David Z. D'Argenio

A program package for simulation and parameter estimation in pharmacokinetic systems

A set of programs is presented which has been developed for parameter estimation and simulation of models arising from pharmacokinetic applications. The programs can accommodate linear and nonlinear models with multiple inputs and multiple outputs. When the model is defined by differential equations, non-uniform repetitive dosage regimens can be handled. The model may also be entered in integrated form when single dose studies or uniform multiple dose studies are being considered. The programs employ a variable-step, variable-order integration routine to solve the model differential equations, and the Nelder-Mead simplex procedure to determine the parameter values which minimize a weighted least squares criterion. The programs have been written for an interactive time-sharing environment with the experimental data and model equations stored in files for future use.

Optimal sampling times for pharmacokinetic experiments

A sequential estimation procedure is presented which uses optimal sampling times to estimate the parameters of a model from data obtained from a group of subjects. This optimal sampling sequential estimation procedure utilizes parameter estimates from previous subjects in the group to determine the optimal sampling times for the next subject. Parameter estimates obtained from the optimal sampling procedure are compared to those obtained from a conventional sampling scheme by using Monte Carlo simulations which include noise terms for both assay error and intersubject variability. The results of these numerical experiments, for the two examples considered here, show that the parameter estimates obtained from data collected at optimal sampling times have significantly less variability than those generated using the conventional sampling procedure. We conclude that optimal sampling and preexperiment simulation may be useful tools for designing informative pharmacokinetic experiments.

Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments

An experiment design procedure is proposed for nonlinear parameter estimation studies that formally incorporates prior parameter uncertainty. The design criterion derives from information theory considerations and involves an asymptotic interpretation of the expected posterior information provided by an experiment. A pharmacokinetic sample schedule design problem is used to illustrate and evaluate this information theoretic design strategy. The model considered is commonly used to describe the plasma concentration of a drug following its oral administration. The limitations and advantages of the proposed design procedure are discussed in relation to other previously reported design techniques for incorporating parameter uncertainty.

Plasma Pharmacokinetics, Oral Bioavailability, and Interspecies Scaling of the DNA Methyltransferase Inhibitor, Zebularine

Purpose: Zebularine is a DNA methyltransferase inhibitor proposed for clinical evaluation. Experimental Design: We developed a liquid chromatography/mass spectrometry assay and did i.v. and oral studies in mice, rats, and rhesus monkeys. Results: In mice, plasma zebularine concentrations declined with terminal half-lives (t1/2) of 40 and 91 minutes after 100 mg/kg i.v. and 1,000 mg/kg given orally, respectively. Zebularine plasma concentration versus time curves (area under the curve) after 100 mg/kg i.v. and 1,000 mg/kg given orally were 7,323 and 4,935 μg/mL min, respectively, corresponding to a total body clearance (CLtb) of 13.65 mL/min/kg, apparent total body clearance (CLapp) of 203 mL/min/kg, and oral bioavailability of 6.7%. In rats, plasma zebularine concentrations declined with t1/2 of 363, 110, and 126 minutes after 50 mg/kg i.v., 250 mg/kg given orally, and 500 mg/kg given orally, respectively. Zebularine areas under the curve after 50 mg/kg i.v., 250 mg/kg given orally, and 500 mg/kg given orally were 12,526, 1,969, and 7,612 μg/mL min, respectively, corresponding to a CLtb of 3.99 mL/min/kg for 50 mg/kg i.v. and CLapp of 127 and 66 mL/min/kg for 250 and 500 mg/kg given orally, respectively. Bioavailabilities of 3.1% and 6.1% were calculated for the 250 and 500 mg/kg oral doses, respectively. In monkeys, zebularine t1/2 was 70 and 150 minutes, CLtb was 3.55 and 10.85 mL/min/kg after i.v. administration, and CLapp was 886 and 39,572 mL/min/kg after oral administration of 500 and 1,000 mg/kg, respectively. Zebularine oral bioavailability was <1% in monkeys. Interspecies scaling produced the following relationship: CLtb = 6.46(weight0.9). Conclusions: Zebularine has limited oral bioavailability. Interspecies scaling projects a CLtb of 296 mL/min in humans.

Vitreous VEGF clearance is increased after vitrectomy.

Purpose. Pars plana vitrectomy (PPV) has been reported to reduce macular thickness and improve visual acuity in patients with diabetic macular edema (ME). The hypothesis for the study was that after PPV, clearance is accelerated and VEGF concentrations are reduced. To test this hypothesis, hVEGF(165) injections were performed in rabbit eyes, with and without PPV, and vitreous VEGF levels were measured as a function of time. Methods. The PPV group rabbits had a bilateral 25-gauge PPV, and in the no-PPV group, rabbits had intact vitreous. Intravitreal injections of hVEGF(165) were performed, and the animals were euthanatized at time points up to 7 days. The vitreous was isolated and an enzyme-linked immunosorbent assay was used to measure the VEGF levels. Pharmacokinetic parameters were determined in a noncompartmental analysis approach. Results. Mean vitreous VEGF levels decreased more rapidly in eyes subjected to PPV than in no-PPV eyes. The vitreous VEGF half-life (t([)(1/2)(])) in PPV eyes was 10 times shorter than that in normal eyes. In addition, mean clearance and mean area under the curve (AUC) increased and decreased, respectively, in eyes that underwent PPV. Conclusions. VEGF clearance is increased after PPV. Reducing VEGF concentrations in the vitreous post-PPV may partially explain the improvement in macular thickness in some patients with ME. Unexpectedly, the half-life of VEGF in the vitreous, even in no-PPV eyes, was <3 hours, whereas compounds of similar molecular weight typically have longer vitreous half-lives. The back of the eye may be uniquely adapted with rapid-clearance mechanisms to regulate vitreous VEGF levels. Further study is suggested.

Physiologically-based pharmacokinetics and molecular pharmacodynamics of 17-(allylamino)-17-demethoxygeldanamycin and its active metabolite in tumor-bearing mice.

A whole-body physiologically-based model was developed to describe the pharmacokinetics of the ansamycin benzoquinone antibiotic 17-(allylamino)-17-demethoxygeldanamycin (17AAG) and its active metabolite 17-(amino)-17-demethoxygeldanamycin (17AG) in blood, normal organs (lung, brain, heart, spleen, liver, kidney, skeletal muscle) and implanted human tumor xenograft in nude mice. The distribution of 17AAG in all organs was described by diffusion-limited exchange models, while that of 17AG was described by perfusion-limited models. The intrinsic clearances of 17AAG and 17AG in the liver were uniquely identified using local models and were estimated to be 4.93 ml/hr and 3.34 ml/hr. It was also estimated that the formation of 17AG in liver accounted for 40% of the 17AAG intrinsic clearance. The model for the distribution of both 17AAG and 17AG in the human breast cancer tumor xenograft included vascular, interstitial and intracellular compartments, which yielded the predicted cellular concentrations of 17AAG and 17AG two to three times higher than the corresponding whole tissue measurements at steady state. Estimates of the vascular-interstitial permeability surface-area product were similar for 17AAG and 17AG (0.23 ml/hr and 0.26 ml/hr). However, the interstitial to cellular transport rate of 17AG was three-fold greater than that of 17AAG, which resulted in the preferential uptake of 17AG over 17AAG in tumor. Indirect response models were developed to describe the combined action of 17AAG and 17AG on the onco-proteins Raf-1 and p185erbB2 in tumor. The half-life of endogenous protein turnover was estimated to be 22.6 hr for Raf-1 and 8.6 hr for p185erbB2, and both were comparable to corresponding values measured in vitro. A model for the molecular chaperon heat shock proteins HSP70 and HSP90 was developed based on the molecular mechanism of heat shock auto-regulation and the action of 17AAG and 17AG on these proteins. The model provided in vivo estimates of endogenous HSP70 and HSP90 turnover. In modeling pharmacokinetics and pharmacodynamics, Bayesian inference was employed to estimate the kinetic, physiological and molecular parameters when prior information was available.

Advanced Methods of Pharmacokinetic and Pharmacodynamic Systems Analysis

Advanced Methods of Pharmacokinetic and Pharmocodynamic Systems Analysis Volume 3 is vital to professionals and academicians working in drug development and bioengineering. Both basic and clinical scientists will benefit from this work.This book contains chapters by leading researchers in pharmacokinetic/pharmacodynamic modeling and will be of interest to anyone involved with the application of pharmacokinetic and pharmacodynamics to drug development. The use of mathematical modeling and associated computational methods is central to the study of the absorption, distribution and elimination of therapeutic drugs (pharmacokinetics) and to understanding how drugs produce their effects (pharmacodynamics). From its inception, the field of pharmacokinetics and pharmacodynamics has incorporated methods of mathematical modeling, simulation and computation in an effort to better understand and quantify the processes of uptake, disposition and action of therapeutic drugs. These methods for pharmacokinetic/pharmacodynamic systems analysis impact all aspects of drug development. In vitro, animal and human testing, as well as drug therapy are all influenced by these methods. Modeling methodologies developed for studying pharmacokinetic/ pharmacodynamic processes confront many challenges. This is related in part to the severe restrictions on the number and type of measurements that are available from laboratory experiments and clinical trials, as well as the variability in the experiments and the uncertainty associated with the processes themselves. The contributions are organized in three main areas: Mechanism-Based PK/PD, Pharmacometrics and Pharmacotherapy. Both professionals and academics will profit from this extensive work.

Adaptive control of theophylline therapy: Importance of blood sampling times

A two-observation protocol for estimating theophylline clearance during a constant-rate intravenous infusion is used to examine the importance of blood sampling schedules with regard to the information content of resulting concentration data. Guided by a theory for calculating maximally informative sample times, population simulations are used to assess the effect of specific sampling times on the precision of resulting clearance estimates and subsequent predictions of theophylline plasma concentrations. The simulations incorporated noise terms for intersubject variability, dosing errors, sample collection errors, and assay error. Clearance was estimated using Chiou s method, least squares, and a Bayesian estimation procedure. The results of these simulations suggest that clinically significant estimation and prediction errors may result when using the above two-point protocol for estimating theophylline clearance if the time separating the two blood samples is less than one population mean elimination half-life.

Simulation of linear compartment models with application to nuclear medicine kinetic modeling

Several techniques are evaluated for solving the linear ordinary differential equations arising from compartment models. The methods involve approximating the matrix exponential of the state matrix (i.e. the transition matrix). The computational efficiencies of these techniques, together with that of a general purpose differential equation solver, are compared for several models arising from radiopharmacokinetic studies. The matrix exponential calculations are performed using both Wards Padé approximation method and an eigenvalue-eigenvector decomposition (QR factorization) of the matrix A. These two algorithms have been incorporated as simulation options into the programs of the ADAPT package. ADAPT consists of a set of high-level programs for simulation, parameter estimation and experiment design, developed primarily for basic and clinical research modeling and data analysis applications involving pharmacokinetic and pharmacodynamic processes. The advantages and disadvantages of these simulation strategies for solving linear kinetic models within a parameter estimation setting are illustrated and discussed.

Implementation and evaluation of control strategies for individualizing dosage regimens, with application to the aminoglycoside antibiotics

Three strategies are implemented for controlling serum concentrations by determining individualized dosage regimens. The methods incorporate, respectively, nonlinear least squares parameter estimation, Bayesian maximum a posterioriprobability estimation, and a stochastic control procedure that minimizes the expected value of an appropriate therapeutic cost. The performance of the three dose regimen calculation strategies was evaluated using Monte Carlo simulations of a typical therapeutic protocol for tobramycin.