Bayesian Population Physiologically-Based Pharmacokinetic (PBPK) Approach for a Physiologically Realistic Characterization of Interindividual Variability in Clinically Relevant Populations

<div><p>Interindividual variability in anatomical and physiological properties results in significant differences in drug pharmacokinetics. The consideration of such pharmacokinetic variability supports optimal drug efficacy and safety for each single individual, e.g. by identification of individual-specific dosings. One clear objective in clinical drug development is therefore a thorough characterization of the physiological sources of interindividual variability. In this work, we present a Bayesian population physiologically-based pharmacokinetic (PBPK) approach for the mechanistically and physiologically realistic identification of interindividual variability. The consideration of a generic and highly detailed mechanistic PBPK model structure enables the integration of large amounts of prior physiological knowledge, which is then updated with new experimental data in a Bayesian framework. A covariate model integrates known relationships of physiological parameters to age, gender and body height. We further provide a framework for estimation of the <i>a posteriori</i> parameter dependency structure at the population level. The approach is demonstrated considering a cohort of healthy individuals and theophylline as an application example. The variability and co-variability of physiological parameters are specified within the population; respectively. Significant correlations are identified between population parameters and are applied for individual- and population-specific visual predictive checks of the pharmacokinetic behavior, which leads to improved results compared to present population approaches. In the future, the integration of a generic PBPK model into an hierarchical approach allows for extrapolations to other populations or drugs, while the Bayesian paradigm allows for an iterative application of the approach and thereby a continuous updating of physiological knowledge with new data. This will facilitate decision making e.g. from preclinical to clinical development or extrapolation of PK behavior from healthy to clinically significant populations.</p></div

Exemplary representation of derived distributions of correlation between the population parameters.

<p>The correlation of a pair of parameters along all individuals was calculated for each of the 500 subsamples of the posterior distribution. For each pair of parameters the histogram of all correlations is shown, representing the uncertainty of the respective correlation.</p

Comparison of visual predictive checks of population pharmacokinetics.

<p>(<b>a</b>) Visual predicive check (VPC) of the pharmacokinetic behavior using the posterior distributions based on the presented Bayesian population PBPK approach. The uncertainty in population parameters was included in the VPC. (<b>b</b>) Visual predicive check of the pharmacokinetic behavior using the prior distributions of all parameters. (<b>c</b>) Visual predicive check (VPC) of the pharmacokinetic behavior using the maximum posterior estimates of the posterior distribution based on the presented Bayesian population PBPK approach. Each VPC is presented in linear scale (left) and logarithmic scale (right). The VPCs were performed as described in the text. In each VPC, the 5% and 95% percentiles (black dotted lines) and the median (black line) of the experimental data (red dots) are compared against the 95% confidence intervals of the 5% and 95% percentile of the simulation (light blue area) and the median (blue area).</p

Individual-specific model simulations of theophylline venous plasma concentrations.

<p>For each of the 12 individuals the PBPK model was subsequently parameterized and simulated with each of 500 individual and independent parameter vectors out of the posterior distribution. The 95% confidence interval of all simulations (grey area) is shown together with the mean value curve (blue dotted line) and the experimental data (red circles). Dark grey dotted lines depict the upper and lower bound of the 95% confidence interval of all simulations including the inferred measurement error.</p

Comparison of characteristic parameters of the prior and posterior population distributions.

<p>Prior and posterior geometric mean values and coefficients of variations (CV) are shown for nine exemplary physiological parameters.</p

Schematic illustration of the presented Bayesian population PBPK approach.

<p>(A) A Bayesian framework is combined with a detailed mechanistic PBPK model, where a Markov chain Monte Carlo (MCMC) approach is considered to identify the high dimensional parameter distribution. (B) Prior population-specific anatomical and physiological information is integrated into an hierarchical model approach. (C) Individual-specific experimental data and physiological parameters are considered to parameterize the model and to generate individual model outputs. (D) Due to the model structure of the PBPK model, substance parameters can be differentiated from physiological parameters. This allows a global determination of the substance information, since it does not vary individually or from population to population.</p

Comparison of observed experimental data and simulated values.

<p>Mean simulated values are plotted against the observed data at the same time points for all individuals (different markers, see legend in the figure).</p

Comparison of marginal prior and posterior distributions of nine exemplary physiological parameters.

<p>For each parameter, the marginal posterior density estimate out of the full posterior (red line) is compared to the corresponding prior distribution (green dotted line). Limits on x axis represent physiological constraints as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139423#pone.0139423.s004" target="_blank">S1 Table</a> (except for intP where the maximum x value was reduced by a factor of 20 and for specCL were the maximum x value was reduced by a factor of 2 for better visualization)</p