Elsevier

Bone

Volume 125, August 2019, Pages 87-95
Bone

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

https://doi.org/10.1016/j.bone.2019.04.022Get rights and content

Highlights

  • Mineralization is an essential mechanism for bone density gain (BDG) after treatment with denosumab.

  • Mineralization rate strongly affects the changes in BDG over time. High values lead to earlier saturation.

  • The slope of BDG vs. time curves is increased with turnover rate.

  • The drug accessibility factor is essential in controlling how denosumab is distributed from the serum to the bone tissue compartment.

  • The effect of denosumab on BDG is site specific, being more effective in the lumbar spine than in the hip.

Abstract

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.

Introduction

Osteoporosis is a major skeletal disease linked to an imbalance in bone remodeling, with bone resorption exceeding bone formation [1]. This results in continuous bone loss and deterioration of the bone microarchitecture, which ultimately leads to impaired bone strength and increased risk of bone fracture [2], [3]. Postmenopausal osteoporosis (PMO) has been linked to a decrease in estrogen production in mid-age women. The rate of bone loss is relatively high in the first year following menopause and then follows a linear pattern of approximately 1% bone loss per year [4], [5]. Fractures related to osteoporosis are a major global health concern. With the increasing elderly population in first world countries, the risk of fracture is estimated to significantly increase over the next few years. In order to counteract this trend, a number of so-called anti-resorptive therapies have been developed including bisphosphonates and denosumab [6]. These therapies decrease osteoclastic bone resorption and have been shown to decrease the risk of osteoporotic fractures in PMO [2]).

Denosumab is one of the most commonly prescribed anti-resorptive drugs for the treatment of PMO [2]. The therapeutic effect of denosumab is based on its ability to inhibit osteoclast formation and activity. The FREEDOM study indicates that after 3 years of denosumab treatment the incidence of new morphometric vertebral fractures decreased from 7.2% with placebo to 2.3% with denosumab (68% relative reduction) [2]. Short-term treatment (i.e. Phase 2 study) of PMO with denosumab has been shown to reduce relative risk of hip fractures by 40% and non-vertebral fractures by 20%. These clinical results clearly indicate high efficacy of denosumab for treatment of PMO. The therapeutic effects of denosumab can be monitored by looking at a variety of bone biomarkers including non-specific (i.e., blood or urine based) markers such as NTx, uTX, PICP/PINP and specific biomarkers, i.e. measured at a particular bone site such as bone mineral density (BMD) [4]. BMD is most commonly assessed at the femoral neck, wrist and vertebrae and it has been shown that denosumab has different effects on BMD depending on the bone site [4]. Largest increases in BMD are observed at bone sites exhibiting high bone turnover rate, while more moderate increases are observed at sites of lower turnover rate [3].

These experimental findings can be explained based on the conceptual model of bone mineralization, which links the rate of bone remodeling with the degree of bone tissue mineralization (BTM) [7], [8]. Bone mineralization is characterized by a fast primary phase, which takes place over several days to weeks and achieves a degree of mineralization of approximately 70%, followed by a slow secondary phase, which can take from months to years and may achieve degrees of mineralization of up to 95%. This conceptual model states that bone sites undergoing high turnover are characterized by a lower BTM (and BMD) based on the fact that continuous remodeling prevents excessive secondary mineralization to occur. On the contrary, at sites of low turnover there is sufficient time for secondary mineralization to occur. Consequently, based on the fact that denosumab significantly reduces bone turnover due to inhibition of osteoclast activity, the treatment effects are more pronounced at bone sites exhibiting higher bone turnover [8].

The time dependent dose-effect response of drugs is most commonly described using pharmacokinetics (PK) − pharmacodynamics (PD) modeling approaches [9]. Among these, mechanistic PK−PD models allow taking into account organ-specific signaling pathways and regulatory mechanisms [4]. A variety of different mechanistic PK−PD models describing the bone remodeling process have been developed [[10], [11], [12]]. The majority of these models are based on the fundamental models of bone cell interactions in bone remodeling proposed by Lemaire et al. [13] and Pivonka et al. [14]. These models incorporate the RANK-RANKL-OPG signaling pathway together with action of TGF− β on bone cells. Particularly, the models of Pivonka et al. also provide a mechanistic description of changes in bone porosity and bone volume faction (BV/TV) which are linked to bone cell numbers [14], [15], [12]. These bone cell population models provide a mechanistic means on how to link the action of denosumab to the bone remodeling process based on competitive binding reactions between OPG, denosumab and RANKL. Several authors have utilized this approach in different ways [10], [11], [16], [12]. However, none of these models included a mechanistic description of the mineralization process.

In the present paper, we present a comprehensive mechanistic PK−PD model for quantifying the effect of denosumab on bone turnover and BMD taking into account the mineralization process. This model is an extension of a previously developed model of bone remodeling taking into account the process of bone mineralization. The bone remodeling model accounts for bone cell interactions via the RANK-RANKL-OPG pathway, the action of TGF− β and mechanobiological feedback [14], [15], [12]. The PK model of denosumab is a one-compartment model including a drug saturation term for high doses and has been previously described by Marathe et al. 2011 [11]. The mineralization model is based on the work of Martí-Reina and co-workers [17] and takes into account the balance of mineral within bone tissue: input, due to the mineralization process, distinguishing the primary and secondary phases; removal, due to bone resorption, that takes mineral back into the blood serum.

Utilizing this model, we investigate some model features in a drug treatment scenario whose clinical results were available in the literature [18]. This includes the following parametric studies: taking or not taking into account the bone mineralization process and its effect on BMD; different drug distribution factors accounting for ease of accessibility of denosumab from the central compartment to the bone tissue compartment; and different bone sites undergoing high and low turnover. Based on the proposed mechanistic PK−PD model we are showing temporal evolution of bone biomarkers for these cases including bone porosity, BMD and the degree of mineralization.

This paper is organized as follows: In Section 2 we provide a detailed description of the mechanistic PK−PD model. The comparison of simulation results and experimentally observed changes in BMD are reported in Section 3, together with parametric studies of essential model parameters. The results are discussed in detail with respect to the clinical bone biology literature in Section 4.

Section snippets

One compartment PK model of denosumab

Several pharmacokinetic (PK) models of denosumab have been proposed including one- and two-compartment models [19]. We here follow the approach suggested by Marathe et al. and use a one-compartment model with Michaelis-Menten kinetics in order to characterize the serum denosumab PK profiles. A first-order rate process (ka) governs the absorption of drug (Doseden) from the subcutaneous (SC) injection site into the central compartment (CP,den, Vc). The drug elimination from the central

Results

We follow the approach described in detail in Lemaire et al. [13] and Pivonka et al. [14], [15] to simulate disease progression in PMO with subsequent denosumab treatment. The following biomarkers are investigated: bone cell numbers and BMD. While the former are representative for non-specific bone resorption and formation markers, the latter are bone specific and reflects the material properties.

PMO was simulated by introducing a disease-related increase in RANKL production over time [12]: P

Discussion

In this paper we presented a novel mechanistic PK-PD model describing the effect of the anti-catabolic drug denosumab on bone remodeling and the associated changes in bone mineral density. Unlike for anabolic drugs, where bone volume (and consequently bone mineral density) is gained due to bone formation by osteoblasts, for anti-catabolic drugs the existing bone matrix has the ability to embed more mineral in the extrafibrillar space, so increasing bone tissue density. The latter phenomenon of

Summary and conclusions

In this paper, a comprehensive mechanistic PK-PD model has been presented which allows simulating the effects of denosumab treatment on bone remodeling and bone mineral density (BMD) in postmenopausal osteoporosis. For this purpose, a PK model of denosumab has been coupled to a bone cell population model of bone remodeling taking into account the mineralization process. The latter accounts for the mineral balance in bone tissue and distinguishes between primary and secondary mineralization and

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    Departmento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla. Escuela Técnica Superior de Ingeniería. Camino de los Descrubrimientos s/n, 41092. Sevilla.

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