Basic pharmacodynamic models for agents that alter production of natural cells

Scaling Pharmacodynamics from Rats to Humans to Support Erythropoietin and Romiplostim Combination Therapy to Treat Erythropoietin-Resistant Anemia

Recombinant human erythropoietin (rHuEPO) is one of the most effective drugs for the treatment of anemia in patients with chronic kidney disease. However, EPO-resistance is an important contributor to the increased risk of adverse effects. We previously showed that EPO treatment could induce precursor cell depletion, resulting in EPO-resistance. We further found that the combination of EPO with romiplostim, a thrombopoietin receptor agonist that can stimulate the expansion of hematopoietic stem cells, can treat EPO-resistance. In this study, we performed interspecies pharmacodynamic (PD) scaling of this combination therapy for human dose prediction. The pharmacokinetic parameters of both rHuEPO and romiplostim in humans were obtained from previous studies. The PD parameters obtained in rats were scaled to humans using allometric equations. The relationship between PD parameters of the megakaryocyte lineage from rats, monkeys, and humans was in agreement with those from the literature on allometric scaling. The PD response was translated to humans based on allometric scaling and agreed with the observed data. These parameters were used to simulate hemoglobin and platelet response in humans. RHuEPO 50 IU/kg thrice weekly and romiplostim 1 μg/kg once every 4 weeks from the second week is the recommended combination dosing regimen according to the model prediction. Our work successfully scaled the PD of rHuEPO and romiplostim monotherapy from rats to humans. The predicted dosing regimen of each drug in the combination therapy is less intensive than the approved starting dose of each drug, which supports additional evaluations of the combination therapy in humans.

An Extended Model Including Target Turnover, Ligand-Target Complex Kinetics, and Binding Properties to Describe Drug-Receptor Interactions

Since the beginning of this century, target-mediated drug disposition has become a central concept in modeling drug action in drug development. It combines a range of processes, such as turnover, protein binding, internalization, and non-specific elimination, and often serves as a nucleus of more complex pharmacokinetic models. It is simple enough to comprehend but complex enough to be able to describe a wide range of phenomena and data sets. However, the complexity comes at a price: many parameters. In this chapter, we present an overview of the temporal development of the compounds involved after different types of drug doses and offer convenient handles for dissecting data sets in a sophisticated manner in order to estimate the values of these parameters, such as rate constants and pertinent concentrations.

Pharmacokinetic/Pharmacodynamic Modelling and Simulation of Lusutrombopag, a Novel Thrombopoietin Receptor Agonist, for the Treatment of Thrombocytopenia in Patients with Chronic Liver Disease Undergoing Invasive Procedures

BACKGROUND

Patients with thrombocytopenia associated with chronic liver disease (CLD) are at greater risk of bleeding during invasive procedures. This study characterized the pharmacokinetic/pharmacodynamic (PK/PD) profile of lusutrombopag, a novel thrombopoietin-receptor agonist, using modelling and simulation, and evaluated the appropriate dose regimen for treatment of thrombocytopenia in CLD patients undergoing invasive procedures.

METHODS

A population PK/PD model was developed using plasma lusutrombopag concentrations from 78 healthy subjects and 349 CLD patients, as well as platelet counts from 347 of these 349 patients. Covariates were explored from subject characteristics. Monte-Carlo simulations were performed to assess a dose response for efficacy (platelet counts ≥ 50,000/μL) and a risk for platelet overshooting (platelet counts > 200,000/μL).

RESULTS

Visual predictive checks indicated the developed models described the PK/PD profile of lusutrombopag well. In the simulations, without stopping criteria, lusutrombopag 3 mg once daily for 7 days before scheduled invasive procedures provided effective platelet response (85.2% probability for efficacy). The probability of platelet overshooting was 1.2%, indicating that platelet monitoring is not necessary. Although body weight was an influential covariate on the pharmacokinetics of lusutrombopag, individually estimated peak platelet counts overlapped among the body weight groups, suggesting no clinically significant effect on body weight.

CONCLUSION

The modelling and simulation support lusutrombopag 3 mg once daily for 7 days without platelet monitoring.

Transitioning from Basic toward Systems Pharmacodynamic Models: Lessons from Corticosteroids

Technology in bioanalysis, -omics, and computation have evolved over the past half century to allow for comprehensive assessments of the molecular to whole body pharmacology of diverse corticosteroids. Such studies have advanced pharmacokinetic and pharmacodynamic (PK/PD) concepts and models that often generalize across various classes of drugs. These models encompass the "pillars" of pharmacology, namely PK and target drug exposure, the mass-law interactions of drugs with receptors/targets, and the consequent turnover and homeostatic control of genes, biomarkers, physiologic responses, and disease symptoms. Pharmacokinetic methodology utilizes noncompartmental, compartmental, reversible, physiologic [full physiologically based pharmacokinetic (PBPK) and minimal PBPK], and target-mediated drug disposition models using a growing array of pharmacometric considerations and software. Basic PK/PD models have emerged (simple direct, biophase, slow receptor binding, indirect response, irreversible, turnover with inactivation, and transduction models) that place emphasis on parsimony, are mechanistic in nature, and serve as highly useful "top-down" methods of quantitating the actions of diverse drugs. These are often components of more complex quantitative systems pharmacology (QSP) models that explain the array of responses to various drugs, including corticosteroids. Progressively deeper mechanistic appreciation of PBPK, drug-target interactions, and systems physiology from the molecular (genomic, proteomic, metabolomic) to cellular to whole body levels provides the foundation for enhanced PK/PD to comprehensive QSP models. Our research based on cell, animal, clinical, and theoretical studies with corticosteroids have provided ideas and quantitative methods that have broadly advanced the fields of PK/PD and QSP modeling and illustrates the transition toward a global, systems understanding of actions of diverse drugs. SIGNIFICANCE STATEMENT: Over the past half century, pharmacokinetics (PK) and pharmacokinetics/pharmacodynamics (PK/PD) have evolved to provide an array of mechanism-based models that help quantitate the disposition and actions of most drugs. We describe how many basic PK and PK/PD model components were identified and often applied to the diverse properties of corticosteroids (CS). The CS have complications in disposition and a wide array of simple receptor-to complex gene-mediated actions in multiple organs. Continued assessments of such complexities have offered opportunities to develop models ranging from simple PK to enhanced PK/PD to quantitative systems pharmacology (QSP) that help explain therapeutic and adverse CS effects. Concurrent development of state-of-the-art PK, PK/PD, and QSP models are described alongside experimental studies that revealed diverse CS actions.

Application of Pharmacokinetic-Pharmacodynamic Modeling in Drug Delivery: Development and Challenges

With the advancement of technology, drug delivery systems and molecules with more complex architecture are developed. As a result, the drug absorption and disposition processes after administration of these drug delivery systems and engineered molecules become exceedingly complex. As the pharmacokinetic and pharmacodynamic (PK-PD) modeling allows for the separation of the drug-, carrier- and pharmacological system-specific parameters, it has been widely used to improve understanding of the in vivo behavior of these complex delivery systems and help their development. In this review, we summarized the basic PK-PD modeling theory in drug delivery and demonstrated how it had been applied to help the development of new delivery systems and modified large molecules. The linkage between PK and PD was highlighted. In particular, we exemplified the application of PK-PD modeling in the development of extended-release formulations, liposomal drugs, modified proteins, and antibody-drug conjugates. Furthermore, the model-based simulation using primary PD models for direct and indirect PD responses was conducted to explain the assertion of hypothetical minimal effective concentration or threshold in the exposure-response relationship of many drugs and its misconception. The limitations and challenges of the mechanism-based PK-PD model were also discussed.

Unraveling Disease Pathophysiology with Mathematical Modeling

Modeling has enabled fundamental advances in our understanding of the mechanisms of health and disease for centuries, since at least the time of William Harvey almost 500 years ago. Recent technological advances in molecular methods, computation, and imaging generate optimism that mathematical modeling will enable the biomedical research community to accelerate its efforts in unraveling the molecular, cellular, tissue-, and organ-level processes that maintain health, predispose to disease, and determine response to treatment. In this review, we discuss some of the roles of mathematical modeling in the study of human physiology and pathophysiology and some challenges and opportunities in general and in two specific areas: in vivo modeling of pulmonary function and in vitro modeling of blood cell populations.

Model-based approach for methoxy polyethylene glycol-epoetin beta drug development in paediatric patients with anaemia of chronic kidney disease

AIMS

Methoxy polyethylene glycol-epoetin beta (continuous erythropoietin receptor activator, C.E.R.A.) is used for the treatment of anaemia in adults with chronic kidney disease (CKD). Patients treated with shorter-acting erythropoiesis-stimulating agents up to three times weekly can be switched to once-monthly C.E.R.A.. Doses can be adjusted on a monthly basis based on haemoglobin (Hb) levels during the preceding period. A model-based approach was applied to optimise C.E.R.A. development, more specifically the confirmatory trial of the paediatric plan.

METHODS

Pharmacokinetic and pharmacodynamic data from a phase II paediatric study and phase II and III adult studies were analysed together using modelling and simulation to determine the pharmacokinetic/pharmacodynamic characteristics of C.E.R.A. in a broad population. Model-based simulations of C.E.R.A. treatment outcomes in paediatric patients were performed, notably when administered subcutaneously and compared to clinical and real-world data.

RESULTS

Age and body weight explained differences in pharmacokinetics, while the pharmacodynamic characteristics of C.E.R.A. were similar between adult and paediatric populations. Simulated Hb levels (mean and 95% prediction interval 10.9 [10.6, 11.2] g dL^-1 ) and C.E.R.A. doses (median and 95% prediction interval 105 [72, 159] μg) 20 weeks after switching to subcutaneous C.E.R.A. were confirmed by observed real-world data from International Pediatric Dialysis Network registries (mean Hb was 10.8 g dL^-1 and median C.E.R.A. dose was 100 μg).

CONCLUSIONS

These analyses have facilitated optimisation of the C.E.R.A. development programme in paediatric patients with anaemia of CKD to provide this patient population with faster access to the drug while avoiding unnecessary clinical trial exposure and related monitoring burden in children.

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.

Delayed logistic indirect response models: realization of oscillating behavior

Indirect response (IDR) models are probably the most frequently applied tools relating the effect of a signal to a baseline response. A response modeled by such a classical IDR model will always return monotonously to its baseline after drug administration. We extend IDR models with a delay process, i.e. a retarded response state, that leads to oscillating response behavior. First, IDR models with a first-order production and second-order loss term based on the famous logistic equation are constructed. Second, a delay process similar to the delayed logistic equation is included. Relations of the classical IDR model with our extended IDR model concerning response and model parameters are revealed. Simulations of typical response profiles are presented and data fitting of a model for leptin and cholesterol dynamics after administration of methylprednisolone is performed. The influence of the delay parameter on the other model parameters is discussed.

Population Pharmacokinetic and Pharmacodynamic Modeling of Lusutrombopag, a Newly Developed Oral Thrombopoietin Receptor Agonist, in Healthy Subjects

OBJECTIVES

The aim of this study was to develop a population pharmacokinetic (PK)/pharmacodynamic (PD) model for describing plasma lusutrombopag concentrations and platelet response following oral lusutrombopag dosing and for evaluating covariates in the PK/PD profiles.

METHODS

A population PK/PD model was developed using a total of 2539 plasma lusutrombopag concentration data and 1408 platelet count data from 78 healthy adult subjects following oral single and multiple (14-day once-daily) dosing. Covariates in PK and PK/PD models were explored for subject age, body weight, sex, and ethnicity.

RESULTS

A three-compartment model with first-order rate and lag time for absorption was selected as a PK model. A three-transit and one-platelet compartment model with a sigmoid E _max model for drug effect and feedback of platelet production was selected as the PD model. The PK and PK/PD models well described the plasma lusutrombopag concentrations and the platelet response, respectively. Body weight was a significant covariate in PK. The bioavailability of non-Japanese subjects (White and Black/African American subjects) was 13 % lower than that of Japanese subjects, while the simulated platelet response profiles using the PK/PD model were similar between Japanese and non-Japanese subjects. There were no significant covariates of the tested background data including age, sex, and ethnicity (Japanese or non-Japanese) for the PD sensitivity.

CONCLUSION

A population PK/PD model was developed for lusutrombopag and shown to provide good prediction for the PK/PD profiles. The model could be used as a basic PK/PD model in the drug development of lusutrombopag.

Estimation of adult and neonatal RBC lifespans in anemic neonates using RBCs labeled at several discrete biotin densities

BACKGROUND

Prior conclusions that autologous neonatal red blood cells (RBC) have substantially shorter lifespans than allogeneic adult RBCs were not based on direct comparison of autologous neonatal vs. allogeneic adult RBCs performed concurrently in the same infant. Biotin labeling of autologous neonatal RBCs and allogeneic adult donor RBCs permits concurrent direct comparison of autologous vs. allogeneic RBC lifespan.

METHODS

RBCs from 15 allogeneic adult donors and from 15 very-low-birth-weight (VLBW) neonates were labeled at separate biotin densities and transfused simultaneously into the 15 neonates. Two mathematical models that account for the RBC differences were employed to estimate lifespans for the two RBC populations.

RESULTS

Mean ± SD lifespan for adult allogeneic RBC was 70.1 ± 19.1 d, which is substantially shorter than the 120 d lifespan of both autologous and adult allogeneic RBC in healthy adults. Mean ± SD lifespan for neonatal RBC was 54.2 ± 11.3 d, which is only about 30% shorter than that of the adult allogeneic RBCs.

CONCLUSION

This study provides evidence that extrinsic environmental factors primarily determine RBC survival (e.g., small bore of the capillaries of neonates, rate of oxygenation/deoxygenation cycles) rather than factors intrinsic to RBC.

Models for the red blood cell lifespan

The lifespan of red blood cells (RBCs) plays an important role in the study and interpretation of various clinical conditions. Yet, confusion about the meanings of fundamental terms related to cell survival and their quantification still exists in the literature. To address these issues, we started from a compartmental model of RBC populations based on an arbitrary full lifespan distribution, carefully defined the residual lifespan, current age, and excess lifespan of the RBC population, and then derived the distributions of these parameters. For a set of residual survival data from biotin-labeled RBCs, we fit models based on Weibull, gamma, and lognormal distributions, using nonlinear mixed effects modeling and parametric bootstrapping. From the estimated Weibull, gamma, and lognormal parameters we computed the respective population mean full lifespans (95 % confidence interval): 115.60 (109.17-121.66), 116.71 (110.81-122.51), and 116.79 (111.23-122.75) days together with the standard deviations of the full lifespans: 24.77 (20.82-28.81), 24.30 (20.53-28.33), and 24.19 (20.43-27.73). We then estimated the 95th percentiles of the lifespan distributions (a surrogate for the maximum lifespan): 153.95 (150.02-158.36), 159.51 (155.09-164.00), and 160.40 (156.00-165.58) days, the mean current ages (or the mean residual lifespans): 60.45 (58.18-62.85), 60.82 (58.77-63.33), and 57.26 (54.33-60.61) days, and the residual half-lives: 57.97 (54.96-60.90), 58.36 (55.45-61.26), and 58.40 (55.62-61.37) days, for the Weibull, gamma, and lognormal models respectively. Corresponding estimates were obtained for the individual subjects. The three models provide equally excellent goodness-of-fit, reliable estimation, and physiologically plausible values of the directly interpretable RBC survival parameters.

Pattern Recognition in Pharmacodynamic Data Analysis

Pattern recognition is a key element in pharmacodynamic analyses as a first step to identify drug action and selection of a pharmacodynamic model. The essence of this process is going from data to insight through exploratory data analysis. There are few formal strategies that scientists typically use when the experiment has been done and data collected. This report attempts to ameliorate this deficit by identifying the properties of a pharmacodynamic model via dissection of the pattern revealed in response-time data. Pattern recognition in pharmacodynamic analyses contrasts with pharmacokinetic analyses with respect to time course. Thus, the time course of drug in plasma usually differs markedly from the time course of the biomarker response, as a consequence of a myriad of interactions (transport to biophase, binding to target, activation of target and downstream mediators, physiological response, cascade and amplification of biosignals, homeostatic feedback) between the events of exposure to test compound and the occurrence of the biomarker response. Homing in on this important-but less often addressed-element, 20 datasets of varying complexity were analyzed, and from this, we summarize a set of points to consider, specifically addressing baseline behavior, number of phases in the response-time course, time delays between concentration- and response-time courses, peak shifts in response with increasing doses, saturation, and other potential nonlinearities. These strategies will hopefully give a better understanding of the complete pharmacodynamic response-time profile.

A Mass Balance-Based Semiparametric Approach to Evaluate Neonatal Erythropoiesis

Postnatal hemoglobin (Hb) production in anemic preterm infants is determined by several factors including the endogenous erythropoietin levels, allogeneic RBC transfusions administered to treat anemia, and developmental age. As a result, their postnatal Hb production rate can vary considerably. This work introduces a novel Hb mass balance-based semiparametric approach that utilizes infant blood concentrations of Hb from the first 30 postnatal days to estimate the amount of Hb produced and the erythropoiesis rate in newborn infants. The proposed method has the advantage of not relying on specific structural pharmacodynamic model assumptions to describe the Hb production, but instead utilizes simple mass balance principles and nonparametric regression analysis. The developed method was applied to the Hb data from 79 critically ill anemic very low birth weight preterm infants to evaluate the dynamic changes in erythropoiesis during the first month of life and to determine the inter-subject variability in Hb production. The estimated mean (±SD) cumulative amount of Hb produced by the infants over the first month of life was 6.6 ± 3.4 g (mean body weight, 0.768 kg), and the mean estimated body weight-scaled Hb production rate over the same period was 0.23 ± 0.12 g/day/kg. A significant positive correlation was observed between infant gestational age and the mean body weight-scaled Hb production rate over the first month of life (P < 0.05). We conclude that the proposed mathematical approach and its implementation provide a flexible framework to evaluate postnatal erythropoiesis in newborn infants.

Pharmacodynamic models of age-structured cell populations

The purpose of this work is to review basic pharmacodynamic (PD) models describing drug effects on cell populations and expand them to age-structured models using the theory of physiologically structured populations. The plasma drug concentrations are interpreted as the environment affecting the cell production and mortality rates. An explicit solution to model equations provides the age density distribution that serves to establish a relationship between the cell lifespan distribution and the hazard of cell removal. Given the lifespan distributions, the age distributions for most commonly applied PD models of cell responses including basic cell turnover, transit compartments, and basic lifespan models have been derived both for the baseline conditions and drug treatment. The steady-state age distribution for basic indirect response models is exponential, and it is uniform for the basic lifespan model. As an example of more complex cell population, the age distribution of human red blood cells has been simulated based on a recent model of red blood cell survival. The age distribution for cells in the transit compartment model is the sum of the gamma functions. Means and variances of age distributions for all discussed models were calculated. A brief discussion of numerical challenges and possible future model developments is presented.

A Systems Pharmacology Model of Erythropoiesis in Mice Induced by Small Molecule Inhibitor of Prolyl Hydroxylase Enzymes

Mammalian erythropoiesis is a conserved process tightly controlled by the hypoxia-inducible factor (HIF1) pathway. In this study, a small molecule inhibitor (PHI-1) of prolyl-hydroxylase-2 (PHD2) enzyme involved in regulating HIF1α levels was orally administered to male BALB/c mice at 10 and 30 mg/kg. A systems pharmacology model was developed based on the measured PHI-1 plasma exposures, kidney HIF1α, kidney erythropoietin (EPO) mRNA, plasma EPO, reticulocyte counts, red blood cells, and hemoglobin levels. The model fit resulted in the estimation of drug potency (IC₅₀: 1.7μM), and systems parameters such as EPO mRNA turnover (k_{deg_EPOmRNA}: 0.43 hr^-1) and mean lifespan of reticulocytes (T_r: 81 hours). The model correctly described the observed 30–40-fold increase in kidney HIF1α protein, ∼1,000 fold increase in EPO mRNA and 2–3-fold increase in the reticulocytes at 30 mg/kg. This study presents the first parsimonious systems model of erythropoiesis to quantitatively describe the in vivo effects of PHD2 inhibition.

Assessment of hemoglobin responsiveness to epoetin alfa in patients on hemodialysis using a population pharmacokinetic pharmacodynamic model

A population pharmacokinetic pharmacodynamic (PK/PD) model describing the effect of epoetin alfa on hemoglobin (Hb) response in hemodialysis patients was developed. Epoetin alfa pharmacokinetics was described using a linear 2-compartment model. PK parameter estimates were similar to previously reported values. A maturation-structured cytokinetic model consisting of 5 compartments linked in a catenary fashion by first-order cell transfer rates following a zero-order input process described the Hb time course. The PD model described 2 subpopulations, one whose Hb response reflected epoetin alfa dosing and a second whose response was unrelated to epoetin alfa dosing. Parameter estimates from the PK/PD model were physiologically reasonable and consistent with published reports. Numerical and visual predictive checks using data from 2 studies were performed. The PK and PD of epoetin alfa were well described by the model.

A Method to Evaluate Fetal Erythropoiesis from Postnatal Survival of Fetal RBCs

Fetal RBCs are produced during a period of very rapid growth and stimulated erythropoiesis under hypoxic intrauterine conditions. Fetal RBC life span varies with gestational age (GA) and is shorter than that in healthy adults. Due to the special kinetic properties of life span-based survival of human RBCs, a mathematical model-based kinetic analysis of the survival of fetal RBCs shortly after birth provides a unique opportunity to "look backward in time" to evaluate fetal erythropoiesis. This work introduces a novel method that utilizes postnatal in vivo RBC survival data collected within 2 days after birth to study both nonsteady-state (non-SS) in utero RBC production and changing fetal RBC life span over time. The effect of changes in erythropoiesis rate and RBC life span and the effect of multiple postnatal phlebotomies on the RBC survival curves were investigated using model-based simulations. This mathematical model, which considers both changes in the rate of erythropoiesis and RBC life span and which accurately accounts for the confounding effect of multiple phlebotomies, was applied to survival curves for biotin-labeled RBCs from ten anemic very low birth weight preterm infants. The estimated mean fetal RBC production rate scaled by body weight was 1.07 × 10(7) RBCs/day g, and the mean RBC life span at birth was 52.1 days; these values are consistent with reported values. The in utero RBC life span increased at a rate of 0.51 days per day of gestation. We conclude that the proposed mathematical model and its implementation provide a flexible framework to study in utero non-SS fetal erythropoiesis in newborn infants.

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.

Optimization of anemia treatment in hemodialysis patients via reinforcement learning

OBJECTIVE

Anemia is a frequent comorbidity in hemodialysis patients that can be successfully treated by administering erythropoiesis-stimulating agents (ESAs). ESAs dosing is currently based on clinical protocols that often do not account for the high inter- and intra-individual variability in the patient's response. As a result, the hemoglobin level of some patients oscillates around the target range, which is associated with multiple risks and side-effects. This work proposes a methodology based on reinforcement learning (RL) to optimize ESA therapy.

METHODS

RL is a data-driven approach for solving sequential decision-making problems that are formulated as Markov decision processes (MDPs). Computing optimal drug administration strategies for chronic diseases is a sequential decision-making problem in which the goal is to find the best sequence of drug doses. MDPs are particularly suitable for modeling these problems due to their ability to capture the uncertainty associated with the outcome of the treatment and the stochastic nature of the underlying process. The RL algorithm employed in the proposed methodology is fitted Q iteration, which stands out for its ability to make an efficient use of data.

RESULTS

The experiments reported here are based on a computational model that describes the effect of ESAs on the hemoglobin level. The performance of the proposed method is evaluated and compared with the well-known Q-learning algorithm and with a standard protocol. Simulation results show that the performance of Q-learning is substantially lower than FQI and the protocol. When comparing FQI and the protocol, FQI achieves an increment of 27.6% in the proportion of patients that are within the targeted range of hemoglobin during the period of treatment. In addition, the quantity of drug needed is reduced by 5.13%, which indicates a more efficient use of ESAs.

CONCLUSION

Although prospective validation is required, promising results demonstrate the potential of RL to become an alternative to current protocols.

A semi-mechanistic red blood cell survival model provides some insight into red blood cell destruction mechanisms

Most mathematical models developed for the survival of haematological cell populations, in particular red blood cells (RBCs), follow the principle of parsimony. They focus on the predominant destruction mechanism of age-related cell death (senescence) and do not account for within subject variability in the RBC lifespan. However, assessment of the underlying physiological destruction mechanisms can be of interest in pathological conditions that affect RBC survival, for example sickle cell anaemia or anaemia of chronic kidney disease. We have previously proposed a semi-mechanistic RBC survival model which accounts for four different types of RBC destruction mechanisms. In this work, it is shown that the proposed model in combination with informative RBC survival data is able to provide a deeper insight into RBC destruction mechanisms. The proposed model was applied in a non-linear mixed effect modelling framework to biotin derived RBC survival data available from literature. Three mechanisms were estimable based on the available data of twelve subjects, including random destruction, senescence and destruction due to delayed failure. It was possible to identify three subjects with a decreased RBC survival in the study population. These three subjects all showed differences in the contribution of the estimated destruction mechanisms: an increased random destruction, versus an accelerated senescence, versus a combination of both.

Modeling of red blood cell life-spans in hematologically normal populations

Despite the impact of red blood cell (RBC) Life-spans in some disease areas such as diabetes or anemia of chronic kidney disease, there is no consensus on how to quantitatively best describe the process. Several models have been proposed to explain the elimination process of RBCs: random destruction process, homogeneous life-span model, or a series of 4-transit compartment model. The aim of this work was to explore the different models that have been proposed in literature, and modifications to those. The impact of choosing the right model on future outcomes prediction--in the above mentioned areas--was also investigated. Both data from indirect (clinical data) and direct life-span measurement (biotin-labeled data) methods were analyzed using non-linear mixed effects models. Analysis showed that: (1) predictions from non-steady state data will depend on the RBC model chosen; (2) the transit compartment model, which considers variation in life-span in the RBC population, better describes RBC survival data than the random destruction or homogenous life-span models; and (3) the additional incorporation of random destruction patterns, although improving the description of the RBC survival data, does not appear to provide a marked improvement when describing clinical data.

Population pharmacokinetic-pharmacodynamic modeling and simulation of platelet decrease induced by peg-interferon-alpha 2a

Peg-interferon-alpha-2a (PEG-IFN) has been used all over the world including Japan as the standard of care for chronic hepatitis C (CHC). PEG-IFN causes platelet count decrease, while CHC patients with compensated liver cirrhosis have a low baseline of platelets. To use PEG-IFN more safely in these patients, we analyzed the effect of PEG-IFN on the longitudinal platelet profile with a pharmacokinetic-pharmacodynamic model. Platelet count and serum PEG-IFN concentration obtained from a Japanese clinical study on 40 patients were analyzed. The serum PEG-IFN concentration profile was fitted with an open 1-compartment model and the platelet profile was fitted with a turnover model. After the final model was fixed, the platelet profiles were simulated with various platelet baselines. The simulation revealed that according to PEG-IFN administration platelets decreased gradually and reached steady state within 12 weeks, and almost subjects would not have a lower platelet count than the criteria for discontinuation of the treatment. Once administration was discontinued, platelets recovered up to the baseline within several weeks. In conclusion, platelet count was predicted to be about a 30% (5th-95th percentiles in 1,000 simulation: 11-66%) decrease and to return to the baseline value in 4 to 8 weeks after the last administration of PEG-IFN.

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.

Population pharmacokinetic and pharmacodynamic model-based comparability assessment of a recombinant human Epoetin Alfa and the Biosimilar HX575

The aim of this study was to develop an integrated pharmacokinetic and pharmacodynamic (PK/PD) model and assess the comparability between epoetin alfa HEXAL/Binocrit (HX575) and a comparator epoetin alfa by a model-based approach. PK/PD data-including serum drug concentrations, reticulocyte counts, red blood cells, and hemoglobin levels-were obtained from 2 clinical studies. In sum, 149 healthy men received multiple intravenous or subcutaneous doses of HX575 (100 IU/kg) and the comparator 3 times a week for 4 weeks. A population model based on pharmacodynamics-mediated drug disposition and cell maturation processes was used to characterize the PK/PD data for the 2 drugs. Simulations showed that due to target amount changes, total clearance may increase up to 2.4-fold as compared with the baseline. Further simulations suggested that once-weekly and thrice-weekly subcutaneous dosing regimens would result in similar efficacy. The findings from the model-based analysis were consistent with previous results using the standard noncompartmental approach demonstrating PK/PD comparability between HX575 and comparator. However, due to complexity of the PK/PD model, control of random effects was not straightforward. Whereas population PK/PD model-based analyses are suited for studying complex biological systems, such models have their limitations (statistical), and their comparability results should be interpreted carefully.

Modeling red blood cell survival data

Anaemia of chronic kidney disease (CKD) is a common complication in patients with renal impairment, especially in end-stage renal failure. As well as erythropoietin deficiency, decreased red blood cell survival is a contributing factor. However, it remains unclear which mechanism underlies the altered survival of red blood cells (RBCs). In this work a previously developed statistical model for RBC survival was applied to clinical data obtained from 14 patients with CKD undergoing hemodialysis as well as 14 healthy controls using radioactive chromium (⁵¹Cr) as random labelling method. A classical two-stage approach and a full population analysis were applied to estimate the key parameters controlling random destruction and senescence in the model. Estimating random destruction was preferred over estimating an accelerated senescence in both approaches and both groups as it provided the better fit to the data. Due to significant nonspecific random loss of the label from the cells that cannot be quantified directly only a relative RBC survival can be obtained from data using ⁵¹Cr as labelling method. Nevertheless, RBC survival was found to be significantly reduced in CKD patients compared to the controls with a relative reduction of 20-30% depending on the analysis method used.

Population modeling of filgrastim PK-PD in healthy adults following intravenous and subcutaneous administrations

Filgrastim is a recombinant human granulocyte colony stimulating factor (G-CSF) that stimulates production of neutrophils. The objective of this analysis was to develop a pharmacokinetic (PK) and pharmacodynamic (PD) model to account for an increase in G-CSF clearance on multiple dosing because of an increase of the G-CSF receptor-mediated endocytosis. Data from 4 randomized studies involving healthy volunteers were used for analysis. Subjects received filgrastim (Neupogen) via subcutaneous (SC) and intravenous (IV) routes. Filgrastim was administered SC daily for 1 week at 2.5, 5, and 10 µg/kg doses and as single IV infusions (5 µg/kg over 0.5 hours) and SC (1 µg/kg) doses. PK data comprised serum concentration-time measurements and the blood absolute neutrophil count (ANC) was used for PD evaluations. Population nonlinear mixed-effect modeling was done using NONMEM VI (Version 6.1.0, Icon Development Solutions, Ellicott City, Maryland). The model depicted the decaying trend in C(max) values with repeated doses and an increase in ANC(max) values consistently with an increase in the G-CSF receptor pool. Simulated time courses of the total clearance exhibited an increasing pattern. The increase in filgrastim clearance on multiple dosing was attributed to the increased neutrophil count in the bone marrow and blood paralleled by an increase in the total G-CSF receptor density.

Exposure-response modeling of darbepoetin alfa in anemic patients with chronic kidney disease not receiving dialysis

A population pharmacokinetic and pharmacodynamic model (PK/PD) of darbepoetin alfa following intravenous (IV) or subcutaneous (SC) administration in participants with chronic kidney disease (CKD) was developed. Darbepoetin alfa concentrations from 96 CKD participants, who received IV or SC darbepoetin alfa, and Hgb concentration from 332 CKD participants not on dialysis, who received SC doses of darbepoetin alfa, were used to develop the PK/PD model. An open 2-compartment model with sequential zero- and first-order absorption was used to characterize darbepoetin alfa pharmacokinetics. Darbepoetin alfa was assumed to trigger concentration-dependent stimulation of production of progenitor cells of red blood cells (RBCs) in bone marrow, which become red blood cells and died after life span expiration. Model evaluation was performed through nonparametric bootstrap and posterior predictive checks. Absolute bioavailability, total mean absorption time, clearance, and volume of distribution were estimated to be 44%, 52 h, 3.4 L/d/70 kg, and 5.9 L/70 kg, respectively. The estimates of drug potency, efficacy, and RBC life span were 0.41 ng/mL, 64%, and 77 days, respectively. Pharmacokinetic or pharmacodynamic parameters of darbepoetin alfa were not affected by age and sex. The qualified model supports the use of darbepoetin alfa administered biweekly (SC) in CKD patients for anemia correction and monthly (SC) for hemoglobin maintenance. In addition, the model is deemed appropriate to conduct simulations to support dose selection for additional clinical studies.

Pharmacodynamics-mediated drug disposition (PDMDD) and precursor pool lifespan model for single dose of romiplostim in healthy subjects

The objective of this study was to characterize the pharmacokinetics and pharmacodynamics (PK-PD) of romiplostim after single-dose administration in healthy subjects. The mean serum romiplostim concentrations (PK data) and mean platelet counts (PD data) collected from 32 subjects receiving a single intravenous (0.3, 1 and 10 μg/kg) or subcutaneous (0.1, 0.3, 1, and 2 μg/kg) dose were fitted simultaneously to a mechanistic PK-PD model based on pharmacodynamics-mediated drug disposition (PDMDD) and a precursor pool lifespan concept. The two-compartment PK model incorporated receptor-mediated endocytosis and linear mechanisms as parallel elimination pathways. The maximal concentration of receptors (assumed to be proportional to the platelet count), the equilibrium dissociation constant, and the first-order internalization rate constant for endocytosis of the drug-receptor complex were 0.022 fg/platelet, 0.131 ng/mL, and 0.173 h⁻¹, respectively. Romiplostim concentration stimulates the production of platelet precursors via the Hill function, where the SC₅₀ was 0.052 ng/mL and S (max) was 11.2. The estimated precursor cell and platelet lifespans were 5.9 and 10.5 days, respectively. Model-based simulations revealed that the romiplostim exposure and the platelet response are both dependent on the dose administered and the baseline platelet counts. Also, weekly dosing produced a sustained PD response while dosing intervals ≥2 weeks resulted in fluctuating platelet counts. Thus, the mechanistic PK-PD model was suitable for describing the romiplostim PK-PD interplay (PDMDD), the dose-dependent platelet stimulation, and the lifespans of thrombopoietic cell populations.

Population pharmacokinetic/pharmacodynamic model for C.E.R.A. in both ESA-naive and ESA-treated chronic kidney disease patients with renal anemia

This study aimed to develop a population pharmacokinetic/pharmacodynamic (PK/PD) model for C.E.R.A., a continuous erythropoietin receptor activator. C.E.R.A. is administered via intravenous (IV) and subcutaneous (SC) routes once every 2 weeks (Q2W) or once every 4 weeks (Q4W), respectively, to correct or maintain hemoglobin levels in chronic kidney disease (CKD) patients. Population models were specified to describe C.E.R.A. (PK) and hemoglobin (PD) concentrations over time, using data from 3 phase III, open-label, randomized, parallel-group, multicenter studies that examined IV or SC C.E.R.A. administration Q2W and Q4W in erythropoiesis-stimulating agent (ESA)-naive and ESA-treated patients. C.E.R.A. PK was described by a 1-compartment model: drug clearance = 0.75 L/d, volume of distribution = 4.72 L, and half-life = 105 hours in accordance with previous reported values. The PD model, a life span sequential PK/PD model, adequately described hemoglobin data. Dosing schedule, administration route, and study type did not affect drug-related PD parameters or system-specific parameters (eg, red blood cell life span). This model adequately described C.E.R.A.'s PK and PD properties according to C.E.R.A. posology, thus permitting simulations exploring alternative drug administration scenarios. It supports use of C.E.R.A. IV and SC; Q2W for anemia correction in ESA-Naïve CKD patients and monthly administration in the hemoglobin maintenance phase.

Scaling pharmacodynamics from in vitro and preclinical animal studies to humans

An important feature of mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) models is the identification of drug- and system-specific factors that determine the intensity and time-course of pharmacological effects. This provides an opportunity to integrate information obtained from in vitro bioassays and preclinical pharmacological studies in animals to anticipate the clinical and adverse responses to drugs in humans. The fact that contemporary PK/PD modeling continues to evolve and seeks to emulate systems level properties should provide enhanced capabilities to scale-up pharmacodynamic data. Critical steps in drug discovery and development, such as lead compound and first in human dose selection, may become more efficient with the implementation and further refinement of translational PK/PD modeling. In this review, we highlight fundamental principles in pharmacodynamics and the basic expectations for in vitro bioassays and traditional allometric scaling in PK/PD modeling. Discussion of PK/PD modeling efforts for recombinant human erythropoietin is also included as a case study showing the potential for advanced systems analysis to facilitate extrapolations and improve understanding of inter-species differences in drug responses.

Pharmacokinetic and pharmacodynamic modeling of pegylated thrombopoietin mimetic peptide (PEG-TPOm) after single intravenous dose administration in healthy subjects

Pegylated thrombopoietin mimetic peptide (PEG-TPOm) is a novel, potent thrombopoietin receptor agonist with low immunotoxicity potential that protects against chemotherapy-induced thrombocytopenia in preclinical animal models. The aim of this study was to develop a population pharmacokinetic and pharmacodynamic model of PEG-TPOm following single intravenous doses in healthy subjects. Data were obtained from a double-blind, randomized, placebo-controlled study. A model based on target-mediated drug disposition and precursor pool life spans was applied. Model evaluation was performed through predictive checks and bootstrap analysis. The half-life of PEG-TPOm ranged between 18 and 36 hours, and the estimated distributional volume was 5 L. The increase in platelet counts was observed after a 4-day delay, consistent with the megakaryocyte cell life span. The platelet life span was estimated to be 5 days. After maximum platelets counts were achieved on day 9, platelets returned back to baseline on day 29. Model-based simulations were undertaken to explore pharmacodynamic effects after multiple dosing. Weekly dosing produced a sustained pharmacodynamic response, whereas an interdosing interval >or=2 weeks resulted in fluctuating pharmacodynamic profiles. Thus, the mechanistic pharmacokinetic/pharmacodynamic model was suitable for describing the complex PEG-TPOm pharmacokinetics/pharmacodynamics, including target-mediated disposition, dose-dependent platelet stimulation, and mean life spans of thrombopoietic cell populations.

Pharmacodynamic modeling of the effect of changes in the environment on cellular lifespan and cellular response

Lifespan-based pharmacodynamic (PD) models of cellular response assume that the lifespan of cells is predetermined at the time of cellular production, despite recognized changes in the cellular environment following production that may alter the survival of the cells. This work extends previously proposed cellular lifespan PD models to incorporate environmental effects on the cell lifespan by considering two basic classes of models from survival analysis: accelerated life and relative risk models. Cellular responses using both model classes were simulated using a steady-state cellular production rate with changes in the environmental effects resulting from three different basic profiles. The environmental effect models were also fitted to the red blood cell (RBC) and hemoglobin concentration data from six sheep following hematopoietic ablation by busulfan administration. The simulations indicated that the basic shapes of the cellular responses were different between the accelerated life and relative risk models. Due to the more direct physical interpretation, relatively simple steady-state relationship between the cellular response and environmental effects, and the ability to reduce the model to a "point" baseline lifespan distribution, the accelerated life model appears to be a more realistic and flexible model. The analysis of the sheep RBC and hemoglobin data indicated that the environmental effect began to decrease the survival of cells 1-2 weeks following initiation of ablation and that the average "severity" of the environmental effect increased 3.49 (29.5%) (mean (C.V.)) fold under the accelerated life model. Alternative models without an environmental effect did not describe the observed data as well. The proposed environmental effect cellular lifespan PD models allow for the incorporation of arbitrary changes in the conditions of the cellular environment and modeling of environmentally dependent cellular survival. These PD models have potential applications in hematological management of end-stage renal disease, transfusion medicine, and patients undergoing chemotherapy, among other diseases and therapies.

Modeling time variant distributions of cellular lifespans: increases in circulating reticulocyte lifespans following double phlebotomies in sheep

Many pharmacodynamic (PD) models of cellular response assume a single and time invariant lifespan of all cells, despite the existence of a true underlying distribution of cellular lifespans and known changes in the lifespan distributions with time. To account for these features of cellular populations, a time variant cellular lifespan distribution PD model was formulated and theoretical aspects of modeling cellular populations presented. The model extends prior work assuming time variant "point distributions" of cellular lifespans (Freise et al. J Pharmacokinet Pharmacodyn 34:519-547, 2007) and models assuming a time invariant lifespan distribution (Krzyzanski et al. J Pharmacokinet Pharmacodyn 33:125-166, 2006). The formulated time variant lifespan distribution model was fitted to endogenous plasma erythropoietin (EPO), reticulocyte, and red blood cell (RBC) concentrations in sheep phlebotomized on two occasions, 8 days apart. The time variant circulating reticulocyte lifespan was modeled as a truncated and scaled Weibull distribution, with the location parameter of the distribution non-parametrically represented by an end constrained quadratic spline function. The formulated time variant lifespan distribution model was compared to the identical time invariant distribution, time variant "point distribution", and time invariant "point distribution" cellular lifespan models. Parameters of the time variant lifespan distribution model were well estimated with low standard errors. The mean circulating reticulocyte lifespan was estimated at 0.304 days, which rapidly increased over 3-fold following the first phlebotomy to a maximum of 1.03 days (P = 0.009). On average, the percentage of erythrocytes being released as reticulocytes maximally increased an estimated two-fold following the phlebotomies. The primary features of immature RBC physiology were captured by the model and gave results consistent with other estimates in sheep and humans. The comparison of the four lifespan models gave similar parameter estimates of the stimulation function and fits to the RBC data. However, the time invariant models fit the reticulocyte data poorly, while the time variant "point distribution" cellular lifespan model gave physiologically unrealistic estimates of the changes in the circulating reticulocyte lifespan under stress erythropoiesis. Thus the underlying physiology must be considered when selecting the most appropriate cellular lifespan model and not just the goodness-of-fit criteria. The proposed PD model and the numerical implementation allows for a flexible framework to incorporate time variant lifespan distributions when modeling populations of cells whose production or stimulation depends on endogenous growth factors and/or exogenous drugs.

Red cell survival in relation to changes in the hematocrit: more important than you think

The management of anemia in patients with chronic renal failure has greatly improved with the availability of recombinant human erythropoietin in the late 1980s, leading to a considerable reduction in mortality and morbidity and to an improvement in quality of life. The findings from recent controlled clinical outcome trials have resulted in a rather narrow, generally accepted therapeutic hematocrit target range. However, currently available dosing algorithms do not permit achievement and maintenance of target values within the therapeutic range in many patients. One possible explanation for this failure may be the ignorance of a finite erythrocyte lifespan not integrated into most algorithms. The purpose of this article is to underline the essential role played by the erythrocyte lifespan in the erythropoietic response to recombinant human erythropoietin and to encourage the integration of this concept in the future development of computer-assisted decision support systems.

Pharmacodynamic model for chemotherapy-induced anemia in rats

Anticancer agents often cause bone marrow toxicity resulting in progressive anemia which may influence the therapeutic effects of erythropoietic-stimulating agents. The objective of this study was to develop a pharmacodynamic (PD) model to describe chemotherapy-induced anemia in rats. Anemia was induced in male Wistar rats with a single intravenous (i.v.) injection of 60 mg/kg carboplatin. Hematological responses including reticulocytes, red blood cells (RBC), hemoglobin, and endogenous rat erythropoietin (EPO) were measured for up to 4 weeks. A catenary, lifespan-based, indirect response model served as a basic PD model to represent erythroid cellular populations in the bone marrow and blood involved in erythropoiesis. The model assumed that actively proliferating progenitor cells in the bone marrow are sensitive to anti-cancer agents and subject to an irreversible removal process. The removal rate of the target cells is proportional to drug activity concentrations and the cell numbers. An additional RBC loss from the circulation resulting from thrombocytopenia was described by a first-order process. The turnover process of rat EPO and EPO-mediated feedback inhibition mechanism regulated by hemoglobin changes were incorporated. Reticulocyte counts decreased rapidly and reached a nadir by day 3 after administration of carboplatin and returned to the baseline by day 13. This was followed by a gradual increase and the rebound peak occurred at about day 15. The hemoglobin nadir was approximately 9 g/dl observed at about 11-13 days compared to its normal value of 13 g/dl and hemoglobin returned to the baseline by day 30. The increase in endogenous rat EPO mirrored inversely hemoglobin changes and the maximum increase was observed soon after the hemoglobin nadir. The carboplatin-treated rats exhibited progressive anemia. The proposed model adequately described the time course of hematological changes after carboplatin in rats and can be a useful tool to explore potential strategies for the management of anemia caused by chemotherapy.

Pharmacodynamic analysis of time-variant cellular disposition: reticulocyte disposition changes in phlebotomized sheep

Most pharmacodynamic (PD) models of cellular response assume a time-invariant (i.e., constant) cellular disposition despite known changes in the disposition with time, such as the reticulocyte residence time in the systemic circulation during stress erythropoiesis. To account for changes in cellular disposition, a comprehensive PD model that involves endogenous erythropoietin (Epo), reticulocytes, and hemoglobin responses was developed in phlebotomized sheep that considers a time-variant reticulocyte residence time and allows for the simultaneous determination of changes in the cellular disposition and cellular production. Five sheep were phlebotomized to hemoglobin concentrations of approximately 4 g/dl. Epo concentrations, reticulocytes, and hemoglobin concentrations were frequently sampled for 5-7 days prior to and 25-30 days following the phlebotomy. Initial steady-state conditions were assumed and the time-variant reticulocyte residence time in the systemic circulation was semiparametrically represented using a constrained spline function. Hemoglobin production was modeled using a Hill function via an effect site compartment. The initial steady state reticulocyte residence time in the systemic circulation was estimated as 0.477 (0.100) (mean (SD)) days, which maximally increased 2.01- to 2.64-fold higher than the initial steady-state residence time 5.95 (0.899) days post-phlebotomy (P < 0.01). On average, the residence time returned to steady-state values 15.4 (2.36) days post-phlebotomy, which was not significantly different from the initial steady-state value (P > 0.05). The baseline hemoglobin production rate was estimated at 0.0929 (0.0472) g/kg/day and the maximum production rate under stress phlebotomy was estimated at 0.504 (0.0422) g/kg/day. These data indicate that endogenously released Epo under acute anemic conditions can increase hemoglobin production approximately 5-fold. The determined increase in reticulocyte residence time produced under stress erythropoiesis is similar to the commonly reported 2- to 3-fold increase observed in human patients.

Contribution of modelling chemotherapy-induced hematological toxicity for clinical practice

Anticancer chemotherapies are responsible for numerous adverse events. Among these, hematological toxicity is one of the main causes for ending treatment. These toxicities decrease production of red blood cells (anemia), production of white blood cells (neutropenia or granulocytopenia), and production of platelets (thrombocytopenia), which may be life-threatening to the patient. Preventing such discontinuation would be valuable for treating patients more effectively. In order to achieve this goal, numerous mathematical and physiological or semiphysiological models have been developed. The complexity of models has increased over the years, from empiric E(max) models to mechanistic models including physiological mechanisms such as feedback control. This review discusses several approaches of modelling hematological toxicities illustrated with some examples: pharmacodynamic models for the hematological toxicity of 5-fluorouracil, epirubicin, melphalan, paclitaxel, topotecan, and indisulam.

Interspecies comparisons of pharmacokinetics and pharmacodynamics of recombinant human erythropoietin

Erythropoietin (EPO) has a highly conserved structure among mammals, and thus recombinant human EPO (rHuEPO) has biological activity in various species. This study explores the interspecies relationships of the pharmacokinetics (PK) and pharmacodynamics (PD) of rHuEPO. The PK parameters such as clearance (CL) and volume of distribution (V(ss)) after i.v. doses of rHuEPO were obtained in several species via noncompartmental analysis and were assessed using the traditional allometric approach. Also, PK/PD modeling of rHuEPO concentrations and responses [reticulocytes, red blood cells (RBCs), and hemoglobin] was performed following a range of i.v. and s.c. doses in rats, monkeys, and humans. Nonlinear disposition (V(max), K(m)) and s.c. absorption rate and bioavailability parameters of rHuEPO were examined. A cascade, indirect, lifespan PD model was applied to recover efficacy (S(max)) and potency (SC(50)) of rHuEPO on erythropoiesis and erythroid cell lifespan parameters. Despite nonlinear rHuEPO disposition, CL and V(ss) were highly correlated with body weight (R(2) > 0.92) with allometric scaling exponents of 0.708 for CL and 0.853 for V(ss). The s.c. bioavailability increased with dose in monkeys and humans but appeared to be dose-independent in rats. A correlation between S(max) or SC(50) and body weight was not obvious. However, RBC lifespans obeyed allometric principles. Size dependence was found for PK and lifespan parameters, whereas pharmacologic parameters were independent of body weight.

G-CSF Control of Neutrophils Dynamics in the Blood

White blood cell neutrophil is a key component in the fast initial immune response against bacterial and fungal infections. Granulocyte colony stimulating factor (G-CSF) which is naturally produced in the body, is known to control the neutrophils production in the bone marrow and the neutrophils delivery into the blood. In oncological practice, G-CSF injections are widely used to treat neutropenia (dangerously low levels of neutrophils in the blood) and to prevent the infectious complications that often follow chemotherapy. However, the accurate dynamics of G-CSF neutrophil interaction has not been fully determined and no general scheme exists for an optimal G-CSF application in neutropenia. Here we develop a two-dimensional ordinary differential equation model for the G-CSF-neutrophil dynamics in the blood. The model is built axiomatically by first formally defining from the biology the expected properties of the model, and then deducing the dynamic behavior of the resulting system. The resulting model is structurally stable, and its dynamical features are independent of the precise form of the various rate functions. Choosing a specific form for these functions, three complementary parameter estimation procedures for one clinical (training) data set are utilized. The fully parameterized model (6 parameters) provides adequate predictions for several additional clinical data sets on time scales of several days. We briefly discuss the utility of this relatively simple and robust model in several clinical conditions.

An assessment of recombinant human erythropoietin effect on reticulocyte production rate and lifespan distribution in healthy subjects

PURPOSE

An empirical pharmacodynamic model was developed to assess the effect of recombinant human erythropoietin (rHu-EPO) treatment on the reticulocyte production rate and lifespan distribution.

MATERIALS AND METHODS

Single doses of rHu-EPO at levels 20, 40, 60, 90, 120, and 160 kIU were administered to healthy volunteers (n = 8 per dose level). Erythropoietin plasma concentrations as well as hematologic responses were measured up to 42 days. The hematological data were used to determine explicit relationships between reticulocyte and red blood cell counts (RBC) and the reticulocytes' production rate and lifespan distribution.

RESULTS

The parameter estimates obtained by simultaneous fitting of the model to the reticulocyte and RBC data revealed that rHu-EPO transiently increased the reticulocyte lifespan from the baseline value of 1.7 days to 3.4 days and the effect lasted for 8.3 days. The dose dependent increase in the reticulocyte production had the maximal value of 77.5 10(9) cells/l/day and was followed by a rebound that was less than 9% of the baseline value. Both reticulocyte and RBC responses were preceded by a dose-independent lag time of 1.7 days.

CONCLUSIONS

The effect of rHu-EPO on the reticulocyte production rate and lifespan distribution was characterized. The results of the present study can be further utilized in building more mechanistic pharmacodynamic models of rHu-EPO stimulatory effects.

Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after intravenous and subcutaneous administration in rats

The pharmacokinetics (PK) and pharmacodynamics (PD) of recombinant human erythropoietin (rHuEPO) were studied in rats after single i.v. and s.c. administration at three dose levels (450, 1350, and 4050 IU/kg). The plasma concentrations of rHuEPO and its erythropoietic effects including reticulocyte (RET), red blood cell (RBC), and hemoglobin (Hb) levels were determined. A two-compartment model with dual input rate and nonlinear disposition was used to characterize the PK of rHuEPO. The catenary indirect response model with several compartments reflecting the bone marrow and circulating erythropoietic cells was applied. The s.c. doses exhibited slow absorption (T(max) = 12 h) and incomplete bioavailability (F = 0.59). In placebo groups, RBC and Hb values gradually increased over time with growth of the rats, and the changes in the baselines monitored from 8 to 32 weeks of age were described by a nonlinear growth function. All doses resulted in dose-dependent increases in RET counts followed by an immediate decline below the baseline at around 6 days and returned to the predose level in 21-24 days after dosing. A subsequent steady increase of RBC and Hb levels followed and reached peaks at 6 days. A tolerance phenomenon observed at all dose levels was modeled by a negative feedback inhibition with the relative change in Hb level. The PK/PD model well described the erythropoietic effects of rHuEPO as well as tolerance, thereby yielding important PD parameters (S(max) = 1.87 and SC(50) = 65.37 mIU/ml) and mean lifespans of major erythropoietic cell populations in rats.