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

Chemotherapy and adjuvant therapies' impact on the internal remodeling process of bone and its mechanical behavior for breast cancer patients

Breast cancer is a significant public health issue affecting women worldwide. While advancements in treatment options have led to improved survival rates, the impact of breast cancer and its treatments on bone health cannot be overlooked. Bone remodeling is a complex process regulated by the delicate balance between bone formation and resorption. Any disruption to this balance can lead to decreased bone density, increased fracture risk, and compromised physical function. To investigate the effects of breast cancer and its treatments on bone remodeling, a finite element model was developed in this study. This model incorporated bone remodeling equations to simulate the mechanical behavior of bone under different conditions. The ABAQUS/UMAT software was used to simulate the behavior of bone tissue under the influence of breast cancer and treatments. Our findings suggest that bone loss is more pronounced after secondary breast cancer and treatment, leading to bone loss (6%-19% decrease in BV/TV), reduced bone stimulation, and decreased effectiveness of physical activity on recovery. These results highlight the importance of early intervention and management of bone health in breast cancer patients to mitigate the negative impact of cancer and treatment on bone remodeling.

Computational Analysis of the Influence of Menopause and Ageing on Bone Mineral Density, Exploring the Impact of Bone Turnover and Focal Bone Balance-A Study on Overload and Underload Scenarios

This study aims to investigate the impact of hormonal imbalances during menopause, compounded by the natural ageing process, on bone health. Specifically, it examines the effects of increased bone turnover and focal bone balance on bone mass. A three-dimensional computational bone remodeling model was employed to simulate the response of the femur to habitual loads over a 19-year period, spanning premenopause, menopause, and postmenopause. The model was calibrated using experimental bone mineral density data from the literature to ensure accurate simulations. The study reveals that individual alterations in bone turnover or focal bone balance do not fully account for the observed experimental outcomes. Instead, simultaneous changes in both factors provide a more comprehensive explanation, leading to increased porosity while maintaining the material-to-apparent density ratio. Additionally, different load scenarios were tested, demonstrating that reaching the clinical osteoporosis threshold is independent of the timing of load changes. However, underload scenarios resulted in the threshold being reached approximately 6 years earlier than overload scenarios. These findings hold significant implications for strategies aimed at delaying the onset of osteoporosis and minimizing fracture risks through targeted mechanical stimulation during the early stages of menopause.

Mathematical models of cystic fibrosis as a systemic disease

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Effect of platelet-rich plasma on the acceleration of graft bone catabolism in lateral lumbar interbody fusion in a short-term assessment

This study aimed to demonstrate whether impregnating the graft bone with platelet-rich plasma (PRP) accelerates graft bone catabolism in lateral lumbar interbody fusion (LLIF). Consecutive patients who underwent LLIF were assessed. Of the two spaces for bone grafts in the intervertebral cage, one space was filled with graft bone impregnated with PRP, and the other was filled with graft bone without PRP, which divided the graft bones into PRP and non-PRP groups. The mean Hounsfield units (HU) of the graft bone at the center of the cage space in the coronal and axial slices were measured using computed tomography (CT) images 1 week and 6 months after surgery. The delta value of HU from 1 week to 6 months after surgery was calculated for the PRP and non-PRP groups. We compared the delta values of the HU between the two groups. The PRP and non-PRP groups comprised 16 bone grafts. In the coronal slices, the HU value in the PRP group (delta value: 526.1 ± 352.2) tended to have a greater decrease at 6 months after surgery compared with that in the non-PRP group (delta value: 217.6 ± 240.4) (p = 0.065). In the axial slices, the HU value in the PRP group (delta value: 501.3 ± 319.6) was significantly decreased at 6 months after surgery compared with that in the non-PRP group (delta value: 159.2 ± 215.3) (p = 0.028). Impregnating the graft-bone with PRP accelerated graft bone catabolism in LLIF within 6 months after surgery.

Research Advances on Stem Cell-Derived Extracellular Vesicles Promoting the Reconstruction of Alveolar Bone through RANKL/RANK/OPG Pathway

Periodontal bone tissue defects and bone shortages are the most familiar and troublesome clinical problems in the oral cavity. Stem cell-derived extracellular vesicles (SC-EVs) have biological properties similar to their sources, and they could be a promising acellular therapy to assist with periodontal osteogenesis. In the course of alveolar bone remodeling, the RANKL/RANK/OPG signaling pathway is an important pathway involved in bone metabolism. This article summarizes the experimental studies of SC-EVs applied for the therapy of periodontal osteogenesis recently and explores the role of the RANKL/RANK/OPG pathway in their mechanism of action. Their unique patterns will open a new field of vision for people, and they will help to advance a possible future clinical treatment.

A coupled mathematical model between bone remodeling and tumors: a study of different scenarios using Komarova's model

This paper aims to construct a general framework of coupling tumor-bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova's model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova's model: first, using a "damage" parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion.

Temporal metabolic profiling of bone healing in a caprine tibia segmental defect model

Bone tissue engineering is an emerging field of regenerative medicine, with a wide array of biomaterial technologies and therapeutics employed. However, it is difficult to objectively compare these various treatments during various stages of tissue response. Metabolomics is rapidly emerging as a powerful analytical tool to establish broad-spectrum metabolic signatures for a target biological system. Developing an effective biomarker panel for bone repair from small molecule data would provide an objective metric to readily assess the efficacy of novel therapeutics in relation to natural healing mechanisms. In this study we utilized a large segmental bone defect in goats to reflect trauma resulting in substantial volumetric bone loss. Characterization of the native repair capacity was then conducted over a period of 12 months through the combination of standard (radiography, computed tomography, histology, biomechanics) data and ultra-high-performance liquid chromatography-high resolution mass spectrometry (UHPLC-HRMS) metabolic profiling. Standard metrics demonstrated that samples formed soft callus structures that later mineralized. Small molecule profiles showed distinct temporal patterns associated with the bone tissue repair process. Specifically, increased lactate and amino acid levels at early time points indicated an environment conducive to osteoblast differentiation and extracellular matrix formation. Citrate and pyruvate abundances increased at later time points indicating increasing mineral content within the defect region. Taurine, shikimate, and pantothenate distribution profiles appeared to represent a shift toward a more homeostatic remodeling environment with the differentiation and activity of osteoclasts offsetting the earlier deposition phases of bone repair. The generation of a comprehensive metabolic reference portfolio offers a potent mechanism for examining novel biomaterials and can serve as guide for the development of new targeted therapeutics to improve the rate, magnitude, and quality of bone regeneration.

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

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

A multi-model approach to predict efficacious clinical dose for an anti-TGF-β antibody (GC2008) in the treatment of osteogenesis imperfecta

Osteogenesis imperfecta (OI) is a heterogeneous group of inherited bone dysplasias characterized by reduced skeletal mass and bone fragility. Although the primary manifestation of the disease involves the skeleton, OI is a generalized connective tissue disorder that requires a multidisciplinary treatment approach. Recent studies indicate that application of a transforming growth factor beta (TGF-β) neutralizing antibody increased bone volume fraction (BVF) and strength in an OI mouse model and improved bone mineral density (BMD) in a small cohort of patients with OI. In this work, we have developed a multitiered quantitative pharmacology approach to predict human efficacious dose of a new anti-TGF-β antibody drug candidate (GC2008). This method aims to translate GC2008 pharmacokinetic/pharmacodynamic (PK/PD) relationship in patients, using a number of appropriate mathematical models and available preclinical and clinical data. Compartmental PK linked with an indirect PD effect model was used to characterize both pre-clinical and clinical PK/PD data and predict a GC2008 dose that would significantly increase BMD or BVF in patients with OI. Furthermore, a physiologically-based pharmacokinetic model incorporating GC2008 and the body's physiological properties was developed and used to predict a GC2008 dose that would decrease the TGF-β level in bone to that of healthy individuals. By using multiple models, we aim to reveal information for different aspects of OI disease that will ultimately lead to a more informed dose projection of GC2008 in humans. The different modeling efforts predicted a similar range of pharmacologically relevant doses in patients with OI providing an informed approach for an early clinical dose setting.

Experimental-based mechanobiological modeling of the anabolic and catabolic effects of breast cancer on bone remodeling

Bone is a biological tissue characterized by its hierarchical organization. This material has the ability to be continually renewed, which makes it highly adaptative to external loadings. Bone renewing is managed by a dynamic biological process called bone remodeling (BR), where continuous resorption of old bone and formation of new bone permits to change the bone composition and microstructure. Unfortunately, because of several factors, such as age, hormonal imbalance, and a variety of pathologies including cancer metastases, this process can be disturbed leading to various bone diseases. In this study, we have investigated the effect of breast cancer (BC) metastases causing osteolytic bone loss. BC has the ability to affect bone quantity in different ways in each of its primary and secondary stages. Based on a BR mathematical model, we modeled the BC cells' interaction with bone cells to assess their effect on bone volume fraction (BV/TV) evolution during the remodeling process. Some of the parameters used in our model have been determined experimentally using the enzyme-linked immune-sorbent assay (ELISA) and the MTT assay. Our numerical simulations show that primary BC plays a significant role in enhancing bone-forming cells' activity leading to a 6.22% increase in BV/TV over 1 year. On the other hand, secondary BC causes a noticeable decrease in BV/TV reaching 15.74% over 2 years.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

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.

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.