OATP1B1, OAT1B3 and OATP2B1, sodium-dependent taurocholate co-transporting polypeptide [NTCP] and breast cancer resistance protein [BCRP]) with one clinical dataset, the PBPK model was used to simulate the drug disposition of rosuvastatin for 11 reported studies that had not been used for development of the rosuvastatin model.

Results

The simulated area under the plasma concentration–time curve (AUC), maximum concentration (C_max) and the time to reach C_max (t_max) values of rosuvastatin over the dose range of 10–80 mg, were within 2-fold of the observed data. Subsequently, the validated model was used to investigate the impact of coadministration of cyclosporine (ciclosporin), an inhibitor of OATPs, BCRP and NTCP, on the exposure of rosuvastatin in healthy volunteers.

Conclusion

The results show the utility of the model to integrate a wide range of in vitro and in vivo data and simulate the outcome of clinical studies, with implications for their design.

Electronic supplementary material

The online version of this article (doi:10.1007/s40262-013-0097-y) contains supplementary material, which is available to authorized users.

Validity of the lipid sink as a mechanism for the reversal of local anesthetic systemic toxicity: a physiologically based pharmacokinetic model study

BACKGROUND

In vitro observations support the lipid sink theory of therapeutic action by confirming the capacity of lipid emulsions to successfully uptake bupivacaine from aqueous media. However, competing hypotheses and some in/ex vivo small animal studies suggest that a metabolic or positive inotropic effect underlies the dramatic effects of lipid therapy. Controlled clinical tests to establish causality and mechanism of action are an impossibility. In an effort to quantitatively probe the merits of a "sink" mechanism, a physiologically based pharmacokinetic model has been developed that considers the binding action of plasma lipid.

METHODS

The model includes no fitting parameters and accounts for concentration dependence of plasma protein and lipid:anesthetic binding as well as the metabolism of the lipid scavenger. Predicted pharmacokinetics were validated by comparison with data from healthy volunteers administered a nontoxic dose of bupivacaine. The model was augmented to simulate lipid therapy and extended to the case of accidental IV infusion of bupivacaine at levels known to cause systemic toxicity.

RESULTS

The model yielded quantitative agreement with available pharmacokinetic data. Simulated lipid infusion following an IV overdose was predicted to yield (1) an increase in total plasma concentration, (2) a decrease in unbound concentration, and (3) a decrease in tissue content of bupivacaine.

CONCLUSIONS

Results suggest that the timescale on which tissue content is reduced varies from organ to organ, with the concentration in the heart falling by 11% within 3 min. This initial study suggests that, in isolation, the lipid sink is insufficient to guarantee a reversal of systemic toxicity.

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.

The corrected traditional equations for calculation of hepatic clearance that account for the difference in drug ionization in extracellular and intracellular tissue water and the corresponding corrected PBPK equation

The estimation of hepatic clearance, Clh, using in vitro data on metabolic stability of compound, its protein binding and blood–plasma equilibrium concentration ratio is commonly performed using well-stirred, parallel tube or dispersion models. It appears that for ionizable drugs there is a difference of the steady-state concentrations in extracelluar and intracellular water (at hepatocytes), where metabolism takes place. This occurs due to the different pH of extra- and intracellular water (7.4 and 7.0, respectively). The account of this fact leads to the novel equations for Clh . These equations include the additional parameter named ionization factor, FI, which is the ratio of the unionized drug fractions in plasma and intracellular tissue water (or the ratio of the unbound drug concentrations in intracellular tissue water and plasma at equilibrium). For neutral drugs FI = 1 and the novel equations coincide with the traditional ones. It is shown that the account of this factor may yield the calculated Clh up to 6.3-fold greater than that obtained by the traditional equations for the strong diprotic basic compounds, and up to 6.3-fold smaller for the strong diprotic acidic compounds. For triprotic acids and bases the difference could be as much as 15-fold. The account of pH difference between extra- and intracellular water also results in the change of the term commonly used to describe drug metabolic elimination rate in physiologically based pharmacokinetic (PBPK) equation. This consequently may lead to a noticeable change of drug concentration-time profiles in plasma and tissues. The effect of ionization factor is especially pronounced for the low-extraction ratio drugs. The examples of significant improvement in the prediction of hepatic clearance due to the account of ionization factor are provided. A more general equation for hepatic clearance, which accounts for ionization factor and possible drug uptake and efflux, is obtained.

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.