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

Bone turnover and mineralisation kinetics control trabecular BMDD and apparent bone density: insights from a discrete statistical bone remodelling model

The mechanical quality of trabecular bone is influenced by its mineral content and spatial distribution, which is controlled by bone remodelling and mineralisation. Mineralisation kinetics occur in two phases: a fast primary mineralisation and a secondary mineralisation that can last from several months to years. Variations in bone turnover and mineralisation kinetics can be observed in the bone mineral density distribution (BMDD). Here, we propose a statistical spatio-temporal bone remodelling model to study the effects of bone turnover (associated with the activation frequency Ac . f ) and mineralisation kinetics (associated with secondary mineralisation T sec ) on BMDD. In this model, individual basic multicellular units (BMUs) are activated discretely on trabecular surfaces that undergo typical bone remodelling periods. Our results highlight that trabecular BMDD is strongly regulated by Ac . f and T sec in a coupled way. Ca wt% increases with lower Ac . f and short T sec . For example, aAc . f = 4 BMU/year/mm3 and T sec = 8 years result in a mean Ca wt% of 25, which is in accordance with Ca wt% values reported in quantitative backscattered electron imaging (qBEI) experiments. However, for lower Ac . f and shorter T sec (from 0.5 to 4 years) one obtains a high Ca wt% and a very narrow skew BMDD to the right. This close link between Ac . f and T sec highlights the importance of considering both characteristics to draw meaningful conclusion about bone quality. Overall, this model represents a new approach to modelling healthy and diseased bone and can aid in developing deeper insights into disease states like osteoporosis.

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.

Clinical Data for Parametrization of In Silico Bone Models Incorporating Cell-Cytokine Dynamics: A Systematic Review of Literature

In silico simulations aim to provide fast, inexpensive, and ethical alternatives to years of costly experimentation on animals and humans for studying bone remodeling, its deregulation during osteoporosis and the effect of therapeutics. Within the varied spectrum of in silico modeling techniques, bone cell population dynamics and agent-based multiphysics simulations have recently emerged as useful tools to simulate the effect of specific signaling pathways. In these models, parameters for cell and cytokine behavior are set based on experimental values found in literature; however, their use is currently limited by the lack of clinical in vivo data on cell numbers and their behavior as well as cytokine concentrations, diffusion, decay and reaction rates. Further, the settings used for these parameters vary across research groups, prohibiting effective cross-comparisons. This review summarizes and evaluates the clinical trial literature that can serve as input or validation for in silico models of bone remodeling incorporating cells and cytokine dynamics in post-menopausal women in treatment, and control scenarios. The GRADE system was used to determine the level of confidence in the reported data, and areas lacking in reported measures such as binding site occupancy, reaction rates and cell proliferation, differentiation and apoptosis rates were highlighted as targets for further research. We propose a consensus for the range of values that can be used for the cell and cytokine settings related to the RANKL-RANK-OPG, TGF-β and sclerostin pathways and a Levels of Evidence-based method to estimate parameters missing from clinical trial literature.

Assessment of Strategies for Safe Drug Discontinuation and Transition of Denosumab Treatment in PMO—Insights From a Mechanistic PK/PD Model of Bone Turnover

Denosumab (Dmab) treatment against postmenopausal osteoporosis (PMO) has proven very efficient in increasing bone mineral density (BMD) and reducing the risk of bone fractures. However, concerns have been recently raised regarding safety when drug treatment is discontinued. Mechanistic pharmacokinetic-pharmacodynamic (PK-PD) models are the most sophisticated tools to develop patient specific drug treatments of PMO to restore bone mass. However, only a few PK-PD models have addressed the effect of Dmab drug holidays on changes in BMD. We showed that using a standard bone cell population model (BCPM) of bone remodelling it is not possible to account for the spike in osteoclast numbers observed after Dmab discontinuation. We show that inclusion of a variable osteoclast precursor pool in BCPMs is essential to predict the experimentally observed rapid rise in osteoclast numbers and the associated increases in bone resorption. This new model also showed that Dmab withdrawal leads to a rapid increase of damage in the bone matrix, which in turn decreases the local safety factor for fatigue failure. Our simulation results show that changes in BMD strongly depend on Dmab concentration in the central compartment. Consequently, bone weight (BW) might play an important factor in calculating effective Dmab doses. The currently clinically prescribed constant Dmab dose of 60 mg injected every 6 months is less effective in increasing BMD for patients with high BW (2.5% for 80 kg in contrast to 8% for 60 kg after 6 years of treatment). However, bone loss observed 24 months after Dmab withdrawal is less pronounced in patients with high BW (3.5% for 80kg and 8.5% for 60 kg). Finally, we studied how to safely discontinue Dmab treatment by exploring several transitional and combined drug treatment strategies. Our simulation results indicate that using transitional reduced Dmab doses are not effective in reducing rapid bone loss. However, we identify that use of a bisphosphonate (BP) is highly effective in avoiding rapid bone loss and increase in bone tissue damage compared to abrupt withdrawal of Dmab. Furthermore, the final values of BMD and damage were not sensitive to the time of administration of the BP.

Effects of Mechanical Stress Stimulation on Function and Expression Mechanism of Osteoblasts

Osteoclasts and osteoblasts play a major role in bone tissue homeostasis. The homeostasis and integrity of bone tissue are maintained by ensuring a balance between osteoclastic and osteogenic activities. The remodeling of bone tissue is a continuous ongoing process. Osteoclasts mainly play a role in bone resorption, whereas osteoblasts are mainly involved in bone remodeling processes, such as bone cell formation, mineralization, and secretion. These cell types balance and restrict each other to maintain bone tissue metabolism. Bone tissue is very sensitive to mechanical stress stimulation. Unloading and loading of mechanical stress are closely related to the differentiation and formation of osteoclasts and bone resorption function as well as the differentiation and formation of osteoblasts and bone formation function. Consequently, mechanical stress exerts an important influence on the bone microenvironment and bone metabolism. This review focuses on the effects of different forms of mechanical stress stimulation (including gravity, continuously compressive pressure, tensile strain, and fluid shear stress) on osteoclast and osteoblast function and expression mechanism. This article highlights the involvement of osteoclasts and osteoblasts in activating different mechanical transduction pathways and reports changings in their differentiation, formation, and functional mechanism induced by the application of different types of mechanical stress to bone tissue. This review could provide new ideas for further microscopic studies of bone health, disease, and tissue damage reconstruction.

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.

A General Mechano-Pharmaco-Biological Model for Bone Remodeling Including Cortisol Variation

The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination is achieved by generating the appropriate number of osteoblasts since osteoblastic-lineage cells govern the bone mass variation and regulate a corresponding number of osteoclasts. Furthermore, diverse hormones, cytokines and growth factors that strongly link osteoblasts to osteoclasts coordinated these two cell populations. The understanding of this complex remodeling process and predicting its evolution is crucial to manage bone strength under physiologic and pathologic conditions. Several mathematical models have been suggested to clarify this remodeling process, from the earliest purely phenomenological to the latest biomechanical and mechanobiological models. In this current article, a general mathematical model is proposed to fill the gaps identified in former bone remodeling models. The proposed model is the result of combining existing bone remodeling models to present an updated model, which also incorporates several important parameters affecting bone remodeling under various physiologic and pathologic conditions. Furthermore, the proposed model can be extended to include additional parameters in the future. These parameters are divided into four groups according to their origin, whether endogenous or exogenous, and the cell population they affect, whether osteoclasts or osteoblasts. The model also enables easy coupling of biological models to pharmacological and/or mechanical models in the future.

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.

Integration of mechanics and biology in computer simulation of bone remodeling

Bone remodeling is a complex physiological process that spans across multiple spatial and temporal scales and is regulated by both mechanical and hormonal cues. An imbalance between bone resorption and bone formation in the process of bone remodeling may lead to various bone pathologies. One powerful and non-invasive approach to gain new insights into mechano-adaptive bone remodeling is computer modeling and simulation. Recent findings in bone physiology and advances in computer modeling have provided a unique opportunity to study the integration of mechanics and biology in bone remodeling. Our objective in this review is to critically appraise recent advances and developments and discuss future research opportunities in computational bone remodeling approaches that enable integration of mechanics and cellular and molecular pathways. Based on the critical appraisal of the relevant recent published literature, we conclude that multiscale in silico integration of personalized bone mechanics and mechanobiology combined with data science and analytics techniques offer the potential to deepen our knowledge of bone remodeling and provide ample opportunities for future research.

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.

Modelling Human Locomotion to Inform Exercise Prescription for Osteoporosis

PURPOSE OF REVIEW

We review the literature on hip fracture mechanics and models of hip strain during exercise to postulate the exercise regimen for best promoting hip strength.

RECENT FINDINGS

The superior neck is a common location for hip fracture and a relevant exercise target for osteoporosis. Current modelling studies showed that fast walking and stair ambulation, but not necessarily running, optimally load the femoral neck and therefore theoretically would mitigate the natural age-related bone decline, being easily integrated into routine daily activity. High intensity jumps and hopping have been shown to promote anabolic response by inducing high strain in the superior anterior neck. Multidirectional exercises may cause beneficial non-habitual strain patterns across the entire femoral neck. Resistance knee flexion and hip extension exercises can induce high strain in the superior neck when performed using maximal resistance loadings in the average population. Exercise can stimulate an anabolic response of the femoral neck either by causing higher than normal bone strain over the entire hip region or by causing bending of the neck and localized strain in the superior cortex. Digital technologies have enabled studying interdependences between anatomy, bone distribution, exercise, strain and metabolism and may soon enable personalized prescription of exercise for optimal hip strength.

Study of the combined effects of PTH treatment and mechanical loading in postmenopausal osteoporosis using a new mechanistic PK-PD model

One of only a few approved and available anabolic treatments for severe osteoporosis is daily injections of PTH (1-34). This drug has a specific dual action which can act either anabolically or catabolically depending on the type of administration, i.e. intermittent or continuous, respectively. In this paper, we present a mechanistic pharmacokinetic-pharmacodynamic model of the action of PTH in postmenopausal osteoporosis. This model accounts for anabolic and catabolic activities in bone remodelling under intermittent and continuous administration of PTH. The model predicts evolution of common bone biomarkers and bone volume fraction (BV/TV) over time. We compared the relative changes in BV/TV resulting from a daily injection of 20 [Formula: see text]g of PTH with experimental data from the literature. Simulation results indicate a site-specific bone gain of 8.66[Formula: see text] (9.4 ± 1.13[Formula: see text]) at the lumbar spine and 3.14[Formula: see text] (2.82 ± 0.72[Formula: see text]) at the femoral neck. Bone gain depends nonlinearly on the administered dose, being, respectively, 0.68[Formula: see text], 3.4[Formula: see text] and 6.16[Formula: see text] for a 10, 20 and 40 [Formula: see text]g PTH dose at the FN over 2 years. Simulations were performed also taking into account a bone mechanical disuse to reproduce elderly frail subjects. The results show that mechanical disuse ablates the effects of PTH and leads to a 1.08% reduction of bone gain at the FN over a 2-year treatment period for the 20 [Formula: see text]g of PTH. The developed model can simulate a range of pathological conditions and treatments in bones including different PTH doses, different mechanical loading environments and combinations. Consequently, the model can be used for testing and generating hypotheses related to synergistic action between PTH treatment and physical activity.

The Effectiveness and Safety of Acupoint Catgut Embedding for the Treatment of Postmenopausal Osteoporosis: A Systematic Review and Meta-Analysis

Purpose

To evaluate the effectiveness and safety of acupoint catgut embedding therapy (ACET) in postmenopausal osteoporosis (PMOP).

Methods

Review of some databases from their inception to June 2018 and randomized controlled trials (RCTs) in which ACET with PMOP were included. Two researchers extracted and evaluated the information independently. Cochrane Collaboration's tool and Jadad scale were used to evaluate the quality of the studies. RevMan V.5.3.3 software was used to carry out the meta-analysis while trial sequential analysis (TSA) performed with TSA 0.9 software.

Results

12 RCTs with 876 participants were included in this review. Meta-analysis showed that ACET alone was not superior to medication in effectiveness rate (RR= 1.11; 95% CI (0.89, 1.40); P=0.35) and E2 (SMD= 0.20; 95% CI (-0.17, 0.57); P=0.28; I ² =20%) while ACET combining medication was more effective on the effectiveness rate (RR= 1.32; 95% CI (1.20, 1.46); P<0.000 01) and E2 (SMD= 1.24; 95% CI (0.63, 1.84); P<0.0001). Additionally, ACET combining calcium could increase the bone mineral density (BMD) of the L2~4 vertebrae and femur-neck [WMD_L2~4 = 0.03; 95% CI (0.01, 0.05); P=0.003; and WMD_Femur-neck = 0.07; 95% CI (0.03, 0.10); P = 0.0006], reduce TCM syndrome score [WMD = -1.85; 95% CI (-2.13, -1.57); P<0.000 01], improve patient's quality of life [WMD_{three  months} = 6.90; 95% CI (3.90, 9.89); P<0.000 01; and WMD_{six  months} = 12.34; 95% CI (5.09, 19.60); P=0.0009], and relieve pain [WMD_VAS = -1.26; 95% CI (-1.66, -0.85); P<0.000 01; and WMD_{Pain  score} = -2.59; 95% CI (-4.76, -0.43); P= 0.02]. The TSA showed that the effectiveness of ACET for PMOP was demonstrated accurately.

Conclusions

ACET combining medication but not ACET alone is more effective than medication as comparison in the treatment of PMOP. As a novel treatment, ACET shows the potential of effectiveness and deserves further high quality of well-designed study.

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.

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.

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.

Automated Scale Reduction of Nonlinear QSP Models With an Illustrative Application to a Bone Biology System

Integrating quantitative systems pharmacology (QSP) into pharmacokinetics/pharmacodynamics (PKPD) has resulted in models that are highly complex and often not amenable to further exploration via estimation or design. Because QSP models are usually depicted using nonlinear differential equations it is not straightforward to apply some model reduction techniques, such as proper lumping. In this study, we explore the combined use of linearization and proper lumping as a general method to simplification of a nonlinear QSP model. We illustrate this with a bone biology model and the reduced model was then applied to describe bone mineral density (BMD) changes due to denosumab dosing. The methodologies used in this study can be applied to other multiscale models for developing a mechanism-based structural model for future analyses.

A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation

While bone tissue is a hierarchically organized material, mathematical formulations of bone remodeling are often defined on the level of a millimeter-sized representative volume element (RVE), "smeared" over all types of bone microstructures seen at lower observation scales. Thus, there is no explicit consideration of the fact that the biological cells and biochemical factors driving bone remodeling are actually located in differently sized pore spaces: active osteoblasts and osteoclasts can be found in the vascular pores, whereas the lacunar pores host osteocytes - bone cells originating from former osteoblasts which were then "buried" in newly deposited extracellular bone matrix. We here propose a mathematical description which considers size and shape of the pore spaces where the biological and biochemical events take place. In particular, a previously published systems biology formulation, accounting for biochemical regulatory mechanisms such as the rank-rankl-opg pathway, is cast into a multiscale framework coupled to a poromicromechanical model. The latter gives access to the vascular and lacunar pore pressures arising from macroscopic loading. Extensive experimental data on the biological consequences of this loading strongly suggest that the aforementioned pore pressures, together with the loading frequency, are essential drivers of bone remodeling. The novel approach presented here allows for satisfactory simulation of the evolution of bone tissue under various loading conditions, and for different species; including scenarios such as mechanical dis- and overuse of murine and human bone, or in osteocyte-free bone.

X-ray physics-based CT-to-composition conversion applied to a tissue engineering scaffold, enabling multiscale simulation of its elastic behavior

Nowadays, the assessment of the mechanical competence of tissue engineering scaffolds based on computer simulations is a well-accepted technology. Typically, such simulations are performed by means of the Finite Element (FE) method, with the underlying structural model being created based on micro-computed tomography (microCT). Here, this analysis modality is applied to a new, ternary composite, consisting of PHBV, i.e. poly(3-hydroxybutyrate-co-3-hydroxyvalerate), PLGA, i.e. poly(lactic-co-glycolide), as well as of TCP, i.e. tricalcium phosphate hydrate. The studied scaffold structure is made up by fibers of this new composite material, manufactured by means of the rapid prototyping method. The data collected from microCT is utilized for adequately defining the mechanical properties of the FE model. In particular, the three-dimensional field of grey values is interpreted in terms of the underlying field of attenuation coefficients, taking into account the photon energy employed in microCT imaging, eventually allowing for calculation of the three-dimensionally distributed, voxel-specific composition of the studied material. For the sake of keeping the FE simulations as efficient as possible, groups of voxels are combined into one finite element; the grey value of the latter is obtained by volume averaging. Employing a two-step micromechanical homogenization scheme, the experimentally accessible stiffness of the three constituents (PHBV, PLGA, and TCP) is then, finite element by finite element, upscaled to the composition-dependent stiffness of the composite material. The plausibility and adequacy of the FE model is demonstrated by simulating the effects of uniaxial compression on the scaffold structure, in terms of resulting stress and strain fields, highlighting the importance of the fiber junctions (as they are the mechanically most stressed regions), and that neglecting the material heterogeneity would lead to a potentially significant underestimation of stresses and strains. Finally, a comparison is made of the employed analysis modality of microCT data with a previously pursued, simplified analysis strategy, highlighting the conceptual superiority of the former, and pointing out the application limits of the latter.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Dynamic modeling of bone metastasis, microenvironment and therapy: Integrating parathyroid hormone (PTH) effect, anti-resorptive and anti-cancer therapy

Bone is a common site for the development of metastasis, as its microenvironment provides the necessary conditions for the growth and proliferation of cancer cells. Several mathematical models to describe the bone remodeling process and how osteoclasts and osteoblasts coupled action ensures bone homeostasis have been proposed and further extended to include the effect of cancer cells. The model proposed here includes the influence of the parathyroid hormone (PTH) as capable of triggering and regulating the bone remodeling cycle. It also considers the secretion of PTH-related protein (PTHrP) by cancer cells, which stimulates the production of receptor activator of nuclear factor kappa-B ligand (RANKL) by osteoblasts that activates osteoclasts, increasing bone resorption and the subsequent release of growth factors entrapped in the bone matrix, which induce tumor growth, giving rise to a self-perpetuating cycle known as the vicious cycle of bone metastases. The model additionally describes how the presence of metastases contributes to the decoupling between bone resorption and formation. Moreover, the effects of anti-cancer and anti-resorptive treatments, through chemotherapy and the administration of bisphosphonates or denosumab, are also included, along with their corresponding pharmacokinetics (PK) and pharmacodynamics (PD). The simulated models, available at http://sels.tecnico.ulisboa.pt/software/, are able to describe bone remodeling cycles, the growth of bone metastases and how treatment can effectively reduce tumor burden on bone and prevent loss of bone strength.

Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure

Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to “feel” the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al. (Bone 46(4):1075–1081, 2010) strongly suggest that the lacunar pores are likely to experience, during typical physiological load cycles, not only fluid transport, but also undrained conditions. The latter entail the buildup of lacunar pore pressures, which we here quantify by means of a thorough multiscale modeling approach. In particular, the proposed model is based on classical poroelasticity theory, and able to account for multiple pore spaces. First, the model reveals distinct nonlinear dependencies of the resulting lacunar (and vascular) pore pressures on the underlying bone composition, highlighting the importance of a rigorous multiscale approach for appropriate computation of the aforementioned pore pressures. Then, the derived equations are evaluated for macroscopic (uniaxial as well as hydrostatic) mechanical loading of physiological magnitude. The resulting model-predicted pore pressures agree very well with the pressures that have been revealed, by means of in vitro studies, to be of adequate magnitude for modulating the responses of biological cells, including osteocytes. This underlines that osteocytes may respond to many types of loading stimuli at the same time, in particular so to fluid flow and hydrostatic pressure.

Changes in the degree of mineralization with osteoporosis and its treatment

The diagnosis of osteoporosis is based on low bone mineral density (BMD) and/or the occurrence of fragility fractures. The majority of patients, however, have also abnormally low bone matrix mineralization. The latter is indicative of alterations in bone turnover rates and/or in kinetics of mineral accumulation within the newly formed bone matrix. Osteoporosis therapies can alter the bone matrix mineralization according to their action on bone turnover and/or mineralization kinetics. Antiresorptives, including the most widely used bisphosphonates, reduce the bone turnover rate resulting in a decrease in heterogeneity and an increase in the degree of mineralization toward to or even beyond normal values. Anabolic agents increase the bone volume and the amount of newly formed bone resulting in a likely transient decrease in mean degree and homogeneity of mineralization. Hence, the measurement of bone matrix mineralization is a sensitive tool to evaluate the response to therapy.

Regenerative orthopaedics: in vitro, in vivo...in silico

In silico, defined in analogy to in vitro and in vivo as those studies that are performed on a computer, is an essential step in problem-solving and product development in classical engineering fields. The use of in silico models is now slowly easing its way into medicine. In silico models are already used in orthopaedics for the planning of complicated surgeries, personalised implant design and the analysis of gait measurements. However, these in silico models often lack the simulation of the response of the biological system over time. In silico models focusing on the response of the biological systems are in full development. This review starts with an introduction into in silico models of orthopaedic processes. Special attention is paid to the classification of models according to their spatiotemporal scale (gene/protein to population) and the information they were built on (data vs hypotheses). Subsequently, the review focuses on the in silico models used in regenerative orthopaedics research. Contributions of in silico models to an enhanced understanding and optimisation of four key elements-cells, carriers, culture and clinics-are illustrated. Finally, a number of challenges are identified, related to the computational aspects but also to the integration of in silico tools into clinical practice.

Vertebral compression fractures in patients under treatment with denosumab: a contraindication for percutaneous vertebroplasty?

BACKGROUND CONTEXT

Denosumab (XGeva) is a receptor activator of nuclear factor-κB ligand (RANKL)-antibody that was approved by the Food and Drug Administration (FDA) in 2010 for the prevention of skeletal fractures in patients with bone metastases from solid tumors. Although there is a widespread use of such drug in patients under risk of pathological fractures, the compatibility of denosumab therapy with percutaneous vertebroplasty (an interventional procedure commonly used for pain control in such population) has not yet been established.

PURPOSE

To present the serial imaging findings and technical report of an attempted percutaneous vertebroplasty in a patient with refractory pain and a lytic pathological vertebral fracture related to small cell lung cancer spinal metastasis and who was actively under medical treatment with denosumab.

STUDY DESIGN

Retrospective review and case report.

METHODS

The authors present the imaging findings and technical report of an attempted percutaneous vertebroplasty in the only patient found to be actively under treatment with denosumab after a retrospective review of the databank of patients with pathological fractures referred to the Department of Radiology of the Ohio State University for percutaneous vertebroplasty (a total sample of 20 patients) since the FDA approval of denosumab (November 2010) until June 2013 (a 30-month period).

RESULTS

Although the computed tomography scan of the thoracic spine, performed 6 weeks after the initiation of the treatment with denosumab, presented a remarkable remodeling of the previously lytic vertebral lesion (which became markedly sclerotic in appearance), the clinical response in terms of pain improvement was not satisfactory. At the time of the percutaneous vertebroplasty (which was indicated for pain control), after advancing the 11-gauge needle through the pedicle with extreme difficulty, the needle repeatedly deviated laterally and, despite several attempts, it was not possible to penetrate the vertebral body and perform the cement injection.

CONCLUSIONS

This is the first report of the technical peculiarities of percutaneous vertebroplasty in patients under medical treatment with denosumab. According to our experience, because of its RANKL-mediated effects on osteoclasts activity, denosumab has been shown to induce a fast and marked sclerotic response on vertebral bodies that may not be accompanied by a satisfactory improvement in pain control (especially in patients with mechanical type of pain) and which may actually prevent the successful performance of percutaneous vertebroplasty. Therefore, it is of paramount importance that future studies evaluating patients with vertebral fractures under treatment with denosumab include long-term pain outcome measures. Additionally, further investigation is warranted to determine the optimal order of treatment and the best timeframe for combining percutaneous vertebroplasty and denosumab therapy in patients presenting with acute vertebral compression fractures and refractory axial pain.