A semimechanistic and mechanistic population PK-PD model for biomarker response to ibandronate, a new bisphosphonate for the treatment of osteoporosis

Optimization of the dosage regimen of zoledronic acid with a kinetic-pharmacodynamic model and exposure-response analysis

Purpose: In order to support the dose optimization of zoledronic acid, the kinetic-pharmacodynamic model and exposure-response analysis were used to describe the changes in bone mineral density in different doses of zoledronic acid and establish the relationship between dose and acute phase reaction. Methods: Data were extracted from literature in accessible public databases. The kinetic-pharmacodynamic model was developed based on the above data using the NONMEM package to estimate parameters describing the relationship between the dose of zoledronic acid and bone mineral density. Exposure-response analysis was developed to establish the relationship between dose and acute phase reaction. Model evaluation was performed using goodness-of-fit, coefficient of variation (CV%). And sensitivity analyses were performed to assess the necessity of related parameters. Then the established model was used to simulate the changes of bone mineral density under different administration regimens, and the literature data was verified. Results: The kinetic-pharmacodynamic model successfully described zoledronic acid dose and change of bone mineral density in osteoporosis patients, with coefficient of variation of most less than 71.5%. The exposure-response analysis showed the incidence of acute phase reaction is dose-dependent. The bone mineral density was simulated based on the developed kinetic-pharmacodynamic model. And the simulated change of bone mineral density and the incidence of acute phase reaction could be helpful to propose a dosage regimen. Conclusion: Overall, the kinetic-pharmacodynamic model described changes of bone mineral density in different doses of zoledronic acid in vivo. And, the model and the exposure-response analysis also showed to provide the assessment of dose-response relationship for zoledronic acid.

Pharmacometrics: The Already-Present Future of Precision Pharmacology

The use of mathematical modeling to represent, analyze, make predictions or providing information on data obtained in drug research and development has made pharmacometrics an area of great prominence and importance. The main purpose of pharmacometrics is to provide information relevant to the search for efficacy and safety improvements in pharmacotherapy. Regulatory agencies have adopted pharmacometrics analysis to justify their regulatory decisions, making those decisions more efficient. Demand for specialists trained in the field is therefore growing. In this review, we describe the meaning, history, and development of pharmacometrics, analyzing the challenges faced in the training of professionals. Examples of applications in current use, perspectives for the future, and the importance of pharmacometrics for the development and growth of precision pharmacology are also presented.

Mechanistic PK-PD model of alendronate treatment of postmenopausal osteoporosis predicts bone site-specific response

Alendronate is the most widely used drug for postmenopausal osteoporosis (PMO). It inhibits bone resorption, affecting osteoclasts. Pharmacokinetics (PK) and pharmacodynamics (PD) of alendronate have been widely studied, but few mathematical models exist to simulate its effect. In this work, we have developed a PK model for alendronate, valid for short- and long-term treatments, and a mechanistic PK-PD model for the treatment of PMO to predict bone density gain (BDG) at the hip and lumbar spine. According to our results, at least three compartments are required in the PK model to predict the effect of alendronate in both the short and long terms. Clinical data of a 2-year treatment of alendronate, reproduced by our PK-PD model, demonstrate that bone response is site specific (hip: 7% BDG, lumbar spine: 4% BDG). We identified that this BDG is mainly due to an increase in tissue mineralization and a decrease in porosity. The difference in BDG between sites is linked to the different loading and dependence of the released alendronate on the bone-specific surface and porosity. Osteoclast population diminishes quickly within the first month of alendronate treatment. Osteoblast population lags behind but also falls due to coupling of resorption and formation. Two dosing regimens were studied (70 mg weekly and 10 mg daily), and both showed very similar BDG evolution, indicating that alendronate accumulates quickly in bone and saturates. The proposed PK-PD model could provide a valuable tool to analyze the effect of alendronate and to design patient-specific treatments, including drug combinations.

A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation

The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA (kXGZ) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 (kXGU). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on γδ T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches.

Model-Based Anticancer Effect of Botulinum Neurotoxin Type A1 on Syngeneic Melanoma Mice

In recent, Botulinum Neurotoxin A1 (BoNT/A1) has been suggested as a potential anticancer agent due to neuronal innervation in tumor cells. Although potential BoNT/A1's mechanism of action for the tumor suppression has been gradually revealed so far, there were no reports to figure out the exposure-response relationships because of the difficulty of its quantitation in the biological matrix. The main objectives of this study were to measure the anticancer effect of BoNT/A1 using a syngeneic mouse model transplanted with melanoma cells (B16-F10) and developed a kinetic-pharmacodynamic (K-PD) model for quantitative exposure-response evaluation. To overcome the lack of exposure information, the K-PD model was implemented by the virtual pharmacokinetic compartment link to the pharmacodynamic compartment of Simeoni's tumor growth inhibition model and evaluated using curve-fitting for the tumor growth-time profile after intratumoral injection of BoNT/A1. The final K-PD model was adequately explained for a pattern of tumor growth depending on represented exposure parameters and simulation studies were conducted to determine the optimal dose under various scenarios considering dose strength and frequency. The optimal dose range and regimen of ≥13.8 units kg^-1 once a week or once every 3 days was predicted using the final model in B16-F10 syngeneic model and it was demonstrated with an extra in-vivo experiment. In conclusion, the K-PD model of BoNT/A1 was well developed to optimize the dosing regimen for evaluation of anticancer effect and this approach could be expandable to figure out quantitative interpretation of BoNT/A1's efficacy in various xenograft and/or syngeneic models.

Osteoporosis treatment with risedronate: a population pharmacokinetic model for the description of its absorption and low plasma levels

To develop a population pharmacokinetic model that describes the absorption and low plasma levels of risedronate in the body. The impact of patients' characteristics on risedronate kinetics is investigated. Simulations revealed the high variability in the concentration levels after different dosage schemes. No dosage adjustment is required in renal impairment.

INTRODUCTION

Risedronate exhibits very low plasma levels and high residence time in the body. The aim of this study is to describe and explain the risedronate transit through the body. The impact of volunteers' characteristics on the kinetics of risedronate is also investigated. Simulations are used to compare the risedronate plasma levels after different dosage schemes and assess the need for dose adjustment in patients with impaired kidney functionality.

METHODS

Plasma concentration-time data were obtained from a four-period, two sequence, single-dose, crossover bioequivalence study. The effects of several covariates (e.g., weight, albumin, creatinine, alkaline phosphatase, and calcium) on model parameters were tested. Non-linear mixed-effect modeling was applied and a variety of models were evaluated placing emphasis on absorption and disposition properties. The modeling and simulation work was implemented in Monolix^TM 2020R1.

RESULTS

Following oral administration, the kinetics of risedronate was best described by a two-compartment model with lag time, first-order absorption, and elimination. The extent of peripheral distribution (i.e., bones) was found to be remarkably high. No volunteer characteristics were identified to affect significantly the disposition of risedronate. Using simulations, risedronate plasma profiles were obtained for different doses and frequencies of administration.

CONCLUSION

The absorption and disposition kinetics of risedronate were successfully characterized. Simulations revealed the high discrepancy in the concentration levels observed after different dosage regimens, implying the safety profile of risedronate. In virtual patients with renal impairment, the blood levels of risedronate are increased, but not in an extent requiring dose adaptation.

Model-based Target Pharmacology Assessment (mTPA): An Approach Using PBPK/PD Modeling and Machine Learning to Design Medicinal Chemistry and DMPK Strategies in Early Drug Discovery

The optimal pharmacokinetic (PK) required for a drug candidate to elicit efficacy is highly dependent on the targeted pharmacology, a relationship that is often not well characterized during early phases of drug discovery. Generic assumptions around PK and potency risk misguiding screening and compound design toward nonoptimal absorption, distribution, metabolism, and excretion (ADME) or molecular properties and ultimately may increase attrition as well as hit-to-lead and lead optimization timelines. The present work introduces model-based target pharmacology assessment (mTPA), a computational approach combining physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling, sensitivity analysis, and machine learning (ML) to elucidate the optimal combination of PK, potency, and ADME specific for the targeted pharmacology. Examples using frequently encountered PK/PD relationships are presented to illustrate its application, and the utility and benefits of deploying such an approach to guide early discovery efforts are discussed.

On the effect of antiresorptive drugs on the bone remodeling of the mandible after dental implantation: a mathematical model

Bone remodeling identifies the process of permanent bone change with new bone formation and old bone resorption. Understanding this process is essential in many applications, such as optimizing the treatment of diseases like osteoporosis, maintaining bone density in long-term periods of disuse, or assessing the long-term evolution of the bone surrounding prostheses after implantation. A particular case of study is the bone remodeling process after dental implantation. Despite the overall success of this type of implants, the increasing life expectancy in developed countries has boosted the demand for dental implants in patients with osteoporosis. Although several studies demonstrate a high success rate of dental implants in osteoporotic patients, it is also known that the healing time and the failure rate increase, necessitating the adoption of pharmacological measures to improve bone quality in those patients. However, the general efficacy of these antiresorptive drugs for osteoporotic patients is still controversial, requiring more experimental and clinical studies. In this work, we investigate the effect of different doses of several drugs, used nowadays in osteoporotic patients, on the evolution of bone density after dental implantation. With this aim, we use a pharmacokinetic-pharmacodynamic (PK/PD) mathematical model that includes the effect of antiresorptive drugs on the RANK/RANK-L/OPG pathway, as well as the mechano-chemical coupling with external mechanical loads. This mechano-PK/PD model is then used to analyze the evolution of bone in normal and osteoporotic mandibles after dental implantation with different drug dosages. We show that using antiresorptive agents such as bisphosphonates or denosumab increases bone density and the associated mechanical properties, but at the same time, it also increases bone brittleness. We conclude that, despite the many limitations of these very complex models, the one presented here is capable of predicting qualitatively the evolution of some of the main biological and chemical variables associated with the process of bone remodeling in patients receiving drugs for osteoporosis, so it could be used to optimize dental implant design and coating for osteoporotic patients, as well as the drug dosage protocol for patient-specific treatments.

Establishment of a Disease-Drug Trial Model for Postmenopausal Osteoporosis: A Zoledronic Acid Case Study

Costly and lengthy clinical trials hinder the development of safe and effective treatments for postmenopausal osteoporosis. To reduce the expense associated with these trials, we established a mechanistic disease-drug trial model for postmenopausal osteoporosis that can predict phase 3 trial outcome based on short-term bone turnover marker data. To this end, we applied a previously developed model for tibolone to bisphosphonates using zoledronic acid as paradigm compound by (1) linking the mechanistic bone cell interaction model to bone turnover markers as well as bone mineral density in lumbar spine and total hip, (2) employing a mechanistic disease progression function, and (3) accounting for zoledronic acid's mechanism of action. Once developed, we fitted the model to clinical trial data of 581 postmenopausal women receiving (1) 5-mg zoledronic acid in year 1 and saline in year 2, (2) 5-mg zoledronic acid in year 1 and year 2, or (3) placebo (saline), calcium (500 mg), and vitamin D (400 IU). All biomarker data was fitted reasonably well, with no apparent bias or model misspecification. Age, years since menopause, and body mass index at baseline were identified as significant covariates. In the future, the model can be modified to explore the link between short-term biomarkers and fracture risk.

On the pharmacological evaluation of bisphosphonates in humans

One of the key parameters for a successful treatment with any drug is the use of an optimal dose regimen. Bisphosphonates (BPs) have been in clinical use for over five decades and during this period clinical pharmacokinetic (PK) and pharmacodynamic (PD) evaluations have been instrumental for the identification of optimal dose regimens in patients. Ideal clinical PK and PD studies help drug developers explain variability in responses and enable the identification of a dose regimen with an optimal effect. PK and PD studies of the unique and rather complex pharmacological properties of BPs also help determine to a significant extent ideal dosing for these drugs. Clinical PK and PD evaluations of BPs preferably use study designs and assays that enable the assessment of both short- (days) and long-term (years) presence and effect of these drugs in patients. BPs are mainly used for metabolic bone diseases because they inhibit osteoclast-mediated bone resorption and the best way to quantify their effects in humans is therefore by measuring biochemical markers of bone resorption in serum and urine. In these very same samples BP concentrations can also be measured. Short-term serum and urine data after both intravenous (IV) and oral administration enable the assessment of oral bioavailability as well as the amount of BP delivered to the skeleton. Longer-term data provide information on the anti-resorptive effect as well as the elimination of the BP from the skeleton. Using PK-PD models to mathematically link the anti-resorptive action of the BPs to the amount of BP at the skeleton provides a mechanism-based explanation of the pattern of bone resorption during treatment. These models have been used successfully during the clinical development of BPs. Newer versions of such models, which include systems pharmacology and disease progression models, are more comprehensive and include additional PD parameters such as BMD and fracture risk. Clinical PK and PD studies of BPs have been useful for the identification of optimal dose regimens for metabolic bone diseases. These analyses will also continue to be important for newer research directions, such as BP use in the delivery of other drugs to the bone to better treat bone metastases and bone infections, as well as the potential benefit of BPs at non-skeletal targets for the prevention and treatments of soft tissue cancers, various fibroses, and other cardiovascular and neurodegenerative diseases, and reduction in mortality and extension of lifespan.

Pharmacology of bisphosphonates

The biological effects of the bisphosphonates (BPs) as inhibitors of calcification and bone resorption were first described in the late 1960s. In the 50 years that have elapsed since then, the BPs have become the leading drugs for the treatment of skeletal disorders characterized by increased bone resorption, including Paget's disease of bone, bone metastases, multiple myeloma, osteoporosis and several childhood inherited disorders. The discovery and development of the BPs as a major class of drugs for the treatment of bone diseases is a paradigm for the successful journey from "bench to bedside and back again". Several of the leading BPs achieved "blockbuster" status as branded drugs. However, these BPs have now come to the end of their patent life, making them highly affordable. The opportunity for new clinical applications for BPs also exists in other areas of medicine such as ageing, cardiovascular disease and radiation protection. Their use as inexpensive generic medicines is therefore likely to continue for many years to come. Fifty years of research into the pharmacology of bisphosphonates have led to a fairly good understanding about how these drugs work and how they can be used safely in patients with metabolic bone diseases. However, while we seemingly know much about these drugs, a number of key aspects related to BP distribution and action remain incompletely understood. This review summarizes the existing knowledge of the (pre)clinical and translational pharmacology of BPs, and highlights areas in which understanding is lacking.

Pharmacometrics and systems pharmacology for metabolic bone diseases

Mathematical modelling and simulation (M&S) of drug concentrations, pharmacologic effects and the (patho)physiologic systems within which they interact can be powerful tools for the preclinical, translational and clinical development of drugs. Indeed, the Prescription Drug User Fee Act (PDUFA VI), incorporated as part of the FDA Reauthorization Act of 2017 (FDARA), highlights the goal of advancing model-informed drug development (MIDD). MIDD can benefit development across many drug classes, including for metabolic bone diseases such as osteoporosis, cancer-related and numerous rare metabolic bone diseases; conditions characterized by significant morbidity and mortality. A drought looms in terms of the availability of new drugs to better treat these devastating diseases. This review provides an overview of several M&S approaches ranging from simple pharmacokinetic to integrated pharmacometric and systems pharmacology modelling. Examples are included to illustrate the use of these approaches during the development of several drugs for metabolic bone diseases such as bisphosphonates, denosumab, teriparatide and sclerostin inhibitors (romosozumab and blosozumab).

Regulatory Perspectives in Pharmacometric Models of Osteoporosis

Osteoporosis is a disorder of the bones in which they are weakened to the extent that they become more prone to fracture. There are various forms of osteoporosis: some of them are induced by drugs, and others occur as a chronic progressive disorder as an individual gets older. As the median age of the population rises across the world, the chronic form of the bone disease is drawing attention as an important worldwide health issue. Developing new treatments for osteoporosis and comparing them with existing treatments are complicated processes due to current acceptance by regulatory authorities of bone mineral density (BMD) and fracture risk as clinical end points, which require clinical trials to be large, prolonged, and expensive to determine clinically significant impacts in BMD and fracture risk. Moreover, changes in BMD and fracture risk are not always correlated, with some clinical trials showing BMD improvement without a reduction in fractures. More recently, bone turnover markers specific to bone formation and resorption have been recognized that reflect bone physiology at a cellular level. These bone turnover markers change faster than BMD and fracture risk, and mathematically linking the biomarkers via a computational model to BMD and/or fracture risk may help in predicting BMD and fracture risk changes over time during the progression of a disease or when under treatment. Here, we discuss important concepts of bone physiology, osteoporosis, treatment options, mathematical modeling of osteoporosis, and the use of these models by the pharmaceutical industry and the Food and Drug Administration.

Kinetic-Pharmacodynamic Model of Chemotherapy-Induced Peripheral Neuropathy in Patients with Metastatic Breast Cancer Treated with Paclitaxel, Nab-Paclitaxel, or Ixabepilone: CALGB 40502 (Alliance)

Chemotherapy-induced peripheral neuropathy (CIPN) is a dose-limiting toxicity caused by several chemotherapeutic agents. Currently, CIPN is managed by empirical dose modifications at the discretion of the treating physician. The goal of this research is to quantitate the dose-CIPN relationship to inform the optimal strategies for dose modification. Data were obtained from the Cancer and Leukemia Group B (CALGB) 40502 trial, a randomized phase III trial of paclitaxel vs. nab-paclitaxel vs. ixabepilone as first-line chemotherapy for locally recurrent or metastatic breast cancer. CIPN was measured using a subset of the Functional Assessment of Cancer Therapy-Gynecologic Oncology Group Neurotoxicity (FACT-GOG-NTX) scale. A kinetic-pharmacodynamic (K-PD) model was utilized to quantitate the dose-CIPN relationship simultaneously for the three drugs. Indirect response models with linear and Smax drug effects were evaluated. The model was evaluated by comparing the predicted proportion of patients with CIPN (score ≥8 or score ≥12) to the observed proportion. An indirect response model with linear drug effect was able to describe the longitudinal CIPN data reasonably well. The proportion of patients that were falsely predicted to have CIPN or were falsely predicted not to have CIPN was 20% or less at any cycle. The model will be utilized to identify an early time point that can predict CIPN at later time points. This strategy will be utilized to inform dose adjustments to prospectively manage CIPN. Clinicaltrials.gov ID: NCT00785291.

Dissociated Agonist of Glucocorticoid Receptor or Prednisone for Active Rheumatoid Arthritis: Effects on P1NP and Osteocalcin Pharmacodynamics

Fosdagrocorat (PF‐04171327), a dissociated agonist of the glucocorticoid receptor, has potent anti‐inflammatory activity in patients with rheumatoid arthritis with reduced adverse effects on bone health. To identify fosdagrocorat doses with bone formation marker changes similar to prednisone 5 mg, we characterized treatment‐related changes in amino‐terminal propeptide of type I collagen (P1NP) and osteocalcin (OC) with fosdagrocorat (1, 5, 10, or 15 mg) and prednisone (5 or 10 mg) in a phase II randomized trial (N = 323). The time course of markers utilized a mixed‐effects longitudinal kinetic‐pharmacodynamic model. Median predicted changes from baseline at week 8 with fosdagrocorat 5, 10, and 15 mg were −18, −22, and −22% (P1NP), and −7, −13, and −17% (OC), respectively. Changes with prednisone 5 and 10 mg were −15% and −18% (P1NP) and −10% and −17% (OC). The probability of fosdagrocorat doses up to 15 mg being noninferior to prednisone 5 mg for P1NP and OC changes was >90%.

Modelling the dose-response relationship: the fair share of pharmacokinetic and pharmacodynamic information

AIMS

The aim of this paper is to investigate the role of drug concentration samplings in the modelling of the dose-response relationship.

METHODS

Using an initial PK/PD model, a reference dataset was simulated. PK and PD samples were extracted to create reduced datasets. PK/PD and K-PD models were fitted to theses reduced datasets. Post hoc estimates from both types of models were compared to the initial PK/PD model and performance was assessed.

RESULTS

K-PD models were largely biased when the drug has a nonlinear elimination. PK/PD models with 1 PK and 2 PD samples were superior to K-PD models with 3 PD samples. PK/PD models with 1 or 2 PK samples and 3 PD samples proved to be superior to K-PD models with 4 PD samples.

CONCLUSIONS

K-PD models should not be used when the drug has nonlinear elimination. K-PD models should not replace PK/PD modelling but are an alternative approach if the PD information is large enough.

Pharmacokinetics, pharmacodynamics and adverse event profile of GSK2256294, a novel soluble epoxide hydrolase inhibitor

AIMS

Endothelial-derived epoxyeicosatrienoic acids may regulate vascular tone and are metabolized by soluble epoxide hydrolase enzymes (sEH). GSK2256294 is a potent and selective sEH inhibitor that was tested in two phase I studies.

METHODS

Single escalating doses of GSK2256294 2-20 mg or placebo were administered in a randomized crossover design to healthy male subjects or obese smokers. Once daily doses of 6 or 18 mg or placebo were administered for 14 days to obese smokers. Data were collected on safety, pharmacokinetics, sEH enzyme inhibition and blood biomarkers. Single doses of GSK2256294 10 mg were also administered to healthy younger males or healthy elderly males and females with and without food. Data on safety, pharmacokinetics and biliary metabolites were collected.

RESULTS

GSK2256294 was well-tolerated with no serious adverse events (AEs) attributable to the drug. The most frequent AEs were headache and contact dermatitis. Plasma concentrations of GSK2256294 increased with single doses, with a half-life averaging 25-43 h. There was no significant effect of age, food or gender on pharmacokinetic parameters. Inhibition of sEH enzyme activity was dose-dependent, from an average of 41.9% on 2 mg (95% confidence interval [CI] -51.8, 77.7) to 99.8% on 20 mg (95% CI 99.3, 100.0) and sustained for up to 24 h. There were no significant changes in serum VEGF or plasma fibrinogen.

CONCLUSIONS

GSK2256294 was well-tolerated and demonstrated sustained inhibition of sEH enzyme activity. These data support further investigation in patients with endothelial dysfunction or abnormal tissue repair, such as diabetes, wound healing or COPD.

A semi-mechanistic model of bone mineral density and bone turnover based on a circular model of bone remodeling

Development of novel therapies for bone diseases can benefit from mathematical models that predict drug effect on bone remodeling biomarkers. Therefore, a bone cycle model (BCM) was developed that takes into consideration the concept of the basic multicellular unit and the dynamic equilibrium of bone remodeling. The model is a closed form cyclical model with four compartments representing resorption, formation, primary mineralization, and secondary mineralization. Equations describing the time course of bone turnover biomarkers were developed using the flow rate of bone cycle units (BCU) between the compartments or the amount of BCU in each compartment. A disease progression model representing bone loss in osteoporosis, a vitamin D and calcium supplementation (placebo) model, and a drug model for antiresorptive treatments were added to the model. Initial model parameter values were derived from published bone turnover data. The BCM accurately described biomarker-time profiles in postmenopausal women receiving either placebo or bisphosphonate treatment. The slow continual increase in bone mineral density (BMD) observed after 1 year of treatment was accurately described when changes in bone turnover were combined with increases in mineralization. For this purpose, the secondary mineralization compartment was replaced by three catenary chain compartments representing increasing mineral content. The refined BCM satisfactorily predicted biomarker profiles after long-term (10-year) bisphosphonate treatment. Furthermore, the model successfully described individual bone turnover markers and BMD results following treatment with denosumab in postmenopausal women. Analyses with this model could be used to optimize dosing regimens and to predict effects of novel osteoporotic treatments.

HIF targets in bone remodeling and metastatic disease

The bone marrow is a hypoxic microenvironment that is rich in growth factors and blood vessels and is readily colonized by tumor cells disseminated from numerous cancers including tumors of the breast, prostate, lung, and skin. The origin of metastatic growth promoting factors for tumor cells disseminated to the bone marrow is derived from multiple sources: the bone matrix, which is a reservoir for growth factors, and cells residing in the marrow and along bone surfaces, such as osteoblasts, osteoclasts, macrophages, and T cells, which secrete cytokines and chemokines. Low oxygen levels within the bone marrow induce hypoxia signaling pathways such as hypoxia inducible factor (HIF), which is regulated by oxygen requiring prolyl hydroxylases (PHDs) and von Hippel-Lindau (VHL) tumor suppressor. These hypoxia signaling pathways have profound effects on bone development and homeostasis. Likewise, hypoxic conditions observed in local breast and prostate tumors point to a role for hypoxia-inducible genes in metastasis to and colonization of the bone marrow. This review will explore the role of hypoxia-regulated factors in bone development and remodeling, and how these elements may contribute to solid tumor metastasis to the bone.

The optimal oral dose selection of ibandronate in Japanese patients with osteoporosis based on pharmacokinetic and pharmacodynamic properties

Ibandronate is a drug widely used outside Japan for the treatment of osteoporosis. It is available in formulations for intermittent intravenous (i.v.) administration and for intermittent (once monthly) oral administration. Ibandronate was recently approved in Japan as an i.v. injection with a dosing regimen of 1.0 mg once a month. To establish the optimal dose for oral administration of ibandronate in Japanese osteoporotic patients, we investigated the pharmacokinetics of and pharmacodynamic response to ibandronate following oral and intravenous administrations to Japanese subjects. Ibandronate (20, 50, 100, or 150 mg) was given orally to healthy postmenopausal Japanese women and to Japanese patients with primary osteoporosis. Serial measurements were obtained for the concentrations of serum ibandronate and urinary cross-linked C-telopeptide of Type I collagen (uCTX). Pharmacokinetic parameters and the time profiles of creatinine-corrected uCTX were compared with those obtained from postmenopausal Japanese women with osteopenia after administration of 1.0 mg i.v. ibandronate. Following oral administration of ibandronate, the area under the serum ibandronate concentration–time curve (AUC_inf) increased dose-proportionally for doses up to 100 mg; at 150 mg, AUC_inf increased beyond the dose-proportionality seen with doses up to 100 mg. The AUC_inf within the linear range following administration of 100 mg oral ibandronate was similar to that following 1.0 mg i.v. ibandronate. Additionally, corrected uCTX decreased after administration of 100 mg oral ibandronate and remained decreased for 1 month; the magnitude of the decrease was similar to or greater than that obtained after 1.0 mg i.v. ibandronate. From a clinical pharmacological perspective, administration of 100 mg/month oral ibandronate was equivalent to that of 1.0 mg/month i.v. ibandronate.

Application of modeling and simulation to a long-term clinical trial: a direct comparison of simulated data and data actually observed in Japanese osteoporosis patients following 3-year ibandronate treatment

Ibandronate, a nitrogen-containing bisphosphonate, is a bone resorption inhibitor widely used to prevent and treat osteoporosis. To optimize the design for a long-term clinical study of ibandronate, modeling and simulation (M&S) was performed based on the result of population pharmacodynamic analysis using the data of a short-term clinical study. A population pharmacodynamic model was constructed by the urinary C-terminal telopeptide of type I collagen (uCTx) and the lumbar spine bone mineral density (BMD) data obtained in clinical studies, including a phase II study of Japanese osteoporosis patients treated with ibandronate for 6 months. Changes in BMD over a period of 3 years were simulated from the population pharmacodynamic parameters of the patients in this phase II study. The relationship between uCTx and BMD was well described by this modeling. The functions of disease progression and supplemental treatment were incorporated into the model to simulate a long-term clinical study with high accuracy. A long-term clinical study with a 3-year treatment was conducted after this M&S. The percentage change from baseline in observed BMD values were found to be similar to the prospectively simulated values. This study showed that M&S could be a useful and powerful tool for designing and conducting long-term clinical studies when carried out in the following sequence: (1) conduct a short-term clinical study; (2) perform M&S; and (3) conduct the long-term clinical study. Application of this procedure to various other treatment agents will establish the usefulness of M&S for long-term clinical studies and bring further efficiencies to drug development.

A network modeling approach for the spatial distribution and structure of bone mineral content

This study aims to develop a spatial model of bone for quantitative assessments of bone mineral density and microarchitecture. A spatially structured network model for bone microarchitecture was systematically investigated. Bone mineral-forming foci were distributed radially according to the cumulative normal distribution, and Voronoi tessellation was used to obtain edges representing bone mineral lattice. Methods to simulate X-ray images were developed. The network model recapitulated key features of real bone and contained spongy interior regions resembling trabecular bone that transitioned seamlessly to densely mineralized, compact cortical bone-like microarchitecture. Model-simulated imaging profiles were similar to patients' X-ray images. The morphometric metrics were concordant with microcomputed tomography results for real bone. Simulations comparing normal and diseased bone of 20-30 to 70-80 year-olds demonstrated the method's effectiveness for modeling osteoporosis. The novel spatial model may be useful for pharmacodynamic simulations of bone drugs and for modeling imaging data in clinical trials.

Romiplostim dose-response in patients with myelodysplastic syndromes

AIM

To characterize the romiplostim dose-response in subjects with low or intermediate-1 risk myelodysplastic syndromes (MDS) receiving subcutaneous romiplostim.

METHODS

Data from 44 MDS subjects receiving subcutaneous romiplostim (dose range 300-1500 μg week(-1) ) were used to develop a pharmacodynamic model consisting of a romiplostim-sensitive progenitor cell compartment linked to the peripheral blood compartment through four transit compartments representing the maturation in the bone marrow from megakaryocytes to platelets. A kinetics of drug effect model was used to quantify the stimulatory effect of romiplostim on the proliferation of sensitive progenitor cells and pharmacodynamics-mediated disposition was modelled by assuming the kinetics of drug effect constant (kDE ) to be proportional to the change in platelet count relative to baseline.

RESULTS

The estimated values (between subject variability) for baseline platelet count, mean transit time, and kDE were 24 × 10(9) l(-1) (47%), 9.6 days (44%) and 0.28 days(-1) , respectively. MDS subjects had a shorter platelet lifespan (42 h) than healthy subjects (257 h). Romiplostim effect was described for responders (78%) and non-responders (22%). The average weekly stimulatory effect of romiplostim on the production rate of sensitive progenitor cells at baseline was 269% per 100 μg week(-1) for responders. Body weight, age, gender and race were not statistically related to romiplostim pharmacodynamic parameters. Visual predictive checks confirmed the model adequacy.

CONCLUSION

The time course of platelet counts in MDS subjects receiving subcutaneous administration of escalating doses of romiplostim was characterized and showed a linear dose-response for romiplostim responders to increase the platelet counts.

Basic concepts in population modeling, simulation, and model-based drug development: part 3-introduction to pharmacodynamic modeling methods

Population pharmacodynamic (PD) models describe the time course of drug effects, relating exposure to response, and providing a more robust understanding of drug action than single assessments. PD models can test alternative dose regimens through simulation, allowing for informed assessment of potential dose regimens and study designs. This is the third paper in a three-part series, providing an introduction into methods for developing and evaluating population PD models. Example files are available in the Supplementary Data.

Population pharmacokinetic and pharmacodynamic modeling of different formulations of ONO-5334, cathepsin K inhibitor, in Caucasian and Japanese postmenopausal females

ONO-5334, a selective inhibitor of cathepsin K, is a potential new treatment for osteoporosis. The objectives of this study were to (1) develop population pharmacokinetic-pharmacodynamic (PK-PD) models for ONO-5334 using dose-ascending data from healthy postmenopausal females, (2) examine comparability of PK and/or PD profile between Caucasian and Japanese, and (3) compare PK-PD profile between immediate release tablet (IRT) and sustained release tablet (SRT). The population PK-PD models were developed for each formulation for post-dose levels of bone resorption markers (serum CTX and NTX). The data were provided from 4 phase 1 studies with total of 201 Caucasian and 94 Japanese subjects. Plasma concentrations of ONO-5334 and bone resorption markers were thoroughly evaluated in those studies. An indirect response model described relationships between bone resorption markers and plasma concentrations of ONO-5334. There was no significant difference in PK and pharmacodynamic potency (IC50 ) between Caucasian and Japanese. Based on the developed model, serum CTX and NTX after administration of ONO-5334 IRT or SRT were simulated, and the results showed that ONO-5334 SRT would provide comparable PD effect on bone resorption markers with lower dose relative to IRT.

Romiplostim dose response in patients with immune thrombocytopenia

A pharmacodynamic model was developed for platelet counts in 52 patients with immune thrombocytopenia (ITP) receiving subcutaneous romiplostim in 3 phase I/II studies (dose range, 0.2-10 µg/kg). The model consisted of a drug-sensitive progenitor cell compartment linked to a peripheral blood compartment through 4 transition compartments. The baseline platelet count, mean transit time, and kinetics of drug effect constant were 11.1 × 10(9)/L, 170 hours, and 0.6 day(-1), respectively. The ITP patients had a shorter platelet life span and lower progenitor cell production rates than healthy volunteers. Romiplostim response was described for 2 subpopulations. The romiplostim stimulatory effect in ITP patients was 351%/100 µg/wk and 12%/100 µg/wk in 68% and 32% of patients, respectively. Visual and numerical predictive checks suggested accurate prediction of platelet time course and durable response rate in ITP patients. Model-based simulations confirmed the effectiveness of dose reduction to prevent platelet counts >400 × 10(9)/L.

Structural models describing placebo treatment effects in schizophrenia and other neuropsychiatric disorders

Large variation in placebo response within and among clinical trials can substantially affect conclusions about the efficacy of new medications in psychiatry. Developing a robust placebo model to describe the placebo response is important to facilitate quantification of drug effects, and eventually to guide the design of clinical trials for psychiatric treatment via a model-based simulation approach. In addition, high dropout rates are very common in the placebo arm of psychiatric clinical trials. While developing models to evaluate the effect of placebo response, the data from patients who drop out of the trial should be considered for accurate interpretation of the results. The objective of this paper is to review the various empirical and semi-mechanistic models that have been used to quantify the placebo response in schizophrenia trials. Pros and cons of each placebo model are discussed. Additionally, placebo models used in other neuropsychiatric disorders like depression, Alzheimer's disease and Parkinson's disease are also reviewed with the objective of finding those placebo models that could be useful for clinical studies of both acute and chronic schizophrenic disease conditions. Better understanding of the patterns of dropout and the factors leading to dropouts are crucial in identifying the true placebo response. We therefore also review dropout models that are used in the development of models for treatment effects and in the optimization of clinical trials by simulation approaches. The use of an appropriate modelling strategy that is capable of identifying the potential sources of variable placebo responses and dropout rates is recommended for improving the sensitivity in discriminating between the effects of active treatment and placebo.

Integrated model for denosumab and ibandronate pharmacodynamics in postmenopausal women

This study aims to characterize the pharmacodynamic properties of denosumab, a RANK ligand inhibitor, and ibandronate, a bisphosphonate, using an integrated bone homeostasis model in postmenopausal women. Mean temporal profiles of denosumab, serum and urine N-telopeptide (sNTX, uNTX), lumbar spine bone mineral density (BMD) following denosumab administration, and urine C-telopeptide (uCTX) and lumbar spine BMD upon ibandronate administration were extracted from the literature. A mechanistic model was developed that integrates denosumab pharmacokinetics with binding to RANK ligand and ibandronate inhibition of osteoclast precursor differentiation to active osteoclasts (AOC). Biomarker concentrations were linked to the AOC pool. The BMD was characterized by a turnover model with stimulation of bone formation and degradation by AOB (active osteoblasts) and AOC pools. The estimated basal sNTX, uNTX and uCTX concentrations were 7.24 nm, 14.4 nmol/mmolCr and 31µg/mmolCr. The BMD degradation rate was 0.00161 day(-1) with stimulation constants associated with AOB and AOC of 1214 and 790 pm(-1) . The plasma ibandronate concentration producing 50% of maximum inhibition of osteoclast differentiation was 522 ng/l. The integrated model, which incorporates multiple pathways of therapeutic intervention, quantitatively describes changes in clinical biomarkers of bone turnover and BMD after denosumab and ibandronate exposures in postmenopausal women.

Pharmacology of bisphosphonates

Four decades of preclinical and clinical research of the pharmacology of bisphosphonates have generated data and concepts that have considerably improved their clinical use. However, despite this progress several pharmacological aspects relevant to bisphosphonate action on bone are still incompletely understood. This is mainly due to the complex, unique pharmacological properties of bisphosphonates. We review here the pharmacokinetic and pharmacodynamic data of bisphosphonates that are relevant for their clinical application and for the potential choice of a given compound, focusing on uncertainties that still exist.

Assessment of a bone biopsy technique for measuring tiludronate in horses: a preliminary study

This study assessed the feasibility of measuring tiludronate in horses using a minimally invasive bone biopsy technique. Eight horses were treated with intravenous (IV) tiludronate [1 mg/kg bodyweight (BW)], either once (n = 4) or twice, 28 d apart (n = 4). The horses that were treated once were euthanized on days 1, 43, 57, or 92 and those that were treated twice, were euthanized on days 112, 154, 194, or 364. Bone samples were taken bilaterally from each horse at 4 sites: the third metacarpal bone (MCIII), the 13th rib (R13), the tuber coxae (TC), and the cuboid bone (CB). Test samples were taken with a 5-mm diameter dental drill, while larger reference samples were taken with an osteotome. The concentrations of tiludronate were measured by high performance liquid chromatography (HPLC) with ultraviolet (UV) detection. The TC was the easiest site to sample, and no technical difficulties were encountered for extraction and measurement. Drill sampling at the MCIII was difficult. Moreover, both the extraction and measurement caused technical problems and results were unreliable in most cases (93%). Drill samples obtained from the R13 were very small and access to the CB required considerable dissection, which would not be feasible in vivo. Forty-six percent and 36% of the tiludronate measurements performed on the R13 and CB samples, respectively, were unreliable. The ratio of tiludronate concentrations ranged from 73% to 185% (median: 118%) in the TC, 65% to 208% (median: 81%) in the R13, and 26% to 110% (median: 57%) in the CB. In all but 1 horse, the highest concentrations of tiludronate were found in the TC. It was concluded that bone biopsies performed at the TC were adequate for measuring tiludronate in horses and should be considered in future for repeated measurements over time in living animals.

Population pharmacodynamic model of the longitudinal FEV1 response to an inhaled long-acting anti-muscarinic in COPD patients

The precise assessment of the dose-response to bronchodilators in the treatment of chronic obstructive pulmonary disease is hindered by the low signal to noise ratio of the typical clinical endpoint FEV(1). Kinetic-pharmacodynamic (K-PD) models which use time course of response over a range of doses are in principle suited for the assessment of the dose response relationship of pulmonary administered drugs. A K-PD model was successfully developed using the longitudinal FEV1 data collected in the clinical study for a novel bronchodilator X. A superposition of two cosine functions was selected to describe the circadian variability in FEV(1) at baseline. The onset (ka) and offset (kde) of drug action were described with first-order rate constants of 0.214/h and 0.141/h, respectively. Drug potency, EKD(50,) was estimated as 6.56 μg/h, and the maximum response, Emax as 0.631 L. Between-subject variability for kde, EKD(50) and Emax were 65, 84.7 or 34.4% (expressed as coefficient variation). The model-based simulation predicted that for the same total daily dose of once-daily and twice-daily regimens, the trough FEV(1) response to a twice-daily regimen was higher, and the maximum FEV(1) response to once-daily regimen was higher, while the predicted average FEV(1) response was about the same.

A systematic review and empirical analysis of the relation between dose and duration of drug action

There is a log-linear relation between the dose and duration of action of drugs with single-compartment pharmacokinetics and direct, reversible mechanisms of action. However, it has been suggested that this relation does not extend to drugs whose metabolites are active or slowly eliminated, drugs with saturable kinetics, and drugs with hit-and-run effects. The purpose of this study is to test this hypothesis and to quantify the relationship by way of a systematic review coupled to an empirical analysis. All issues of 4 clinical pharmacology journals from 1980 to 2005 are hand-searched for articles that present pharmacodynamic response versus time curves for 4 or more different doses. Data on duration of action, dose, and area under the plasma concentration versus time curve from zero to infinity (AUC) are abstracted and analyzed by panel data regression modeling, with within-study fixed effects. Duration of drug action is defined as the time during which a pharmacodynamic effect (or response) exceeds a nominal threshold. The generalized models of all observations from 33 publications, with duration of action as the dependent variable and the logarithm of the dose (or AUC) as the explanatory variable, yield significant log-linear relationships. The regressions for individual studies are correctly specified in 27 cases; there are insufficient data for analysis in 10 studies, and a log-linear specification is deemed inappropriate in 6. Analysis of published dose-ranging studies shows that the duration of action of a drug is directly proportional to the logarithm of dose across a wide range of different drugs, extending a result that was previously documented for very few compounds.

Semi-mechanistic model for neutropenia after high dose of chemotherapy in breast cancer patients

PURPOSE

To describe the absolute neutrophil counts (ANC) profile in breast cancer patients receiving high-dose of chemotherapy and peripheral blood stem-cells (PBSC) transplantation.

METHODS

Data from 41 subjects receiving cyclophosphamide, thiotepa and carboplatin were used to develop the ANC model consisting of a drug-sensitive progenitor cell compartment, linked to the peripheral blood compartment, through three transition compartments. PBSC were incorporated into the first transit compartment following a zero-order process, k(in), and the rebound effect was explained by a feedback mechanism. A 'kinetics of drug action' model was used to quantify the HDC effect on the progenitor cells according to a linear function, with a slope (alpha).

RESULTS

The typical of the ANC at baseline (Circ(0)), mean transit time (MTT), feedback parameter (gamma), k(in) and alpha were estimated to be 5,610 x 10(6)/L, 3.25 days, 0.145, 0.954 cell/kg/day and 2.50 h/U, respectively. rHuG-CSF shortens the MTT by 92% and increases the mitotic activity by 120%. Bootstrap analysis, visual predictive check and numerical predictive checks evidenced accurate prediction of the ANC nadir, time to ANC nadir and time to grade 4 neutropenia recovery.

CONCLUSION

The time course of neutropenia following high-dose of chemotherapy and PBSC transplantation was accurately predicted. Higher amount of CD34+ cells in the PBSC transplantation and earlier administration rHuG-CSF were associated with faster haematological recovery.

Evaluation of drugs in pediatrics using K-PD models: perspectives

Some pharmacodynamic (PD) models, called K-PD models, have been developed for the description of drug action kinetics in the absence of drug concentration measurements. Because blood samples for drug measurements are not needed, these models may be very useful in pediatric studies, by reducing their invasiveness. In addition, a number of PD measurements are also non-invasive and specific devices exist for measures in children. Therefore, the kinetics of drug action may be characterized with minimal invasiveness. A brief description of the key features of these models is given, and a number of examples of application are presented. K-PD models are expected to be most useful when the drug kinetics is simple (i.e. when the one-compartment model is a reasonable description), or when the response kinetics is slow compared with drug kinetics. K-PD models have already demonstrated their usefulness in animal and adult studies. They are very attractive for pediatric studies and they should facilitate the assessment of drug efficacy and safety.

Minutes from the round table held in Paris on July 6, 2007: 'Contribution of modelling in the paediatric drug development'

A symposium called "Contribution of modelling in the paediatric drug development" was organized at Paris on July 5-6, 2007 under the auspices of INSERM. The following issues were highlighted and discussed by the participants at the end of the meeting during a round table: *What is the place of modelling at a preclinical stage in the paediatric development? *What is the place of modelling at a clinical stage in the paediatric development? *What are the requirements for an evaluation based on modelling? *What are the recommendations and guidelines need to be established to facilitate the use of modelling techniques in paediatrics? This paper summarizes the discussion around these four questions.

A non-parametric method to analyse time-course of effect in the absence of pharmacokinetic data: application to inhaled bronchodilators

In spite of the extensive use of long-acting beta(2)-agonist (LABA) bronchodilators in asthma, the actual mechanism of their in vivo duration of action is not well understood, primarily due to limitations of standard pharmacokinetic-pharmacodynamic (PKPD) analysis methodologies. We have developed a novel method of analysing lung efficacy vs. time profiles for LABAs that can be used to provide comparative information on the lung PK. We hypothesised that for compounds that do not differ in their PK at the site of PD action, but differ in their in vivo potencies, the relationship between the area under the effect curve (AUEC) and the observed maximum effect (OME) at different doses is described by the same sigmoid curve. We have illustrated this property for standard PKPD models by obtaining analytical solution and through simulations. Anaesthetised dog in vivo effect vs. time profiles were gathered for six inhaled LABA candidates that differ in their in vitro potencies. Neither lung nor systemic PK was available for any compound. Analysis of the AUEC vs. OME data, derived from the efficacy profiles, using nonlinear mixed effects modelling indicated that for four compounds, the observed differences in in vivo duration of action was due to differences in their in vivo potencies and not because of lung PK differences. Therefore, it was concluded that for these compounds, characterisation of lung PK was unlikely to differentiate their PKPD characteristics. Thus, the proposed approach helped focus resources during translational research leading to lead candidate selection.