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

Bone 186 (2024) 117140 Available online 3 June 2024 8756-3282/© 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Review Article Advances in mechanobiological pharmacokinetic-pharmacodynamic models of osteoporosis treatment – Pathways to optimise and exploit existing therapies Peter Pivonka a , * , Jos´ e Luis Calvo-Gallego b , Stephan Schmidt c , Javier Martínez-Reina b a School of Mechanical, Medical and Process Engineering, Queensland University of Technology, QLD 4000, Australia b Departmento de Ingeniería Mec´ anica y Fabricaci´ on, Universidad de Sevilla, Seville 41092, Spain c Center for Pharmacometrics and Systems Pharmacology, Department of Pharmaceutics, College of Pharmacy, University of Florida, Orlando, FL 32827, USA ARTICLE INFO Keywords: Mechanobiological PK-PD models Osteoporosis Anti-catabolic drugs Anabolic drugs Sequential drug treatments Bone matrix mineralisation Microstructural damage Bone remodelling In-silico modelling ABSTRACT 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. 1. Introduction Osteoporosis (OP) is a chronic progressive bone disease which is characterised by reduction of bone matrix volume and changes in the bone matrix properties, i.e. bone quality, which leads to a reduction in whole (organ) bone strength and to bone fractures. The latter are most often low energy fractures such as vertebral compression fractures. The most common forms of OP are age-related and postmenopausal. The age-related decline in bone properties is due to an imbalance in the bone remodelling process, i.e. bone resorption exceeds bone formation. Age- and environmental related factors that contribute to the onset and progression of OP are vitamin D and calcium deficiency, decreased physical activity and hypogonadism [1–4]. Other forms of OP include secondary OP, which may be linked to adverse effects of drug therapies (e.g. glucocorticoids or proton pump inhibitors), endocrine disorders, eating disorders, immobilisation, marrow-related disorders, disorders of * Corresponding author. E-mail address: [email protected] (P. Pivonka). Contents lists available at ScienceDirect Bone journal homepage: www.elsevier.com/locate/bone https://doi.org/10.1016/j.bone.2024.117140 Received 20 March 2024; Received in revised form 17 May 2024; Accepted 29 May 2024 Bone 186 (2024) 117140 2 the gastrointestinal or biliary tract, renal disease and cancer [5]. The standard of care for OP patients includes general recommendations (e.g., adequate calcium and vitamin D intake, moderate exercise) and, based on the level of fracture risk, drug treatments are assigned. Different drug treatments can be distinguished according to the following characteristics: mechanisms of action; specific sites and modes of action; route of administration (oral, intravenous, nasal); dosage regimes; degrees of efficacy and effectiveness [6,7]. Current bone therapeutic guidelines use bone mineral density (BMD) and bone turnover markers (BTMs) as classification criteria for anabolic and anti-catabolic (previously also referred to as antiresorptive) drugs [8]. According to the terminology of Riggs and Parfitt, anti-catabolic drugs, e.g., bisphosphonates (alendronate, risedronate, ibandronate, zoledronic acid), denosumab and estrogen agonist/antagonists (raloxifene), act to reduce bone turnover (i.e., reduce bone remodelling) causing an increase in bone strength. These drugs are also associated with a moderately increase of bone mass resulting from the increased mineralisation of the existing bone matrix. On the other hand, anabolic drugs, e.g., intermittent PTH (teriparatide, abaloparatide) and sclerostin antibody (romosozumab), strongly increase bone mass by increasing bone remodelling (i.e., high bone turnover) and consequently bone strength. Interestingly, most agents decrease bone resorption (i.e., anti-catabolic treatment), some increase bone formation (i.e., anabolic treatment) and others have been reported to have a dual action [9]. Note that anabolic drugs are generally reserved for patients at high risk of fracture. While it is often argued that new treatments are needed to reduce the burden of OP and to overcome adverse effects of current therapies, another point of view is that there is already a large number of drugs available to treat OP and that the combined actions of these drugs have not been exploited in detail. Among negative therapeutic effects that have been reported are: (i) osteonecrosis of the jaw, a relatively rare event occurring in individuals on nitrogen-containing bisphosphonate treatment [10] or denosumab [11] 1 and (ii) increased fracture risk after denosumab drug withdrawal, due to increased osteoclastic resorption [12]. Because of these contraindications, the duration of treatment is usually limited in time, but if discontinuation can lead to a rebound in bone loss, what to do after that time needs to be carefully considered. Switching to other drugs and in general the combination of drugs has not been explored in much detail, nor has the use of other alternative or complementary therapies such as physical exercise, which is known to have an anabolic effect on bone. In-silico testing can be of great use to address the above questions and help paving the way for confirmatory clinical trials. As has been stated in Madrasi et al. [13], different types of quantitative models can be established at various levels of spatial and/or temporal complexity. These models may range from purely data driven (phenomenological) to fully mechanobiological models. Based on a particular research question, a suitable model needs to be chosen. In order to facilitate this choice, scientists are required to have a good understanding of bone disease, its progression and potential sources of between- and within-subject variability in the presence and absence of drug treatment, as well as their physiological plausibility. Developing the “right model” is, consequently, not a trivial task and frequently requires cross talk between disciplines and among scientists with different expertise. In the case of new drug candidates, it also requires the evaluation of the efficacy of the drug and safety profiles during different stages of pre-clinical and clinical development programs and the proper communication of the science and discovery community to the medical community and, ultimately, the patient. We also note that drug development requires a modelling continuum (rather than a modelling competition) as different stages of drug developments require different models that may be mutually informative [14]. This work has been made possible due to collaboration between a pharmacologist (SS), mechanical engineers (JMR, JLCG) and a biomedical engineer (PP). This review focuses on recent advances made in mechanobiological PK-PD modelling of OP and its treatments. We first review the original work of Lemaire et al. [15] which included major bone cell types and signalling pathways and paved the way for many subsequent mechanobiological model developments of bone diseases and their treatments. Another highlight of this review is the work of Pivonka and co-workers who extended the model of Lemaire et al. by including mechanistic aspects of bone remodelling. We will show how BMD, mineralisation and damage can be included in such a modelling framework. While the former approach is now commonly used by the pharmacology scientific community, the latter mechanobiological approach is heavily employed by the engineering research community. We will provide a variety of examples of how the different types of models have enhanced our current understanding of bone pathologies and their treatments. Finally, we provide a future outlook on the direction in which we envision this field would move and hopefully provide osteoporotic patients with the best possible treatment strategies to reduce their risk of fracture and improve their quality of life. 2. Bone physiology and pathology In this section we will briefly introduce bone physiology, by describing the main regulatory pathways that drive cellular responses; bone pathology with focus on OP, by describing how those pathways are altered by disease; and drug therapeutics, aiming at restoring or at least compensating those alterations, together with references for a more detailed review. As part of the musculoskeletal system, the main function of bones is to bear loads and support locomotion, though they also provide protection to organs and serve as reservoir of stem cells and calcium and phosphorus, in the homeostasis of which they are passively involved in. The load bearing function is responsible for the accumulation of microstructural damage that must be continuously removed in order to preserve bone integrity, i.e. stiffness and strength. For this reason, bone is undergoing continuous renewal and adaptation to its mechanical microenvironment. Renewal is carried out by osteoclasts, which resorb old and probably damaged tissue, and osteoblasts, which form new, and therefore, intact tissue. Adaptation can also be achieved by the activity of both types of cells. Thus, if the mechanical stimulus on the bone is intense, osteoblastic activity predominates over osteoclastic activity and bone volume increases. The opposite occurs when the mechanical stimulus is low. Renewal and/or adaptation can take place through two specific mechanisms termed as bone remodelling and bone modelling. The former is characterised by bone resorption and bone formation taking place asynchronously but in a coordinated manner at the same bone site, throughout the skeleton and throughout life. Bone remodelling is responsible for the internal renewal of bone and, less frequently, for its adaptation through changes in bone porosity, which is most commonly a reduction due to senescence or pathology. On the other hand, the process of bone modelling is characterised by resorption and formation occurring at the same time, but at spatial distinct bone sites; not necessarily coordinated but independent. Bone modelling is mainly responsible for adaptation and mostly occurs at childhood or senescence, being respectively linked to skeletal growth and recession, thus shaping or reshaping the different bones of the skeleton and their trabecular architecture. In recent years there has been a significant shift from a generic view of bone remodelling and modelling events to a consideration of the different bone envelopes in which these events take place. One can distinguish four bone compartments (see Fig. 1): (i) periosteal compartment (in cortical bone); (ii) intra-cortical compartment; (iii) endosteal or endocortical compartment and (iv) trabecular 1 The reference is based on a single patient and the authors are not sure that denosumab caused osteonecrosis of the jaw. P. Pivonka et al. Bone 186 (2024) 117140 3 compartment. These compartments are characterized by different microenvironments and mechanical loading conditions which may affect remodelling and modelling events in different ways. Notably, drugs and physiological exercise also affect these compartments in different ways. Periosteal surfaces undergo bone modelling leading either to expansion, in modelling-based bone formation, or to recession, in modelling-based bone resorption. Endosteal surfaces can undergo either modelling or remodelling. In the former case, resorption is responsible, for instance, for the medullary expansion seen at long bones and ribs with aging [16]. Modelling-based formation, both at the periosteum or endosteum, has been observed, for example, in the playing arm of tennis players [17] or following antiresorptive treatments [18]. During skeletal reshaping, processes such as radial growth or bone drift arise from the coordination of modelling-based resorption and formation in periosteal and endosteal surfaces. Internal bone compartments, i.e. trabecular and intracortical, are governed primarily by remodelling throughout life [19]. 2.1. Catabolic and anabolic bone regulation In Fig. 2 the bone remodelling process is schematically shown indicating the different cell types taken into account in mechanobiological PK-PD models together with catabolic and anabolic regulatory pathways. Also, bone remodelling coupling factors such as TGF-β are shown in this figure together with mechanobiological feedback of osteocytes. Below, we briefly describe these regulatory pathways and factors. RANK–RANKL–OPG is one of the most important signalling pathways controlling bone remodelling and explains how the osteoblast lineage regulates the differentiation and activity of osteoclasts [20,21]. It involves three major components: (i) receptor activator of nuclear factor κ B (RANK) is expressed on the surface of hematopoietic precursor cells; (ii) RANK ligand (RANKL), a polypeptide found on the surface of osteoblastic cells and in soluble form after proteolytic cleavage; (iii) osteoprotegrin (OPG), a “decoy receptor” molecule released by osteoblastic cells [22]. Differentiation and activation of osteoclast precursor cells into mature (active) osteoclasts requires the binding of RANKL to RANK, which can be inhibited by OPG as it also binds to RANKL. Thus, OPG prevents the differentiation of resorbing osteoclasts and acts as an anti-catabolic factor. Increased production of RANKL following the estrogen decay observed during menopause and thereafter has been identified as one of possible factors leading to post-menopausal osteoporosis (PMO) [23]. It is important to note that drugs targeting the RANK–RANKL–OPG pathway, such as denosumab, mainly aim at suppressing bone resorption, but they also end up suppressing bone formation, due to the coupling between both processes. The Wnt/β-catenin, or canonical Wnt pathway, comprises a family of proteins that play critical roles in embryonic development and adult tissue regeneration. In the absence of Wnt, the transmembrane receptors Frizzled and lipoprotein receptor-related protein 5 or 6 (LRP5/6) are separated, on the plasma membrane. In this scenario, a “destruction complex” comprising different proteins activate β-catenin degradation in the cytoplasm. When Wnts are present, they bind the receptors of Frizzled and LRP5/6 together and the “destruction complex” is recruited to the cell membrane and loses its ability to degrade β-catenin [24]. Thus, β-catenin translocates to the nucleus where it interacts with the Tcf/Lef family of transcription factors to regulate the expression of a number of genes important to the differentiation, proliferation, apoptosis and functionality of bone cells [25] with a more likely incidence on the osteoblastic lineage. In this regard, some authors have demonstrated that the Wnt/β-catenin pathway is essential for determining whether mesenchymal precursor cells differentiate into osteoblasts or chondrocytes [26] or that Wnt10b initiates the differentiation of mesenchymal stem cells along an osteoblast lineage rather than an adipocyte lineage [27]. Several proteins, such as Dkk1 and sclerostin, can bind to LRP5/6 so inhibiting Wnt signal transduction and disrupting the anabolic function of the Wnt/β-catenin pathway. Sclerostin is a protein secreted by osteocytes in response to various signals including mechanical stimulus. This fact highlights two fundamental insights: that the anabolic pathway is largely controlled by mechanical stimulus and that osteocytes play a very important role here, as discussed next. Fig. 1. Different envelopes of cortical and trabecular bone where bone remodelling and modelling events occur. Oc a: active osteoclasts; Oba: active osteoblasts; grey region: bone matrix; orange region: osteoid; pink region: blood vessel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) P. Pivonka et al. Bone 186 (2024) 117140 4 2.2. Bone biomarkers As part of the cellular actions of bone cells during bone remodelling and modelling events, biochemicals are released into the bone microenvironment which then enter systemic body compartments, i.e. blood and urine. Fig. 2 shows different bone resorption and formation markers that are released during bone remodelling and modelling events. Note that a distinction is made between the so-called non-specific biomarkers and specific biomarkers. The former are measured in the blood or urine and reflect the response of the entire skeleton to disease, exercise or drug treatments, i.e. they are not bone site specific. These biomarkers are often referred to as bone turnover markers (BTMs). On the other hand, specific biomarkers are measuring bone site specific quantities such as areal bone mineral density (aBMD), ratio of bone volume to total volume (BV/TV) and/or trabecular microarchitecture indexes. In a clinical context we limit our discussion to BMD and BV/TV, which is typically measured using dual energy x-ray absorption (DEXA) and quantitative computed tomography (qCT). Mechanobiological coupling of different bone cell types is achieved through expression of a multitude of cytokines expressed by bone cells and other cells in the bone microenvironment. Apart from these local paracrine regulations of bone cells, endocrine regulators such as parathyroid hormone (PTH) and vitamin D allow for systemic regulations. We note that both PTH and vitamin D play a vital role in calcium and phosphate homeostasis. Below we summarise some of the main catabolic (i.e. bone resorbing) and anabolic (i.e. bone forming) regulators which will serve for our discussion on pharmacokineticpharmacodynamic (PK/PD) models of bone remodelling. 2.3. The role of osteocytes in bone remodelling Osteocytes have the capacity of sensing the mechanical stimulus through mechanisms that are not yet fully understood, but have been acknowledged by different authors [25,28]. Therefore, they would act as coordinators of skeletal responses to mechanical loading. For instance, the production of sclerostin by osteocytes is enhanced if these cells sense a low strain level, i.e. in disuse states [29]. Conversely, high mechanical stimulus is associated to low production of sclerostin by osteocytes and hence the Wnt/β-catenin pathway is not interfered, leading to the wellknown anabolic effect of mechanical loading and exercise. Osteocytes produce high levels of nitric oxide (NO) in response to mechanical loading both in vitro and in vivo [30] and, since NO decreases the RANKL/OPG ratio [31], their activity also affects the catabolic RANKL-RANK-OPG pathway. The above highlights the importance of osteocytes in the mechanical regulation of bone tissue, due to their performance in cases of disuse and normal load. But their activity is not limited to those cases, since they also play a paramount role in overload cases, which are usually associated to the appearance of microcracks in bone tissue. Verborgt et al. [32] probed that damage induces apoptosis very locally, in the ostecytes closest to the microcrack. Later, Kurata et al. [33] showed in cultured osteocyte-like cell line MLO-Y4 cells that the application of overphysiological stretching significantly increased the number of cells undergoing apoptosis and an overexpression of the tartrate-resistant acid Fig. 2. Schematic illustration of bone remodelling. a) Cell lineages together with catabolic and anabolic biomarkers produced by bone cells. b) Influence of RANKRANKL-OPG pathway and NO. c) Influence of TGF-β. d) Influence of Wnt-Scl-LRP5/6 pathway. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) P. Pivonka et al. Bone 186 (2024) 117140 5 phosphatase (TRACP) enzyme, an indicator of the presence of osteoclasts. Whether this was caused by RANKL remained unclear until Kennedy et al. [34] measured RANKL levels in vivo in an ulnar loading model, where they induced microdamage in mid-diaphyseal cortical bone. These authors identified apoptotic osteocytes at the damaged area, but these did not upregulate pro-osteoclastogenic markers. Instead, RANKL peaked at around 150 to 200 μ m from the damaged site, likely due to soluble RANKL circulating through the canalicular network from apoptotic cells to the nearest bone surface at which osteoclast precursors can be recruited, as Schaffler and Kennedy [35] noted. These are the generic “eat-me” signals that bone lining cells would express to attract osteoclasts in order to resorb the damaged tissue, as suggested by Martin [36] in the theory of targeted bone remodelling, a theory that could also explain the orientation of osteons in cortical bone [37]. 2.4. Drugs targeting OP In Section 3.3.1 we will discuss in more detail the cytokines affected by OP and how they are counteracted by medication, in the context of how to model the disease and treatment. In this section, we will focus on the mechanisms of action of the main drugs currently used in clinical practice. Based on the above described distinction between catabolic and anabolic regulatory pathways, the actions of therapeutic agents is distinguished based on how they interact with those pathways. Thus, anti-catabolic drugs target to switch off excessive bone resorption, whereas anabolic drugs aim at promoting bone formation. Indeed, things are even more complex because the administration protocol seem to play a role as well. For example, PTH shows catabolic effects when administered continuously, whereas it shows anabolic effects when administered intermittently. Among the anti-catabolic drug category the most commonly prescribed drugs are denosumab and bisphosphonates. Denosumab (AMG 162; Amgen Inc., Thousand Oaks, CA) is a human IgG2 monoclonal antibody that binds to RANKL with high affinity and specificity thus inhibiting RANK-RANKL binding [38], similar to the action of OPG. Bisphosphonates constitute a group of drugs with a very high affinity for bone mineral to which they bind [39] and a mechanism of action consisting in the inhibition of osteoclastic activity through cytoskeletal disruption, changing intracellular protein traffic, blocking intracellular signal transduction pathways and induction of osteoclast apoptosis [40]. Bisphosphonates get infiltrated within bone matrix and are released during bone resorption, where they impair the already activated osteoclasts to continue resorbing bone matrix. The action of anti-catabolic drugs ultimately leads to a blockage of bone turnover owing to the coupling between resorption and formation phases. This results in bone mass gain due to mineralisation of the existing tissue, but, in general, with a non-significant reduction of porosity. The most common anabolic drug treatments are intermittent administration of PTH (either teriparatide or abaloparatide daily injections) and romosozumab. The anabolic effect of the former is achieved through attenuation of osteoblast apoptosis. Romosozumab (AMG 785; Amgen Inc., Thousand Oaks, CA) is a human monoclonal antibody that inhibits sclerostin and thus facilitates the anabolic effect of the Wnt/ β-catenin pathway. Some studies have confirmed that, in high doses, sclerostin may enhance osteoclastic activity by increasing the RANKL levels [41]. For this reason, romosozumab is considered to have a dual action (anabolic and anti-catabolic) [42]. Anabolic treatments are less widespread because they are more costly and in the case of daily injections (teriparatide or abaloparatide) because of their low adherence. For this reason they are usually prescribed in cases of severe OP or to patients for whom the anti-catabolic treatment failed to prevent fracture. Finally, we mention a different type of drug, raloxifene, a member of the class of selective estrogen receptor modulators (SERM) whose action against OP consists in counteracting the decay in estrogen production that follows menopause. For this reason, it is mainly prescribed to combat post-menopausal OP [43]. Table 1 summarises the most commonly prescribed drugs for the treatment of OP. 3. Mechanobiological models of bone (re)modelling This section is organised as follows: we start with a description of the commonly used bone cell population model (BCPM) approach which describes the bone remodelling process including different bone cell types and regulatory factors (Section 3.1). In Section 3.2 we discuss how osteoblast and osteoclast cell concentrations obtained from the BCPM are used to either formulate concentrations of various non-site-specific bone biomarkers that are experimentally measured in blood or urine (Subsection 3.2.1) or to site-specific bone biomarkers, i.e. BV/TV or bone volume fraction (Subsection 3.2.2). In Section 3.3 we discuss how bone disease progression can be simulated using BCPMs with emphasis on postmenopausal osteoporosis (Subsection 3.3.1) and advanced-age osteoporosis (Subsection 3.3.2). Section 3.4 describes, based on the example of denosumab, how to apply drug treatments in BCPMs leading to formulation of mechanobiological PK/PD models. Table 1 Summary of most commonly prescribed drugs for treatment of OP. Drug Type Action Common regimen for osteporosis treatment Alendronate Bisphosphonate Antiresorptive 10 mg oral once daily 70 mg oral once weekly Risendronate Bisphosphonate Antiresorptive 5 mg oral once daily 35 mg oral once weekly 150 mg oral once monthly Zolendronic acid Bisphosphonate Antiresorptive 5 mg IV once yearly Ibandronate Bisphosphonate Antiresorptive 2.5 mg oral once daily 150 mg oral once monthly 3 mg IV every 3 months Denosumab Rankl inhibitor Antiresorptive 60 mg subcutaneously every 6 months Raloxifene SERM Antiresorptive 60 mg oral once daily Bazedoxifen/ Estrogen SERM / Hormonal therapy Antiresorptive 20 mg bazedoxifene / 0.45 mg conjugated estrogens orally once daily Estrogen/ Progestin Hormonal therapy Antiresorptive Wide variety. Once daily tablet, once daily transdermal gel, twice/ once weekly transdermal patch, once daily spray. Different doses Tibolone Hormonal therapy Antiresorptive 1.25/2.5 mg orally once daily Calcitonin Hormonal therapy Antiresorptive 200 IU (1 spray) intranasal once daily 100 IU subcutaneously/ intramuscularly once daily Teriparatide Parathyroid Hormone Analogue Anabolic 20 μ g subcutaneously once daily. Duration limited to 2 years Abaloparatide Parathyroid Hormone Analogue Anabolic 80 μ g SC once daily. Duration limited to 2 years Romozosumab Sclerostin and RANKL inhibitor Antiresorptive and anabolic 210 mg subcutaneously once monthly. Duration limited to 1 year P. Pivonka et al. Bone 186 (2024) 117140 6 3.1. Bone cell population models of bone remodelling With the continuously increasing knowledge of the bone remodelling process and the cells and regulatory factors involved in it (see previous section) a major milestone in putting this complex information together into a mathematical model was made in 2004. Lemaire et al. [15] proposed a biochemical model of the remodelling process which included osteoblast precursor cells, active osteoblasts and active osteoclasts, together with the RANK-RANKL-OPG pathway and TGF-β, which couples the osteoblastic and osteoclastic cell lineages. PTH was used as a catabolic regulator of RANKL and OPG and consequently of bone resorption. However, no mechanical aspects were included by these authors. This model was then used to investigate different bone diseases and treatment options. In subsequent works, Pivonka and co-workers [44,45] made various improvements to the original Lemaire model, most notably, swapping of the expression of OPG and RANKL on osteoblastic cells and introducing an evolution equation for BV/TV as a function of the concentration of active osteoblasts and active osteoclasts in a bone volume of interest (VOI) at a particular bone site. The latter evolution equation opened the door to the Mechanics community, which now had a way of coupling complex biology of the bone remodelling process with mechanical aspects of bone, since BV/TV has been shown to be a major determinant of bone stiffness and strength. These types of models are commonly referred to as bone cell population models (BCPM) in the literature. The consistent extension of this biochemical model towards a mechanobiological model was achieved by Scheiner et al. [46] and incorporated mechanical loading at a particular bone site and activity of bone cells in the VOI. In that work, it was hypothesized that the strain energy density in the bone matrix (Ψbm) is sensed by osteocytes and then translated into anabolic and/or catabolic mechanobiological feedback stimuli, which control the behaviour of bone cells. In this context, an anabolic regulatory function was used to control the proliferation of osteoblast precursors, while a RANKL production term was used to regulate the catabolic feedback control. Using this model, Scheiner et al. showed that long-term effects of bone loss can be counteracted by the “Mechanostat” regulation. This was tested for the case of mechanical disuse and reuse conditions. A follow up work [47] also included the influence of bone specific surface of the VOI on the differentiation rates of both cell lineages. This was based on the idea that both active osteoclasts and active osteoblasts develop their function on the surface of bone matrix. The most notable recent improvement to the model was made by Martínez-Reina and Pivonka [48] with respect to including the bone mineralisation process into the BCPM. The authors realised that capturing in-silico the effects of anticatabolic drug treatments required the simulation of the process of secondary mineralisation. It was originally pointed out by Scheiner et al. [49] when analyzing the effects of denosumab treatment on BMD that no significant bone gains could be obtained by using the above described bone remodelling models, which was in contradiction to the experimental reported data [50,51]. The authors discussed that two processes, not considered in their model, could lead to BMD gains obtained in the experiments. One process was the presence of osteoid in a particular VOI that would become mineralised (i.e. primary mineralisation) when denosumab treatment is commenced, while the other mechanism was related to the secondary mineralisation of the existing bone matrix. It was found that the former mechanism is quite unlikely to significantly contribute to BMD increases, due to the low amounts of osteoid in bone. However, the latter has a strong potential, due to a relatively large amount of bone matrix that could mineralise to high levels [52]. In parallel to the above described efforts to consistently integrate biochemical and mechanical aspects of bone, there have been a number of developments driven by the pharmacology and mathematics community. The latter model improvements and extensions are mostly phenomenological with the aim of matching experimental findings with equations rather than describing the underlying physiology [53–55]. Fig. 3 shows the most important milestones in the historical development of bone cell population models (BCPM) including the various extensions and improvements of the original model of Lemaire et al. In order to describe the typical BCPM approach we choose one of the recently published models as an example on how to formulate the evolution equations of bone cells and briefly describe the mechanical coupling process. This will also allow to consistently introduce the modelling of the mineralisation process and the accumulation of microdamage in the bone matrix, as discussed in detail in the next section. Fig. 2 schematically shows the BCPM including major regulatory mechanisms. Bone cell balance equations for osteoblast precursors (Obu), active osteoblasts (Oba), osteoclast precursors (Ocu), active osteoclasts (Oca) and osteocytes (Ot) in the VOI can be formulated as in [56–58]: dObp dt =DObu⋅Obu⋅ π TGF−β act,Obu−DObp⋅Obp⋅ π TGF−β rep,Obp +PObp⋅Obp⋅ π mech act,Obp (1) dOba dt =DObp⋅Obp⋅ π TGF−β rep,Obp− (DOba+AOba)⋅Oba(2) dOcp dt =DOcu⋅Ocu⋅ π RANKL act,Ocu−DOcp⋅Ocp⋅ π RANKL act,Ocp(3) dOca dt =DOcp⋅Ocp⋅ π RANKL act,Ocp−AOca⋅Oca⋅ π TGF−β act,Ocp(4) dOt dt = η dfbm dt (5) where DObu, DOcu, DObp, DOcp and DOba are the differentiation rates of uncommitted osteoblast/osteoclast progenitor cells, osteoblast/osteoclast precursor cells, and active osteoblasts respectively. PObp denotes the proliferation rate of osteoblast precursor cells. AOba and AOca are respectively the apoptosis rates of active osteoblasts and osteoclasts. Eq. (5) assumes that osteocytes population is proportional to the change in bone matrix volume fraction (fbm =BV/TV), with the proportionality constant η . Cell differentiation, proliferation, and apoptosis are regulated by several “activator” ( π act) and “repressor” ( π rep) functions, which model respectively the promotion or inhibition of the biological processes of differentiation, proliferation or apoptosis. In these regulatory functions, subscripts of cell type indicate the type of bone cell that is regulated by these functions while the superscript indicates which regulatory molecule (e.g. RANKL, WNT, TGF-β) is responsible for the respective cell responses. 3.2. Evolution of bone biomarkers 3.2.1. Non-specific bone biomarkers As described in Section 2, there are a number of bone turnover markers that can be measured in blood (serum) or urine which give an indication of bone cell activity at a systemic level. These markers can be used to assess whether a particular drug suppresses or increases bone cell activities. We note that the original Lemaire et al. model considered systemic bone remodelling (i.e., accounting for all remodelling events in the skeleton) [15]. Hence, systemic bone cell activity can be directly linked to mathematical expressions of bone turnover quantities. However, no direct link to non-specific bone turnover markers was made. Table 2 summarises a variety of commonly used expressions of nonspecific bone turnover marker concentrations. Note that the equations are typically scaled with respect to the steady state concentration value of the biomarker, i.e. at t0, and cell numbers are also made dimensionless by scaling with respect to their values at the steady state. The sensitivity of variation of biomarkers is controlled via a power law P. Pivonka et al. Bone 186 (2024) 117140 7 expression of the dimensionless cell numbers. 3.2.2. Site-specific bone biomarkers Section 2 also mentioned a variety of site-specific bone turnover markers such as BV/TV (measured by volumetric QCT) and aBMD (measured by DEXA). Given that the majority of clinical trials report aBMD as an outcome measure, most PK-PD studies have focused on comparing model predictions with aBMD (or short BMD). Table 2 summarises commonly found phenomenological BMD equations from the literature. We note that the expressions for BMD changes in Table 3 are only meaningful from a phenomenological point of view, i.e. formulated as balance equations of in-flux and out-flux terms. However, these equations are not mechanically motivated nor do they make use of the information of the activity of active osteoclasts and osteoblasts in the VOI, i.e. they use cell concentrations that have been obtained from a systemic analysis. Pivonka and co-workers were the first to propose that the bone cell activities within the VOI are changing the bone volume fraction locally over time: dfbm dt =kform Oba−kres Oca(6) Fig. 3. Timeline of Bone Cell Population Models developed in recent years. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) P. Pivonka et al. Bone 186 (2024) 117140 8 where it is assumed that osteoclasts resorb bone and osteoblasts form bone at constant rates, respectively kres and kform. The bone volume fraction fbm can be linked, as a first approximation, to the apparent bone density, ρ app, which also depends on the mineral content of bone matrix (see Section 4.1). This mineral content was assumed constant in the first models but it can be considered variable by modelling the mineralisation process, as will be discussed later in Section 4.3. By doing so, an alternative way of evaluating BMD changes is proposed in two steps: porosity through Eq. (6) and mineral content independently. 3.3. Simulation of bone disease progression While conventional PK/PD analysis considers a system baseline status (often denoted as E0) that is constant, degenerative musculoskeletal diseases such as OP, sarcopenia and osteoarthritis are characterized by a slow deterioration of health condition with time. To take into account the changes in the system due to the progression of the disease, mechanism-based PK/PD models also include a disease progression analysis [60,62,63]. Furthermore, the use of disease progression models is fundamental when drug treatments specifically aim to modify the progression of the disease [64]. In particular, clinical pharmacology can be described in terms of disease progression, i.e. changes in the disease status over time, and drug action, i.e. the effect of the drug on the disease progression [62]. Drug treatments can be distinguished according to their actions into symptomatic, disease-modifying or curative, depending on their action to either reduce, stop or reverse the natural process of a disease. A symptomatic treatment effect improves the severity of the symptoms without modifying disease progression, while a disease-modifying therapy, on the other hand, involves a modification of the underlying disease progression leading to an improved disease status [63]. Mechanobiological simulation of bone diseases was originally proposed by Lemaire et al. [15]. In that work four bone diseases were addressed: (i) PMO, (ii) vitamin D deficiency, (iii) OP of advanced age and (iv) glucocorticoid-induced OP. The different bone diseases were introduced as an instantaneous perturbation of some selected model parameters from the healthy, i.e. steady-state condition. Below we discuss how to model PMO and OP of advanced age. 3.3.1. Postmenopausal osteoporosis (PMO) Experimental studies on the pathophysiology of PMO reveal that several mechanisms might occur simultaneously, together inducing the disease pattern known as PMO. Among these, estrogen deficiency has been widely accepted as the main cause of PMO [65,66]. The skeletal manifestation of PMO is an increase in bone turnover with an imbalance of bone resorption and bone formation in favour of excessive bone resorption [67]. Estrogen deficiency affects several elements in the RANK-RANKL- OPG pathway: (i) it enhances RANKL expression by stromal cells and lymphocytes [68]; (ii) it increases the responsiveness of osteoclasts to RANKL [69]; and (iii) it reduces OPG secretion in osteoblasts [70]. We note that estrogen and its role in bone remodelling was not directly simulated in many works including [15,49], but only considered indirectly, by prescribing a perturbation function which acts as a driver for disease progression. In Lemaire et al. [15] this was achieved by suggesting that the OPG production (by osteoblasts) significantly decreases due to estrogen deficiency in PMO. In the model this was simulated by changing the OPG production rate to a constant reduced value (compared to normal). In Scheiner et al. [49] PMO was modelled by prescribing an external RANKL production term, which was made time dependent using a sigmoidal function, in order to account for the temporal change of the disease. We note that due to the fact that the RANK-RANKL-OPG pathway is included as a catabolic pathway in typical bone remodelling models, the Table 2 Expressions of non-specific bone biomarkers found in the literature. CXu and CXs designate the concentration of biomarker X measured in urine and serum, respectively. NTX: N-terminal telopeptide of type I collagen. CTX: C-terminal telopeptide of type I collagen. BSAP: bone-specific alkaline phosphatase. OST: osteocalcin. Non-specific biomarker equation Description Reference CNTXs=Eb,NTXs+(CNTXs(t0) − Eb,NTXs)(Oca Oca(t0))n Eb,NTXs: basal concentration of serum NTX (NTXs) Marathe et al. [59] n: Hill coefficient CNTXu=Eb,NTXu+(CNTXu(t0) − Eb,NTXu)(Oca Oca(t0))n Eb,NTXu: basal concentration of urine NTX (NTXu) Marathe et al. [59] n: Hill coefficient CCTXu=Eb,CTXu+(CCTXu(t0) − Eb,CTXu)(Oca Oca(t0))n Eb,CTXu: basal concentration of urine CTX (CTXu) Marathe et al. [59] n: Hill coefficient CNTXs=CNTXs(t0)(Oca Oca(t0)) ρ NTXs ρ NTXs: Positive transduction Post et al. [60] parameter CBSAPs=CBSAPs(t0)(Oba Oba(t0)) ρ BSAPs ρ BSAPs: Positive transduction Post et al. [60] parameter COST =COST(t0)(Oba Oba(t0)⋅Oca Oca(t0)) ρ OST ρ OST: Positive transduction parameter Post et al. [60] Table 3 Expressions of site-specific bone biomarkers found in the literature. BMD: bone mineral density averaged in the entire skeleton. BMDLS: bone mineral density averaged in the lumbar spine. BMDTH: bone mineral density averaged in total hip. Site-specific biomarker equation Description Reference dBMD dt =kin⋅(1+SObaOba) kin: zero-order production rate constant Marathe et al. [59] kout: first-order degradation rate constant −kout⋅(1+SOcaOca)⋅BMD SOba: coefficient for stimulation by Oba SOca: coefficient for stimulation by Oca dBMDLS dt =kLS (1−S ρ BMD ) kLS: turnover rate parameter for lumbar spine (LS) Post et al. [60] kTH: turnover rate parameter for total hip (TH) dBMDTH dt =kTH (1−S ρ BMD ) with S = (Oca Oca(t0))( Oba Oba(t0))−1 ρ BMD: transduction parameter used to translate changes in bone cell dynamics into those of BMD dBMDLS dt = kin,BMD (CBSAP CBSAP(t0))γOb − kout,BMD (CCTX CCTX(t0))γOc ⋅BMDLS kin,BMD: zero-order production rate affected by Oba function Peterson and Riggs [61] kout,BMD: first-order degradation rate affected by Oca function γOb: sigmoidicity term for BSAP to describe the steepness of BMDLS change relative to the proportional change in the marker γOc: sigmoidicity term for CTX to describe the steepness of BMDLS change relative to the proportional change in the marker Ci: concentration of bone marker i, with i =BSAP,CTX P. Pivonka et al. Bone 186 (2024) 117140 9 simulation of PMO can be equivalently achieved by targeting different parameters in this pathway. For example increasing RANKL, decreasing OPG, and increasing RANKL sensitivity all give rise to high bone turnover catabolic bone response as was studied by Pivonka et al. [45]. 3.3.2. Osteoporosis of advanced age Factors leading to age related bone resorption are manyfold including increased osteocyte apoptosis [71], a reduced number of osteoblast precursors and stem cells from which these precursors are derived or reduced osteoblast lifespan [72]. Additionally, increased glucocorticoid production and sensitivity with advancing age decrease skeletal hydration and thereby increase skeletal fragility [73]. With aging, cortical porosity increases more in women than in men, while trabecular thickness declines more in men than in women, and bone expansion at the periosteal surface increases more in men than in women so that the total bone area becomes larger in men than in women [74]. Older women show dramatically greater medullary expansion and cortical thinning, due to endocortical resorption outpacing periosteal apposition [74]. The osteopenia associated with advanced age appears to be universal in humans and animals [75]. Although the mechanisms responsible are not completely understood, it seems that a decrease in the production of TGF-β is a critical step in disease progression [75–77]. Lemaire et al. [15] modelled age-related OP by reducing the TGF-β content in the bone matrix by a factor of 5.5. This leads to an increased bone turnover and increased negative bone balance. We conclude this section by re-emphasizing that modelling of bone disease progression is not trivial as in many cases the underlying drivers of the disease are not fully known. Using latest findings from the bone biology literature it is possible to justify modifications of (healthy) bone remodelling parameters. In some instances, such as for example in the case of PMO and the altered RANKL/OPG ratio, there is ambiguity on how that alteration can be achieved, i.e. either by increasing RANKL production, by decreasing OPG production, or by altering both. 3.4. Simulation of drug interventions Once a sufficiently complex mechanobiological bone remodelling disease model has been developed, the action of OP drugs can be introduced in a straight forward manner. The terminology “sufficiently complex” refers to the fact that biochemical signalling pathways targeted by the drug must be included in the model. For example, in the case of denosumab the RANKL-RANK-OPG signalling pathway must be properly modelled as denosumab tends to bind to RANKL, so that the normal signalling pathway turns into a more complex RANKL-RANK- OPG-denosumab pathway, with RANK, OPG and now denosumab competing for binding to RANKL. PK models describe the relationship between the dose administered to an individual and the resulting concentrations of the drug inside various body compartments. The model depicted in Fig. 4 was proposed for denosumab by Martínez-Reina et al. [57] and considers the subcutaneous (SC) injection site, the central compartment and the bone compartment. A first-order rate process (ka) governs the absorption of the drug (Dose) from the SC site into the central compartment (serum). The drug elimination from the central compartment is described by a combination of a linear first-order process and a Michaelis-Menten saturation process (not distinguished in the figure), resulting in the amount “Elim”. A fraction (1−ζ)is assumed to be excreted to urine and the remaining fraction passes into the bone compartment, where it interacts with the RANKL-RANK-OPG signalling pathway by binding to RANKL. The input to the PD model is the concentration of denosumab in the bone compartment and is taken into account in this part of the model along with the concentrations of RANK, OPG and RANKL (see Fig. 2). Analogous models can be found in the literature for romosozumab [78], teriparatide [79] and alendronate [56]. In the latter case, it is important to note that the drug infiltrates into bone matrix when it reaches the bone compartment and is stored there until bone matrix is dissolved by osteoclasts. This is when the drug comes into action by impairing the resorptive capacity of osteoclasts and promoting their apoptosis [80]. 4. Mechanoregulation of bone (re)modelling Traditional PK-PD models do not consider a mechanobiological description of bone volume changes (i.e., BV/TV) or BMD changes nor include mechanical feedback in the description of bone cell populations. Furthermore, material effects such as bone matrix mineralisation and the accumulation of damage in bone matrix and micro-crack development due to fatigue loading are not considered. The latter effects, e.g. bone matrix mineralisation, can be modelled phenomenologically by introducing additional parameters into these models to reproduce certain aspects of the experimental data. On the other hand, mechanobiological PK-PD models allow physicsbased incorporation of these phenomena in a rigorous way which does not require ad hoc equations. Particularly, they allow to incorporate the following phenomena: (i) BV/TV evolution laws for different bone sites, Fig. 4. Schematic representation of the PK/PD model of denosumab proposed by Martínez-Reina et al. [57]. The drug dose is injected subcutaneously at the SC site. Then it is absorbed into the central compartment. A fraction (1−ζ)of the drug eliminated from the central compartment (Elim) is assumed to be excreted via urine and the remaining fraction ζ passes into the bone compartment where it interacts with the RANKL-RANK-OPG signalling pathway. This interaction is modelled with the PD model (see Fig. 2). P. Pivonka et al. Bone 186 (2024) 117140 16 severely as HPT in mild stages of the disease. Normal glomerular filtration rate was assumed to be GFR =6 L/h [105] and used in the simulations corresponding to black and red lines in Fig. 10 right. In the cases of CKD, the value assumed for GFR in L/h is specified. Renal deficiency hinders phosphorus filtration to urine and high phosphorus levels downregulates calcitriol production in the kidney. This in turn decreases calcium serum levels and increases PTH production, which enhances bone loss. In case of CKD, efficacy of Dmab is slightly reduced in absolute terms, probably because the calcium available for mineralisation is decreased. However, since BMD is lower at the beginning of the treatment, that efficacy is unaffected in relative terms. Thus, at the end of the 2-year treatment BDG is equal to 3.7 % in the normal case (black line), 3.4 % in the mild disease case (GFR =4 L/h) and 3.8 % in the severe disease case (GFR =2 L/h), which is in agreement with the clinical results of Jamal et al. [140], who obtained BDG around 5 % in the 3-year treatment with no significant differences between groups. 7. Conclusions and future directions In silico modelling and simulation are powerful tools that complement traditional methods for gathering evidence including bench-top (in vitro) testing, and animal or clinical (in vivo) studies. Many world regulatory bodies, i.e. the Food and Drug Administration (FDA, USA), European Medicines Agency (EMA, Europe), Therapeutic Goods Administration (TGA, Australia) recognise that the use of in silico models has the potential to revolutionize the future of healthcare and is among the recognized emerging health technologies. In this review, we have presented the state-of-the-art of in silico mechanobiological models of bone remodelling and their application to optimise existing drugs for osteoporosis. We have particularly focused on including essential mechanistic processes such as 1 mineralization, microdamage and mechanobiological feedback. Based on four examples we have shown how such mechanobiological PK/PD models for OP can provide important insight into best treatment options. These mechanobiological models are continuously advancing, but there are still some modelling challenges which we discuss below. Fig. 9. Left: Effect of patient’s body weight (BW) on the evolution of apparent density in a Dmab treatment 60Q6. Right: Effect of variation of the applied load with respect to the homeostatic load for a patient of BW =60 kg. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 10. Left: Effect of an extra 10 % calcium intake and a vitamin D supplement producing a 10 % increase in serum calcitriol levels on the evolution of apparent density in a Dmab treatment (60Q6). Right: Effect of the concurrence of diseases: PMO, hyperparathyroidism (HPT) and renal deficiency (GFR is specified in L/h in these cases) on the efficacy of the Dmab treatment (60Q6). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) P. Pivonka et al. Bone 186 (2024) 117140 17 We want to point out that major challenges in the use of mechanobiological PK-PD models for OP treatment are the model calibration and validation. These models require many parameters to be estimated from in-vitro experiments (e.g., reaction binding constants for ligand binding to their respective receptors), mechanical testing (e.g. fatigue damage evolution law) and clinical studies (e.g. PK-PD models of drugs) among others. We note that while there are many model parameters, the influence of many of these parameters on model behaviour is constrained, e.g. all binding reaction parameters of the OPG-RANK-RANKL pathway are ultimately controlling π RANKL act,Ocu and π RANKL act,Ocp in Eqs. (3)–(4) which regulates differentiation of osteoclasts. As was shown by Larcher and Scheiner, the number of parameters of mechanobiological models of bone remodelling can be significantly reduced [141]. Also, that contribution demonstrated sensitivity and reliability of mechanobiological models of bone remodelling. However, for the purpose of mechanobiological PK-PD modelling of OP treatment, one would like to have access to all receptors and ligands that play a role in bone remodelling and are drug targets. As highlighted in this review, mineralisation of bone matrix is a key mechanism of the bone remodelling process, but many mathematical models developed today neglect this process together with the availability (or an excess) of Ca2+and PO 3− 4 in the blood serum that modulates the mineralisation rate. Coupling bone remodelling models with models of calcium and phosphorus homeostasis at the whole body level, as in [105,139] are promising future direction. This coupling will also allow to study the effect of other concomitant conditions with PMO, such as vitamin D or dietary deficiencies, kidney diseases, hyper- and hypoparathyroidism among others. The majority of models reviewed here were applied locally at a RVE (VOI). Recently, some work has been presented that applies similar models at a structural scale (i.e., macroscopic pieces of bone) [142] or at the entire organ level [143]. Such models are computationally expensive, but are particularly important for the estimation of fracture risk. We note that the estimation of local damage in the RVE might be insufficient as it does not take into account damage propagation leading to fracture. Bisphosphonates get infiltrated within bone matrix as they bind to hydroxyapatite crystals [39,40]. This fact prolongs the action of these drugs and requires a special PK-PD modelling that considers their deposition into bone matrix and its subsequent release through bone resorption. Finally, the use of physical exercise as a therapeutical tool against osteoporosis, alone or in combination with drugs, must be further investigated by mechanobiological models for its potential use in cases where drugs have failed, are contraindicated or cannot be extended. Author contributions All the authors have contributed equally. CRediT authorship contribution statement Peter Pivonka: Writing – review & editing, Writing – original draft, Supervision, Project administration, Conceptualization. Jos´ e Luis Calvo-Gallego: Writing – review & editing, Visualization, Conceptualization. Stephan Schmidt: Writing – review & editing, Writing – original draft, Conceptualization. Javier Martínez-Reina: Writing – review & editing, Writing – original draft, Supervision, Conceptualization. Declaration of competing interest The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. 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