An introduction to the use of physiologically based pharmacokinetic models in risk assessment

Many extrapolation issues surface in quantitative risk assessments. The extrapolation from high-dose animal studies to low-dose human exposures is of particular concern. Physiologically based pharmacokinetic (PBPK) models are often proposed as tools to mitigate the problems of extrapolation. These models provide a representation of the disposition, metabolism, and excretion of xenobiotics that are believed to possess the potential of inducing adverse human health responses. Given a model of xenobiotic disposition that is applicable for multiple species and appropriate for nonlinearity of the xenobiotic biotransformation process, better extrapolation may be possible. Unfortunately, the true structure of these models (e.g. number of compartments, type of metabolism, etc.) is seldom known, and attributes of these models (tissue volumes, partition coefficients, etc.) are often experimentally determined and often only central measures of these quantities are reported. We describe the use of PBPK models in risk assessment, the structural and parameter uncertainty in these models, and provide a simple illustration of how these characteristics can be incorporated in a statistical analysis of PBPK models. Additional complexity in the analysis of variability in the models is also outlined. This discussion is illustrated using data from methylene chloride.     

A physiologically based pharmacokinetic and pharmacodynamic model for paraoxon in rainbow trout

Trout were exposed to an aqueous solution of 75 ng/ml paraoxon for 5 days at 12 degrees C. The relationships among paraoxon concentration in water and target organs, AChE inhibition, and carboxylesterase (CaE) detoxification of paraoxon were characterized quantitatively by development of a PBPK-PD model. The PKPD model structure consisted of brain, heart, liver, kidney, and remainder of the body, which were interconnected by blood circulation. The paraoxon tissue/blood partition coefficients were: plasma/water, 1.46; liver/plasma, 5.89; brain/plasma, 3.90; heart/plasma, 2.91; kidney/plasma, 0.45; and blood/plasma, 0.91. Turnover of AChE was characterized from a dose-response study, in which its zero-order synthesis rate and first-order degradation rate constant were determined in several tissues; for brain they were 7.67 pmol/min and 7.31 x 10(-5) hr(-1). The uptake and depuration clearances of paraoxon (Cl(u) = 0.651 and Cl(d) = 0.468 ml min(-1) g body wt(-1)) were determined using a compartmental model. During continuous water exposure to paraoxon, AChE activity in the tissues declined to new steady state values that were maintained by the synthesis of new AChE. CaE was shown by simulation to be an important pathway for detoxification of paraoxon.     

Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty

PURPOSE: We explore use of "bootstrapping" methods to obtain a measure of reliability of predictions made in part from fits of individual drug level data with a pharmacokinetic (PK) model, and to help clarify parameter identifiability for such models. METHODS: Simulation studies use four sets (A-D) of drug concentration data obtained following a single oral dose. Each set is fit with a two compartment PK model, and the "bootstrap" is employed to examine the potential predictive variation in estimates of parameter sets. This yields an empirical distribution of plausible steady state (SS) drug concentration predictions that can be used to form a confidence interval for a prediction. RESULTS: A distinct, narrow confidence region in parameter space is identified for subjects A and B. The bootstrapped sets have a relatively large coefficient of variation (CV) (35-90% for A), yet the corresponding SS drug levels are tightly clustered (CVs only 2-9%). The results for C and D are dramatically different. The CVs for both the parameters and predicted drug levels are larger by a factor of 5 and more. The results reveal that the original data for C and D, but not A and B, can be represented by at least two different PK model manifestations, yet only one provides reliable predictions. CONCLUSIONS: The insights gained can facilitate making decisions about parameter identifiability. In particular, the results for C and D have important implications for the degree of implicit overparameterization that may exist in the PK model. In cases where the data support only a single model manifestation, the "bootstrap" method provides information needed to form a confidence interval for a prediction.     

Development and application of a physiologically based pharmacokinetic model for ethanol in the mouse

The purpose of the present study was to develop a physiologically based pharmacokinetic (PBPK) model in the mouse and to utilize it to evaluate the relative contribution, if any, of gastric alcohol dehydrogenase (ADH) to the bioavailability of ethanol. The PBPK model developed in Swiss Webster male mice accurately simulated blood and brain ethanol concentrations following an intraperitoneal administration of 0.82 and 3.2 g of ethanol/kg body weight. Application of the model illustrated that inclusion of gastric ADH into the model provided a less accurate fit to the experimental data, and therefore gastric ADH did not contribute to the overall disposition of an orally administered ethanol dose of 0.75 g/kg. Furthermore, the model also indicated that changes in percentage cardiac output to the liver had a minimal effect on the blood ethanol concentration (BEC) time curve. The results illustrate the validity of the PBPK model developed for ethanol and demonstrate that in the Swiss Webster male mouse the bioavailability of ethanol is minimally affected, if at all, by metabolism by gastric ADH.     

Predicting cancer risk from vinyl chloride exposure with a physiologically based pharmacokinetic model

A physiologically based pharmacokinetic (PBPK) model capable of describing the metabolism of vinyl chloride (VC) in rats, mice, and humans has been developed and validated by comparison with experimental data from experiments not used in model development. This PBPK model has been used to predict measures of delivered dose (reactive VC metabolites produced in the livers of the affected species) hypothesized to be involved in the induction of liver angiosarcoma in rats, mice, and human populations exposed to VC. Measures of delivered dose in rats were fit to an empirical dose-response model (the linearized multistage model of Crump et al.) and used to make predictions of liver angiosarcoma incidence in mice and human populations exposed to VC. This procedure gave a good prediction of angiosarcoma incidence in mice. Predictions of angiosarcoma incidence in humans were more than two orders of magnitude lower than risk estimations which did not utilize pharmacokinetic data, but were still almost an order of magnitude higher than actually observed in exposed human populations.     

Construction of a physiologically based pharmacokinetic model for 2,4-dichlorophenoxyacetic acid dosimetry in the developing rabbit brain

A physiologically based pharmacokinetic (PBPK) model that describes the kinetics of organic anions by using 2,4-dichlorophenoxyacetic (2,4-D) as a representative compound was constructed for the developing rabbit brain at near-term pregnancy (Gestation Day 30). The model consisted of brain, body, and venous and arterial compartments for the mother which were linked to the fetus by a placenta. Maternal brain compartments in the model were brain plasma, cerebrospinal fluid (CSF), and brain tissue including hypothalamus, caudate nucleus, hippocampus, forebrain, brainstem, and cerebellum. The fetus consisted of brain, body, amniotic fluid, and venous and arterial compartments. the maternal body had both a central and a deep compartment; the fetal body had only one compartment. Maternal blood flow to the fetus was modeled as blood flowing to the placenta, where it was equilibrated before it reached the fetus. The brain uptake was membrane-limited by the blood-brain barrier, with saturable clearance from the CSF into the venous blood by the choroid plexus in both fetus and mother. The model was used to compare concentrations of 2,4-D in maternal and fetal brain, maternal and fetal plasma, and amniotic fluid over time with experimental data from pregnant rabbits given 2,4-D intravenously (1, 10, or 40 mg/kg). The model adequately simulated the 2-hr time course of 2,4-D concentrations in both mother and fetus. With continued development, this generic PBPK model should be a useful tool for evaluating the safety of organic acid neurotoxicants in the developing brain.     

Combining physiologically based pharmacokinetic modeling with Monte Carlo simulation to derive an acute inhalation guidance value for trichloroethylene

Using the Monte Carlo method and physiologically based pharmacokinetic modeling, an occupational inhalation exposure to trichloroethylene consisting of 7 h of exposure per day for 5 days was simulated in populations of men and women of 5000 individuals each. The endpoint of concern for occupational exposure was drowsiness. The toxicologic condition leading to drowsiness was assumed to be high levels of both trichloroethanol and trichloroethylene. Therefore, the output of the simulation or dose metric was the maximum value of the sum of the concentration of trichloroethylene in blood and the concentration of trichloroethanol within its volume of distribution occurring within 1 week of exposure. The distributions of the dose metric in the simulated populations were lognormal. To protect 99% of a worker population, a concentration of 30 ppm over a 7-h period of the work day should not be exceeded. Subjecting a susceptible individual (the 99th percentile of the dose metric) to 200 ppm (the ACGIH short-term exposure limit or STEL) for 15 min twice a day over a work week necessitates a 2.5-h rest in fresh air following the STEL exposure to allow the blood concentrations of trichloroethylene and trichloroethanol to drop to levels that would not cause drowsiness. Both the OSHA PEL and the ACGIH TLV are greater than the value of 30 ppm derived here. As well as suggesting a new occupational guidance value, this study provides an example of this method of guidance value derivation.     

Physiologically based pharmacokinetic models of 2'',3''-dideoxyinosine

In this paper, the construction, evaluation, and application of cDNA libraries from eight unfertilized oocytes and single four-cell-, seven-cell-, and blastocyst-stage embryos are described. Rapid, reproducible, and efficient procedures for the construction of PCR-based cDNA libraries from fewer than 10 cells were first developed in small populations of fibroblast cells. The human embryo libraries display complexities sufficient (between 10(5) and 10(6) clones) to represent the entire active gene population at these early stages of human development. The ubiquitous cytoskeletal elements, beta-actin, keratin-18, and alpha-tubulin, were detected at the expected frequency. Sequencing of consecutively picked random clones, without selection, showed the presence of a variety of sequences, such as the human transposable element, LINE-1 and Alu repeat sequences, housekeeping genes, and tissue-specific genes, such as alpha-globin and FMR-1. In addition to cDNAs corresponding to known ESTs (expressed sequence tags) in the GenBank and dbEST databases, a high proportion of novel sequences were detected. Applications of the libraries to several areas of interest, such as expression of CpG-island-containing "tissue-specific" genes, developmental genes expressed in a stage-specific manner, and a search for monoallelic expression of imprinted genes, are described. The libraries are a valuable resource for the study of gene expression during human preimplantation development and obviate the need for research on the human embryos themselves.     

Physiologically relevant one-compartment pharmacokinetic models for skin. 2. Comparison of models when combined with a systemic pharmacokinetic model

The discovery of a second isoform of cyclooxygenase (cyclooxygenase-2) that is expressed in inflammatory cells and the central nervous system, but not in the gastric mucosa, offers the possibility of developing anti-inflammatory and analgesic agents that lack the gastrointestinal side effects of currently available nonsteroidal anti-inflammatory drugs. Lead compounds from several different structural classes have been identified and shown to be slow, tight-binding inhibitors that express their selectivity for cyclooxygenase-2 in the time-dependent step. The determination of structures of enzyme-inhibitor co-crystals along with site-directed mutagenesis experiments reveal the molecular basis for selectivity of some, but not all, inhibitors. Preclinical and clinical studies suggest cyclooxygenase-2 inhibitors are highly promising new agents for the treatment of pain and inflammation, and for the prevention of cancer.     

A physiologically based pharmacokinetic model of zidovudine (AZT) in the mouse: model development and scale-up to humans

After having been used in treating HIV infection for a decade, zidovudine (AZT) continues to be an essential component of antiretroviral regimens. Because antiviral responses and toxicity of AZT seem to be related to cells in specific target tissues, being able to understand and predict the distribution of AZT into different pharmacologically and toxicologically relevant tissues is therefore critically important to improving the efficacy and minimizing the toxicity of AZT therapy. This study was designed to develop a physiologically based pharmacokinetic model to help describe and predict the time course of AZT levels in different tissues. The model was developed in the mouse and then scaled up to predict human situations.     

Physiologically relevant one-compartment pharmacokinetic models for skin. 1. Development of models

Many studies have used pharmacokinetic (compartment) models for skin to predict or analyze absorption of chemicals through skin. In these studies, several different definitions of the rate constants were used. The purpose of this study was to develop a general procedure for relating compartment model rate constants to dermal absorption parameters, such as permeability and partition coefficients, and to assess whether different definitions of the rate constants produce different results. Rate constant expressions were developed by requiring a one-compartment model to match a one-membrane model at specific conditions. Because a membrane model contains more information than a compartment model, a compartment model cannot match the membrane model in all respects. Consequently, many compartment models (i.e., different definitions of the rate constants) can be developed which match the membrane model for different conditions. Using this procedure, 11 different compartment models were developed and compared to the membrane model for four different dermal absorption scenarios. The compartment model that most closely matches the membrane model depends on the specific exposure scenario and what is to be predicted. One of the new compartment models agrees reasonably well with the membrane model, for the cases considered.     

Local identifiability for two and three-compartment pharmacokinetic models with time-lags

Parkinson's disease (PD), a disorder of unknown etiology, is associated with the degeneration of dopaminergic neurons in nigro-striatal pathways. MPTP, a meperidine analog, causes parkinsonism in human and nonhuman primates. MPP+, the active metabolite of MPTP, inhibits the activity of respiratory chain complex I. In patients with PD, a reduced complex I activity was found in substantia nigra, skeletal muscle, and platelets. Because complex I is partially encoded by the mitochondrial genome, several studies have searched for mitochondrial (mt) DNA abnormalities in patients with PD. Our aim was to answer the following questions: (1) are there some abnormalities of mtDNA in PD? (2) if there are some, what are these abnormalities? and (3) what is the pathogenic role of these abnormalities? METHODS: The literature review was performed using Medline [National Library of Medicine, Washington] and Current Contents [Institute for Scientific Information, Philadelphia] databases. Periods screened were 1966-March, 1998 (Medline) and March 17, 1997-March 9, 1998 (Current Contents). Keywords were: "Parkinson" or "Parkinson's", and "mitochondrial DNA" or "mtDNA". We limited our research to articles in English and French. RESULTS: Medline search provided 59 articles. Current Contents search provided 22 articles. Twelve articles were found in both databases. Thirty-eight of the 69 articles were either reviews about mitochondrial diseases (19 articles) or original articles not related to mtDNA (19 articles). Our final selection included the remaining 31 articles.     

Identifiability and indistinguishability of nonlinear pharmacokinetic models

Three nonlinear model structures of interest in pharmacokinetics are analyzed to determine whether the unknown, independent, model parameters can be deduced if perfect input-output data were available. This is the problem of identifiability. The method used is based on the local state isomorphism theorem. In certain circumstances, the modeler may be undecided between several model structures and it is then of interest to determine whether different model structures can be distinguished from perfect input-output data. This is the problem of model indistinguishability. The technique used, again based on the local state isomorphism theorem, parallels the similarity transformation approach for linear systems described previously in this journal. The analysis is performed on three two-compartment examples having one linear and one nonlinear (Michaelis-Menten) elimination pathway. In each model there is, on physiological and other grounds, some uncertainty over the precise location (central compartment or peripheral compartment) of one of the elimination pathways.     

Three-dimensional visualization of physiologically based kinetic model outputs

Outputs from a physiologically based toxicokinetic (PB-TK) model for fish were visualized by mapping time-series data for specific tissues onto a three-dimensional representation of a rainbow trout. The trout representation was generated in stepwise fashion: 1) cross-section images were obtained from an anesthetized fish using a magnetic resonance imaging system, 2) images were processed to classify tissue types and eliminate unnecessary detail. 3) processed images were imported to a visualization software package (Application Visualization System) to create a three-dimensional representation of the fish, encapsulating five volumes corresponding to the liver, kidney, muscle, gastrointestinal tract, and fat, Kinetic data for the disposition of pentachloroethane in trout were generated using a PB-TK model. Model outputs were mapped onto corresponding tissues volumes, representing chemical concentration as color intensity. The workstation software was then used to animate the images, illustration the accumulation of pentachloroethane in each tissue during a continuous branchial (gill) exposure.     

Testing a model for the dynamics of actin structures with biological parameter values

A simple mathematical model for the dynamics of network-bundle transitions in actin filaments has been previously proposed and some of its mathematical properties have been described. Other models in this class have since been considered and investigated mathematically. In this paper, we have made the first steps in connecting parameters in the model with biologically measurable quantities such as published values of rate constants for filament-crosslinker association. We describe how this connection was made, and give some preliminary numerical simulation results for the behavior of the model under biologically realistic parameter regimes. A key result is that filament length influences the bundle-network transition.     

Simulation of toluene kinetics in the rat by a physiologically based pharmacokinetic model with application of biotransformation parameters derived independently in vitro and in vivo

The biokinetic behavior of toluene was modeled in the rat with a physiologically based pharmacokinetic (PB-PK) model. The model was parameterized by using reference physiological parameter values and partition coefficients that were reported earlier from in vitro studies. Biotransformation parameters for toluene, reported from two in vivo and six in vitro studies, were subsequently substituted in the model while keeping all other model parameters constant. Simulations of toluene kinetics, based on these eight biotransformation parameter sets, were compared with empirical data reported on toluene uptake in blood and/or brain tissue after inhalation exposure. It was observed that most empirical data on toluene blood concentrations were adequately predicted by the model for almost each of the eight biotransformation parameter sets. It was also observed that differences between model predictions, based on either in vivo- or in vitro-derived biotransformation parameters, were generally small. It is concluded that the results from most in vitro studies on toluene biotransformation can be applied successfully to predict the kinetics of toluene in vivo. It is also concluded that the brain-blood partition coefficient may be at least as important for the outcome of the model as the biotransformation parameters are. These results support earlier reported findings in the literature on application of in vitro techniques to derive parameters for PB-PK models.     

Bayesian population pharmacokinetic and pharmacodynamic analyses using mixture models

Population studies of the pharmacokinetics or pharmacodynamics of drugs help us, learn about the variability in drug disposition and effects, information that can be used to treat future patients at safe and effective doses. We present a new approach to population modeling based on a weighted mixture of normal distributions having random weights and means. This method allows estimation of underlying continuous population distributions without prespecifying the parametric form or shape of these probability distributions. Additionally, this method can carry out nonparametric regression of pharmacokinetic or dynamic parameters on patient covariates while estimating the underlying distributions. Two examples illustrate the method and its flexibility.