Development and application of physiologically based pharmacokinetic-modeling tools to support drug discovery

Physiologically based pharmacokinetic (PBPK) modeling integrates physicochemical (PC) and in vitro pharmacokinetic (PK) data using a mechanistic framework of principal ADME (absorption, distribution, metabolism, and excretion) processes into a physiologically based whole-body model. Absorption, distribution, and clearance are modeled by combining compound-specific PC and PK properties with physiological processes. Thereby, isolated in vitro data can be upgraded by means of predicting full concentration-time profiles prior to animal experiments. The integrative process of PBPK modeling leads to a better understanding of the specific ADME processes driving the PK behavior in vivo, and has the power to rationally select experiments for a more focussed PK project support. This article presents a generic disposition model based on tissue-composition-based distribution and directly scaled hepatic clearance. This model can be used in drug discovery to identify the critical PK issues of compound classes and to rationally guide the optimization path of the compounds toward a viable development candidate. Starting with a generic PBPK model, which is empirically based on the most common PK processes, the model will be gradually tailored to the specifics of drug candidates as more and more experimental data become available. This will lead to a growing understanding of the 'drug in the making', allowing a range of predictions to be made for various purposes and conditions. The stage is set for a wide penetration of PK modeling and simulations to form an intrinsic part of a project starting from lead discovery, to lead optimization and candidate selection, to preclinical profiling and clinical trials.     

Separating Pharmacokinetic and Pharmacodynamic Components in Empirical Adjustment Factor Distributions

For a particular chemical, one can treat the chemical-by-chemical variation in relative doses for equal toxicity in experimental animals and humans as a characterization of the likelihoods of extrapolation factors of different magnitudes. An emerging approach to noncancer risk assessment is to use such empirical distributions in place of fixed Uncertainty Factors. This paper discusses dividing the overall variation into two sub-distributions representing pharmacokinetic (PK) and pharmacodynamic (PD) contributions to the variation among chemicals in the animal-to-human toxicologically equivalent dose. If a physiologically based pharmacokinetic model (PBPK model) is used to derive a compound specific adjustment factor (CSAF) for the pharmacokinetic component, the deconvolution of the PK and PD components allows one to remove the PK component (to be replaced with the CSAF), while retaining the uncertainty in pharmacodynamics that PBPK models do not address. One must then add back the uncertainty in the PBPK determination of the CSAF (which may be considerable). A candidate criterion for whether one can use an uncertain PBPK model is whether the generic uncertainty about cross-species pharmacokinetics (reflected in the PK component of the overall empirical distribution) is larger than the chemical-specific uncertainty in the determination of kinetically equivalent doses in experimental animals and humans.     

2BAD: an application to estimate the parental contributions during two independent admixture events

Several approaches have been developed to calculate the relative contributions of parental populations in single admixture event scenarios, including Bayesian methods. In many breeds and populations, it may be more realistic to consider multiple admixture events. However, no approach has been developed to date to estimate admixture in such cases. This report describes a program application, 2BAD (for 2-event Bayesian ADmixture), which allows the consideration of up to two independent admixture events involving two or three parental populations and a single admixed population, depending on the number of populations sampled. For each of these models, it is possible to estimate several parameters (admixture, effective sizes, etc.) using an approximate Bayesian computation approach. In addition, the program allows comparing pairs of admixture models, determining which is the most likely given data. The application was tested through simulations and was found to provide good estimates for the contribution of the populations at the two admixture events. We were also able to determine whether an admixture model was more likely than a simple split model.     

A calculator program for clinical application of the Bayesian method of predicting plasma drug levels

A pharmacokinetic program that allows individualization of drug dosage regimens through the Bayesian method is described. The program, which is designed for the Hewlett-Packard HP-41 CV calculator, is based upon the one-compartment open model with either instantaneous or zero-order absorption. Individualized estimation of the patient's kinetic parameters (clearance and volume of distribution) is performed by analyzing the plasma levels measured in the patient as well as considering the population data of the drug. After estimating the individual kinetic parameters by the Bayesian method, the program predicts the dosage regimen that will elicit the desired peak and trough plasma levels at steady state. For comparison purposes, the least-squares estimates for clearance and volume of distribution are calculated, and dosage prediction can also be made on the basis of the least-squares estimates. The least-squares estimates can be used to calculate population pharmacokinetic parameters according to the Standard Two-Stage method. Several examples of clinical use of the program are presented. The examples refer to patients with classic hemophilia who were treated with Factor VIII concentrates. In these patients, the Bayesian kinetic parameters of Factor VIII have been estimated through the calculator program. The Bayesian parameter estimates generated by the HP-41 have been compared with those determined by a Bayesian program (ADVISE) designed for microcomputers.     

Establishing the dose-dependent daily variations of a low molecular weight heparin (Fraxiparine) through a population approach analysis in the rat

The effects of dose and dosing time on the anticoagulant activity of a low molecular weight heparin (Fraxiparine®) were studied in rats. Three doses were administered at four evenly spaced dosing times. Rats were kept under a light-dark cycle of 24h, and all the main external factors were constant. The bleeding time, the anti-Xa activity of the drug, and the activated partial thromboplastin time (APTT) were measured. A population approach analysis to assess daily variations was used. With standard methods, interindividual variability may mask potential time-related effects, while the population approach analysis overcomes this difficulty.

Bleeding time was at its peak at 04:00 and at its trough at 22:00, suggesting that platelet activity was time of day dependent. For the pharmacological activity of the drug, we compared several pharmacokinetic models derived from a monocompartmental model. The model that describes the anti-Xa pharmacological activity best is expressed through parameters that depend on animal weight and drug level. The model for APTT is of a sinusoidal type for which the clearance depends on the dosing time. The most interesting result is that the amplitude of this daily variation is linearly dependent on drug level. (Chronobiology International, 17(2), 173-185, 2000)     

PKQuest: volatile solutes - application to enflurane,nitrous oxide,halothane, methoxyflurane and toluene pharmacokinetics

BACKGROUND: The application of physiologically based pharmacokinetic models (PBPK) to human studies has been limited by the lack of the detailed organ information that is required for this analysis. PKQuest is a new generic PBPK that is designed to avoid this problem by using a set of "standard human" default parameters that are applicable to most solutes. RESULTS: PKQuest is used to model the human pharmacokinetics of the volatile solutes. A "standard human" value for the lipid content of the blood and each organ (klip) was chosen. This set of klip and the oil/water partition coefficient then specifies the organ/blood partition for each organ. Using this approach, the pharmacokinetics of inert volatile solute is completely specified by just 2 parameters: the water/air and oil/water partition coefficients. The model predictions of PKQuest were in good agreement with the experimental data for the inert solutes enflurane and nitrous oxide and the metabolized solutes halothane and toluene. METHODS: The experimental data that was modeled was taken from previous publications. CONCLUSIONS: This approach greatly increases the predictive power of the PBPK. For inert volatile solutes the pharmacokinetics are determined just from the water/air and oil/water partition coefficient. Methoxyflurane cannot be modeled by this PBPK because the arterial and end tidal partial pressures are not equal (as assumed in the PBPK). This inequality results from the "washin-washout" artifact in the large airways that is established for solutes with large water/air partition coefficients.PKQuest and the worked examples are available on the web www.pkquest.com.     

ESTABLISHING THE DOSE-DEPENDENT DAILY VARIATIONS OF A LOW MOLECULAR WEIGHT HEPARIN (FRAXIPARINE®) THROUGH A POPULATION APPROACH ANALYSIS IN THE RAT

The effects of dose and dosing time on the anticoagulant activity of a low molecular weight heparin (Fraxiparine®) were studied in rats. Three doses were administered at four evenly spaced dosing times. Rats were kept under a light-dark cycle of 24h, and all the main external factors were constant. The bleeding time, the anti-Xa activity of the drug, and the activated partial thromboplastin time (APTT) were measured. A population approach analysis to assess daily variations was used. With standard methods, interindividual variability may mask potential time-related effects, while the population approach analysis overcomes this difficulty.

Bleeding time was at its peak at 04:00 and at its trough at 22:00, suggesting that platelet activity was time of day dependent. For the pharmacological activity of the drug, we compared several pharmacokinetic models derived from a monocompartmental model. The model that describes the anti-Xa pharmacological activity best is expressed through parameters that depend on animal weight and drug level. The model for APTT is of a sinusoidal type for which the clearance depends on the dosing time. The most interesting result is that the amplitude of this daily variation is linearly dependent on drug level. (Chronobiology International, 17(2), 173–185, 2000)     

Bayesian Inference for Generalized Linear Mixed Model Based on the Multivariate t Distribution in Population Pharmacokinetic Study

This article provides a fully Bayesian approach for modeling of single-dose and complete pharmacokinetic data in a population pharmacokinetic (PK) model. To overcome the impact of outliers and the difficulty of computation, a generalized linear model is chosen with the hypothesis that the errors follow a multivariate Student t distribution which is a heavy-tailed distribution. The aim of this study is to investigate and implement the performance of the multivariate t distribution to analyze population pharmacokinetic data. Bayesian predictive inferences and the Metropolis-Hastings algorithm schemes are used to process the intractable posterior integration. The precision and accuracy of the proposed model are illustrated by the simulating data and a real example of theophylline data.     

Mechanistic prediction of food effects for Compound A tablet using PBPK model

Physiologically based pharmacokinetic (PBPK) modeling has been extensively used to study the factors of effect drug absorption, distribution, metabolize and extraction progress in human. In this study, Compound A(CPD A) is a BCS Class II drug, which has been extensive applied in clinical as lipid-lowering drug, administered orally after food, they displayed positive food effects in human, A PBPK model was built to mechanistic investigate the food effect of CPD A tablet in our study. By using gastroplus™ software, the PBPK models accurately predicted the results of food effects and predicted data were within 2-fold error of the observed results. The PBPK model mechanistic illuminated the changes of pharmacokinetic values for the positive food effects of the compound in human. Here in, the PBPK modeling which were combined with ACAT absorption models in it, successfully simulated the food effect in human of the drug. The simulation results were proved that PBPK model can be able to serve as a potential tool to predict the food effect on certain oral drugs.     

PKQuest: volatile solutes – application to enflurane, nitrous oxide, halothane, methoxyflurane and toluene pharmacokinetics

Background  

The application of physiologically based pharmacokinetic models (PBPK) to human studies has been limited by the lack of the detailed organ information that is required for this analysis. PKQuest is a new generic PBPK that is designed to avoid this problem by using a set of "standard human" default parameters that are applicable to most solutes.     

Frog population viability under present and future climate conditions: a Bayesian state-space approach

1.?World-wide extinctions of amphibians are at the forefront of the biodiversity crisis, with climate change figuring prominently as a potential driver of continued amphibian decline. As in other taxa, changes in both the mean and variability of climate conditions may affect amphibian populations in complex, unpredictable ways. In western North America, climate models predict a reduced duration and extent of mountain snowpack and increased variability in precipitation, which may have consequences for amphibians inhabiting montane ecosystems. 2.?We used Bayesian capture-recapture methods to estimate survival and transition probabilities in a high-elevation population of the Columbia spotted frog (Rana luteiventris) over 10?years and related these rates to interannual variation in peak snowpack. Then, we forecasted frog population growth and viability under a range of scenarios with varying levels of change in mean and variance in snowpack. 3.?Over a range of future scenarios, changes in mean snowpack had a greater effect on viability than changes in the variance of snowpack, with forecasts largely predicting an increase in population viability. Population models based on snowpack during our study period predicted a declining population. 4.?Although mean conditions were more important for viability than variance, for a given mean snowpack depth, increases in variability could change a population from increasing to decreasing. Therefore, the influence of changing climate variability on populations should be accounted for in predictive models. The Bayesian modelling framework allows for the explicit characterization of uncertainty in parameter estimates and ecological forecasts, and thus provides a natural approach for examining relative contributions of mean and variability in climatic variables to population dynamics. 5.?Longevity and heterogeneous habitat may contribute to the potential for this amphibian species to be resilient to increased climatic variation, and shorter-lived species inhabiting homogeneous ecosystems may be more susceptible to increased variability in climate conditions.     

The combination of population pharmacokinetic studies

Pharmacokinetic data consist of drug concentrations with associated known sampling times and are collected following the administration of known dosage regimens. Population pharmacokinetic data consist of such data on a number of individuals, possibly along with individual-specific characteristics. During drug development, a number of population pharmacokinetic studies are typically carried out and the combination of such studies is of great importance for characterizing the drug and, in particular, for the design of future studies. In this paper, we describe a model that may be used to combine population pharmacokinetic data. The model is illustrated using six phase I studies of the antiasthmatic drug fluticasone propionate. Our approach is Bayesian and computation is carried out using Markov chain Monte Carlo. We provide a number of simplifications to the model that may be made in order to ease simulation from the posterior distribution.     

Spiking networks for Bayesian inference and choice

Systems neuroscience traditionally conceptualizes a population of spiking neurons as merely encoding the value of a stimulus. Yet, psychophysics has revealed that people take into account stimulus uncertainty when performing sensory or motor computations and do so in a nearly Bayes-optimal way. This suggests that neural populations do not encode just a single value but an entire probability distribution over the stimulus. Several such probabilistic codes have been proposed, including one that utilizes the structure of neural variability to enable simple neural implementations of probabilistic computations such as optimal cue integration. This approach provides a quantitative link between Bayes-optimal behaviors and specific neural operations. It allows for novel ways to evaluate probabilistic codes and for predictions for physiological population recordings.     

Application of Physiologically Based Absorption Modeling to Formulation Development of a Low Solubility,Low Permeability Weak Base: Mechanistic Investigation of Food Effect

Physiologically based pharmacokinetic (PBPK) modeling has been broadly used to facilitate drug development, hereby we developed a PBPK model to systematically investigate the underlying mechanisms of the observed positive food effect of compound X (cpd X) and to strategically explore the feasible approaches to mitigate the food effect. Cpd X is a weak base with pH-dependent solubility; the compound displays significant and dose-dependent food effect in humans, leading to a nonadherence of drug administration. A GastroPlus Opt logD Model was selected for pharmacokinetic simulation under both fasted and fed conditions, where the biopharmaceutic parameters (e.g., solubility and permeability) for cpd X were determined in vitro, and human pharmacokinetic disposition properties were predicted from preclinical data and then optimized with clinical pharmacokinetic data. A parameter sensitivity analysis was performed to evaluate the effect of particle size on the cpd X absorption. A PBPK model was successfully developed for cpd X; its pharmacokinetic parameters (e.g., C _max, AUC_inf, and t _max) predicted at different oral doses were within ±25% of the observed mean values. The in vivo solubility (in duodenum) and mean precipitation time under fed conditions were estimated to be 7.4- and 3.4-fold higher than those under fasted conditions, respectively. The PBPK modeling analysis provided a reasonable explanation for the underlying mechanism for the observed positive food effect of the cpd X in humans. Oral absorption of the cpd X can be increased by reducing the particle size (<100 nm) of an active pharmaceutical ingredient under fasted conditions and therefore, reduce the cpd X food effect correspondingly.     

PBPK models in risk assessment--A focus on chloroprene

Mathematical models are increasingly being used to simulate events in the exposure-response continuum, and to support quantitative predictions of risks to human health. Physiologically based pharmacokinetic (PBPK) models address that portion of the continuum from an external chemical exposure to an internal dose at a target site. Essential data needed to develop a PBPK model include values of key physiological parameters (e.g., tissue volumes, blood flow rates) and chemical specific parameters (rate of chemical absorption, distribution, metabolism, and elimination) for the species of interest. PBPK models are commonly used to: (1) predict concentrations of an internal dose over time at a target site following external exposure via different routes and/or durations; (2) predict human internal concentration at a target site based on animal data by accounting for toxicokinetic and physiological differences; and (3) estimate variability in the internal dose within a human population resulting from differences in individual pharmacokinetics. Himmelstein et al. [M.W. Himmelstein, S.C. Carpenter, P.M. Hinderliter, Kinetic modeling of beta-chloroprene metabolism. I. In vitro rates in liver and lung tissue fractions from mice, rats, hamsters, and humans, Toxicol. Sci. 79 (1) (2004) 18-27; M.W. Himmelstein, S.C. Carpenter, M.V. Evans, P.M. Hinderliter, E.M. Kenyon, Kinetic modeling of beta-chloroprene metabolism. II. The application of physiologically based modeling for cancer dose response analysis, Toxicol. Sci. 79 (1) (2004) 28-37] developed a PBPK model for chloroprene (2-chloro-1,3-butadiene; CD) that simulates chloroprene disposition in rats, mice, hamsters, or humans following an inhalation exposure. Values for the CD-PBPK model metabolic parameters were obtained from in vitro studies, and model simulations compared to data from in vivo gas uptake studies in rats, hamsters, and mice. The model estimate for total amount of metabolite in lung correlated better with rodent tumor incidence than did the external dose. Based on this PBPK model analytical approach, Himmelstein et al. [M.W. Himmelstein, S.C. Carpenter, M.V. Evans, P.M. Hinderliter, E.M. Kenyon, Kinetic modeling of beta-chloroprene metabolism. II. The application of physiologically based modeling for cancer dose response analysis, Toxicol. Sci. 79 (1) (2004) 28-37; M.W. Himmelstein, R. Leonard, R. Valentine, Kinetic modeling of beta-chloroprene metabolism: default and physiologically-based modeling approaches for cancer dose response, in: IISRP Symposium on Evaluation of Butadiene & Chloroprene Health Effects, September 21, 2005, TBD--reference in this proceedings issue of Chemical-Biological Interactions] propose that observed species differences in the lung tumor dose-response result from differences in CD metabolic rates. The CD-PBPK model has not yet been submitted to EPA for use in developing the IRIS assessment for chloroprene, but is sufficiently developed to be considered. The process that EPA uses to evaluate PBPK models is discussed, as well as potential applications for the CD-PBPK model in an IRIS assessment.     

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.     

Assessing antiangiogenic therapy response by DCE-MRI: development of a physiology driven multi-compartment model using population pharmacometrics

Dynamic contrast enhanced (DCE-) MRI is commonly applied for the monitoring of antiangiogenic therapy in oncology. Established pharmacokinetic (PK) analysis methods of DCE-MRI data do not sufficiently reflect the complex anatomical and physiological constituents of the analyzed tissue. Hence, accepted endpoints such as Ktrans reflect an unknown multitude of local and global physiological effects often rendering an understanding of specific local drug effects impossible. In this work a novel multi-compartment PK model is presented, which for the first time allows the separation of local and systemic physiological effects. DCE-MRI data sets from multiple, simultaneously acquired tissues, i.e. spinal muscle, liver and tumor tissue, of hepatocellular carcinoma (HCC) bearing rats were applied for model development. The full Markov chain Monte Carlo (MCMC) Bayesian analysis method was applied for model parameter estimation and model selection was based on histological and anatomical considerations and numerical criteria. A population PK model (MTL3 model) consisting of 3 measured and 6 latent (unobserved) compartments was selected based on Bayesian chain plots, conditional weighted residuals, objective function values, standard errors of model parameters and the deviance information criterion. Covariate model building, which was based on the histology of tumor tissue, demonstrated that the MTL3 model was able to identify and separate tumor specific, i.e. local, and systemic, i.e. global, effects in the DCE-MRI data. The findings confirm the feasibility to develop physiology driven multi-compartment PK models from DCE-MRI data. The presented MTL3 model allowed the separation of a local, tumor specific therapy effect and thus has the potential for identification and specification of effectors of vascular and tissue physiology in antiangiogenic therapy monitoring.     

Robust estimation of local genetic ancestry in admixed populations using a nonparametric bayesian approach

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.