Comparative performance of cell life span and cell transit models for describing erythropoietic drug effects

Evaluation of Hemoglobin Response to Treatment With Enarodustat Using Pharmacometric Approach in Japanese Anemic Patients With Chronic Kidney Disease

Enarodustat (JTZ-951) is a hypoxia-inducible factor prolyl hydroxylase inhibitor that has been approved and marketed in Japan for patients with anemia with chronic kidney disease (CKD). The pharmacometric approach was applied to assess the relationship between plasma concentrations of enarodustat and hemoglobin (Hb) levels, and to provide information regarding the optimal use of enarodustat in clinical practice by simulations based on the pharmacokinetic and pharmacodynamic (PK/PD) model that was developed. The PK/PD data of enarodusat obtained from phase 2 and phase 3 studies in Japanese patients with CKD were well described by the models: a 1-compartment model with first-order absorption and elimination for PK, and a semimechanistic model based on transit compartment model for PD. Although several factors were identified as statistically significant covariates on the PK/PD of enarodustat, model-based simulations showed that none of them had clinically relevant impacts on the treatment effect (ie, Hb levels) of enarodustat. Hence, enarodustat treatment provides the stable Hb control with the initial dose (hemodialysis-dependent CKD: 4 mg/day, non-dialysis-dependent CKD: 2 mg/day) and maintenance dose (1-8 mg/day) to the patients with varied demographic characteristics.

Application of the relationship between pharmacokinetics and pharmacodynamics in drug development and therapeutic equivalence: a PEARRL review

Objectives

The objective of this review was to provide an overview of pharmacokinetic/pharmacodynamic (PK/PD) models, focusing on drug-specific PK/PD models and highlighting their value added in drug development and regulatory decision-making.

Key findings

Many PK/PD models, with varying degrees of complexity and physiological understanding have been developed to evaluate the safety and efficacy of drug products. In special populations (e.g. paediatrics), in cases where there is genetic polymorphism and in other instances where therapeutic outcomes are not well described solely by PK metrics, the implementation of PK/PD models is crucial to assure the desired clinical outcome. Since dissociation between the pharmacokinetic and pharmacodynamic profiles is often observed, it is proposed that physiologically based pharmacokinetic and PK/PD models be given more weight by regulatory authorities when assessing the therapeutic equivalence of drug products.

Summary

Modelling and simulation approaches already play an important role in drug development. While slowly moving away from ‘one-size fits all’ PK methodologies to assess therapeutic outcomes, further work is required to increase confidence in PK/PD models in translatability and prediction of various clinical scenarios to encourage more widespread implementation in regulatory decision-making.

Semi-mechanistic Pharmacokinetic/Pharmacodynamic model of three pegylated rHuEPO and ior®EPOCIM in New Zealand rabbits

Marketed formulations of erythropoietin (EPO) ior®EPOCIM, MIRCERA® and two newly developed pegylated-EPO analogues (PEG-EPO 32 and 40 kDa) formulations were intravenously administered to New Zealand rabbits. A semi-mechanistic Pharmacokinetic/Pharmacodynamic (PK/PD) model describing in a simultaneous and integrated form the time course of reticulocytes, red blood cells and hemoglobin was built to account for the time course of hematopoiesis stimulation after erythropoietin administration. Data analysis was performed based on the population approach with the software NONMEM version 7.3. Erythropoietin disposition of each of the administered formulations was best described with a two compartment model and linear elimination. Different formulations show different clearance and apparent volume of distribution of the central compartment but share estimates of inter-compartmental clearance and apparent peripheral volume of distribution. A semi-mechanistic model including cell proliferation, maturation, and homeostatic regulation provided a good description of the data regardless the type of erythropoietin formulation administered. The system-, and drug-related parameters showed consistency and differed across formulations, respectively. A single IV administration of PEG-EPO 32 and 40 kDa formulations in New Zealand rabbits achieves a median change of 27% and 22% on RET levels, and of 47% and 63% on RBC and HGB levels, respectively compared to MIRCERA®. The administration of new branched PEG-chains formulations improves PK and PD properties of EPO, in terms of increasing elimination half-lives and pharmacological activity on RET, RBC and HGB compared to commercially available formulations (ior®EPOCIM and MIRCERA®).

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.

Clinical pharmacokinetics and pharmacodynamics of erythropoiesis-stimulating agents

The cloning of the EPO gene in the early 1980s allowed for the development of recombinant erythropoietins and analogues [erythropoiesis-stimulating agents (ESAs)], offering an alternative to transfusion as a method of raising haemoglobin (Hb) levels, which have been used for more than 20 years to treat anaemia in millions of anaemic patients. There are now a number of ESAs available worldwide for the treatment of anaemia, approved for different routes of administration (intravenous and subcutaneous) and dosing intervals (three times weekly, weekly, biweekly and monthly). In this review, we discuss the pharmacokinetic characteristics, including absorption, distribution and elimination processes, across the different ESAs. Incomplete and slow lymphatic absorption, with limited extravascular distribution, and minor contributions of the target-mediated drug disposition to the overall elimination are the common characteristics across the marketed ESA. Additionally, we assess the similarities and differences of ESAs related to pharmacodynamics in the context of the different biomarkers used to monitor the magnitude and duration of the effect, and introduce the concept of the minimum effective concentration of the ESA. The relationship between the minimum effective concentration and the half-life suggests that the time during which drug concentrations are above the minimum effective concentration is the main determinant of ESA efficacy in increasing Hb levels. The tolerance phenomenon and its physiological mechanism and implications for ESA dosing are discussed. Finally, the areas of future clinical pharmacology research are envisioned.

Pharmacokinetics and pharmacokinetic-pharmacodynamic correlations of therapeutic peptides

Peptides, defined as polymers of less than 50 amino acids with a molecular weight of less than 10 kDa, represent a fast-growing class of new therapeutics which has unique pharmacokinetic characteristics compared to large proteins or small molecule drugs. Unmodified peptides usually undergo extensive proteolytic cleavage, resulting in short plasma half-lives. As a result of their low permeability and susceptibility to catabolic degradation, therapeutic peptides usually have very limited oral bioavailability and are administered either by the intravenous, subcutaneous, or intramuscular route, although other routes such as nasal delivery are utilized as well. Distribution processes are mainly driven by a combination of diffusion and to a lesser degree convective extravasation dependent on the size of the peptide, with volumes of distribution frequently not larger than the volume of the extracellular body fluid. Owing to the ubiquitous availability of proteases and peptidases throughout the body, proteolytic degradation is not limited to classic elimination organs. Since peptides are generally freely filtered by the kidneys, glomerular filtration and subsequent renal metabolism by proteolysis contribute to the elimination of many therapeutic peptides. Although small peptides have usually limited immunogenicity, formation of anti-drug antibodies with subsequent hypersensitivity reactions has been described for some peptide therapeutics. Numerous strategies have been applied to improve the pharmacokinetic properties of therapeutic peptides, especially to overcome their metabolic instability, low permeability, and limited tissue residence time. Applied techniques include amino acid substitutions, modification of the peptide terminus, inclusion of disulfide bonds, and conjugation with polymers or macromolecules such as antibody fragments or albumin. Application of model-based pharmacokinetic-pharmacodynamic correlations has been widely used for therapeutic peptides in support of drug development and dosage regimen design, especially because their targets are often well-described endogenous regulatory pathways and processes.

Computational approaches to analyse and predict small molecule transport and distribution at cellular and subcellular levels

Quantitative structure-activity relationship (QSAR) studies and mechanistic mathematical modeling approaches have been independently employed for analysing and predicting the transport and distribution of small molecule chemical agents in living organisms. Both of these computational approaches have been useful for interpreting experiments measuring the transport properties of small molecule chemical agents, in vitro and in vivo. Nevertheless, mechanistic cell-based pharmacokinetic models have been especially useful to guide the design of experiments probing the molecular pathways underlying small molecule transport phenomena. Unlike QSAR models, mechanistic models can be integrated from microscopic to macroscopic levels, to analyse the spatiotemporal dynamics of small molecule chemical agents from intracellular organelles to whole organs, well beyond the experiments and training data sets upon which the models are based. Based on differential equations, mechanistic models can also be integrated with other differential equations-based systems biology models of biochemical networks or signaling pathways. Although the origin and evolution of mathematical modeling approaches aimed at predicting drug transport and distribution has occurred independently from systems biology, we propose that the incorporation of mechanistic cell-based computational models of drug transport and distribution into a systems biology modeling framework is a logical next step for the advancement of systems pharmacology research.

Lifespan based indirect response models

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.