Multimolecular process in a packed-bed immobilized enzyme reactor: numerical simulation and back-mixing effects.

In a previous report, we presented a new analytical model describing the performance of a packed-bed catalytic unit, where the reaction between two cosubstrates is catalyzed by an enzyme immobilized on a porous carrier. The model explicitly takes into account the changes in concentrations of both cosubstrates along the reactor, as well as the hydrodynamic regimen (i.e., back-mixing) prevailing in the packed bed. In the present report, and on the basis of the procedures developed, we present a detailed analysis of the performance of the reactor. With numerical simulations, the effects of internal diffusion limitations, the depth of the pores, the substrates' concentration in the feed, and kinetic parameters are evaluated. Particular attention is also given here to the back-mixing effects prevailing in the reactor. An experimental procedure for assessing their extent is described.

Validation of a decision support system for use in drug development: pharmacokinetic data.

PURPOSE: Single dose pharmacokinetic data from several individuals can be used to predict the fraction of the population that is expected to be within a therapeutic range. Without having some measure of its reliability, however, that prediction is only likely to marginally influence critical drug development decision making. The system (Forecaster) described generates an approximate prediction interval that contains the original prediction and where, for example, the probability is approximately 85% that a similar prediction from a new set of data will also be within the range. The goal is to validate that the system functions as designed. METHODS: The strategy requires having a Surrogate Population (SP), which is a large number (> or = 1500) of hypothetical individuals each represented by set of model parameter values having unique attributes. The SP is generated so that a sample taken from it will give data that is statistically indistinguishable from the available experimental data. The automated method for building the SP is described. RESULTS: Validation studies using 300 independent samples document that for this example the SP can be used to make useful predictions, and that the approximate prediction interval functions as designed. CONCLUSIONS: For the boundary conditions and assumptions specified, the Forecaster can make valid predictions of pharmacokinetic-based population targets that without a SP would not be possible. Finally, the approximate prediction interval does provide a useful measure of prediction reliability.

Measures of uncertainty of pharmacokinetic and pharmacodynamic parameter estimates: a new computerized algorithm.

Numerous algorithms exist to fit data to nonlinear models of the type used in chemistry, pharmacology, physiology, etc. Most include modules that provide some measure of the reliability of the estimated model parameters. The variance-covariance matrix (VCM) is the common tabulation of information that is used to quantify the parameter uncertainty as well as correlations between parameters. The VCM has its mathematical foundation in the linear regression world, where the dependent variable is a linear function of the parameters. However, when the model is not linear in its parameters, then the VCM is no longer an absolute quantitative measure of reliability of the parameter estimates and should be interpreted with caution. If the goal is to obtain a realistic and quantitative rather than a qualitative measurement of the parameter reliability, then it is necessary to have an alternative approach to describe the parameter likelihood region. We present a computerized algorithm that fills that need, and we compare its performance with the traditional VCM approach for different data sets. We also discuss criteria that may be used to determine when the VCM approach should and should not be used.

A forecasting approach to accelerate drug development.

The clinical phase of drug development should be concluded sooner and at a lower cost if primarily only the pivotal and supportive studies were to be conducted. Such improved efficiency requires development of a decision support system that delivers five new capabilities: (i) it enables one to predict a result of a clinical study and to identify those studies that are expected to have an acceptable probability of success; (ii) it will allow one to optimally utilize available pharmacokinetic and pharmacodynamic (PK/PD) data and improve its predictive capability as more data become available; (iii) it will enable one to project useful population results, not just mean results; (iv) predictions will be accompanied by a measure of reliability; and (v) expected initial clinical results will be predictable from animal and related drug class data. With such a tool population targets could be specified very early in the drug development programme, challenged, and then rationally revised at each step during the development process. This report describes progress in developing and testing a clinical trials Forecaster, a prototype for such a system. The Forecaster generates estimates of the joint density for a population of combined PK/PD parameters. That population then serves as a surrogate for the population of individuals. When the resulting joint density is sampled, the obtained sets of parameters may be used to generate data that is statistically indistinguishable from the original experimental data. Such simulated data can be used to validate assumptions, and make inferences on specified population targets that are accompanied by a measure of prediction reliability. We demonstrate use of the forecaster by employing N = 22 PK/PD parameter sets for an orally administered analgesic.

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.