A priori prediction of tissue:plasma partition coefficients of drugs to facilitate the use of physiologically-based pharmacokinetic models in drug discovery

The tissue:plasma (P(t:p)) partition coefficients (PCs) are important drug-specific input parameters in physiologically based pharmacokinetic (PBPK) models used to estimate the disposition of drugs in biota. Until now the use of PBPK models in early stages of the drug discovery process was not possible, since the estimation of P(t:p) of new drug candidates by using conventional in vitro and/or in vivo methods is too time and cost intensive. The objectives of the study were (i) to develop and validate two mechanistic equations for predicting a priori the rabbit, rat and mouse P(t:p) of non-adipose and non-excretory tissues (bone, brain, heart, intestine, lung, muscle, skin, spleen) for 65 structurally unrelated drugs and (ii) to evaluate the adequacy of using P(t:p) of muscle as predictors for P(t:p) of other tissues. The first equation predicts P(t:p) at steady state, assuming a homogenous distribution and passive diffusion of drugs in tissues, from a ratio of solubility and macromolecular binding between tissues and plasma. The ratio of solubility was estimated from log vegetable oil:water PCs (K(vo:w)) of drugs and lipid and water levels in tissues and plasma, whereas the ratio of macromolecular binding for drugs was estimated from tissue interstitial fluid-to-plasma concentration ratios of albumin, globulins and lipoproteins. The second equation predicts P(t:p) of drugs residing predominantly in the interstitial space of tissues. Therefore, the fractional volume content of interstitial space in each tissue replaced drug solubilities in the first equation. Following the development of these equations, regression analyses between P(t:p) of muscle and those of the other tissues were examined. The average ratio of predicted-to-experimental P(t:p) values was 1.26 (SD = 1.40, r = 0.90, n = 269), and 85% of the 269 predicted values were within a factor of three of the corresponding literature values obtained under in vivo and in vitro conditions. For predicted and experimental P(t:p), linear relationships (r > 0.9 in most cases) were observed between muscle and other tissues, suggesting that P(t:p) of muscle is a good predictor for the P(t:p) of other tissues. The two previous equations could explain the mechanistic basis of these linear relationships. The practical aim of this study is a worthwhile goal for pharmacokinetic screening of new drug candidates.     

Estimation of tissue-to-plasma partition coefficients used in physiological pharmacokinetic models

An important parameter in the development of pharmacokinetic models is the ratio of tissue drug concentration to the concentration of the drug in the arterial plasma or the effluent plasma. The relationship between these two tissue/plasma ratios is derived analytically for different routes of drug administration. The two are equal only in compartments with no elimination when the drug is infused at constant rate. For other routes of administration, the two ratios are identical in all compartments only when there is no elimination process. The tissue/plasma concentration ratios for infusion equilibrium are not equal to the corresponding values for the postdistribution phase after an intravenous bolus injection. When the plasma concentration for infusion and injection are the same, more drug will appear in the lung during infusion steady state than during the postdistribution equilibrium. The reverse is true for the other organs. The importance of properly defining the tissue/plasma ratio and its implication for pharmacokinetic modeling are discussed. The results may have important therapeutic implications for the availability of drugs using different routes of administration.This work was supported by Grant CA-17094 from the National Cancer Institute.     

Development of appropriate equations for physiologically based pharmacokinetic modeling of permeability-limited and flow-limited transport

Although the implementation of a flow-limited, well-stirred tank (WST) single-compartment tissue model in pharmacokinetics and toxicokinetics is widespread, its use is not always justified biophysically or physiologically. The WST model introduces a loss of biophysical detail, specifically the vascular space, which is present in the standard permeability-limited two-subcompartment (PLT) tissue model. To address this loss of detail when evaluating the in vivo kinetics of drugs, toxins, nutrients, and endogenous metabolites, a novel set of physiologically based pharmacokinetic tissue compartment equations is developed through application of an asymptotic approximation to a two-region vascular–extravascular system to arrive at a permeability-limited two-region asymptotically reduced (P-TAR) model and a flow-limited (F-TAR) model. Development of the TAR modeling approach illustrates the importance of relative timescales in PBPK tissue compartment model selection and the conditions under which improved biophysical realism is advantageous. In the permeability-limited regime, the TAR model formulations enable drug or toxicant concentration to be modeled in the vascular and extravascular spaces equivalent to the PLT tissue model while invoking only one state variable to represent the vascular and extravascular spaces. In the flow-limited regime, the F-TAR model is more biophysically realistic than the WST model because it maintains the anatomical distinction between the vascular and extravascular spaces, and hence offers greater pharmacological and physiological insight than the WST model, without introducing additional computational complexity.     

Estimation of tissue-to-plasma partition coefficients used in physiological pharmacokinetic models.

An important parameter in the development of pharmacokinetic models is the ratio of tissue drug concentration to the concentration of the drug in the arterial plasma or the effluent plasma. The relationship between these two tissue/plasma ratios is derived analytically for different routes of drug administration. The two are equal only in compartments with no elimination when the drug is infused at constant rate. For other routes of administration, the two ratios are identical in all compartments only when there is no elimination process. The tissue/plasma concentration ratios for infusion equilibrium are not equal to the corresponding values for the postdistribution phase after an intravenous bolus injection. When the plasma concentration for infusion and injection are the same, more drug will appear in the lung during infusion steady state than during the postdistribution equilibrium. The reverse is true for the other organs. The importance of properly defining the tissue/plasma ratio and its implication for pharmacokinetic modeling are discussed. The results may have important therapeutic implications for the availability of drugs using different routes of administration.     

Interspecies prediction of pharmacokinetics and tissue distribution of doxorubicin by physiologically-based pharmacokinetic modeling

The aim of the study was to develop a physiologically-based pharmacokinetic (PBPK) model to describe and predict whole-body disposition of doxorubicin following intravenous administration. The PBPK model was established using previously published data in mice and included 10 tissue compartments: lungs, heart, brain, muscle, kidneys, pancreas, intestine, liver, spleen, adipose tissue, and plasma. Individual tissues were described by either perfusion-limited or permeability-limited models. All parameters were simultaneously estimated and the final model was able to describe murine data with good precision. The model was used for predicting doxorubicin disposition in rats, rabbits, dogs, and humans using interspecies scaling approaches and was qualified using plasma and tissue observed data. Reasonable prediction of the plasma pharmacokinetics and tissue distribution was achieved across all species. In conclusion, the PBPK model developed based on a rich dataset obtained from mice, was able to reasonably predict the disposition of doxorubicin in other preclinical species and humans. Applicability of the model for special populations, such as patients with hepatic impairment, was also demonstrated. The proposed model will be a valuable tool for optimization of exposure profiles of doxorubicin in human patients.     

Applications of minimal physiologically-based pharmacokinetic models

Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue (usually total body weight) volumes, fractions (f _d ) of cardiac output with Fick??s Law of Perfusion, tissue/blood partitioning (K _p ), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mammillary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated K _p values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common K _p and f _d values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.     

Area method for the estimation of partition coefficients for physiological pharmacokinetic models

A new technique, the area method, is derived for the determination of partition coefficients for both blood-flow limited and membrane limited physiological pharmacokinetic models. This method was compared to a standard technique by Monte Carlo simulation. Partition coefficients were calculated for the blood-flow limited case for both eliminating and noneliminating organs. It was found that the area method compared favorably to a standard technique and was less prone to error. This may be attributed to the more subjective interpretation as to which data points are included in the terminal phase, since the standard method relies on the accurate determination of the terminal slope for the calculation of partition coefficients. Both methods are satisfactory for the calculation of partition coefficients with the area method being more accurate and precise.     

Area method for the estimation of partition coefficients for physiological pharmacokinetic models

A new technique, the area method, is derived for the determination of partition coefficients for both blood-flow limited and membrane limited physiological pharmacokinetic models. This method was compared to a standard technique by Monte Carlo simulation. Partition coefficients were calculated for the blood-flow limited case for both eliminating and noneliminating organs. It was found that the area method compared favorably to a standard technique and was less prone to error. This may be attributed to the more subjective interpretation as to which data points are included in the terminal phase, since the standard method relies on the accurate determination of the terminal slope for the calculation of partition coefficients. Both methods are satisfactory for the calculation of partition coefficients with the area method being more accurate and precise.     

Determination of the rat tissue partitioning of endotoxin in vitro for physiologically-based pharmacokinetic (PBPK) modeling

The biosynthetically double-labeled lipopolysaccharide (LPS), containing (3)H-labeled on the fatty acyl-chains and (14)C-labeled on the glucosamine of Salmonella enterica serotype typhimurium, was isolated from bacteria grown in proteose peptone-beef extract (PPBE) medium in the presence of labeled precursors; 133 micro Ci/ml of [2-(3)H] acetate sodium salt and 0.167 micro Ci/ml of N-acetyl[D-1-(14)C]glucosamine. The LPS was extracted from the bacteria with 90% phenol/chloroform/petroleum ether, purified and stored in 0.1% (v/v) triethylamine/10 mM Tris HCl at -70 degrees C. Tissue slices and portions of the meninges were prepared and incubated in artificial cerebrospinal fluid (CSF) or Krebs phosphate buffer (Krebs) containing 150 ng/ml LPS with [(3)H] LPS (0.004 micro Ci/ml, sp. act. 28 micro Ci/mg LPS). The tissues were incubated under 95% oxygen/5% carbon dioxide at 37 degrees C with constant agitation until steady-state uptake was reached (60 min). At the end of the incubation period, tissues were processed for radioactivity measurement. The rat tissue partitioning of LPS in artificial CSF for brain and Krebs for other organs was measured by using the ratio of tissue to medium at the steady state in vitro. The following results were obtained from the study: Heart, 0.15; liver, 0.19; spleen, 0.12; kidney, 0.18; stomach, 0.17; small intestine, 0.18; brain stem, 0.10; cerebellum, 0.11; meninges, 0.77; hippocampus, 0.12; hypothalamus, 0.12; frontal cortex, 0.09 and caudate nucleus, 0.10. This information, along with plasma or blood/buffer partition coefficients, is a requisite for constructing a physiologically-based pharmacokinetic (PBPK) model of endotoxins for quantitative risk assessment.     

Application of physiologically-based pharmacokinetic modeling to investigate the toxicological interaction between chlorpyrifos and parathion in the rat

Environmental exposure is usually due to the presence of multiple chemicals. In most cases, these chemicals interact with each other at both pharmacokinetic and pharmacodynamic toxicity mechanisms. In the absence of data, joint toxicity assessment of a mixture is based on default dose or response additivity. Although, the concept of additivity is mostly accepted at low dose levels, these levels need to be determined quantitatively to validate the use of additivity as an absence of any possible synergistic or antagonistic interactions at low environmental exposure levels. The doses at which interaction becomes significant define the interaction threshold. In most cases, estimation of these low-dose interaction thresholds experimentally is economically costly and challenging because of the need to use a large number of laboratory animals. Computational toxicology methods provide a feasible alternative to establish interaction thresholds. For example, a physiologically based pharmacokinetic (PBPK) model was developed to estimate an interaction threshold for the joint toxicity between chlorpyrifos and parathion in the rat. Initially, PBPK models were developed for each chemical to estimate the blood concentrations of their respective metabolite. The metabolite concentrations in blood out-put was then linked to acetylcholinesterase kinetics submodel. The resulting overall PBPK model described interactions between these pesticides at two levels in the organism: (a) the P450 enzymatic bioactivation site, and (b) acetylcholinesterase binding sites. Using the overall model, a response surface was constructed at various dose levels of each chemical to investigate the mechanism of interaction and to calculate interaction threshold doses. The overall model simulations indicated that additivity is obtained at oral dose levels below 0.08mg/kg of each chemical. At higher doses, antagonism by enzymatic competitive inhibition is the mode of interaction.     

Second-generation minimal physiologically-based pharmacokinetic model for monoclonal antibodies

Minimal physiologically-based pharmacokinetic (mPBPK) models provide a sensible modeling approach when fitting only plasma (or blood) data yielding physiologically-relevant PK parameters that may provide more practical value than parameters of mammillary models. We propose a second-generation mPBPK model specifically for monoclonal antibodies (mAb) by including (lumping) several essential components of mAb PK used in full PBPK models. These components include convection as the primary mechanism of antibody movement from plasma into tissues and return to plasma with interstitial fluid as the major extravascular distribution space. The model divides tissue spaces into two groups according to their vascular endothelial structure, leaky and tight, which consequently allows discernment of two types and general sites of distribution. This mPBPK model was applied to two mAbs in mice and ten mAbs with linear kinetics in humans. The model captured their plasma PK profiles well with predictions of concentrations in interstitial fluid for two types of tissues. Predictions of tissue concentrations for mAb 7E3 and 8C2 were consistent with actual measurements in mice, indicating the feasibility of this model in assessing extravascular distribution in the two categories of tissues. The vascular reflection coefficients (σ ₁) of tight tissues (V _tight ) ranged 0.883–0.987 and coefficients (σ ₂) for leaky tissues (V _leaky ) ranged 0.311 to 0.837. The plasma clearance (CL _p ) varied among the mAbs in humans from 0.0054 to 0.03 L/h. In addition, applying this model generates parameters for mAb transcapillary escape rates and assesses major sites of elimination. Four of ten mAbs exhibited better fitting statistics premised on elimination from interstitial fluid than from plasma. This approach allows comparisons of mAb PK when only plasma data are available, provides more realistic parameters and predictions than mammillary models, and may provide an intermediate step towards utilizing full PBPK models for mAbs.     

Predicting neonatal perchlorate dose and inhibition of iodide uptake in the rat during lactation using physiologically-based pharmacokinetic modeling.

Perchlorate (ClO4-), a contaminant in drinking water, competitively inhibits active uptake of iodide (I-) into various tissues, including mammary tissue. During postnatal development, inhibition of I- uptake in the mammary gland and neonatal thyroid and the active concentration ClO4- in milk indicate a potentially increased susceptibility of neonates to endocrine disruption. A physiologically based pharmacokinetic (PBPK) model was developed to reproduce measured ClO4- distribution in the lactating and neonatal rat and predict resulting effects on I- kinetics from competitive inhibition at the sodium iodide symporter (NIS). Kinetic I- and ClO4- behavior in tissues with NIS (thyroid, stomach, mammary gland, and skin) was simulated with multiple subcompartments, Michaelis-Menten (M-M) kinetics and competitive inhibition. Physiological and kinetic parameters were obtained from literature and experiment. Systemic clearance and M-M parameters were estimated by fitting simulations to tissue and serum data. The model successfully describes maternal and neonatal thyroid, stomach, skin, and plasma, as well as maternal mammary gland and milk data after ClO4- exposure (from 0.01 to 10 mg/kg-day ClO4-) and acute radioiodide (2.1 to 33,000 ng/kg I-) dosing. The model also predicts I- uptake inhibition in the maternal thyroid, mammary gland, and milk. Model simulations predict a significant transfer of ClO4- through milk after maternal exposure; approximately 50% to 6% of the daily maternal dose at doses ranging from 0.01 to 10.0 mg ClO4-/kg-day, respectively. Comparison of predicted dosimetrics across life-stages in the rat indicates that neonatal thyroid I- uptake inhibition is similar to the adult and approximately tenfold less than the fetus.     

Optimizing pharmacokinetic bridging studies in paediatric oncology using physiologically-based pharmacokinetic modelling: application to docetaxel

Aim

Applying physiologically-based pharmacokinetic (PBPK) modelling in paediatric cancer drug development is still challenging. We aimed to demonstrate how PBPK modelling can be applied to optimize dose and sampling times for a paediatric pharmacokinetic (PK) bridging study in oncology and to compare with the allometric scaling population PK (AS-popPK) approach, using docetaxel as an example.

Methods

A PBPK model for docetaxel was first developed for adult cancer patients using Simcyp® and subsequently used to predict its PK profiles in children by accounting for age-dependent physiological differences. Dose (mg m^–2) requirements for children aged 0–18 years were calculated to achieve targeted exposure in adults. Simulated data were then analyzed using population PK modelling with MONOLIX® in order to perform design optimization with the population Fisher information matrix (PFIM). In parallel, the AS-popPK approach was performed for the comparison.

Results

The PBPK model developed for docetaxel adequately predicted its PK profiles in both adult and paediatric cancer patients (predicted clearance and volume of distribution within 1.5 fold of observed data). The revised dose of docetaxel for a child over 1.5 years old was higher than the adult dose. Considering clinical constraints, the optimal design contained two groups of 15 patients, having three or four sampling times and had good predicted relative standard errors (RSE<30%) for almost all parameters. The AS-popPK approach performed reasonably well but could not predict for very young children.

Conclusion

This research shows the clinical utility of PBPK modelling in combination with population PK modelling and optimal design to support paediatric oncology development.     

Cancer risk assessment for dioxane based upon a physiologically-based pharmacokinetic approach

A cancer bioassay conducted in 1974 (Kociba et al.) indicated that rats given drinking water containing dioxane at a dose of 1184 mg.kg-1.d-1 produced an increased incidence of liver tumors. Applying the linearized multistage extrapolation model to these data, the administered dose estimated to present a human cancer risk of 1 in 100,000 (10(-5)) was 0.01 mg.kg-1.d-1. As in customary regulatory policy, this estimate assumed that humans were about 5.5 times more sensitive than rats on a mg/kg basis. However, this approach did not consider that the metabolism of dioxane is saturable at high doses. Based on experience with similar chemicals, it is known that the conventional risk extrapolation method may overestimate the most likely human cancer risk. In order to determine more accurately the likely human response following lifetime exposure to dioxane, a physiologically-based pharmacokinetic (PB-PK) model was developed. The objective of this study was to establish a quantitative relationship between the administered dose of dioxane and the internal dose delivered to the target organ. Using this PB-PK model, and assuming that the best dose surrogate for estimating the liver tumor response was the time-weighted average lifetime liver dioxane concentration, the cancer risk for humans exposed to low doses of dioxane was estimated. The dose surrogate in humans most likely to be associated with a tumorigenic response of 1 in 100,000 is 280 mumol/l, equivalent to an administered dose of about 59 mg.kg-1.d-1. The 95% lower confidence limit on the dose surrogate at the same response level is 1.28 mumol/l, equivalent to an administered dose of 0.8 mg.kg-1.d-1. This PB-PK analysis indicated that conventional approaches based on the administered doses in the rodent bioassay, if uncorrected for metabolic and physiological differences between rats and humans, will overestimate the human cancer risk of dioxane by as much as 80-fold.     

A physiologically-based pharmacokinetic (PBPK) model of squalene-containing adjuvant in human vaccines

Squalene is used in the oil phase of certain emulsion vaccine adjuvants, but its fate as a vaccine component following intramuscular (IM) injection in humans is unknown. In this study, we constructed a physiologically-based pharmacokinetic (PBPK) model for intramuscularly injected squalene-in-water (SQ/W) emulsion, in order to make a quantitative estimation of the tissue distribution of squalene following a single IM injection in humans. The PBPK model incorporates relevant physicochemical properties of squalene; estimates of the time course of cracking of a SQ/W emulsion; anatomical and physiological parameters at the injection site and beyond; and local, preferential lymphatic transport. The model predicts that a single dose of SQ/W emulsion will be removed from human deltoid muscle within six days following IM injection. The major proportion of the injected squalene will be distributed to draining lymph nodes and adipose tissues. The model indicates slow decay from the latter compartment most likely due to partitioning into neutral lipids and a low rate of squalene biotransformation there. Parallel pharmacokinetic modeling for mouse muscle suggests that the kinetics of SQ/W emulsion correspond to the immunodynamic time course of a commercial squalene-containing adjuvant reported in that species. In conclusion, this study makes important pharmacokinetic predictions of the fate of a squalene-containing emulsion in humans. The results of this study may be relevant for understanding the immunodynamics of this new class of vaccine adjuvants and may be useful in future quantitative risk analyses that incorporate mode-of-action data.     

Survey of monoclonal antibody disposition in man utilizing a minimal physiologically-based pharmacokinetic model

Minimal physiologically based pharmacokinetic (mPBPK) models provide a simple and sensible approach that incorporates physiological elements into pharmacokinetic (PK) analysis when only plasma data are available. With this modeling concept, a second-generation mPBPK model was further developed with specific accommodations for the unique PK properties of monoclonal antibodies (mAb). This study applied this model to extensively survey mAb PK in man in order to seek general perspectives on mAb distributional and elimination features. Profiles for 72 antibodies were successfully analyzed with this model. The model results provide assessment regarding: (1) predominant clearance site, in plasma or interstitial fluid (ISF); (2) mAb ISF concentrations in two groups of lumped tissues with continuous (V _tight ) or fenestrated (V _leaky ) vascular endothelium; (3) Transcapillary escape rate (TER), an indicator of systemic vascular permeability. For 93 % of surveyed mAbs, the model assuming clearance from plasma (CL _p ) produced better or at least equivalent model performance than the model with clearance from ISF and yielded most consistent values of vascular reflection coefficients (σ₁ and σ₂) among all antibodies. The average mAb ISF concentration in V _tight and V _leaky at equilibrium was predicted to be about 6.8 and 37.9 % of that in plasma. A positive correlation was detected between plasma clearance and TER among most mAbs, which could be interpreted as both parameters having common determinants related to ISF tissue distribution in this model context. The mAbs with relative higher plasma clearance (>0.035 L/h/70 kg) did not reveal such positive correlation between clearance and TER, implying that the factors contributing to high clearance may not necessarily increase tissue distribution and penetration. In conclusion, this mPBPK model offers a more mechanistic approach for analyzing plasma mAb PK than compartment models and generates parameters providing useful intrinsic distributional and elimination insights for a large number of mAbs that were examined in man.