Use of partition coefficients in flow-limited physiologically-based pharmacokinetic modeling

Permeability-limited two-subcompartment and flow-limited, well-stirred tank tissue compartment models are routinely used in physiologically-based pharmacokinetic modeling. Here, the permeability-limited two-subcompartment model is used to derive a general flow-limited case of a two-subcompartment model with the well-stirred tank being a specific case where tissue fractional blood volume approaches zero. The general flow-limited two-subcompartment model provides a clear distinction between two partition coefficients typically used in PBPK: a biophysical partition coefficient and a well-stirred partition coefficient. Case studies using diazepam and cotinine demonstrate that, when the well-stirred tank is used with a priori predicted biophysical partition coefficients, simulations overestimate or underestimate total organ drug concentration relative to flow-limited two-subcompartment model behavior in tissues with higher fractional blood volumes. However, whole-body simulations show predicted drug concentrations in plasma and lower fractional blood volume tissues are relatively unaffected. These findings point to the importance of accurately determining tissue fractional blood volume for flow-limited PBPK modeling. Simulations using biophysical and well-stirred partition coefficients optimized with flow-limited two-subcompartment and well-stirred models, respectively, lead to nearly identical fits to tissue drug distribution data. Therefore, results of whole-body PBPK modeling with diazepam and cotinine indicate both flow-limited models are appropriate PBPK tissue models as long as the correct partition coefficient is used: the biophysical partition coefficient is for use with two-subcompartment models and the well-stirred partition coefficient is for use with the well-stirred tank model.     

Physiologically based pharmacokinetic study on a cyclosporin derivative,SDZ IMM 125

The immunosuppressant, SDZ IMM 125 (IMM), is a derivative of cyclosporin A (CyA). The disposition kinetics of IMM in plasma, blood cells, and various tissues of the rat was characterized by a physiologically based pharmacokinetic (PBPK) model; the model was then applied to predict the disposition kinetics in dog and human. Accumulation of IMM in blood cell is high (equilibrium blood cell/plasma ratio=8), although the kinetics of drug transference between plasma and blood cell is moderately slow, taking approximately 10 min to reach equilibrium, implying a membranelimited distribution into blood cells. A local PBPK model, assuming blood-flow limited distribution and tissue/blood partition coefficient (K _P) data, failed to adequately describe the observed kinetics of distribution, which were slower than predicted. A membrane transport limitation is therefore needed to model dynamic tissue distribution data. Moreover, a slowly interacting intracellular pool was also necessary to adequately describe the kinetics of distribution in some organs. Three elimination pathways (metabolism, biliary secretion, and glomerular filtration) of IMM were assessed at steady statein vivo and characterized independently by the corresponding clearance terms. A whole-body PBPK model was developed according to these findings, which described closely the IMM concentration-time profiles in arterial blood as well as 14 organs/tissues of the rat after intravenous administration. The model was then scaled up to larger mammals by modifying physiological parameters, tissue distribution and elimination clearances;in vivo enzymatic activity was considered in the scale-up of metabolic clearance. The simulations agreed well with the experimental measurements in dog and human, despite the large interspecies difference in the metabolic clearance, which does not follow the usual allometric relationship. In addition, the nonlinear increase in maximum blood concentration andAUC with increasing dose, observed in healthy volunteers after intravenous administration, was accommodated quantitatively by incorporating the known saturation of specific binding of IMM to blood cells. Overall, the PBPK model provides a promising tool to quantitatively link preclinical and clinical data.     

BioDMET: a physiologically based pharmacokinetic simulation tool for assessing proposed solutions to complex biological problems

We developed a detailed, whole-body physiologically based pharmacokinetic (PBPK) modeling tool for calculating the distribution of pharmaceutical agents in the various tissues and organs of a human or animal as a function of time. Ordinary differential equations (ODEs) represent the circulation of body fluids through organs and tissues at the macroscopic level, and the biological transport mechanisms and biotransformations within cells and their organelles at the molecular scale. Each major organ in the body is modeled as composed of one or more tissues. Tissues are made up of cells and fluid spaces. The model accounts for the circulation of arterial and venous blood as well as lymph. Since its development was fueled by the need to accurately predict the pharmacokinetic properties of imaging agents, BioDMET is more complex than most PBPK models. The anatomical details of the model are important for the imaging simulation endpoints. Model complexity has also been crucial for quickly adapting the tool to different problems without the need to generate a new model for every problem. When simpler models are preferred, the non-critical compartments can be dynamically collapsed to reduce unnecessary complexity. BioDMET has been used for imaging feasibility calculations in oncology, neurology, cardiology, and diabetes. For this purpose, the time concentration data generated by the model is inputted into a physics-based image simulator to establish imageability criteria. These are then used to define agent and physiology property ranges required for successful imaging. BioDMET has lately been adapted to aid the development of antimicrobial therapeutics. Given a range of built-in features and its inherent flexibility to customization, the model can be used to study a variety of pharmacokinetic and pharmacodynamic problems such as the effects of inter-individual differences and disease-states on drug pharmacokinetics and pharmacodynamics, dosing optimization, and inter-species scaling. While developing a tool to aid imaging agent and drug development, we aimed at accelerating the acceptance and broad use of PBPK modeling by providing a free mechanistic PBPK software that is user friendly, easy to adapt to a wide range of problems even by non-programmers, provided with ready-to-use parameterized models and benchmarking data collected from the peer-reviewed literature.     

A Simplified PBPK Modeling Approach for Prediction of Pharmacokinetics of Four Primarily Renally Excreted and CYP3A Metabolized Compounds During Pregnancy

During pregnancy, a drug’s pharmacokinetics may be altered and hence anticipation of potential systemic exposure changes is highly desirable. Physiologically based pharmacokinetics (PBPK) models have recently been used to influence clinical trial design or to facilitate regulatory interactions. Ideally, whole-body PBPK models can be used to predict a drug’s systemic exposure in pregnant women based on major physiological changes which can impact drug clearance (i.e., in the kidney and liver) and distribution (i.e., adipose and fetoplacental unit). We described a simple and readily implementable multitissue/organ whole-body PBPK model with key pregnancy-related physiological parameters to characterize the PK of reference drugs (metformin, digoxin, midazolam, and emtricitabine) in pregnant women compared with the PK in nonpregnant or postpartum (PP) women. Physiological data related to changes in maternal body weight, tissue volume, cardiac output, renal function, blood flows, and cytochrome P450 activity were collected from the literature and incorporated into the structural PBPK model that describes HV or PP women PK data. Subsequently, the changes in exposure (area under the curve (AUC) and maximum concentration (C _max)) in pregnant women were simulated. Model-simulated PK profiles were overall in agreement with observed data. The prediction fold error for C _max and AUC ratio (pregnant vs. nonpregnant) was less than 1.3-fold, indicating that the pregnant PBPK model is useful. The utilization of this simplified model in drug development may aid in designing clinical studies to identify potential exposure changes in pregnant women a priori for compounds which are mainly eliminated renally or metabolized by CYP3A4.     

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.     

Are Physiologically Based Pharmacokinetic Models Reporting the Right Cmax? Central Venous Versus Peripheral Sampling Site

Physiologically based pharmacokinetic (PBPK) models can over-predict maximum plasma concentrations (C_max) following intravenous administration. A proposed explanation is that invariably PBPK models report the concentration in the central venous compartment, rather than the site where the samples are drawn. The purpose of this study was to identify and validate potential corrective models based on anatomy and physiology governing the blood supply at the site of sampling and incorporate them into a PBPK platform. Four models were developed and scrutinised for their corrective potential. All assumed the peripheral sampling site concentration could be described by contributions from surrounding tissues and utilised tissue-specific concentration-time profiles reported from the full-PBPK model within the Simcyp Simulator. Predicted concentrations for the peripheral site were compared to the observed C_max. The models results were compared to clinical data for 15 studies over seven compounds (alprazolam, imipramine, metoprolol, midazolam, omeprazole, rosiglitazone and theophylline). The final model utilised tissue concentrations from adipose, skin, muscle and a contribution from artery. Predicted C_max values considering the central venous compartment can over-predict the observed values up to 10-fold whereas the new sampling site predictions were within 2-fold of observed values. The model was particularly relevant for studies where traditional PBPK models over-predict early time point concentrations. A successful corrective model for C_max prediction has been developed, subject to further validation. These models can be enrolled as built-up modules into PBPK platforms and potentially account for factors that may affect the initial mixing of the blood at the site of sampling.

Electronic supplementary material

The online version of this article (doi:10.1208/s12248-015-9796-7) contains supplementary material, which is available to authorized users.KEY WORDS: C_max, intravenous, PBPK modelling, pharmacokinetics, physiological model     

Simplification of Complex Physiologically Based Pharmacokinetic Models of Monoclonal Antibodies

Monoclonal antibodies (mAbs) exhibit biexponential profiles in plasma that are commonly described with a standard two-compartment model with elimination from the central compartment. These models adequately describe mAb plasma PK. However, these models ignore elimination from the peripheral compartment. This may lead to underestimation of the volume of distribution of the peripheral compartment and thus over-predicts concentration in the peripheral compartment. We developed a simple and physiologically relevant model that incorporates information on binding and dissociation rates between mAb and FcRn receptor, mAb uptake, reflection, and catabolic degradation. We employed a previously published PBPK model and, with assumptions regarding rates of processes controlling mAb disposition, reduced the complex PBPK model to a simpler circular model with central, peripheral, and lymph compartments specifying elimination from both central and peripheral. We successfully applied the model to describe the PK of an investigational mAb. Our model presents an improvement over standard two-compartmental models in predicting whole-body average tissue concentrations while adequately describing plasma PK with minimal complexity and physiologically more meaningful parameters.     

Pharmacokinetic modeling of manganese in the rat IV: Assessing factors that contribute to brain accumulation during inhalation exposure

A recently published physiologically based pharmacokinetic (PBPK) model successfully accounted for steady-state tissue manganese (Mn) concentration seen with normal dietary intakes and for biphasic, whole-body time-course profiles observed with tracer (54Mn) dosing. In this present study, PBPK modeling was used to evaluate Mn kinetics and brain concentrations in rats exposed to Mn both in their diet and by inhalation. Three published studies were used: (1) rats fed on diets ranging from 2 to 100 ppm, (2) rats on 125 ppm in diet and exposed via inhalation at 0.0 to 3.00 mg Mn/m3 each day for 14 d, and (3) rats to 0.1 or 0.5 mg Mn/m3 for 6 h/d, 5 d/wk over a 90-d period. The original model structure with well-mixed and "deep" compartments for each tissue could not describe rapid increases in tissue concentrations and rapid declines seen in high concentration inhalation studies. A second structure was developed that included (1) saturable, high-affinity binding of Mn in all tissues and (2) asymmetric diffusion from blood into brain (i.e., transport into and out of specific brain regions such as the striatum was described with different diffusion constants). This second model was consistent with liver and striatum experimental data. Preferential increases in some brain regions were predicted for exposures above 0.2 mg/m3 and had a rapid (i.e., 1 or 2 wk) return to steady-state levels. Multi-dose-route PBPK models for Mn based on this alternative model structure can be readily scaled to evaluate tissue Mn kinetics in other species and for human populations. Once validated across test animals, these PBPK models will be useful in tissue-dose based risk assessment with manganese.     

Pharmacokinetics in organs and the intact body: model validation and reduction

Physiological pharmacokinetic models are based on the structure of the circulatory system reflecting the convective transport of drug by blood flow to the various organs and tissues. Distribution kinetics at the organ level is mostly simplified as transfer between well-stirred compartments neglecting a priori the effects of intravascular dispersion and diffusion within tissue parenchyma. Recirculatory models based on residence time theory overcome these structural limitations since they allow in a most general way the decomposition of the body into its natural subsystems. Because of the unidentifiability of the global multi-organ model on the basis of plasma concentration–time curves the following methods/experimental designs will be discussed which provide quantitative information regarding the subsystems under in vivo conditions: (i) determination of tissue concentration–time profiles (destructive sampling), (ii) estimation of the organ transit time density from input/output profiles and (iii) application of a recirculatory model with reduced complexity to clinical pharmacokinetic data.     

Early identification of drug-induced impairment of gastric emptying through physiologically based pharmacokinetic (PBPK) simulation of plasma concentration-time profiles in rat

Inhibition of gastric emptying rate can have adverse effects on the absorption of food and nutrients. The absorption phase of the plasma concentration-time profile of a compound administered orally to pre-clinical species reflects among others, the gastric and intestinal transit kinetics, and can thus assist in the early identification of delayed gastric emptying. The purpose of this article is to demonstrate the value of Physiologically Based Pharmacokinetic (PBPK) modelling in the early identification of drug induced impairment of gastric emptying from pharmacokinetic profiles. To our knowledge, this is first time that the value of a generic PBPK model for hypothesis testing has been demonstrated with examples. A PBPK model built in-house using MATLAB package and incorporating absorption, metabolism, distribution, biliary and renal elimination models has been employed for the simulation of concentration-time profiles. PBPK simulations of a few compounds that are currently in drug discovery projects show that the observed initial absorption phase of their concentration-time profiles in rat were consistent with reduced gastric emptying rates. The slow uptake of these compounds into the systemic circulation is reflected in their pharmacokinetic profiles but it is not obvious until PBPK simulations are done. Delayed gastric emptying rates of these compounds in rats were also independently observed in x-ray imaging. PBPK simulations can provide early alerts to drug discovery projects, besides aiding the understanding of complex mechanisms that determine the lineshapes of pharmacokinetic profiles. The application of PBPK simulations in the early detection of gastric emptying problems with existing data and without the need to resort to additional animal studies, is appealing both from an economic and ethical standpoint.     

Physiologically Based Pharmacokinetic (PBPK) Modeling of Everolimus (RAD001) in Rats Involving Non-Linear Tissue Uptake

Everolimus is a novel macrolide immunosuppressant developed for the prophylaxis of allogeneic renal or cardiac transplant rejection. Treatments with immunosuppressants are often associated with organ toxicity that is linked to high organ exposure. Therefore, gaining insight into the pharmacokinetics of everolimus in various organs is highly desirable especially those organs of therapeutic interest or those that pose safety concerns. The aim of this work was to characterize the disposition kinetics of everolimus in rats by physiologically based pharmacokinetic (PBPK) modeling. Blood and tissue samples were collected from male Wistar rats over 24 hr following intravenous (iv) bolus and iv infusion of 1 mg/kg and 10 mg/kg/2 hr of everolimus. Further blood samples were collected between 1 and 170 hr from a third group of rats, which received iv infusion of 1 mg/kg/2 hr of everolimus. Drug concentrations in blood and tissues were determined by a liquid chromatography reverse dilution method. Distribution of everolimus between blood fractions was determined in vitro at 37°C. The results of the study demonstrated that everolimus exhibited moderate non-linear binding to red blood cells. Also, the tissue-to-blood concentration ratio decreased in all tissues as blood concentration increased. A PBPK model involving non-linear tissue binding was able to successfully describe the observed data in blood and all the organs investigated. The highest binding potential was observed in thymus, lungs, and spleen with the greatest tissue affinity observed in thymus, skin, and muscle as compared to other tissues. Everolimus exhibited a high clearance rate that was limited to the hepatic blood flow (47.2 ml/min/kg). The PBPK model was also able to predict the venous blood concentration reasonably well following oral administration. The oral bioavailability value, as estimated with the PBPK, was 12% and was similar to the value obtained by non-compartmental analysis. In conclusion, A PBPK model has been developed that successfully predicts the time course of everolimus in blood and a variety of organs. This model takes into account the non- linear binding of everolimus to red blood cells and tissues. This model may be used to predict everolimus concentration–time course in organs from other species including humans.     

Cellular Pharmacokinetics: Effects of Cytoplasmic Diffusion and Binding on Organ Transit Time Distribution

Distribution between well-stirred compartments is the classical paradigm in pharmacokinetics. Also in capillary–issue exchange modeling a barrier-limited approach is mostly adopted. As a consequence of tissue binding, however, drug distribution cannot be regarded as instantaneous even at the cellular level and the distribution process consists of at least two components: transmembrane exchange and cytoplasmic transport. Two concepts have been proposed for the cytoplasmic distribution process of hydrophobic or amphipathic molecules, (i) slowing of diffusion due to instantaneous binding to immobile cellular structures and (ii) slow binding after instantaneous distribution throughout the cytosol. The purpose of this study was to develop a general approach for comparing both models using a stochastic model of intra- and extravascular drug distribution. Criteria for model discrimination are developed using the first three central moments (mean, variance, and skewness) of the cellular residence time and organ transit time distribution, respectively. After matching the models for the relative dispersion the remaining differences in relative skewness are predicted, discussing the relative roles of membrane permeability, cellular binding and cytoplasmic transport. It is shown under which conditions the models are indistinguishable on the basis of venous organ outflow concentration–time curves. The relative dispersion of cellular residence times is introduced as a model-independent measure of cytoplasmic equilibration kinetics, which indicates whether diffusion through the cytoplasm is rate limiting. If differences in outflow curve shapes (their relative skewness) cannot be detected, independent information on binding and/or diffusion kinetics is necessary to avoid model misspecification. The method is applied to previously published hepatic outflow data of enalaprilat, triiodothyronine, and diclofenac. It provides a general framework for the modeling of cellular pharmacokinetics.     

Modelling and PBPK Simulation in Drug Discovery

Physiologically based pharmacokinetic (PBPK) models are composed of a series of differential equations and have been implemented in a number of commercial software packages. These models require species-specific and compound-specific input parameters and allow for the prediction of plasma and tissue concentration time profiles after intravenous and oral administration of compounds to animals and humans. PBPK models allow the early integration of a wide variety of preclinical data into a mechanistic quantitative framework. Use of PBPK models allows the experimenter to gain insights into the properties of a compound, helps to guide experimental efforts at the early stages of drug discovery, and enables the prediction of human plasma concentration time profiles with minimal (and in some cases no) animal data. In this review, the application and limitations of PBPK techniques in drug discovery are discussed. Specific reference is made to its utility (1) at the lead development stage for the prioritization of compounds for animal PK studies and (2) at the clinical candidate selection and “first in human” stages for the prediction of human PK.     

Identification of intestinal loss of a drug through physiologically based pharmacokinetic simulation of plasma concentration-time profiles

BACKGROUND AND OBJECTIVE: Despite recent advances in understanding of the role of the gut as a metabolizing organ, recognition of gut wall metabolism and/or other factors contributing to intestinal loss of a compound has been a challenging task due to the lack of well characterized methods to distinguish it from first-pass hepatic extraction. The implications of identifying intestinal loss of a compound in drug discovery and development can be enormous. Physiologically based pharmacokinetic (PBPK) simulations of pharmacokinetic profiles provide a simple, reliable and cost-effective way to understand the mechanisms underlying pharmacokinetic processes. The purpose of this article is to demonstrate the application of PBPK simulations in bringing to light intestinal loss of orally administered drugs, using two example compounds: verapamil and an in-house compound that is no longer in development (referred to as compound A in this article). METHODS: A generic PBPK model, built in-house using MATLAB software and incorporating absorption, metabolism, distribution, biliary and renal elimination models, was employed for simulation of concentration-time profiles. Modulation of intrinsic hepatic clearance and tissue distribution parameters in the generic PBPK model was done to achieve a good fit to the observed intravenous pharmacokinetic profiles of the compounds studied. These optimized clearance and distribution parameters are expected to be invariant across different routes of administration, as long as the kinetics are linear, and were therefore employed to simulate the oral profiles of the compounds. For compounds with reasonably good solubility and permeability, an area under the concentration-time curve for the simulated oral profile that far exceeded the observed would indicate some kind of loss in the intestine. RESULTS: PBPK simulations applied to compound A showed substantial loss of the compound in the gastrointestinal tract in humans but not in rats. This accounted for the lower bioavailability of the compound in humans than in rats. PBPK simulations of verapamil identified gut wall metabolism, well established in the literature, and showed large interspecies differences with respect to both gut wall metabolism and drug-induced delays in gastric emptying. CONCLUSIONS: Mechanistic insights provided by PBPK simulations can be very valuable in answering vital questions in drug discovery and development. However, such applications of PBPK models are limited by the lack of accurate inputs for clearance and distribution. This article demonstrates a successful application of PBPK simulations to identify and quantify intestinal loss of two model compounds in rats and humans. The limitation of inaccurate inputs for the clearance and distribution parameters was overcome by optimizing these parameters through fitting intravenous profiles. The study also demonstrated that the large interspecies differences associated with gut wall metabolism and gastric emptying, evident for the compounds studied, make animal model extrapolations to humans unreliable. It is therefore important to do PBPK simulations of human pharmacokinetic profiles to understand the relevance of intestinal loss of a compound in humans.     

Physiologically based pharmacokinetic tissue compartment model selection in drug development and risk assessment

A well-stirred tank (WST) has been the predominant flow-limited tissue compartment model in physiologically based pharmacokinetic (PBPK) modeling. Recently, we developed a two-region asymptotically reduced (TAR) PBPK tissue compartment model through an asymptotic approximation to a two-region vascular-extravascular system to incorporate more biophysical detail than the WST model. To determine the relevance of a flow-limited TAR (F-TAR) approach, 75 structurally diverse drugs were evaluated herein using a priori predicted tissue:plasma partition coefficients along with hybrid and whole-body PBPK of eight rat tissues to determine the impact of model selection on simulation and optimization. Simulations showed that the F-TAR model significantly improved the ability to predict drug exposure, with hybrid and whole-body WST model error approaching 50% for tissues with larger vascular volumes. When optimization was used to fit F-TAR and WST models to pseudo data, WST-optimized drug partition coefficients more appropriately represented curve-fitting parameters rather than biophysically meaningful partition coefficients. Median F-TAR-optimized error ranged from -0.4% to +0.3%, whereas WST-optimized median error ranged from -22.2% to +1.8%. These studies demonstrated that the use of F-TAR represents a more accurate, biophysically realistic PBPK tissue model for predicting tissue exposure to drug and that it should be considered for use in drug development and regulatory review.     

Characterization of small intestinal transit time distribution in humans

This report is aimed at characterizing small intestinal transit time distribution and presenting a slope-based method to determine compartmental transit and dispersion model parameters. The intradose, intrasubject, and intersubject means and variances were defined to examine small intestinal transit time distribution in individuals and populations. Equations were derived to determine the optimum number of compartments and the dispersion coefficient. It was found that the intra- or intersubject variance was significantly smaller than the intradose variance. The optimum number of compartments and the dispersion coefficient were estimated to be seven and 0.78 cm²/s, respectively, in agreement with the literature data.     

Lumping of physiologically-based pharmacokinetic models and a mechanistic derivation of classical compartmental models

In drug discovery and development, classical compartment models and physiologically based pharmacokinetic (PBPK) models are successfully used to analyze and predict the pharmacokinetics of drugs. So far, however, both approaches are used exclusively or in parallel, with little to no cross-fertilization. An approach that directly links classical compartment and PBPK models is highly desirable. We derived a new mechanistic lumping approach for reducing the complexity of PBPK models and establishing a direct link to classical compartment models. The proposed method has several advantages over existing methods: Perfusion and permeability rate limited models can be lumped; the lumped model allows for predicting the original organ concentrations; and the volume of distribution at steady state is preserved by the lumping method. To inform classical compartmental model development, we introduced the concept of a minimal lumped model that allows for prediction of the venous plasma concentration with as few compartments as possible. The minimal lumped parameter values may serve as initial values for any subsequent parameter estimation process. Applying our lumping method to 25 diverse drugs, we identified characteristic features of lumped models for moderate-to-strong bases, weak bases and acids. We observed that for acids with high protein binding, the lumped model comprised only a single compartment. The proposed lumping approach established for the first time a direct derivation of simple compartment models from PBPK models and enables a mechanistic interpretation of classical compartment models.