Integrated cellular bone homeostasis model for denosumab pharmacodynamics in multiple myeloma patients

Advances in mechanobiological pharmacokinetic-pharmacodynamic models of osteoporosis treatment - Pathways to optimise and exploit existing therapies

Osteoporosis (OP) is a chronic progressive bone disease which is characterised by reduction of bone matrix volume and changes in the bone matrix properties which can ultimately lead to bone fracture. The two major forms of OP are related to aging and/or menopause. With the worldwide increase of the elderly population, particularly age-related OP poses a serious health issue which puts large pressure on health care systems. A major challenge for development of new drug treatments for OP and comparison of drug efficacy with existing treatments is due to current regulatory requirements which demand testing of drugs based on bone mineral density (BMD) in phase 2 trials and fracture risk in phase 3 trials. This requires large clinical trials to be conducted and to be run for long time periods, which is very costly. This, together with the fact that there are already many drugs available for treatment of OP, makes the development of new drugs inhibitive. Furthermore, an increased trend of the use of different sequential drug therapies has been observed in OP management, such as sequential anabolic-anticatabolic drug treatment or switching from one anticatabolic drug to another. Running clinical trials for concurrent and sequential therapies is neither feasible nor practical due to large number of combinatorial possibilities. In silico mechanobiological pharmacokinetic-pharmacodynamic (PK-PD) models of OP treatments allow predictions beyond BMD, i.e. bone microdamage and degree of mineralisation can also be monitored. This will help to inform clinical drug usage and development by identifying the most promising scenarios to be tested clinically (confirmatory trials rather than exploratory only trials), optimise trial design and identify subgroups of the population that show benefit-risk profiles (both good and bad) that are different from the average patient. In this review, we provide examples of the predictive capabilities of mechanobiological PK-PD models. These include simulation results of PMO treatment with denosumab, implications of denosumab drug holidays and coupling of bone remodelling models with calcium and phosphate systems models that allows to investigate the effects of co-morbidities such as hyperparathyroidism and chronic kidney disease together with calcium and vitamin D status on drug efficacy.

Pharmacokinetics, pharmacodynamics, safety, and immunogenicity of Gerilimzumab (GB224), a recombinant humanized interleukin-6 monoclonal antibody, in healthy Chinese adults: A randomized controlled dose-escalation study

OBJECTIVES

This study aimed to investigate the safety, pharmacokinetics (PK), pharmacodynamics (PD), and immunogenicity of Gerilimzumab (GB224), a recombinant humanized IgG1λ monoclonal antibody against interleukin-6, in healthy Chinese adults.

METHODS

Fifty-eight subjects were randomly assigned to receive a single subcutaneous dose of 2, 5, 10, 15, 20, 30 mg GB224 or placebo. Safety assessments were performed, and blood samples were collected for PK, PD, and immunogenicity analyses during a follow-up of 112 days.

RESULTS

The most frequent adverse event was decreased fibrinogen (43.1%). GB224 was absorbed relatively fast with a median T_max of 48 h (24-168 h) but eliminated slowly with a long mean half-life (839.38-981.63 h). Dose proportionality was shown to be in the dose range of 10-30 mg. A dose-dependent increase in serum interleukin-6 concentration from baseline was observed in the subjects receiving GB224. Only two subjects tested positive for antidrug antibodies after administration of GB224.

CONCLUSION

GB224 had a well-tolerated safety profile, desirable PK, and a low immunogenicity following a single-dose subcutaneous administration in healthy Chinese subjects. These findings warrant further investigation.

Breast Cancer Exosomal microRNAs Facilitate Pre-Metastatic Niche Formation in the Bone: A Mathematical Model

Pre-metastatic niche is a location where cancer cells, separating from a primary tumor, find "fertile soil" for growth and proliferation, ensuring successful metastasis. Exosomal miRNAs of breast cancer are known to enter the bone and degrade it, which facilitates cancer cells invasion into the bone interior and ensures its successful colonization. In this paper, we use a mathematical model to first describe, in health, the continuous remodeling of the bone by bone-forming osteoblasts, bone-resorbing osteoclasts and the RANKL-OPG-RANK signaling system, which keeps the balance between bone formation and bone resorption. We next demonstrate how breast cancer exosomal miRNAs disrupt this balance, either by increasing or by decreasing the ratio of osteoclasts/osteoblasts, which results in abnormal high bone resorption or abnormal high bone forming, respectively, and in bone weakening in both cases. Finally we consider the case of abnormally high resorption and evaluate the effect of drugs, which may increase bone density to normal level, thus protecting the bone from invasion by cancer cells.

Modeling osteoporosis to design and optimize pharmacological therapies comprising multiple drug types

For the treatment of postmenopausal osteoporosis, several drug classes with different mechanisms of action are available. Since only a limited set of dosing regimens and drug combinations can be tested in clinical trials, it is currently unclear whether common medication strategies achieve optimal bone mineral density gains or are outperformed by alternative dosing schemes and combination therapies that have not been explored so far. Here, we develop a mathematical framework of drug interventions for postmenopausal osteoporosis that unifies fundamental mechanisms of bone remodeling and the mechanisms of action of four drug classes: bisphosphonates, parathyroid hormone analogs, sclerostin inhibitors, and receptor activator of NF-κB ligand inhibitors. Using data from several clinical trials, we calibrate and validate the model, demonstrating its predictive capacity for complex medication scenarios, including sequential and parallel drug combinations. Via simulations, we reveal that there is a large potential to improve gains in bone mineral density by exploiting synergistic interactions between different drug classes, without increasing the total amount of drug administered.

A Randomized Controlled Dose-Escalation Study of LY06006, a Recombinant Humanized Monoclonal Antibody to RANKL, in Chinese Healthy Adults

Background: This study was conducted to explore the safety, tolerance, pharmacokinetics, pharmacodynamics, and immunogenicity of LY06006, a recombinant humanized monoclonal antibody to RANKL, when administrated subcutaneously in Chinese healthy adults.

Research design and methods: This was a randomized, double-blinded, placebo-controlled, single ascending dose study performed in 32 healthy Chinese adults, who were randomly assigned to receive a single injection dose of 18, 60, 120 mg study drug or placebo with a follow-up of 140–252 days.

Results: No deaths or drug-related serious adverse events occurred. LY06006 was rapidly absorbed in the 60 mg group with a T_max range of 120–480 h and serum LY06006 concentrations decreased slowly 11–13 days after dosing with a long mean (SD) half-life of 389.58 (63.44) h. The most frequent AEs were elevated serum parathyroid hormone (PTH) level (83.3%), hypocalcemia (54.2%), and hypophosphatemia (45.8%). None of the 32 subjects tested positive for anti-drug antibody during the trial.

Conclusion: Single-dose subcutaneous administration of LY06006 was safe and well-tolerated in healthy Chinese adults. C_max showed linear pharmacokinetic characteristics in the dose range of 18–120 mg based on dose-exposure proportionality analysis.

Parameter reduction, sensitivity studies, and correlation analyses applied to a mechanobiologically regulated bone cell population model of the bone metabolism

When striving for reconstructing and predicting bone remodeling processes by means of mathematical models, cell population models have become a popular option. From a conceptual point of view, these models are able to take into account an arbitrary amount of regulatory mechanisms driving the development of bone cells and their activities. However, in most cases, the models include a large number of parameters; and most of those parameters cannot be measured, which certainly compromises the credibility of cell population models. Here, new insights are presented as to the potential improvement of this unsatisfactory situation. In particular, a previously published bone remodeling model was considered, and based on combination and merging of the original parameters, the total number of parameters could be reduced from 28 to 18, without impairing the model's versatility and significance. Furthermore, a comprehensive number of one- and two-variable sensitivity studies were performed, pointing out which parameters (alone and in combination with other parameters) influence the model predictions significantly - for that purpose, the mean squared relative error (MSRE) between simulations based on the original parameters and based on varied parameters was considered as failure measure. It has turned out that the model is significantly more sensitive to parameters which can be considered as phenomenological (such as differentiation, proliferation, and apoptosis rates) than to parameters which are directly related to specific processes (such as dissociation rate constants, and maximum concentrations of the involved factors). Using common correlation measures (such as Pearson, Spearman, and partial ranked correlation coefficients), correlation studies revealed that the correlations between most parameters and the MSRE are weak, while a few parameters exhibited moderate correlations. In conclusion, the results shown in this paper provide valuable insights concerning the design of new experiments allowing for measurement of the parameters which are most influential in the context of bone remodeling simulation.

Combined Effects of Exercise and Denosumab Treatment on Local Failure in Post-menopausal Osteoporosis-Insights from Bone Remodelling Simulations Accounting for Mineralisation and Damage

Denosumab has been shown to increase bone mineral density (BMD) and reduce the fracture risk in patients with post-menopausal osteoporosis (PMO). Increase in BMD is linked with an increase in bone matrix mineralisation due to suppression of bone remodelling. However, denosumab anti-resorptive action also leads to an increase in fatigue microdamage, which may ultimately lead to an increased fracture risk. A novel mechanobiological model of bone remodelling was developed to investigate how these counter-acting mechanisms are affected both by exercise and long-term denosumab treatment. This model incorporates Frost's mechanostat feedback, a bone mineralisation algorithm and an evolution law for microdamage accumulation. Mechanical disuse and microdamage were assumed to stimulate RANKL production, which modulates activation frequency of basic multicellular units in bone remodelling. This mechanical feedback mechanism controls removal of excess bone mass and microdamage. Furthermore, a novel measure of bone local failure due to instantaneous overloading was developed. Numerical simulations indicate that trabecular bone volume fraction and bone matrix damage are determined by the respective bone turnover and homeostatic loading conditions. PMO patients treated with the currently WHO-approved dose of denosumab (60 mg administrated every 6 months) exhibit increased BMD, increased bone ash fraction and damage. In untreated patients, BMD will significantly decrease, as will ash fraction; while damage will increase. The model predicted that, depending on the time elapsed between the onset of PMO and the beginning of treatment, BMD slowly converges to the same steady-state value, while damage is low in patients treated soon after the onset of the disease and high in patients having PMO for a longer period. The simulations show that late treatment PMO patients have a significantly higher risk of local failure compared to patients that are treated soon after the onset of the disease. Furthermore, overloading resulted in an increase of BMD, but also in a faster increase of damage, which may consequently promote the risk of fracture, specially in late treatment scenarios. In case of mechanical disuse, the model predicted reduced BMD gains due to denosumab, while no significant change in damage occurred, thus leading to an increased risk of local failure compared to habitual loading.

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.

Toward a Mathematical Modeling of Diseases' Impact on Bone Remodeling: Technical Review

A wide variety of bone diseases have hitherto been discovered, such as osteoporosis, Paget’s disease, osteopetrosis, and metastatic bone disease, which are not well defined in terms of changes in biochemical and mechanobiological regulatory factors. Some of these diseases are secondary to other pathologies, including cancer, or to some clinical treatments. To better understand bone behavior and prevent its deterioration, bone biomechanics have been the subject of mathematical modeling that exponentially increased over the last years. These models are becoming increasingly complex. The current paper provides a timely and critical analysis of previously developed bone remodeling mathematical models, particularly those addressing bone diseases. Besides, mechanistic pharmacokinetic/pharmacodynamic (PK/PD) models, which englobe bone disease and its treatment’s effect on bone health. Therefore, the review starts by presenting bone remodeling cycle and mathematical models describing this process, followed by introducing some bone diseases and discussing models of pathological mechanisms affecting bone, and concludes with exhibiting the available bone treatment procedures considered in the PK/PD models.

Are drug holidays a safe option in treatment of osteoporosis? - Insights from an in silico mechanistic PK-PD model of denosumab treatment of postmenopausal osteoporosis

Recent reviews by the clinical bone research community suggest caution with prescription of drug holidays for patients with postmenopausal osteoporosis (PMO) treated with denosumab for an extended period of time. Main reasons for this suggestion are based on the fact that discontinuation of denosumab treatment leads to a relapse of osteoclastic bone resorption and a loss of bone mineral density (BMD) to pre-treatment levels at only 12-28 months. The question remains what is the best treatment option for cases where it is required to discontinue and/or reduce the drug dose and what are the consequences on BMD and bone turnover markers (BTMs). The latter questions are difficult to be addressed using clinical trials alone given the large number of parameter combinations involved to answer this problem. In this paper, we apply a recently developed in silico mechanistic pharmacokinetic-pharmacodynamic (PK-PD) model of the effect of denosumab on bone remodelling in PMO. To address the above clinical relevant questions, we design a wide range of current and virtual treatment regimens to study the effect of drug holiday duration and therapy resumption on the evolution of BTMs, BMD and mineral content. Our numerical simulation results indicate the symptomatic effect of denosumab, which is lost once treatment is stopped. This effect is most clearly seen on rapid loss of BMD to pre-treatment levels 12 months after the last injection (8% and 3.6% per year in the lumbar spine and femoral neck, respectively). Also, we identify that independently of the duration of drug holiday (i.e. 12, 16 or 18 months) resuming treatment can restore BMD quite effectively. However, the latter result does not consider the possibility of potential fractures that can occur during the drug holiday. Finally, we identify a treatment case most promising for achieving maintenance of BMD and mineral content, while moderately increasing BTMs. The latter case uses no drug holiday, but reduces the most commonly prescribed denosumab dose (60 mg every 6 months) by half at same interval.

A new era for migraine: Pharmacokinetic and pharmacodynamic insights into monoclonal antibodies with a focus on galcanezumab, an anti-CGRP antibody

PURPOSE

To review pharmacokinetic and pharmacodynamic characteristics of antibodies that bind to soluble ligands within the framework of calcitonin gene-related peptide antibodies.

OVERVIEW

Calcitonin gene-related peptide has been implicated in the pathophysiology of migraine. Galcanezumab is an antibody that binds to the ligand calcitonin gene-related peptide. Other antibodies that target calcitonin gene-related peptide include eptinezumab and fremanezumab. To understand how antibodies can affect the extent and duration of free ligand concentrations, it is important to consider the dose and pharmacokinetics of an antibody, and the kinetics of the ligand and antibody-ligand complex. Insights regarding the pharmacokinetic/pharmacodynamic properties of galcanezumab as a probe antibody drug and calcitonin gene-related peptide as its binding ligand regarding its clinical outcomes are provided.

DISCUSSION

Antibodies are administered parenterally because oral absorption is limited by gastrointestinal degradation and inefficient diffusion through the epithelium. The systemic absorption of antibodies following intramuscular or subcutaneous administration most likely occurs via convective transport through lymphatic vessels into blood. The majority of antibody elimination occurs via intracellular catabolism into peptides and amino acids following endocytosis. Binding of ligand to an antibody reduces the free ligand that is available to interact with the receptor and efficacy is driven by the magnitude and duration of the reduction in free ligand concentration. A galcanezumab pharmacokinetic/pharmacodynamic model shows that galcanezumab decreases free calcitonin gene-related peptide concentrations in a dose- and time-dependent manner and continues to suppress free calcitonin gene-related peptide with repeated dosing. The model provides evidence for a mechanistic linkage to galcanezumab therapeutic effects for the preventive treatment of migraine.

Effects of long-term treatment of denosumab on bone mineral density: insights from an in-silico model of bone mineralization

Denosumab is one of the most commonly prescribed anti-resorptive drugs for the treatment of postmenopausal osteoporosis. The therapeutic effect of denosumab is to inhibit osteoclast differentiation and consequently bone resorption. Gains in bone mineral density (BMD) are achieved based on the ability of the bone matrix to undergo secondary mineralization. Experimental data show that the increase of BMD after commencing denosumab treatment are bone site specific. In this paper, we developed a comprehensive mechanistic pharmacokinetic-pharmacodymamic (PK-PD) model of the effect of denosumab on bone remodeling in postmenopausal osteoporosis (PMO). The PD model is based on a bone cell population model describing the bone remodeling process at the tissue scale. The conceptual model of the bone mineralization process, originally proposed by Boivin and Meunier, is quantitatively incorporated using a FIFO (First-In-First-Out) queue algorithm. The latter takes into account the balance of mineral within bone tissue due to the mineralization process, distinguishing the primary and secondary phases and removal of bone matrix due to bone resorption. The numerical simulations show that the model is able to predict the bone-site specific increase in BMD as was observed in the experimental data of Bone et al. 2008 for a typical denosumab administration pattern of 60 mg every 6 months. At the hip a 5 % increase in BMD was observed, while at the lumbar spine a 7.5 % increase of BMD was achieved after a 2 year treatment period. The difference in BMD is due to the fact that bone turnover at the hip is lower compared to lumbar spine and consequently has less potential for secondary mineralization. Parametric studies revealed that the rate of bone mineralization is an essential parameter regulating BMD gains. If mineralization is neglected only minimal increases in BMD are observed.

Trial Design and Statistical Considerations on the Assessment of Pharmacodynamic Similarity

Pharmacodynamics (PD) similarity is an important component to support the claim of similarity between two drugs or devices. This article investigates the trial design and statistical considerations in the equivalence test of PD endpoints. Using bone resorption marker CTX as a case study, the relationship between the PD readouts and drug potency was explored to evaluate the sensitivity of the PD endpoint and guide equivalence margin selection. For PD data that have high baseline variability, one conventional similarity assessment method was to apply baseline-normalization followed by the standard bioequivalence (BE) test (Lancet Haematol. 4:e350-61, 2017, Ann Rheum Dis. 2017). This study showcased the drawbacks of the conventional method for PD data that were close to inhibition saturation, as the baseline-normalization significantly skewed the distribution of the PD data toward non-log-normal. In such cases, the standard BE test can produce an inflated type I error. Alternatively, ANCOVA, when applied to the un-normalized PD data with the baseline as a covariate, produced a satisfactory type I error with sufficient power. Therefore, ANCOVA was recommended for equivalence test of PD markers that has a saturated inhibition profile and high variability at baseline. Moreover, the relationship between PD readouts and drug potency was used to explore the sensitivity of the PD endpoint and it could help justify the equivalence margins, since the standard 80% to 125% BE margin often does not apply to PD. Finally, a decision tree was proposed to help guide the design of the PD equivalence study in the choice of PD endpoints and statistical methods.

Acute hypercalcemia and excessive bone resorption following anti-RANKL withdrawal: Case report and brief literature review

Denosumab is an anti-RANKL antibody that is commonly used for the treatment of osteoporosis; in oncology, bisphosphonates and denosumab have become the standard therapies for the treatment and prevention of skeletal complications in patients with myeloma and solid tumors. In recent years, excessive bone remodeling following the discontinuation of denosumab has raised concerns. Several cases of hypercalcemia have been reported after the discontinuation of high-dose denosumab (120 mg every 4 weeks), mainly in children. In this study, we report a new case of severe refractory hypercalcemia in a 54-year-old woman who received high-dose denosumab for 5 years as an adjuvant therapy for breast cancer. She is currently in remission and undergoing treatment with anastrazole, an aromatase inhibitor. The peculiarities of this case are the presence of associated bone pain with subperiosteal bone resorption on hand X-rays, and diffuse, long bone diaphyseal uptake on a bone scan. Hyperparathyroidism has been ruled out, and existing evidence suggests that this high-level of bone remodeling could be due to a rebound hyperactivation of the RANKL pathway. In addition to rehydration, repeated use of i.v. bisphosphonates was required to control recurrent hypercalcemia. As hypercalcemia is a serious metabolic complication, a gradual dose reduction should be considered when interruption of high dose denosumab therapy is planned.

Integrative modeling of drug therapy and the bone turnover

BACKGROUND

Denosumab has been successfully used for the postmenopausal osteoporosis treatment. This research is focused on the computational analysis of the effect of denosumab on bone remodeling.

METHODS

Inspired by the advancement in the field of multiscale modeling , this research encompasses on the cellular and molecular bone remodeling key players. The model is designed to cover all the dominant interacting factors and their respective gradients. During this research, we have performed numerical experiments to validate our mathematical model, by interfacing it with the parametric values available in the literature.

FINDINGS

The novelty of our work relies in the fact that we have considered the effect of estrogen, sclerostin and NFATc1 during osteoporosis and their combined effect with the variable effect of denosumab during therapy.

INTERPRETATIONS

From our analysis, we have concluded that denosumab suppresses osteoclast differentiation, that results in reduced bone resorption. These results are in agreement with the experimental findings.

Systems Modeling of Bortezomib and Dexamethasone Combinatorial Effects on Bone Homeostasis in Multiple Myeloma Patients

Osteolytic bone disease is one of the most debilitating manifestations of multiple myeloma (MM). Bortezomib is a proteasome inhibitor that shows both anticancer and bone anabolic properties and is being evaluated for its positive effects in MM patients with skeletal complications. Dexamethasone is a potent corticosteroid that is often given in combination with bortezomib for its antineoplastic effects; however, bone loss and osteoporosis are major adverse effects of long-term steroid-based therapies. In this study, a small systems pharmacological model was developed to integrate the bone anabolic effects of bortezomib with the osteolytic activity of dexamethasone in MM patients with bone disease. The final model parameters were all estimated with good precision. The interaction model is based on codifying multiple regulatory mechanisms of drug action and provides a platform for probing optimized bortezomib and dexamethasone combination dosing regimens to minimize skeletal side effects during myeloma therapy.

Dynamics of Bone Cell Interactions and Differential Responses to PTH and Antibody-Based Therapies

We propose a mathematical model describing the dynamics of osteoblasts and osteoclasts in bone remodeling. The goal of this work is to develop an integrated modeling framework for bone remodeling and bone cell signaling dynamics that could be used to explore qualitatively combination treatments for osteoporosis in humans. The model has been calibrated using 57 checks from the literature. Specific global optimization methods based on qualitative objectives have been developed to perform the model calibration. We also added pharmacokinetics representations of three drugs to the model, which are teriparatide (PTH(1-34)), denosumab (a RANKL antibody) and romosozumab (a sclerostin antibody), achieving excellent goodness-of-fit of human clinical data. The model reproduces the paradoxical effects of PTH on the bone mass, where continuous administration of PTH results in bone loss but intermittent administration of PTH leads to bone gain, thus proposing an explanation of this phenomenon. We used the model to simulate different categories of osteoporosis. The main attributes of each disease are qualitatively well captured by the model, for example changes in bone turnover in the disease states. We explored dosing regimens for each disease based on the combination of denosumab and romosozumab, identifying adequate ratios and doses of both drugs for subpopulations of patients in function of categories of osteoporosis and the degree of severity of the disease.

Modeling and simulation of bone mineral density in Japanese osteoporosis patients treated with zoledronic acid using tartrate-resistant acid phosphatase 5b, a bone resorption marker

Annual intravenous administration of zoledronic acid is used in the treatment of osteoporosis. A mathematical model was developed to predict bone mineral density up to 2 years after two annual doses of zoledronic acid from the early values of a bone resorption marker in osteoporosis patients.

INTRODUCTION

The measurement of bone mineral density (BMD) has been used as a surrogate marker instead of the observation of incident fractures to detect the efficacy of treatment. However, this method requires a long time to obtain significant changes. On the other hand, bone resorption markers respond to bone resorption inhibitors within a few weeks. Therefore, the aim of this study was to develop a mathematical model predicting long-term BMD after two annual doses of zoledronic acid (ZOL) using the early response of a bone resorption marker in osteoporosis patients.

METHODS

The model was constructed using 3410 tartrate-resistant acid phosphatase 5b (TRACP-5b) serum concentrations and 1146 lumbar spine (L2-L4) BMD values from 306 patients with primary osteoporosis. A mathematical model was developed to describe the time-dependent profiles of TRACP-5b and BMD.

RESULTS

The percentage changes from baseline of the BMD (%BMD) at up to 2 years were predicted from patients' baseline BMD and baseline and 12-week TRACP-5b values by the model obtained. The simulated 90% prediction interval almost covered the observed %BMD distribution at each time point, and the predictions were comparable to the observed %BMD.

CONCLUSIONS

This is the first model to predict BMD for up to 2 years following two annual doses of ZOL using patients' background characteristics and the early response of TRACP-5b. This model allows us to inform patients at the initial stage of ZOL treatment of their predicted response to treatment.

Systems pharmacology and enhanced pharmacodynamic models for understanding antibody-based drug action and toxicity

Pharmacokinetic (PK) and pharmacodynamic (PD) models seek to describe the temporal pattern of drug exposures and their associated pharmacological effects produced at micro- and macro-scales of organization. Antibody-based drugs have been developed for a large variety of diseases, with effects exhibited through a comprehensive range of mechanisms of action. Mechanism-based PK/PD and systems pharmacology models can play a major role in elucidating and integrating complex antibody pharmacological properties, such as nonlinear disposition and dynamical intracellular signaling pathways triggered by ligation to their cognate targets. Such complexities can be addressed through the use of robust computational modeling techniques that have proven powerful tools for pragmatic characterization of experimental data and for theoretical exploration of antibody efficacy and adverse effects. The primary objectives of such multi-scale mathematical models are to generate and test competing hypotheses and to predict clinical outcomes. In this review, relevant systems pharmacology and enhanced PD (ePD) models that are used as predictive tools for antibody-based drug action are reported. Their common conceptual features are highlighted, along with approaches used for modeling preclinical and clinically available data. Key examples illustrate how systems pharmacology and ePD models codify the interplay among complex biology, drug concentrations, and pharmacological effects. New hybrid modeling concepts that bridge cutting-edge systems pharmacology models with established PK/ePD models will be needed to anticipate antibody effects on disease in subpopulations and individual patients.

Mathematical Model of Bone Remodeling Captures the Antiresorptive and Anabolic Actions of Various Therapies

A better understanding of the molecular pathways regulating the bone remodeling process should help in the development of new antiresorptive regulators and anabolic regulators, that is, regulators of bone resorption and of bone formation. Understanding the mechanisms by which parathyroid hormone (PTH) influences bone formation and how it switches from anabolic to catabolic action is important for treating osteoporosis (Poole and Reeve in Curr Opin Pharmacol 5:612-617, 2005). In this paper we describe a mathematical model of bone remodeling that incorporates, extends, and integrates several models of particular aspects of this biochemical system (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013; Lemaire et al. in J Theor Biol 229:293-309, 2004; Peterson and Riggs in Bone 46:49-63, 2010; Raposo et al. in J Clin Endocrinol Metab 87(9):4330-4340, 2002; Ross et al. in J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012). We plan to use this model as a bone homeostasis platform to develop anabolic and antiresorptive compounds. The model will allow us to test hypotheses about the dynamics of compounds and to test the potential benefits of combination therapies. At the core of the model is the idealized account of osteoclast and osteoblast signaling given by Lemaire et al. (J Theor Biol 229:293-309, 2004). We have relaxed some of their assumptions about the roles of osteoprotegerin, transforming growth factor [Formula: see text], and receptor activator of nuclear factor [Formula: see text]B ligand; we have devised more detailed models of the interactions of these species. We have incorporated a model of the effect of calcium sensing receptor antagonists on remodeling (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013). We have also incorporated a basic model of the effects of vitamin D on calcium homeostasis. We have included a simple model of the mechanism proposed by Bellido et al. (2003), Ross et al. (J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012), of the influence of PTH on osteoblast apoptosis, a mechanism that accounts for the anabolic response to pulsatile PTH administration. Finally, we have devised a simple model of the administration and effects of bisphosphonates. The biomarkers in the model are procollagen type 1 amino-terminal propeptide and C-terminal telopeptide. Bone mineral density is the model's principal endpoint.

Utility of free and total target measurements as target engagement and efficacy biomarkers in biotherapeutic development--opportunities and challenges

For biotherapeutics directed against soluble targets, most often monoclonal antibodies (mAbs), their therapeutic efficacy theoretically is driven by the magnitude and duration of free target suppression. However, for soluble targets of rapid turnover and low abundance, it can be technically challenging to directly measure the lowering of free target following treatment with biologics. The opportunities, challenges, and practical approaches to assess free and bound soluble targets and the utility of free and bound target measurements as biomarkers for target engagement and efficacy are covered in this review. In particular, case examples are presented to illustrate the interplay between drug and free/bound target, and how an integrated bioanalytical and pharmacokinetic/target engagement/pharmacodynamic (PK/TE/PD) modeling approach can be used to assess the target engagement for biologics directed against soluble targets with rapid turnover. Important caveats of the modeling approach in the absence of free target measurements are also discussed.

A Tutorial on Target-Mediated Drug Disposition (TMDD) Models

Target-mediated drug disposition (TMDD) is the phenomenon in which a drug binds with high affinity to its pharmacological target site (such as a receptor) to such an extent that this affects its pharmacokinetic characteristics.1 The aim of this Tutorial is to provide an introductory guide to the mathematical aspects of TMDD models for pharmaceutical researchers. Examples of Berkeley Madonna2 code for some models discussed in this Tutorial are provided in the Supplementary Materials.

Improved efficacy of soluble human receptor activator of nuclear factor kappa B (RANK) fusion protein by site-directed mutagenesis

Soluble human receptor activator of nuclear factor kappa B fusion immunoglobulin (hRANK-Ig) has been considered as one of the therapeutic agents to treat osteoporosis or diseases associated with bone destruction by blocking the interaction between RANK and the receptor activator of nuclear factor kappa B ligand (RANKL). However, no scientific record showing critical amino acid residues within the structural interface between the human RANKL and RANK complex is yet available. In this study, we produced several mutants of hRANK-Ig by replacement of amino acid residue(s) and tested whether the mutants had increased binding affinity to human RANKL. Based on the results from flow cytometry and surface plasmon resonance analyses, the replacement of E(125) with D(125), or E(125) and C(127) with D(125) and F(127) within loop 3 of cysteine-rich domain 3 of hRANK-Ig increases binding affinity to human RANKL over the wild-type hRANK-Ig. This result may provide the first example of improvement in the efficacy of hRANK-Ig by protein engineering and may give additional information to understand a more defined structural interface between hRANK and RANKL.

Application of human FcRn transgenic mice as a pharmacokinetic screening tool of monoclonal antibody

1. For drug discovery, useful screening tools are essential to select superior candidates. Here, we evaluated the applicability of transgenic mice expressing human neonatal Fc receptor (FcRn) (hFcRn Tgm) as a pharmacokinetic screening tool of therapeutic monoclonal antibodies (mAbs) and Fc-fusion proteins that overcomes the species difference in FcRn binding. 2. Marketed 11 mAbs and 2 Fc-fusion proteins were intravenously administered to hFcRn Tgm and WT mice. The half-lives in hFcRn Tgm and WT mice were compared with those in human obtained from literature. The linear half-lives in human and monkey were also calculated by nonlinear pharmacokinetic analysis. For comparison, correlations of half-lives between monkey and human were also evaluated. 3. The half-lives of mAbs and Fc-fusion proteins after intravenous administration ranged from 1.1 to 13.2 days in hFcRn Tgm and from 1.2 to 30.3 days in WT mice. The half-lives in human correlated more closely with those in hFcRn Tgm than in WT mice and monkey. 4. Our results suggest that hFcRn Tgm are a valuable and useful tool for pharmacokinetic screening of mAbs and Fc-fusion proteins in the preclinical stage. Furthermore, we believe that hFcRn Tgm are broadly applicable to preclinical pharmacokinetic screening of mAbs-based therapeutics.

Mathematical modeling of postmenopausal osteoporosis and its treatment by the anti-catabolic drug denosumab

Denosumab, a fully human monoclonal antibody, has been approved for the treatment of postmenopausal osteoporosis. The therapeutic effect of denosumab rests on its ability to inhibit osteoclast differentiation. Here, we present a computational approach on the basis of coupling a pharmacokinetics model of denosumab with a pharmacodynamics model for quantifying the effect of denosumab on bone remodeling. The pharmacodynamics model comprises an integrated systems biology-continuum micromechanics approach, including a bone cell population model, considering the governing biochemical factors of bone remodeling (including the action of denosumab), and a multiscale micromechanics-based bone mechanics model, for implementing the mechanobiology of bone remodeling in our model. Numerical studies of postmenopausal osteoporosis show that denosumab suppresses osteoclast differentiation, thus strongly curtailing bone resorption. Simulation results also suggest that denosumab may trigger a short-term bone volume gain, which is, however, followed by constant or decreasing bone volume. This evolution is accompanied by a dramatic decrease of the bone turnover rate by more than one order of magnitude. The latter proposes dominant occurrence of secondary mineralization (which is not anymore impeded through cellular activity), leading to higher mineral concentration per bone volume. This explains the overall higher bone mineral density observed in denosumab-related clinical studies.

Mechanistic pharmacokinetic/target engagement/pharmacodynamic (PK/TE/PD) modeling in deciphering interplay between a monoclonal antibody and its soluble target in cynomolgus monkeys

For therapeutic monoclonal antibodies (mAbs) against soluble ligands, the free ligand level can, theoretically, be used as a surrogate for efficacy. However, it can be extremely challenging technically to measure free ligand level in the presence of an excessive amount of antibody-ligand complex. The interplay among such mAbs, ligands, and the downstream pharmacodynamic (PD) effects has not been well defined. Using siltuximab and interleukin-6 (IL-6) as model compounds, a pharmacokinetic (PK)/target engagement (TE) model was established via simultaneous fitting of total siltuximab, total IL-6, and free IL-6 concentration profiles following a low dose of siltuximab in cynomolgus monkeys. The model adequately captured the observed data and provided estimation of model parameters with good precision. The PK/TE model was used to predict free IL-6 profiles at higher siltuximab doses, where the accurate determination of free IL-6 concentration became technically too difficult. The measured free IL-6 levels from the low-dose groups and PK/TE model-predicted free IL-6 levels from the high-dose groups were used to drive an indirect response TE/PD model to describe the concentration-effect relationship between free IL-6 and C-reactive protein (CRP). The TE/PD model adequately captured both CRP elevation and CRP suppression in response to free IL-6 concentration change from baseline with a linear stimulation function, providing direct evidence that the PK/TE model-predicted free IL-6 levels from the high-dose groups were accurate. Overall, the results provided an integrated PK/TE/PD modeling and bioanalytical framework for prediction of efficacious dose levels and duration of action for mAbs against soluble ligands with rapid turnover.

Pharmacokinetics, pharmacodynamics and physiologically-based pharmacokinetic modelling of monoclonal antibodies

Development of monoclonal antibodies (mAbs) and their functional derivatives represents a growing segment of the development pipeline in the pharmaceutical industry. More than 25 mAbs and derivatives have been approved for a variety of therapeutic applications. In addition, around 500 mAbs and derivatives are currently in different stages of development. mAbs are considered to be large molecule therapeutics (in general, they are 2-3 orders of magnitude larger than small chemical molecule therapeutics), but they are not just big chemicals. These compounds demonstrate much more complex pharmacokinetic and pharmacodynamic behaviour than small molecules. Because of their large size and relatively poor membrane permeability and instability in the conditions of the gastrointestinal tract, parenteral administration is the most usual route of administration. The rate and extent of mAb distribution is very slow and depends on extravasation in tissue, distribution within the particular tissue, and degradation. Elimination primarily happens via catabolism to peptides and amino acids. Although not definitive, work has been published to define the human tissues mainly involved in the elimination of mAbs, and it seems that many cells throughout the body are involved. mAbs can be targeted against many soluble or membrane-bound targets, thus these compounds may act by a variety of mechanisms to achieve their pharmacological effect. mAbs targeting soluble antigen generally exhibit linear elimination, whereas those targeting membrane-bound antigen often exhibit non-linear elimination, mainly due to target-mediated drug disposition (TMDD). The high-affinity interaction of mAbs and their derivatives with the pharmacological target can often result in non-linear pharmacokinetics. Because of species differences (particularly due to differences in target affinity and abundance) in the pharmacokinetics and pharmacodynamics of mAbs, pharmacokinetic/pharmacodynamic modelling of mAbs has been used routinely to expedite the development of mAbs and their derivatives and has been utilized to help in the selection of appropriate dose regimens. Although modelling approaches have helped to explain variability in both pharmacokinetic and pharmacodynamic properties of these drugs, there is a clear need for more complex models to improve understanding of pharmacokinetic processes and pharmacodynamic interactions of mAbs with the immune system. There are different approaches applied to physiologically based pharmacokinetic (PBPK) modelling of mAbs and important differences between the models developed. Some key additional features that need to be accounted for in PBPK models of mAbs are neonatal Fc receptor (FcRn; an important salvage mechanism for antibodies) binding, TMDD and lymph flow. Several models have been described incorporating some or all of these features and the use of PBPK models are expected to expand over the next few years.

Merging systems biology with pharmacodynamics

The emerging discipline of systems pharmacology aims to combine analysis and computational modeling of cellular regulatory networks with quantitative pharmacology approaches to drive the drug discovery processes, predict rare adverse events, and catalyze the practice of personalized precision medicine. Here, we introduce the concept of enhanced pharmacodynamic (ePD) models, which synergistically combine the desirable features of systems biology and current PD models within the framework of ordinary or partial differential equations. ePD models that analyze regulatory networks involved in drug action can account for a drug's multiple targets and for the effects of genomic, epigenomic, and posttranslational changes on the drug efficacy. This new knowledge can drive drug discovery and shape precision medicine.

In silico investigations of the anti-catabolic effects of pamidronate and denosumab on multiple myeloma-induced bone disease

It is unclear whether the new anti-catabolic agent denosumab represents a viable alternative to the widely used anti-catabolic agent pamidronate in the treatment of Multiple Myeloma (MM)-induced bone disease. This lack of clarity primarily stems from the lack of sufficient clinical investigations, which are costly and time consuming. However, in silico investigations require less time and expense, suggesting that they may be a useful complement to traditional clinical investigations. In this paper, we aim to (i) develop integrated computational models that are suitable for investigating the effects of pamidronate and denosumab on MM-induced bone disease and (ii) evaluate the responses to pamidronate and denosumab treatments using these integrated models. To achieve these goals, pharmacokinetic models of pamidronate and denosumab are first developed and then calibrated and validated using different clinical datasets. Next, the integrated computational models are developed by incorporating the simulated transient concentrations of pamidronate and denosumab and simulations of their actions on the MM-bone compartment into the previously proposed MM-bone model. These integrated models are further calibrated and validated by different clinical datasets so that they are suitable to be applied to investigate the responses to the pamidronate and denosumab treatments. Finally, these responses are evaluated by quantifying the bone volume, bone turnover, and MM-cell density. This evaluation identifies four denosumab regimes that potentially produce an overall improved bone-related response compared with the recommended pamidronate regime. This in silico investigation supports the idea that denosumab represents an appropriate alternative to pamidronate in the treatment of MM-induced bone disease.

Population pharmacokinetic meta-analysis of denosumab in healthy subjects and postmenopausal women with osteopenia or osteoporosis

BACKGROUND AND OBJECTIVE

Inhibition of the receptor activator of nuclear factor κ-B ligand (RANKL) is a therapeutic target for treatment of bone disorders associated with increased bone resorption, such as osteoporosis. The objective of this analysis was to characterize the population pharmacokinetics of denosumab (AMG 162; Prolia®), a fully human IgG2 monoclonal antibody that binds to RANKL, in healthy subjects and postmenopausal women with osteopenia or osteoporosis.

METHODS

A total of 22944 serum free denosumab concentrations from 495 healthy subjects and 1069 postmenopausal women with osteopenia or osteoporosis were pooled. Denosumab was administered as either a single intravenous dose (n = 36), a single subcutaneous dose (n = 469) or multiple subcutaneous doses (n = 1059), ranging from 0.01 to 3 mg/kg (or 6-210 mg as fixed mass dosages), every 3 or 6 months for up to 48 months. An open, two-compartment pharmacokinetic model with a quasi-steady-state approximation of the target-mediated drug disposition model was used to describe denosumab pharmacokinetics, using NONMEM Version 7.1.0 software. Subcutaneous absorption was characterized by the first-order absorption rate constant (k(a)), with constant absolute bioavailability over the range of doses that were evaluated. Clearance and volume of distribution parameters were scaled by body weight, using a power model. Model evaluation was performed through visual predictive checks.

RESULTS

The subcutaneous bioavailability of denosumab was 64%, and the k(a) was 0.00883 h-1. The central volume of distribution and linear clearance were 2.49 L/66 kg and 3.06 mL/h/66 kg, respectively. The baseline RANKL level, quasi-steady-state constant and RANKL degradation rate were 614 ng/mL, 138 ng/mL and 0.00148 h-1, respectively. Between-subject variability in model parameters was moderate. A fixed dose of 60 mg provided RANKL inhibition similar to that achieved by equivalent body weight-based dosing. The effects of age and race on the area under the serum concentration-time curve of denosumab were less than 15% over the range of covariate values that were evaluated.

CONCLUSIONS

The non-linearity in denosumab pharmacokinetics is probably due to RANKL binding, and denosumab dose adjustment based on the patient demographics is not warranted.

Monoclonal antibodies: what are the pharmacokinetic and pharmacodynamic considerations for drug development?

INTRODUCTION

The number of monoclonal antibodies available for clinical use and under development has dramatically increased in the last 10 years. Understanding their pharmacokinetics and pharmacodynamics is essential for selecting the right clinical candidate, correct dose and regimen for a target indication.

AREAS COVERED

This article reviews the existing literature and knowledge of monoclonal antibodies. Specifically, the authors discuss monoclonal antibodies with respect to their pharmacokinetics (including absorption, distribution and elimination) and their pharmacodynamics. The authors also look at the pharmacokinetic/pharmacodynamic relationship, scaling from preclinical to clinical studies and selection of the first-in-human dose.

EXPERT OPINION

Monoclonal antibodies have complex pharmacokinetic and pharmacodynamic characteristics that are dependent on several factors. Therefore, it is important to improve our understanding of the pharmacokinetics and pharmacodynamics of monoclonal antibodies from a basic research standpoint. It is also equally important to apply mechanistic pharmacokinetic/pharmacodynamic models to interpret the experimental results and facilitate efforts to predict the safety and efficacy of monoclonal antibodies.

Pharmacokinetic/pharmacodynamic modeling in inflammation

Inflammation is an array of immune responses to infection and injury. It results from a complex immune cascade and is the basis of many chronic diseases such as arthritis, diabetes, and cancer. Numerous mathematical models have been developed to describe the disease progression and effects of anti-inflammatory drugs. This review illustrates the state of the art in modeling the effects of diverse drugs for treating inflammation, describes relevant biomarkers amenable to modeling, and summarizes major advantages and limitations of the published pharmacokinetic/ pharmacodynamic (PK/PD) models. Simple direct inhibitory models are often used to describe in vitro effects of anti-inflammatory drugs. Indirect response models are more mechanism based and have been widely applied to the turnover of symptoms and biomarkers. These, along with target-mediated and transduction models, have been successfully applied to capture the PK/PD of many anti-inflammatory drugs and describe disease progression of inflammation. Biologics have offered opportunities to address specific mechanisms of action, and evolve small systems models to quantitatively capture the underlying physiological processes. More advanced mechanistic models should allow evaluation of the roles of some key mediators in disease progression, assess drug interactions, and better translate drug properties from in vitro and animal data to patients.

Population pharmacokinetic meta-analysis of denosumab in healthy subjects and postmenopausal women with osteopenia or osteoporosis

BACKGROUND AND OBJECTIVE

Inhibition of the receptor activator of nuclear factor κ-B ligand (RANKL) is a therapeutic target for treatment of bone disorders associated with increased bone resorption, such as osteoporosis. The objective of this analysis was to characterize the population pharmacokinetics of denosumab (AMG 162; Prolia®), a fully human IgG2 monoclonal antibody that binds to RANKL, in healthy subjects and postmenopausal women with osteopenia or osteoporosis.

METHODS

A total of 22944 serum free denosumab concentrations from 495 healthy subjects and 1069 postmenopausal women with osteopenia or osteoporosis were pooled. Denosumab was administered as either a single intravenous dose (n = 36), a single subcutaneous dose (n = 469) or multiple subcutaneous doses (n = 1059), ranging from 0.01 to 3 mg/kg (or 6-210 mg as fixed mass dosages), every 3 or 6 months for up to 48 months. An open, two-compartment pharmacokinetic model with a quasi-steady-state approximation of the target-mediated drug disposition model was used to describe denosumab pharmacokinetics, using NONMEM Version 7.1.0 software. Subcutaneous absorption was characterized by the first-order absorption rate constant (k(a)), with constant absolute bioavailability over the range of doses that were evaluated. Clearance and volume of distribution parameters were scaled by body weight, using a power model. Model evaluation was performed through visual predictive checks.

RESULTS

The subcutaneous bioavailability of denosumab was 64%, and the k(a) was 0.00883 h-1. The central volume of distribution and linear clearance were 2.49 L/66 kg and 3.06 mL/h/66 kg, respectively. The baseline RANKL level, quasi-steady-state constant and RANKL degradation rate were 614 ng/mL, 138 ng/mL and 0.00148 h-1, respectively. Between-subject variability in model parameters was moderate. A fixed dose of 60 mg provided RANKL inhibition similar to that achieved by equivalent body weight-based dosing. The effects of age and race on the area under the serum concentration-time curve of denosumab were less than 15% over the range of covariate values that were evaluated.

CONCLUSIONS

The non-linearity in denosumab pharmacokinetics is probably due to RANKL binding, and denosumab dose adjustment based on the patient demographics is not warranted.

Theoretical considerations of target-mediated drug disposition models: simplifications and approximations

PURPOSE

To clarify relationships among various types of target-mediated disposition (TMD) models including the Michaelis-Menten, quasi-steady-state (Qss), and rapid binding models and propose measures for the closeness of some models as approximations to the general TMD model (Mager and Jusko, J Pharmacokinet Pharmacodyn 28(6):507-532, 2001).

METHODS

Based on the classic singular perturbation theory by selecting appropriate scales of time, we derive requirements with which the Michaelis-Menten and Qss models are suitable approximations. Under the Qss assumption we show that other simplifications of the general TMD model can be similarly obtained as the Michaelis-Menten and Qss models. We compare these models by simulations using known application examples.

RESULTS

The Michaelis-Menten and Qss models are direct simplifications of the general TMD model and, moreover, suitable approximations if certain specific requirements on the parameters are met.

CONCLUSIONS

As a first attempt to quantify the closeness of some simplifications to the general TMD model, our work should provide a more rigorous basis for the theoretical and practical research of TMD models, which are important for investigating the pharmacokinetic-pharmacodynamic relationships of many biological compounds.

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.

Performance and robustness of the Monte Carlo importance sampling algorithm using parallelized S-ADAPT for basic and complex mechanistic models

The Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm can approximate the true log-likelihood as precisely as needed and is efficiently parallelizable. Our objectives were to evaluate an importance sampling version of the MC-PEM algorithm for mechanistic models and to qualify the default estimation settings in SADAPT-TRAN. We assessed bias, imprecision and robustness of this algorithm in S-ADAPT for mechanistic models with up to 45 simultaneously estimated structural parameters, 14 differential equations, and 10 dependent variables (one drug concentration and nine pharmacodynamic effects). Simpler models comprising 15 parameters were estimated using three of the ten dependent variables. We set initial estimates to 0.1 or 10 times the true value and evaluated 30 bootstrap replicates with frequent or sparse sampling. Datasets comprised three dose levels with 16 subjects each. For simultaneous estimation of the full model, the ratio of estimated to true values for structural model parameters (median [5-95% percentile] over 45 parameters) was 1.01 [0.94-1.13] for means and 0.99 [0.68-1.39] for between-subject variances for frequent sampling and 1.02 [0.81-1.47] for means and 1.02 [0.47-2.56] for variances for sparse sampling. Imprecision was ≤25% for 43 of 45 means for frequent sampling. Bias and imprecision was well comparable for the full and simpler models. Parallelized estimation was 23-fold (6.9-fold) faster using 48 threads (eight threads) relative to one thread. The MC-PEM algorithm was robust and provided unbiased and adequately precise means and variances during simultaneous estimation of complex, mechanistic models in a 45 dimensional parameter space with rich or sparse data using poor initial estimates.

Development of a new pre- and post-processing tool (SADAPT-TRAN) for nonlinear mixed-effects modeling in S-ADAPT

Mechanistic modeling greatly benefits from automated pre- and post-processing of model code and modeling results. While S-ADAPT provides many state-of-the-art parametric population estimation methods, its pre- and post-processing capabilities are limited. Our objective was to develop a fully automated, open-source pre- and post-processor for nonlinear mixed-effects modeling in S-ADAPT. We developed a new translator tool (SADAPT-TRAN) based on Perl scripts. These scripts (a) automatically translate the core model components into robust Fortran code, (b) perform extensive mutual error checks across all input files and the raw dataset, (c) extend the options of the Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm, and (d) improve the numerical robustness of the model code. The post-processing scripts automatically summarize the results of one or multiple models as tables and, by generating problem specific R scripts, provide an extended series of standard and covariate-stratified diagnostic plots. The SADAPT-TRAN package substantially improved the efficiency to specify, debug, and evaluate models and enhanced the flexibility of using the MC-PEM algorithm for parallelized estimation in S-ADAPT. The parameter variability model can take any combination of normally, log-normally, or logistically distributed parameters and the SADAPT-TRAN package can automatically generate the Fortran code required to specify between occasion variability. Extended estimation features are available to avoid local minima, estimate means with negligible variances, and estimate variances for fixed means. The SADAPT-TRAN package significantly facilitated model development in S-ADAPT, reduced model specification errors, and provided useful error messages for beginner and advanced users. This benefit was greatest for complex mechanistic models.

Biotherapeutic bioanalysis: a multi-indication case study review

A thorough understanding of the structure and biology of a biotherapeutic is crucial to defining a suitable strategy for pharmacokinetic characterization in proof-of-concept disease models, toxicology species as well as the healthy and disease indication patient populations. This manuscript summarizes parameters that impact bioanalytical strategy for over 50 biotherapeutics indicated for the treatment of oncology, rheumatoid arthritis, allergy, multiple sclerosis, hematology, metabolism and infectious disease. We have addressed numerous therapeutic modalities including chimeric, humanized and fully human monoclonal antibodies, replacement proteins, peptides and fusion proteins, including polyethylene glycol and Fc fusions, as well as antibody–drug conjugates. With the rapid evolution of biotherapeutics over the last 20 years and the contraction of the pharmaceutical and biotechnology labor force, efficient workflow management becomes a crucial bioanalytical component. Thus, we have also addressed new technologies that have demonstrated either increased throughput or enhanced characterization, including Meso Scale Discovery, Gyrolab and affinity MS.

Population pharmacokinetics of therapeutic monoclonal antibodies

A growing number of population pharmacokinetic analyses of therapeutic monoclonal antibodies (mAbs) have been published in the scientific literature. The aims of this article are to summarize the findings from these studies and to relate the findings to the general pharmacokinetic and structural characteristics of therapeutic mAbs. A two-compartment model was used in the majority of the population analyses to describe the disposition of the mAb. Population estimates of the volumes of distribution in the central (V(1)) and peripheral (V(2)) compartments were typically small, with median (range) values of 3.1 (2.4-5.5) L and 2.8 (1.3-6.8) L, respectively. The estimated between-subject variability in the V(1) was usually moderate, with a median (range) coefficient of variation (CV) of 26% (12-84%). Between-subject variability in other distribution-related parameters such as the V(2) and intercompartmental clearance were often not estimated. Although the pharmacokinetic models used most frequently in the population analyses were models with linear clearance, other models with nonlinear, or parallel linear and nonlinear clearance pathways were also applied, as many therapeutic mAbs are eliminated via saturable target-mediated mechanisms. Population estimates of the maximum elimination rate (V(max)) and the mAb concentration at which elimination was at half maximum for Michaelis-Menten-type elimination pathways varied considerably among the different therapeutic mAbs. However, estimates of the total clearance (CL) of mAbs with linear clearance characteristics and of the clearance of mAbs via the linear clearance pathway (CL(L)) with parallel linear and nonlinear clearance were quite similar for the different mAbs and typically ranged from 0.2 to 0.5 L/day, which is relatively close to the estimated clearance of endogenous IgG of 0.21 L/day. The between-subject variability in the V(max), CL and CL(L) was moderate to high, with estimated CVs ranging from 15% to 65%. Measures of body size were the covariates most commonly identified as influencing the pharmacokinetics of therapeutic mAbs. In summary, many features of the population pharmacokinetics of currently used therapeutic mAbs are similar, despite differences in their pharmacological targets and studied patient populations.

Properties of a general PK/PD model of antibody-ligand interactions for therapeutic antibodies that bind to soluble endogenous targets

Antibodies that target endogenous soluble ligands are an important class of biotherapeutic agents. While much focus has been placed on characterization of antibody pharmacokinetics, less emphasis has been given to characterization of antibody effects on their soluble targets. We describe here the properties of a generalized mechanism-based PK/PD model used to characterize the in vivo interaction of an antibody and an endogenous soluble ligand. The assumptions and properties of the model are explored, and situations are described when deviations from the basic assumptions may be necessary. This model is most useful for in vivo situations where both antibody and ligand levels are available following drug administration. For a given antibody exposure, the extent and duration of suppression of free ligand is impacted by the apparent affinity of the interaction, as well as by the rate of ligand turnover. The applicability of the general equilibrium model of in vivo antibody-ligand interaction is demonstrated with an anti-Aß antibody.

Pharmacokinetics of anti-hepcidin monoclonal antibody Ab 12B9m and hepcidin in cynomolgus monkeys

Hepcidin is a key regulator responsible for systemic iron homeostasis. A semi-mechanistic PK model for hepcidin and a fully human anti-hepcidin monoclonal antibody (Ab 12B9m) was developed to describe their total (free + bound) serum concentration-time data after single and multiple weekly intravenous or subcutaneous doses of Ab 12B9m. The model was based on target mediated drug disposition and the IgG-FcRn interaction concepts published previously. Both total Ab 12B9m and total hepcidin exhibited nonlinear kinetics due to saturable Fc-FcRn interaction. Ab 12B9m showed a limited volume of distribution and negligible linear elimination from serum. The nonlinear elimination of Ab 12B9m was attributed to the endosomal degradation of Ab 12B9m that was not bound to the FcRn receptor. The terminal half-life, assumed to be the same for free and total serum Ab 12B9m, was estimated to be 16.5 days. The subcutaneous absorption of Ab 12B9m was described with a first-order absorption rate constant k(a) of 0.0278 h⁻¹, with 86% bioavailability. The model suggested a rapid hepcidin clearance of approximately 800 mL h⁻¹ kg⁻¹. Only the highest-tested Ab 12B9m dose of 300 mg kg⁻¹ week⁻¹ was able to maintain free hepcidin level below the baseline during the dosing intervals. Free Ab 12B9m and free hepcidin concentrations were simulated, and their PK profiles were nonlinear as affected by their binding to each other. Additionally, the total amount of FcRn receptor involved in Ab 12B9m recycling at a given time was calculated empirically, and the temporal changes in the free FcRn levels upon Ab 12B9m administration were inferred.