An approach for identifiability of population pharmacokinetic-pharmacodynamic models

Clinical Utility of A Model-based Amoxicillin Dosage Regimen in Neonates with Early-Onset Sepsis

Early-onset sepsis (EOS) is one of the most significant causes of morbidity and mortality in neonates. Currently, amoxicillin is empirically used to treat neonates with EOS. However, data on its effectiveness in neonates with EOS are still limited. Therefore, we aimed to evaluate the pharmacodynamics (PD) target attainment and effectiveness of a model-based amoxicillin dosage regimen in these neonates. We used a previously developed model and collected additional clinical data from the EOS neonates who used the model-based dosage regimen (25 mg/kg q12h). The primary outcomes were PD target attainment (free drug concentration above MIC during 70% of the dosing interval) and treatment failure rate. The secondary endpoints were length of amoxicillin treatment, duration of hospitalization, etc. Seventy-five neonates (postmenstrual age 28.4-41.6 weeks) were enrolled. A total of 70 (93.3%) neonates reached their PD target using 1 mg/L as the MIC breakpoint. The treatment failure rate was 10.7%.

Metaheuristics for pharmacometrics

Metaheuristics is a powerful optimization tool that is increasingly used across disciplines to tackle general purpose optimization problems. Nature-inspired metaheuristic algorithms is a subclass of metaheuristic algorithms and have been shown to be particularly flexible and useful in solving complicated optimization problems in computer science and engineering. A common practice with metaheuristics is to hybridize it with another suitably chosen algorithm for enhanced performance. This paper reviews metaheuristic algorithms and demonstrates some of its utility in tackling pharmacometric problems. Specifically, we provide three applications using one of its most celebrated members, particle swarm optimization (PSO), and show that PSO can effectively estimate parameters in complicated nonlinear mixed-effects models and to gain insights into statistical identifiability issues in a complex compartment model. In the third application, we demonstrate how to hybridize PSO with sparse grid, which is an often-used technique to evaluate high dimensional integrals, to search for D -efficient designs for estimating parameters in nonlinear mixed-effects models with a count outcome. We also show the proposed hybrid algorithm outperforms its competitors when sparse grid is replaced by its competitor, adaptive gaussian quadrature to approximate the integral, or when PSO is replaced by three notable nature-inspired metaheuristic algorithms.

Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Background

Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities.

Results

Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition.

Conclusions

We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis

The aim of the study is to develop a population pharmacokinetic (PPK) model, of Octreotide long acting repeatable (LAR) formulation in healthy volunteers, which describes the highly variable, multiple peak absorption pattern of the pharmacokinetics of the drug, in individual and population levels. An empirical absorption model, coupled with a one-compartment distribution model with linear elimination was found to describe the data well. Absorption was modelled as a weighted sum of a first order and three transit compartment absorption processes, with delays and appropriately constrained model parameters. Identifiability analysis verified that all twelve parameters of the structural model are identifiable. A machine learning method, i.e., cluster analysis, was performed as pre-processing of the PK profiles, to define subpopulations, before PPK modelling. It revealed that 13% of the patients deviated considerably from the typical absorption pattern and allowed better characterization of the observed heterogeneity and variability of the study, while the approach may have wider applicability in building PPK models. The final model was evaluated by goodness of fit plots, Visual Predictive Check plots and bootstrap. The present model is the first to describe the multiple-peak absorption pattern observed after octreotide LAR administration and may be useful to provide insights and validate hypotheses regarding release from PLGA-based formulations.

A minimal model to describe short-term haemodynamic changes of the cardiovascular system

AIMS

Current pharmacokinetic-pharmacodynamic models describing the haemodynamic changes often do not include necessary feedback mechanisms. These models provide adequate description of current data but may fail to adequately extrapolate to additional scenarios. This study aims to develop a minimal model to describe the short-term changes of haemodynamics that can be used as the basis for model development by future researchers.

METHODS

A minimal haemodynamic model was developed to describe the influence of drugs on blood pressure components. The model structure was defined based on known mechanisms and previously published models. The model was evaluated under 2 different simulation settings. The model parameters were calibrated to describe (without estimation) the haemodynamics of 2 antihypertensive drugs with data extracted from the literature. Structural identifiability analysis was done using various combinations of the observed variable.

RESULTS

The proposed model structure includes mean arterial pressure, heart rate and stroke volume and is composed of 4 states described by differential equations. Model evaluation showed flexibility in describing the haemodynamics at different target perturbations. Overlay plots of model predictions and literature data showed a good description without data fitting. The structural identifiability analysis revealed all model parameters and initial conditions were identifiable only when heart rate, mean arterial pressure and cardiac output were measured together.

CONCLUSIONS

A minimal model of the haemodynamic system was developed and evaluated. The model accounted for short-term haemodynamic feedback processes. We propose that this model can be used as the basis for future pharmacometric analyses of drugs acting on the haemodynamic system.

Saddle-Reset for Robust Parameter Estimation and Identifiability Analysis of Nonlinear Mixed Effects Models

Parameter estimation of a nonlinear model based on maximizing the likelihood using gradient-based numerical optimization methods can often fail due to premature termination of the optimization algorithm. One reason for such failure is that these numerical optimization methods cannot distinguish between the minimum, maximum, and a saddle point; hence, the parameters found by these optimization algorithms can possibly be in any of these three stationary points on the likelihood surface. We have found that for maximization of the likelihood for nonlinear mixed effects models used in pharmaceutical development, the optimization algorithm Broyden–Fletcher–Goldfarb–Shanno (BFGS) often terminates in saddle points, and we propose an algorithm, saddle-reset, to avoid the termination at saddle points, based on the second partial derivative test. In this algorithm, we use the approximated Hessian matrix at the point where BFGS terminates, perturb the point in the direction of the eigenvector associated with the lowest eigenvalue, and restart the BFGS algorithm. We have implemented this algorithm in industry standard software for nonlinear mixed effects modeling (NONMEM, version 7.4 and up) and showed that it can be used to avoid termination of parameter estimation at saddle points, as well as unveil practical parameter non-identifiability. We demonstrate this using four published pharmacometric models and two models specifically designed to be practically non-identifiable.

Bayesian pooling versus sequential integration of small preclinical trials: a comparison within linear and nonlinear modeling frameworks

Bayesian sequential integration is an appealing approach in drug development, as it allows to recursively update posterior distributions as soon as new data become available, thus considerably reducing the computation time. However, preclinical trials are often characterized by small sample sizes, which may affect the estimation process during the first integration steps, particularly when complex PK-PD models are used. In this case, sequential integration would not be practicable, and trials should be pooled together. This work is aimed at comparing simple Bayesian pooling with sequential integration through a simulation study. The two techniques are compared under several scenarios using linear as well as nonlinear models. The results of our simulation study encourage the use of Bayesian sequential integration with linear models. However, in the case of nonlinear models several caveats arise. This paper outlines some important recommendations and precautions in that respect.

Population pharmacokinetics of riociguat and its metabolite in patients with chronic thromboembolic pulmonary hypertension from routine clinical practice

Pharmacokinetic data for riociguat in patients with chronic thromboembolic pulmonary hypertension (CTEPH) have previously been reported from randomized clinical trials, which may not fully reflect the population encountered in routine practice. The aim of the current study was to characterize the pharmacokinetic of riociguat and its metabolite M1 in the patients from routine clinical practice. A population pharmacokinetic model was developed in NONMEM 7.3, based on riociguat and its metabolite plasma concentrations from 49 patients with CTEPH. One sample with riociguat and M1 concentrations was available from each patient obtained at different time points after last dose. Age, bodyweight, sex, smoking status, concomitant medications, kidney and liver function markers were tested as potential covariates of pharmacokinetic of riociguat and its metabolite. Riociguat and M1 disposition was best described with one-compartment models. Apparent volume of distribution (Vd/F) for riociguat and M1 were assumed to be the same. Total bilirubin and creatinine clearance were the most predictive covariates for apparent riociguat metabolic clearance to M1 (CL_f,M1/F) and for apparent riociguat clearance through remaining pathways (CL_e,r/F), respectively. CL_f,M1/F, CL_e,r/F, Vd/F of riociguat and M1, and clearance of M1 (CL_e,M1/F) for a typical individual with 70 mL/min creatinine clearance and 0.69 mg/dL total bilirubin were 0.665 L/h (relative standard error = 17%)), 0.66 (18%) L/h, 3.63 (15%) L and 1.47 (19%) L/h, respectively. Upon visual identification of six outlying individuals, an absorption lag-time of 2.95 (6%) h was estimated for these patients. In conclusion, the only clinical characteristics related to riociguat exposure in patients with CTEPH from routine clinical practice are total bilirubin and creatinine clearance. This confirms the findings of the previous population pharmacokinetic studies based on data from randomized clinical trials.

Bayesian sequential integration within a preclinical pharmacokinetic and pharmacodynamic modeling framework: Lessons learned

The present manuscript aims to discuss the implications of sequential knowledge integration of small preclinical trials in a Bayesian pharmacokinetic and pharmacodynamic (PK-PD) framework. While, at first sight, a Bayesian PK-PD framework seems to be a natural framework to allow for sequential knowledge integration, the scope of this paper is to highlight some often-overlooked challenges while at the same time providing some guidances in the many and overwhelming choices that need to be made. Challenges as well as opportunities will be discussed that are related to the impact of (1) the prior specification, (2) the choice of random effects, (3) the type of sequential integration method. In addition, it will be shown how the success of a sequential integration strategy is highly dependent on a carefully chosen experimental design when small trials are analyzed.

Three novel approaches to structural identifiability analysis in mixed-effects models

BACKGROUND AND OBJECTIVE

Structural identifiability is a concept that considers whether the structure of a model together with a set of input-output relations uniquely determines the model parameters. In the mathematical modelling of biological systems, structural identifiability is an important concept since biological interpretations are typically made from the parameter estimates. For a system defined by ordinary differential equations, several methods have been developed to analyse whether the model is structurally identifiable or otherwise. Another well-used modelling framework, which is particularly useful when the experimental data are sparsely sampled and the population variance is of interest, is mixed-effects modelling. However, established identifiability analysis techniques for ordinary differential equations are not directly applicable to such models.

METHODS

In this paper, we present and apply three different methods that can be used to study structural identifiability in mixed-effects models. The first method, called the repeated measurement approach, is based on applying a set of previously established statistical theorems. The second method, called the augmented system approach, is based on augmenting the mixed-effects model to an extended state-space form. The third method, called the Laplace transform mixed-effects extension, is based on considering the moment invariants of the systems transfer function as functions of random variables.

RESULTS

To illustrate, compare and contrast the application of the three methods, they are applied to a set of mixed-effects models.

CONCLUSIONS

Three structural identifiability analysis methods applicable to mixed-effects models have been presented in this paper. As method development of structural identifiability techniques for mixed-effects models has been given very little attention, despite mixed-effects models being widely used, the methods presented in this paper provides a way of handling structural identifiability in mixed-effects models previously not possible.

Can Population Modelling Principles be Used to Identify Key PBPK Parameters for Paediatric Clearance Predictions? An Innovative Application of Optimal Design Theory

PURPOSE

Physiologically-based pharmacokinetic (PBPK) models are essential in drug development, but require parameters that are not always obtainable. We developed a methodology to investigate the feasibility and requirements for precise and accurate estimation of PBPK parameters using population modelling of clinical data and illustrate this for two key PBPK parameters for hepatic metabolic clearance, namely whole liver unbound intrinsic clearance (CLint_,u,WL) and hepatic blood flow (Qh) in children.

METHODS

First, structural identifiability was enabled through re-parametrization and the definition of essential trial design components. Subsequently, requirements for the trial components to yield precise estimation of the PBPK parameters and their inter-individual variability were established using a novel application of population optimal design theory. Finally, the performance of the proposed trial design was assessed using stochastic simulation and estimation.

RESULTS

Precise estimation of CLint_,u,WL and Qh and their inter-individual variability was found to require a trial with two drugs, of which one has an extraction ratio (ER) ≤ 0.27 and the other has an ER ≥ 0.93. The proposed clinical trial design was found to lead to precise and accurate parameter estimates and was robust to parameter uncertainty.

CONCLUSION

The proposed framework can be applied to other PBPK parameters and facilitate the development of PBPK models.

Automated Scale Reduction of Nonlinear QSP Models With an Illustrative Application to a Bone Biology System

Integrating quantitative systems pharmacology (QSP) into pharmacokinetics/pharmacodynamics (PKPD) has resulted in models that are highly complex and often not amenable to further exploration via estimation or design. Because QSP models are usually depicted using nonlinear differential equations it is not straightforward to apply some model reduction techniques, such as proper lumping. In this study, we explore the combined use of linearization and proper lumping as a general method to simplification of a nonlinear QSP model. We illustrate this with a bone biology model and the reduced model was then applied to describe bone mineral density (BMD) changes due to denosumab dosing. The methodologies used in this study can be applied to other multiscale models for developing a mechanism-based structural model for future analyses.

A Joint Model for Vitamin K-Dependent Clotting Factors and Anticoagulation Proteins

BACKGROUND

Warfarin acts by inhibiting the reduction of vitamin K (VK) to its active form, thereby decreasing the production of VK-dependent coagulation proteins. The aim of this research is to develop a joint model for the VK-dependent clotting factors II, VII, IX and X, and the anticoagulation proteins, proteins C and S, during warfarin initiation.

METHODS

Data from 18 patients with atrial fibrillation who had warfarin therapy initiated were available for analysis. Nine blood samples were collected from each subject at baseline, and at 1-5, 8, 15 and 29 days after warfarin initiation and assayed for factors II, VII, IX and X, and proteins C and S. Warfarin concentration-time data were not available. The coagulation proteins data were modelled in a stepwise manner using NONMEM^® Version 7.2. In the first stage, each of the coagulation proteins was modelled independently using a kinetic-pharmacodynamic model. In the subsequent step, the six kinetic-pharmacodynamic models were combined into a single joint model.

RESULTS

One patient was administered VK and was excluded from the analysis. Each kinetic-pharmacodynamic model consisted of two parts: (1) a common one-compartment pharmacokinetic model with first-order absorption and elimination for warfarin; and (2) an inhibitory E _max model linked to a turnover model for coagulation proteins. In the joint model, an unexpected pharmacodynamic lag was identified and the estimated degradation half-life of VK-dependent coagulation proteins were in agreement with previously published values. The model provided an adequate fit to the observed data.

CONCLUSION

The joint model represents the first work to quantify the influence of warfarin on all six VK-dependent coagulation proteins simultaneously. Future work will expand the model to predict the influence of exogenously administered VK on the time course of clotting factor concentrations after warfarin overdose and during perioperative warfarin reversal procedures.

An evaluation of the operational model when applied to quantify functional selectivity

BACKGROUND AND PURPOSE

Functional selectivity describes the ability of ligands to differentially regulate multiple signalling pathways when coupled to a single receptor, and the operational model is commonly used to analyse these data. Here, we assess the mathematical properties of the operational model and evaluate the outcomes of fixing parameters on model performance.

EXPERIMENTAL APPROACH

The operational model was evaluated using both a mathematical identifiability analysis and simulation.

KEY RESULTS

Mathematical analysis revealed that the parameters R0 and KE were not independently identifiable which can be solved by considering their ratio, τ. The ratio parameter, τ, was often imprecisely estimated when only functional assay data were available and generally only the transduction coefficient R ( τKA) could be estimated precisely. The general operational model (that includes baseline and the Hill coefficient) required either the parameters Em or KA to be fixed. The normalization process largely cancelled out the mean error of the calculated Δlog (R) caused by fixing these parameters. From this analysis, it was determined that we can avoid the need for a full agonist ligand to be included in an experiment to determine Δlog (R).

CONCLUSION AND IMPLICATIONS

This analysis has provided a ready-to-use understanding of current methods for quantifying functional selectivity. It showed that current methods are generally tolerant to fixing parameters. A new method was proposed that removes the need for including a high efficacy ligand in any given experiment, which allows application to large-scale screening to identify compounds with desirable features of functional selectivity.

Selection and Qualification of Simplified QSP Models When Using Model Order Reduction Techniques

Quantitative systems pharmacology (QSP) models are increasingly used in drug development to provide a deep understanding of the mechanism of action of drugs and to identify appropriate disease targets. Such models are, however, not suitable for estimation purposes due to their high dimensionality. Based on any desired and specific input-output relationship, the system may be reduced to a model with fewer states and parameters. However, any simplification process will be a trade-off between model performance and complexity. In this study, we develop a weighted composite criterion which brings together the opposing indices of performance and dimensionality. The weighting factor can be determined by qualification of the simplified model based on a visual predictive check (VPC) using the precision of each parameter. The weighted criterion and model qualification techniques were illustrated with three examples: a simple compartmental pharmacokinetic model, a physiologically based pharmacokinetic (PBPK) example, and a semimechanistic model for bone mineral density. When considering the PBPK example, this automated search identified the same reduced model which had been detected in a previous report, as well as a simpler model which had not been previously identified. The simpler bone mineral density model provided an adequate description of the response even after 1 year from the initiation of treatment. The proposed criterion together with a VPC provides a natural way for model order reduction that can be fully automated and applied to multiscale models.

Extending existing structural identifiability analysis methods to mixed-effects models

The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice.

Population pharmacokinetic model of transdermal nicotine delivered from a matrix-type patch

AIMS

Nicotine addiction is an issue faced by millions of individuals worldwide. As a result, nicotine replacement therapies, such as transdermal nicotine patches, have become widely distributed and used. While the pharmacokinetics of transdermal nicotine have been extensively described using noncompartmental methods, there are few data available describing the between-subject variability in transdermal nicotine pharmacokinetics. The aim of this investigation was to use population pharmacokinetic techniques to describe this variability, particularly as it pertains to the absorption of nicotine from the transdermal patch.

METHODS

A population pharmacokinetic parent-metabolite model was developed using plasma concentrations from 25 participants treated with transdermal nicotine. Covariates tested in this model included: body weight, body mass index, body surface area (calculated using the Mosteller equation) and sex.

RESULTS

Nicotine pharmacokinetics were best described with a one-compartment model with absorption based on a Weibull distribution and first-order elimination and a single compartment for the major metabolite, cotinine. Body weight was a significant covariate on apparent volume of distribution of nicotine (exponential scaling factor 1.42). After the inclusion of body weight in the model, no other covariates were significant.

CONCLUSIONS

This is the first population pharmacokinetic model to describe the absorption and disposition of transdermal nicotine and its metabolism to cotinine and the pharmacokinetic variability between individuals who were administered the patch.

Deterministic identifiability of population pharmacokinetic and pharmacokinetic-pharmacodynamic models

Identifiability is an important component of pharmacokinetic-pharmacodynamic (PKPD) model development. Structural identifiability is concerned with the uniqueness of the model parameters for a set of perfect input-output data and deterministic identifiability with the precision of parameter estimation given imperfect input-output data. We introduce two subcategories of deterministic identifiability, external and internal, and consider factors that distinguish between these forms. We define external deterministic identifiability as a function of externally controllable variables, i.e., the design, and internal deterministic identifiability as a function of the model and its parameter values. The concepts are explored using three common PK and PKPD models, and verified for their precision for the selected set of parameter values under optimal design.

Population pharmacokinetics of doxorubicin and doxorubicinol in patients diagnosed with non-Hodgkin's lymphoma

AIMS

The aims of the study were: (i) to characterize the pharmacokinetics (PK) of doxorubicin (DOX) and doxorubicinol (DOXol) in patients diagnosed with non-Hodgkin's lymphoma (NHL) using a population approach; (ii) to evaluate the influence of various covariates on the PK of DOX; and (iii) to evaluate the role of DOX and DOXol exposure in haematological toxicity.

METHODS

Population PK modelling (using NONMEM) was performed using DOX and DOXol plasma concentration-time data from 45 NHL patients treated with R-CHOP (rituximab, cyclophosphamide, doxorubicin, vincristine and prednisone). The influence of drug exposure on haematological toxicity was analysed using the Mann-Whitney-Wilcoxon test.

RESULTS

A five-compartment model, three for DOX and two for DOXol, with first-order distribution and elimination for both entities best described the data. Population estimates for parent drug (CL) and metabolite (CL_m ) clearance were 62 l h^-1 and 27 l h^-1 , respectively. The fraction metabolized to DOXol (F_m ) was estimated at 0.22. While bilirubin and aspartate aminotransferase showed an influence on the CL and CL_m , the objective function value decrease was not statistically significant. A trend towards an association between the total area under the concentration-time curve (AUC_total ), the area under the concentration-time curve for DOX (AUC) plus the area under the concentration-time curve for DOXol (AUC_m ), and the neutropenia grade (P = 0.068) and the neutrophil counts (P = 0.089) was observed, according to an exponential relationship.

CONCLUSIONS

The PK of DOX and DOXol were well characterized by the model developed, which could be used as a helpful tool to optimize the dosage of this drug. The results suggest that the main active metabolite of DOX, DOXol, is involved in the haematological toxicity of the parent drug.

Children in clinical trials: towards evidence-based pediatric pharmacotherapy using pharmacokinetic-pharmacodynamic modeling

INTRODUCTION

In pediatric pharmacotherapy, many drugs are still used off-label, and their efficacy and safety is not well characterized. Different efficacy and safety profiles in children of varying ages may be anticipated, due to developmental changes occurring across pediatric life.

AREAS COVERED

Beside pharmacokinetic (PK) studies, pharmacodynamic (PD) studies are urgently needed. Validated PKPD models can be used to derive optimal dosing regimens for children of different ages, which can be evaluated in a prospective study before implementation in clinical practice. Strategies should be developed to ensure that formularies update their drug dosing guidelines regularly according to the most recent advances in research, allowing for clinicians to integrate these guidelines in daily practice. Expert commentary: We anticipate a trend towards a systems-level approach in pediatric modeling to optimally use the information gained in pediatric trials. For this approach, properly designed clinical PKPD studies will remain the backbone of pediatric research.

What do we mean by identifiability in mixed effects models?

We discuss the question of model identifiability within the context of nonlinear mixed effects models. Although there has been extensive research in the area of fixed effects models, much less attention has been paid to random effects models. In this context we distinguish between theoretical identifiability, in which different parameter values lead to non-identical probability distributions, structural identifiability which concerns the algebraic properties of the structural model, and practical identifiability, whereby the model may be theoretically identifiable but the design of the experiment may make parameter estimation difficult and imprecise. We explore a number of pharmacokinetic models which are known to be non-identifiable at an individual level but can become identifiable at the population level if a number of specific assumptions on the probabilistic model hold. Essentially if the probabilistic models are different, even though the structural models are non-identifiable, then they will lead to different likelihoods. The findings are supported through simulations.

Pharmacokinetic Modeling of Lamivudine and Zidovudine Triphosphates Predicts Differential Pharmacokinetics in Seminal Mononuclear Cells and Peripheral Blood Mononuclear Cells

The male genital tract is a potential site of viral persistence. Therefore, adequate concentrations of antiretrovirals are required to eliminate HIV replication in the genital tract. Despite higher zidovudine (ZDV) and lamivudine (3TC) concentrations in seminal plasma (SP) than in blood plasma (BP) (SP/BP drug concentration ratios of 2.3 and 6.7, respectively), we have previously reported lower relative intracellular concentrations of their active metabolites, zidovudine triphosphate (ZDV-TP) and lamivudine triphosphate (3TC-TP), in seminal mononuclear cells (SMCs) than in peripheral blood mononuclear cells (PBMCs) (SMC/PBMC drug concentration ratios of 0.36 and 1.0, respectively). Here, we use population pharmacokinetic (PK) modeling-based methods to simultaneously describe parent and intracellular metabolite PK in blood, semen, and PBMCs and SMCs. From this model, the time to steady state in each matrix was estimated, and the results indicate that the PK of 3TC-TP and ZDV-TP in PBMCs are different from the PK of the two in SMCs and different for the two triphosphates. We found that steady-state conditions in PBMCs were achieved within 2 days for ZDV-TP and 3 days for 3TC-TP. However, steady-state conditions in SMCs were achieved within 2 days for ZDV-TP and 2 weeks for 3TC-TP. Despite this, or perhaps because of it, ZDV-TP in SMCs does not achieve the surrogate 50% inhibitory concentration (IC50) (as established for PBMCs, assuming SMC IC50 = PBMC IC50) at the standard 300-mg twice-daily dosing. Mechanistic studies are needed to understand these differences and to explore intracellular metabolite behavior in SMCs for other nucleoside analogues used in HIV prevention, treatment, and cure.

Population pharmacokinetic modelling to assess the impact of CYP2D6 and CYP3A metabolic phenotypes on the pharmacokinetics of tamoxifen and endoxifen

AIMS

Tamoxifen is considered a pro-drug of its active metabolite endoxifen. The major metabolic enzymes involved in endoxifen formation are CYP2D6 and CYP3A. There is considerable evidence that variability in activity of these enzymes influences endoxifen exposure and thereby may influence the clinical outcome of tamoxifen treatment. We aimed to quantify the impact of metabolic phenotype on the pharmacokinetics of tamoxifen and endoxifen.

METHODS

We assessed the CYP2D6 and CYP3A metabolic phenotypes in 40 breast cancer patients on tamoxifen treatment with a single dose of dextromethorphan as a dual phenotypic probe for CYP2D6 and CYP3A. The pharmacokinetics of dextromethorphan, tamoxifen and their relevant metabolites were analyzed using non-linear mixed effects modelling.

RESULTS

Population pharmacokinetic models were developed for dextromethorphan, tamoxifen and their metabolites. In the final model for tamoxifen, the dextromethorphan derived metabolic phenotypes for CYP2D6 as well as CYP3A significantly (P < 0.0001) explained 54% of the observed variability in endoxifen formation (inter-individual variability reduced from 55% to 25%).

CONCLUSIONS

We have shown that not only CYP2D6, but also CYP3A enzyme activity influences the tamoxifen to endoxifen conversion in breast cancer patients. Our developed model may be used to assess separately the impact of CYP2D6 and CYP3A mediated drug-drug interactions with tamoxifen without the necessity of administering this anti-oestrogenic drug and to support Bayesian guided therapeutic drug monitoring of tamoxifen in routine clinical practice.

Lifespan based pharmacokinetic-pharmacodynamic model of tumor growth inhibition by anticancer therapeutics

Accurate prediction of tumor growth is critical in modeling the effects of anti-tumor agents. Popular models of tumor growth inhibition (TGI) generally offer empirical description of tumor growth. We propose a lifespan-based tumor growth inhibition (LS TGI) model that describes tumor growth in a xenograft mouse model, on the basis of cellular lifespan T. At the end of the lifespan, cells divide, and to account for tumor burden on growth, we introduce a cell division efficiency function that is negatively affected by tumor size. The LS TGI model capability to describe dynamic growth characteristics is similar to many empirical TGI models. Our model describes anti-cancer drug effect as a dose-dependent shift of proliferating tumor cells into a non-proliferating population that die after an altered lifespan T_A. Sensitivity analysis indicated that all model parameters are identifiable. The model was validated through case studies of xenograft mouse tumor growth. Data from paclitaxel mediated tumor inhibition was well described by the LS TGI model, and model parameters were estimated with high precision. A study involving a protein casein kinase 2 inhibitor, AZ968, contained tumor growth data that only exhibited linear growth kinetics. The LS TGI model accurately described the linear growth data and estimated the potency of AZ968 that was very similar to the estimate from an established TGI model. In the case study of AZD1208, a pan-Pim inhibitor, the doubling time was not estimable from the control data. By fixing the parameter to the reported in vitro value of the tumor cell doubling time, the model was still able to fit the data well and estimated the remaining parameters with high precision. We have developed a mechanistic model that describes tumor growth based on cell division and has the flexibility to describe tumor data with diverse growth kinetics.

Scale reduction of a systems coagulation model with an application to modeling pharmacokinetic-pharmacodynamic data

Bridging systems biology and pharmacokinetics–pharmacodynamics has resulted in models that are highly complex and complicated. They usually contain large numbers of states and parameters and describe multiple input–output relationships. Based on any given data set relating to a specific input–output process, it is possible that some states of the system are either less important or have no influence at all. In this study, we explore a simplification of a systems pharmacology model of the coagulation network for use in describing the time course of fibrinogen recovery after a brown snake bite. The technique of proper lumping is used to simplify the 62-state systems model to a 5-state model that describes the brown snake venom–fibrinogen relationship while maintaining an appropriate mechanistic relationship. The simplified 5-state model explains the observed decline and recovery in fibrinogen concentrations well. The techniques used in this study can be applied to other multiscale models.

Parameterisation affects identifiability of population models

Identifiability is an important aspect of model development. In this work, using a simple one compartment population pharmacokinetic model, we show that identifiability of the variances of the random effects parameters are affected by the parameterisation of the fixed effects parameters.