Conventional mammillary models are frequently used for pharmacokinetic (PK) analysis when only blood or plasma data are available. Such models depend on the quality of the drug disposition data and have vague biological features. An alternative minimal-physiologically-based PK (minimal-PBPK) modeling approach is proposed which inherits and lumps major physiologic attributes from whole-body PBPK models. The body and model are represented as actual blood and tissue usually total body weight) volumes, fractions (fd) of cardiac output with Fick’s Law of Perfusion, tissue/blood partitioning (Kp), and systemic or intrinsic clearance. Analyzing only blood or plasma concentrations versus time, the minimal-PBPK models parsimoniously generate physiologically-relevant PK parameters which are more easily interpreted than those from mam-millary models. The minimal-PBPK models were applied to four types of therapeutic agents and conditions. The models well captured the human PK profiles of 22 selected beta-lactam antibiotics allowing comparison of fitted and calculated Kp values. Adding a classical hepatic compartment with hepatic blood flow allowed joint fitting of oral and intravenous (IV) data for four hepatic elimination drugs (dihydrocodeine, verapamil, repaglinide, midazolam) providing separate estimates of hepatic intrinsic clearance, non-hepatic clearance, and pre-hepatic bioavailability. The basic model was integrated with allometric scaling principles to simultaneously describe moxifloxacin PK in five species with common Kp and fd values. A basic model assigning clearance to the tissue compartment well characterized plasma concentrations of six monoclonal antibodies in human subjects, providing good concordance of predictions with expected tissue kinetics. The proposed minimal-PBPK modeling approach offers an alternative and more rational basis for assessing PK than compartmental models.
PBPK; Mammillary model; Pharmacokinetics; Compartmental analysis
This investigation evaluated the utility of a physiologically based pharmacokinetic (PBPK) model, which incorporates model parameters representing key determinants of monoclonal antibody (mAb) target-mediated disposition, to predict, a priori, mAb disposition in plasma and in tissues, including tumors that express target antigens. Monte Carlo simulation techniques were employed to predict the disposition of two mAbs, 8C2 (as a non-binding control mouse IgG1 mAb) and T84.66 (a high-affinity murine IgG1 anti-carcinoembryonic antigen mAb), in mice bearing no tumors, or bearing colorectal HT29 or LS174T xenografts. Model parameters were obtained or derived from the literature. 125I-T84.66 and 125I-8C2 were administered to groups of SCID mice, and plasma and tissue concentrations were determined via gamma counting. The PBPK model well-predicted the experimental data. Comparisons of the population predicted versus observed areas under the plasma concentration versus time curve (AUC) for T84.66 were 95.4 ± 67.8 versus 84.0 ± 3.0, 1,859 ± 682 versus 2,370 ± 154, and 5,930 ± 1,375 versus 5,960 ± 317 (nM × day) at 1, 10, and 25 mg/kg in LS174T xenograft-bearing SCID mice; and 215 ± 72 versus 233 ± 30, 3,070 ± 346 versus 3,120 ± 180, and 7,884 ± 714 versus 7,440 ± 626 in HT29 xenograft-bearing mice. Model predicted versus observed 8C2 plasma AUCs were 312.4 ± 30 versus 182 ± 7.6 and 7,619 ± 738 versus 7,840 ± 24.3 (nM × day) at 1 and 25 mg/kg. High correlations were observed between the predicted median plasma concentrations and observed median plasma concentrations (r2 = 0.927, for all combinations of treatment, dose, and tumor model), highlighting the utility ofthe PBPK model forthe a priori prediction of in vivo data.
Monoclonal antibody; Target-mediated disposition (TMD); Physiologically based pharmacokinetic (PBPK); Monte Carlo simulation; Preclinical pharmacokinetic; Tissue disposition
Dulanermin (rhApo2L/TRAIL) and conatumumab bind to transmembrane death receptors and trigger the extrinsic cellular apoptotic pathway through a caspase-signaling cascade resulting in cell death. Tumor size time series data from rodent tumor xenograft (COLO205) studies following administration of either of these two pro-apoptotic receptor agonists (PARAs) were combined to develop a intracellular-signaling tumor-regression model that includes two levels of signaling: upstream signals unique to each compound (representing initiator caspases), and a common downstream apoptosis signal (representing executioner caspases) shared by the two agents. Pharmacokinetic (PK) models for each drug were developed based on plasma concentration data following intravenous and/or intraperitoneal administration of the compounds and were used in the subsequent intracellular-signaling tumor-regression modeling. A model relating the PK of the two PARAs to their respective and common downstream signals, and to the resulting tumor burden was developed using mouse xenograft tumor size measurements from 448 experiments that included a wide range of dose sizes and dosing schedules. Incorporation of a pro-survival signal—consistent with the hypothesis that PARAs may also result in the upregulation of pro-survival factors that can lead to a reduction in effectiveness of PARAs with treatment—resulted in improved predictions of tumor volume data, especially for data from the long-term dosing experiments.
Extrinsic apoptotic pathway; Tumor-regression modeling; Death receptor activation of NF-κB; Pro-apoptotic receptor agonists; Dulanermin; Conatumumab
This report generates efficient experimental designs (dose, sampling times) for parameter estimation for four basic physiologic indirect pharmacodynamic response (IDR) models. The principles underlying IDR models and their response patterns have been well described. Each IDR model explicitly contains four parameters, kin (production), kout (loss), Imax/Smax (capacity) and IC50/SC50 (sensitivity). The pharmacokinetics of an IV dose of drug described by a monoexponential function of time with two parameters, V and kel, is assumed. The random errors in the response variable are assumed to be additive, independent, and normal with zero mean and variance proportional to some power of the mean response. Optimal design theory was used extensively to assess the role of both dose and sampling times. Our designs were generated in Mathematica (ADAPT 5 typically produces identical results). G-optimality was used to verify that the generated designs were indeed D-optimal. Such designs are efficient and robust when good prior knowledge of the estimated parameters is available. The efficiency of unconstrained D-optimal designs (4 dose, sampling time pairs) does not improve much when the drug doses are allowed to differ, compared with constrained single dose designs (4 sampling times) with one maximal feasible dose. Also, explored were efficiencies of alternative study designs and results from parameter misspecification. This analysis substantiates the importance of larger doses yielding greater certainty in parameter estimation in pharmacodynamics.
Pharmacodynamics; D-optimal design; Indirect response models; Parameter estimation
Permeability-limited two-subcompartment and flow-limited, well-stirred tank tissue compartment models are routinely used in physiologically-based pharmacokinetic modeling. Here, the permeability-limited two-subcompartment model is used to derive a general flow-limited case of a two-subcompartment model with the well-stirred tank being a specific case where tissue fractional blood volume approaches zero. The general flow-limited two-subcompartment model provides a clear distinction between two partition coefficients typically used in PBPK: a biophysical partition coefficient and a well-stirred partition coefficient. Case studies using diazepam and cotinine demonstrate that, when the well-stirred tank is used with a priori predicted biophysical partition coefficients, simulations overestimate or underestimate total organ drug concentration relative to flow-limited two-subcompartment model behavior in tissues with higher fractional blood volumes. However, whole-body simulations show predicted drug concentrations in plasma and lower fractional blood volume tissues are relatively unaffected. These findings point to the importance of accurately determining tissue fractional blood volume for flow-limited PBPK modeling. Simulations using biophysical and well-stirred partition coefficients optimized with flow-limited two-subcompartment and well-stirred models, respectively, lead to nearly identical fits to tissue drug distribution data. Therefore, results of whole-body PBPK modeling with diazepam and cotinine indicate both flow-limited models are appropriate PBPK tissue models as long as the correct partition coefficient is used: the biophysical partition coefficient is for use with two-subcompartment models and the well-stirred partition coefficient is for use with the well-stirred tank model.
Physiologically-based pharmacokinetics; Flow-limited; Permeability-limited; Well-stirred tank; Compartmental modeling; Partition coefficient; Biophysical; Diazepam; Cotinine
The dynamics of aging and type 2 diabetes (T2D) disease progression were investigated in normal [Wistar-Kyoto (WKY)] and diabetic [Goto-Kakizaki (GK)] rats and a mechanistic disease progression model was developed for glucose, insulin, and glycosylated hemoglobin (HbA1c) changes over time. The study included 30 WKY and 30 GK rats. Plasma glucose and insulin, blood glucose and HbA1c concentrations and hematological measurements were taken at ages 4, 8, 12, 16 and 20 weeks. A mathematical model described the development of insulin resistance (IR) and β-cell function with age/growth and diabetes progression. The model utilized transit compartments and an indirect response model to quantitate biomarker changes over time. Glucose, insulin and HbA1c concentrations in WKY rats increased to a steady-state at 8 weeks due to developmental changes. Glucose concentrations at 4 weeks in GK rats were almost twice those of controls, and increased to a steady-state after 8 weeks. Insulin concentrations at 4 weeks in GK rats were similar to controls, and then hyperinsulinemia occurred until 12–16 weeks of age indicating IR. Subsequently, insulin concentrations in GK rats declined to slightly below WKY controls due to β-cell failure. HbA1c showed a delayed increase relative to glucose. Modeling of HbA1c was complicated by age-related changes in hematology in rats. The diabetes model quantitatively described the glucose/insulin inter-regulation and HbA1c production and reflected the underlying pathogenic factors of T2D—IR and β-cell dysfunction. The model could be extended to incorporate other biomarkers and effects of various anti-diabetic drugs.
Type 2 diabetes; Disease progression modeling; Insulin resistance; β-cell function
This study derives and assesses modified equations for Indirect Response Models (IDR) for normalizing data for baseline values (R0) and evaluates different methods of utilizing baseline information. Pharmacodynamic response equations for the four basic IDR models were adjusted to reflect a ratio to, a change from (e.g., subtraction), or percent change relative to baseline. The original and modified IDR equations were fitted individually to simulated data sets and compared for recovery of true parameter values. Handling of baseline values was investigated using: estimation (E), fixing at the starting value (F1), and fixing at an average of starting and returning values of response profiles (F2). The performance of each method was evaluated using simulated data with variability under various scenarios of different doses, numbers of data points, type of IDR model, and degree of residual errors. The median error and inter-quartile range relative to true values were used as indicators of bias and precision for each method. Applying IDR models to normalized data required modifications in writing differential equations and initial conditions. Use of an observed/baseline ratio led to parameter estimates of kin = kout and inability to detect differences in kin values for groups with different R0, whereas the modified equations recovered the true values. An increase in variability increased the %Bias and %Imprecision for each R0 fitting method and was more pronounced for ‘F1’. The overall performance of ‘F2’ was as good as that of ‘E’ and better than ‘F1’. The %Bias in estimation of parameters SC50 (IC50) and kout followed the same trend, whereas use of ‘F1’ or ‘F2’ resulted in the least bias for Smax (Imax). The IDR equations need modifications to directly assess baseline-normalized data. In general, Method ‘E’ resulted in lesser bias and better precision compared to ‘F1’. With rich datasets including sufficient information on the return to baseline, Method ‘F2’ is reasonable. Method ‘E’ offers no significant advantage over ‘F1’ with datasets lacking information on the return to baseline phase. Handling baseline responses properly is an essential aspect of applying pharmacodynamic models.
Indirect response models; Turnover models; Baseline responses; Pharmacodynamics; Modeling and simulation
In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.
Cell lifespan; Delay differential equations; Indirect response models; Cell populations
Intermittent drug dosing intervals are usually initially guided by the terminal pharmacokinetic half life and are dependent on drug formulation. For chronic multiple dosing and for extended release dosage forms, the terminal half life often does not predict the plasma drug accumulation or fluctuation observed. We define and advance applications for the operational multiple dosing half lives for drug accumulation and fluctuation after multiple oral dosing at steady-state. Using Monte Carlo simulation, our results predict a way to maximize the operational multiple dosing half lives relative to the terminal half life by using a first-order absorption rate constant close to the terminal elimination rate constant in the design of extended release dosage forms. In this way, drugs that may be eliminated early in the development pipeline due to a relatively short half life can be formulated to be dosed at intervals three times the terminal half life, maximizing compliance, while maintaining tight plasma concentration accumulation and fluctuation ranges. We also present situations in which the operational multiple dosing half lives will be especially relevant in the determination of dosing intervals, including for drugs that follow a direct PKPD model and have a narrow therapeutic index, as the rate of concentration decrease after chronic multiple dosing (that is not the terminal half life) can be determined via simulation. These principles are illustrated with case studies on valproic acid, diazepam, and anti-hypertensives.
dosing interval; half life; pharmacokinetics; pharmacodynamics; drug accumulation; fluctuation
Nanoparticles (NPs) may be capable of reversing the toxic effects of drug overdoses in humans by adsorbing/absorbing drug molecules. This paper develops a model to include the kinetic effects of treating drug overdoses by NPs. Depending on the size and the nature of the NPs, they may either pass through the capillary walls and enter the tissue space or remain only inside the capillaries and other blood vessels; models are developed for each case. Furthermore, the time scale for equilibration between the NP and the blood will vary with the specific type of NP. The NPs may sequester drug from within the capillaries depending on whether this time scale is larger or smaller than the residence time of blood within the capillary. Models are developed for each scenario. The results suggest that NPs are more effective at detoxification if they are confined to the blood vessels and do not enter the tissues. The results also show that the detoxification process is faster if drug uptake occurs within the capillaries. The trends shown by the model predictions can serve as useful guides in the design of the optimal NP for detoxification.
absorption; adsorption; drug detoxification; drug overdose; microemulsion; nanoparticle; pharmacokinetic model
The ability to deliver drug molecules effectively across the blood–brain barrier into the brain is important in the development of central nervous system (CNS) therapies. Cerebral microdialysis is the only existing technique for sampling molecules from the brain extracellular fluid (ECF; also termed interstitial fluid), the compartment to which the astrocytes and neurones are directly exposed. Plasma levels of drugs are often poor predictors of CNS activity. While cerebrospinal fluid (CSF) levels of drugs are often used as evidence of delivery of drug to brain, the CSF is a different compartment to the ECF. The continuous nature of microdialysis sampling of the ECF is ideal for pharmacokinetic (PK) studies, and can give valuable PK information of variations with time in drug concentrations of brain ECF versus plasma. The microdialysis technique needs careful calibration for relative recovery (extraction efficiency) of the drug if absolute quantification is required. Besides the drug, other molecules can be analysed in the microdialysates for information on downstream targets and/or energy metabolism in the brain. Cerebral microdialysis is an invasive technique, so is only useable in patients requiring neurocritical care, neurosurgery or brain biopsy. Application of results to wider patient populations, and to those with different pathologies or degrees of pathology, obviously demands caution. Nevertheless, microdialysis data can provide valuable guidelines for designing CNS therapies, and play an important role in small phase II clinical trials. In this review, we focus on the role of cerebral microdialysis in recent clinical studies of antimicrobial agents, drugs for tumour therapy, neuroprotective agents and anticonvulsants.
Brain; Microdialysis; Pharmacokinetics; Human
Human cerebrospinal fluid (CSF) sampling is of high value as the only general applicable methodology to obtain information on free drug concentrations in individual human brain. As the ultimate interest is in the free drug concentration at the CNS target site, the question is what CSF concentrations may tell us in that respect. Studies have been performed in rats and other animals for which concentrations in brain extracellular fluid (brain ECF) as a target site for many drugs, have been compared to (cisterna magna) CSF concentrations, at presumed steady state conditions,. The data indicated that CSF drug concentrations provided a rather good indication of, but not a reliable measure for predicting brain ECF concentrations. Furthermore, comparing rat with human CSF concentrations, human CSF concentrations tend to be higher and display much more variability. However, this comparison of CSF concentrations cannot be a direct one, as humans probably had a disease for which CSF was collected in the first place, while the rats were healthy. In order to be able to more accurately predict human brain ECF concentrations, understanding of the complexity of the CNS in terms of intrabrain pharmacokinetic relationships and the influence of CNS disorders on brain pharmacokinetics needs to be increased. This can be achieved by expanding a currently existing preclinically derived physiologically based pharmacokinetic model for brain distribution. This model has been shown to successfully predict data obtained for human lumbar CSF concentrations of acetaminophen which renders trust in the model prediction of human brain ECF concentrations. This model should further evolute by inclusion of influences of drug properties, fluid flows, transporter functionalities and different disease conditions. Finally the model should include measures of target site engagement and CNS effects, to ultimately learn about concentrations that best predict particular target site concentrations, via human CSF concentrations.
Target site; Cerebrospinal fluid; Human; Central nervous system; Translational; Physiologically based pharmacokinetic model
A population pharmacokinetic–pharmacodynamic–disease progression (PK/PD/DIS) model was developed to characterize the effects of anakinra in collagen-induced arthritic (CIA) rats and explore the role of interleukin-1β (IL-1β) in rheumatoid arthritis. The CIA rats received either vehicle, or anakinra at 100 mg/kg for about 33 h, 100 mg/kg for about 188 h, or 10 mg/kg for about 188 h by subcutaneous infusion. Plasma concentrations of anakinra were assayed by enzyme-linked immunosorbent assay. Swelling of rat hind paws was measured. Population PK/PD/DIS parameters were computed for the various groups using non-linear mixed-effects modeling software (NONMEM® Version VI). The final model was assessed using visual predictive checks and nonparameter stratified bootstrapping. A two-compartment PK model with two sequential absorption processes and linear elimination was used to capture PK profiles of anakinra. A transduction-based feedback model incorporating logistic growth rate captured disease progression and indirect response model I captured drug effects. The PK and paw swelling versus time profiles in CIA rats were fitted well. Anakinra has modest effects (Imax = 0.28) on paw edema in CIA rats. The profiles are well-described by our PK/PD/DIS model which provides a basis for future mechanism-based assessment of anakinra dynamics in rheumatoid arthritis.
Anakinra; Pharmacokinetics; Pharmacodynamics; Rheumatoid arthritis; Population model
GLP-1 is an insulinotropic hormone that synergistically with glucose gives rise to an increased insulin response. Its secretion is increased following a meal and it is thus of interest to describe the secretion of this hormone following an oral glucose tolerance test (OGTT). The aim of this study was to build a mechanism-based population model that describes the time course of total GLP-1 and provides indices for capability of secretion in each subject. The goal was thus to model the secretion of GLP-1, and not its effect on insulin production. Single 75 g doses of glucose were administered orally to a mixed group of subjects ranging from healthy volunteers to patients with type 2 diabetes (T2D). Glucose, insulin, and total GLP-1 concentrations were measured. Prior population data analysis on measurements of glucose and insulin were performed in order to estimate the glucose absorption rate. The individual estimates of absorption rate constants were used in the model for GLP-1 secretion. Estimation of parameters was performed using the FOCE method with interaction implemented in NONMEM VI. The final transit/indirect-response model obtained for GLP-1 production following an OGTT included two stimulation components (fast, slow) for the zero-order production rate. The fast stimulation was estimated to be faster than the glucose absorption rate, supporting the presence of a proximal–distal loop for fast secretion from L-cells. The fast component (st3 = 8.64·10−5 [mg−1]) was estimated to peak around 25 min after glucose ingestion, whereas the slower component (st4 = 26.2·10−5 [mg−1]) was estimated to peak around 100 min. Elimination of total GLP-1 was characterised by a first-order loss. The individual values of the early phase GLP-1 secretion parameter (st3) were correlated (r = 0.52) with the AUC(0–60 min.) for GLP-1. A mechanistic population model was successfully developed to describe total GLP-1 concentrations over time observed after an OGTT. The model provides indices related to different mechanisms of subject abilities to secrete GLP-1. The model provides a good basis to study influence of different demographic factors on these components, presented mainly by indices of the fast- and slow phases of GLP-1 response.
GLP-1; L-cells; Oral glucose tolerance test (OGTT); Indirect response model; NONMEM
The purpose of this study is to develop a statistical methodology to handle a large proportion of artifactual outliers in a population pharmacokinetic (PK) modeling. The motivating PK data were obtained from a population PK study to examine associations between PK parameters such as clearance of dexmedetomidine and cytochrome P450 2A6 phenotypes. The blood samples were sparsely sampled from patients in intensive care units (ICUs) while different doses of dexmedetomidine were continuously infused. Conventional population PK analysis of these data revealed several challenges and intricacies. Especially, there was strong evidence that some plasma drug concentrations were artifactually high and likely contaminated with the infused drug due to blood sampling processes that are sometimes unavoidable in an ICU setting. If not addressed, or if arbitrarily excluded, these outlying values could lead to biased estimates of PK parameters and miss important relationships between PK parameters and covariates due to increased variability. We propose a novel population PK model, a Bayesian hierarchical nonlinear mixture model, to accommodate the artifactual outliers using a finite mixture as the residual error model. Our results showed that the proposed model handles the outliers well. We also conducted simulation studies with a varying proportion of the outliers. These simulation results showed that the proposed model can accommodate the outliers well so that the estimated PK parameters are less biased.
finite mixture; outlier; nonlinear mixed effect model; pharmacogenetics; pharmacokinetics; NONMEM
The Michaelis–Menten (M–M) approximation of the target-mediated drug disposition (TMDD) pharmacokinetic (PK) model was derived based on the rapid binding (RB) or quasi steady-state (QSS) assumptions that implied that the target and drug binding and dissociation were in equilibrium. However, the initial dose for an IV bolus injection for the M–M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M–M approximation. We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant an identifiable parameter that was not for the original M–M model. Finally, we performed a simulation exercise to check if the correction will impact the model performance and the bias of the M–M parameter estimates. We used literature data to simulate plasma drug concentrations described by the RB/QSS TMDD model. The simulated data were refitted by both models. All the parameters estimated from the original M–M model were substantially biased. On the other hand, the corrected M–M is able to accurately estimate these parameters except for equilibrium constant Km. Weighted sum of square residual and Akaike information criterion suggested a better performance of the corrected M–M model compared with the original M–M model. Further studies are necessary to determine the importance of this correction for the M–M model applications to analysis of TMDD driven PK data.
Michaelis–Menten; Target-mediated drug disposition; Rapid binding; Quasi steady-state; Equilibrium
Although the implementation of a flow-limited, well-stirred tank (WST) single-compartment tissue model in pharmacokinetics and toxicokinetics is widespread, its use is not always justified biophysically or physiologically. The WST model introduces a loss of biophysical detail, specifically the vascular space, which is present in the standard permeability-limited two-subcompartment (PLT) tissue model. To address this loss of detail when evaluating the in vivo kinetics of drugs, toxins, nutrients, and endogenous metabolites, a novel set of physiologically based pharmacokinetic tissue compartment equations is developed through application of an asymptotic approximation to a two-region vascular–extravascular system to arrive at a permeability-limited two-region asymptotically reduced (P-TAR) model and a flow-limited (F-TAR) model. Development of the TAR modeling approach illustrates the importance of relative timescales in PBPK tissue compartment model selection and the conditions under which improved biophysical realism is advantageous. In the permeability-limited regime, the TAR model formulations enable drug or toxicant concentration to be modeled in the vascular and extravascular spaces equivalent to the PLT tissue model while invoking only one state variable to represent the vascular and extravascular spaces. In the flow-limited regime, the F-TAR model is more biophysically realistic than the WST model because it maintains the anatomical distinction between the vascular and extravascular spaces, and hence offers greater pharmacological and physiological insight than the WST model, without introducing additional computational complexity.
Physiologically based pharmacokinetics; Flow-limited; Permeability-limited; Well-stirred tank; Compartmental modeling; Singular perturbation
The objective was to demonstrate the methodology and process of optimal sparse sampling pharmacokinetics (PK). This utilized a single daily dose of pioglitazone for pediatric patients with severe sepsis and septic shock based upon adult and minimal adolescent data. Pioglitazone pharmacokinetics were modeled using non-compartment analysis WinNonlin Pro (version 5.1) and population kinetics using NONMEM (version 7.1) with first order conditional estimation method (FOCE) with interaction. The initial model was generated from single- and multiple-dose pioglitazone PK data (15 mg, 30 mg, and 45 mg) in 36 adolescents with diabetes. PK models were simulated and overlaid upon original data to provide a comparison best described by a single compartment, first order model. The optimal design was based on the simulated oral administration of pioglitazone to three groups of pediatric patients, age 3.8 (2–6 years), weight 14.4 (7–28 kg); age 9.6 (6.1–11.9 years), weight 36.5 (28.1–48 kg) and age 15.5 (12–17 years,) weight 61.6 (48.1–80 kg). PFIM (version 3.2) was used to evaluate sample study size. Datasets were compiled using simulation for each dose (15, 30 and 45 mg) for the potential age/weight groups. A target dose of 15 mg daily in the youngest and middle groups was considered appropriate with area under the curve exposure levels (AUC) comparable to studies in adolescents. The final optimal design suggested time points of 0.5, 2, 6 and 21 h for 24 h dosing. This methodology provides a robust method of utilizing adult and limited adolescent data to simulate allometrically scaled, pediatric data sets that allow the optimal design of a pediatric trial. The pharmacokinetics of pioglitazone were described adequately and simulated data estimates were comparable to literature values. The optimal design provided clinically attainable sample times and windows.
Optimal design; Pediatric; Pioglitazone; Sepsis; Sparse sampling
In this paper we present a mathematical analysis of the basic model for target mediated drug disposition (TMDD). Assuming high affinity of ligand to target, we give a qualitative characterisation of ligand versus time graphs for different dosing regimes and derive accurate analytic approximations of different phases in the temporal behaviour of the system. These approximations are used to estimate model parameters, give analytical approximations of such quantities as area under the ligand curve and clearance. We formulate conditions under which a suitably chosen Michaelis–Menten model provides a good approximation of the full TMDD-model over a specified time interval.
Target; Receptor; Antibodies; Drug-disposition; Michaelis–Menten; Quasi-steady-state; Quasi-equilibrium; Singular perturbation
Influences of methylprednisolone (MPL) and food consumption on body weight (BW), and the effects of MPL on glycemic control including food consumption and the dynamic interactions among glucose, insulin, and free fatty acids (FFA) were evaluated in normal male Wistar rats. Six groups of animals received either saline or MPL via subcutaneous infusions at the rate of 0.03, 0.1, 0.2, 0.3 and 0.4 mg/kg/h for different treatment periods. BW and food consumption were measured twice a week. Plasma concentrations of MPL and corticosterone (CST) were determined at animal sacrifice. Plasma glucose, insulin, and FFA were measured at various times after infusion. Plasma MPL concentrations were simulated by a two-compartment model and used as the driving force in the pharmacodynamic (PD) analysis. All data were modeled using ADAPT 5. The MPL treatments caused reduction of food consumption and body weights in all dosing groups. The steroid also caused changes in plasma glucose, insulin, and FFA concentrations. Hyper-insulinemia was achieved rapidly at the first sampling time of 6 h; significant elevations of FFA were observed in all drug treatment groups; whereas only modest increases in plasma glucose were observed in the low dosing groups (0.03 and 0.1 mg/kg/h). Body weight changes were modeled by dual actions of MPL: inhibition of food consumption and stimulation of weight loss, with food consumption accounting for the input of energy for body weight. Dynamic models of glucose and insulin feedback interactions were extended to capture the major metabolic effects of FFA: stimulation of insulin secretion and inhibition of insulin-stimulated glucose utilization. These models of body weight and glucose regulation adequately captured the experimental data and reflect significant physiological interactions among glucose, insulin, and FFA. These mechanism-based PD models provide further insights into the multi-factor control of this essential metabolic system.
Glucocorticoids; Methylprednisolone; Pharmacodynamics; Food intake; Body weight; Glucose; Insulin; Free fatty acids
A limitation in traditional stepwise population pharmacokinetic model building is the difficulty in handling interactions between model components. To address this issue, a method was previously introduced which couples NONMEM parameter estimation and model fitness evaluation to a single-objective, hybrid genetic algorithm for global optimization of the model structure. In this study, the generalizability of this approach for pharmacokinetic model building is evaluated by comparing (1) correct and spurious covariate relationships in a simulated dataset resulting from automated stepwise covariate modeling, Lasso methods, and single-objective hybrid genetic algorithm approaches to covariate identification and (2) information criteria values, model structures, convergence, and model parameter values resulting from manual stepwise versus single-objective, hybrid genetic algorithm approaches to model building for seven compounds. Both manual stepwise and single-objective, hybrid genetic algorithm approaches to model building were applied, blinded to the results of the other approach, for selection of the compartment structure as well as inclusion and model form of inter-individual and inter-occasion variability, residual error, and covariates from a common set of model options. For the simulated dataset, stepwise covariate modeling identified three of four true covariates and two spurious covariates; Lasso identified two of four true and 0 spurious covariates; and the single-objective, hybrid genetic algorithm identified three of four true covariates and one spurious covariate. For the clinical datasets, the Akaike information criterion was a median of 22.3 points lower (range of 470.5 point decrease to 0.1 point decrease) for the best single-objective hybrid genetic-algorithm candidate model versus the final manual stepwise model: the Akaike information criterion was lower by greater than 10 points for four compounds and differed by less than 10 points for three compounds. The root mean squared error and absolute mean prediction error of the best single-objective hybrid genetic algorithm candidates were a median of 0.2 points higher (range of 38.9 point decrease to 27.3 point increase) and 0.02 points lower (range of 0.98 point decrease to 0.74 point increase), respectively, than that of the final stepwise models. In addition, the best single-objective, hybrid genetic algorithm candidate models had successful convergence and covariance steps for each compound, used the same compartment structure as the manual stepwise approach for 6 of 7 (86 %) compounds, and identified 54 % (7 of 13) of covariates included by the manual stepwise approach and 16 covariate relationships not included by manual stepwise models. The model parameter values between the final manual stepwise and best single-objective, hybrid genetic algorithm models differed by a median of 26.7 % (q1 = 4.9 % and q3 = 57.1 %). Finally, the single-objective, hybrid genetic algorithm approach was able to identify models capable of estimating absorption rate parameters for four compounds that the manual stepwise approach did not identify. The single-objective, hybrid genetic algorithm represents a general pharmacokinetic model building methodology whose ability to rapidly search the feasible solution space leads to nearly equivalent or superior model fits to pharmacokinetic data.
Electronic supplementary material
The online version of this article (doi:10.1007/s10928-012-9258-0) contains supplementary material, which is available to authorized users.
Pharmacokinetics; Model building; Genetic algorithms
The purpose of this study was to examine the role of dose selection on population pharmacokinetic (PK) parameter estimation using a rapid binding approximation of a target-mediated drug disposition (TMDD) model previously developed for interferon-β (IFN-β). A total of 50 replicate datasets each containing 100 subjects were created using NONMEM®. The study design included IV injection of IFN-β followed by the SC route in a crossover manner, with each dose and route of administration separated by a 1,000 h washout period. Serial plasma PK samples were simulated up to 48 h for all subjects following each dose. Population mean PK parameters were re-estimated in NONMEM® for each simulated dataset using the same TMDD model after including the following doses (MIU/kg): (A) 1, 3 and 10 (original study); (B) 1, 3 and 7; (C) 1, 3 and 5; (D) 1, 3 and 4; (E) 1 and 3; (F) 3 and 10; or (G) 10 MIU/kg only. Bias in the model fit was assessed by calculating the percent prediction error (PE%) for each of the population mean PK parameters relative to the estimates obtained from the fit to the 1, 3, and 10 MIU/kg doses (Case A). Relatively unbiased population mean PK parameter estimates (median PE% <8%) were obtained only when the study design included 1, 3 and a minimum higher dose of 7 MIU/kg. Bias increased for various parameters when the highest dose was less than 7 MIU/kg along with 1 and 3 MIU/kg being the low and intermediate dose levels. An increase in the bias for binding capacity, Rtot, and the equilibrium dissociation constant, KD, was observed as the highest dose included in the dataset was reduced from 5 to 3 MIU/kg (median PE% ranged from −4.71 to −23.9% and −4.76 to −34.6%). Similar increases in the range of median PE% were also observed for other model parameters as the highest dose was reduced from 5 to 3 MIU/kg. Severely biased results were obtained from the study design that included only the 10 MIU/kg dose (Case G) suggesting that it is not sufficient to study just a high dose group. This bias was greatly reduced (median PE% <14%) for all parameters except KD when the 3 and 10 MIU/kg doses were co-modeled (Case F). Plots of the PE% for Rtot and KD versus the molar ratio of maximum dose to Rtot suggest that study designs should evaluate at least one IFN-β dose 3.5- to 4-fold higher than Rtot along with the 1 and 3 MIU/kg dose levels to obtain unbiased population PK parameter estimates. In summary, for the IFN-β model and study design, dose selection influences the ability to generate relatively unbiased population mean TMDD parameter estimates, which is based on maximum dose levels relative to Rtot. This simulation study highlights the role of dose selection in optimal study design strategies for drugs such as IFN-β that exhibit TMDD properties.
Target-mediated drug disposition; Rapid binding approximation; NONMEM; Pharmacokinetics; Simulation; Interferon-β
Transit compartments (TC) models are used to describe pharmacodynamic responses that involve drug action on cells undergoing differentiation and maturation. Such pharmacodynamic systems can also be described by lifespan based indirect response (LIDR) models. The purpose of this report is to investigate conditions under which the transit compartments models can be considered a special case of LIDR models. An integral representation of a solution to TC model has been used to determine the lifespan distribution for cell population described by this model. The distribution served as a basis for definition of new LIDRE (lifespan based indirect response with an effect on the lifespan distribution) models. Time courses of responses described by both types of models were simulated for a monoexponential pharmacokinetic function. The limit response was calculated as the number of transit compartments approached infinity. The difference between the limit response and TC responses were evaluated by computer simulations using MATLAB 7.7. TC models are a special case of LIDR models with the lifespan distribution described by the gamma function. If drug affects only the production of cells, then the cell lifespan distribution is time invariant. In this case an increase in the number of compartments results in a basic LIDR model with a point lifespan distribution. When the drug inhibits or stimulates cell aging, the cell lifespan distribution becomes time dependent revealing a new mechanism for drug effect on the gamma probability density function. The TC model with a large number of transit compartments converges to an LIDRE model. The limit LIDR models are approximated by the TC models when the number of compartments is at least 5. A moderate improvement in the approximation is observed if this number exceeds 20. The lifespan distribution for a cell population described by a TC model is described by the gamma probability density function. A drug affects this distribution only if it stimulates or inhibits the rate of cell maturation. If the number of transit compartments increases, then the TC model converges to a new type of LIDR model.
Cell aging models; Lifespan distribution; Gamma probability density function
Cell-level kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while cell-level dynamics are typically neglected. We here present a systematic approach to integrate cell-level kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)-mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multi-level model for anti-EGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of anti-EGFR antibodies on their F(ab)-mediated inhibitory effect. The multi-level model suggests that the F(ab)-mediated inhibitory effect saturates with increasing drug-receptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fc-mediated indirect mechanisms such as antibody-dependent cell cytotoxicity.
Cell-level kinetics; Pharmacokinetic models; Therapeutic proteins; EGFR; Biomedicine; Biomedical Engineering; Biochemistry, general; Pharmacy; Pharmacology/Toxicology; Veterinary Medicine
Dose selection for “first in children” trials often relies on scaling of the pharmacokinetics from adults to children. Commonly used approaches are physiologically-based pharmacokinetic modeling (PBPK) and allometric scaling (AS) in combination with maturation of clearance for early life. In this investigation, a comparison of the two approaches was performed to provide insight into the physiological meaning of AS maturation functions and their interchangeability. The analysis focused on the AS maturation functions established using paracetamol and morphine paediatric data after intravenous administration. First, the estimated AS maturation functions were compared with the maturation functions of the liver enzymes as used in the PBPK models. Second, absolute clearance predictions using AS in combination with maturation functions were compared to PBPK predictions for hypothetical drugs with different pharmacokinetic properties. The results of this investigation showed that AS maturation functions do not solely represent ontogeny of enzyme activity, but aggregate multiple pharmacokinetic properties, as for example extraction ratio and lipophilicity (log P). Especially in children younger than 1 year, predictions using AS in combination with maturation functions and PBPK were not interchangeable. This highlights the necessity of investigating methodological uncertainty to allow a proper estimation of the “first dose in children” and assessment of its risk and benefits.
Allometric scaling; Physiologically-based pharmacokinetic models; Pediatrics; Bridging; Scaling; Extrapolation