Figure - available from: PLOS One
This content is subject to copyright.
Cross section area (ABMU) of the tissue volume unit that a single BMU remodels in cortical and cancellous bone as a function of bone material volume For vb > 0.7, osteonal cross section is considered while for vb < 0.3, hemi-osteonal cross section is used instead. For bone material volume values between 0.3 and 0.7, a linear transition of cross section area is assumed.
Source publication
![Simplified scheme of the bone-remodelling computational model [21]
Note...](publication/315308299/figure/fig2/AS:11431281256797604@1719570943668/Simplified-scheme-of-the-bone-remodelling-computational-model-21-Note-that-for_Q320.jpg)
Bone is a living tissue whose main mechanical function is to provide stiffness, strength and protection to the body. Both stiffness and strength depend on the mineralization of the organic matrix, which is constantly being remodelled by the coordinated action of the bone multicellular units (BMUs). Due to the dynamics of both remodelling and minera...
Similar publications
There is still an urgent need for more efficient biological scaffolds to promote the healing of bone defects. Vessels can accelerate bone growth and regeneration by transporting nutrients, which is an excellent method to jointly increase osteogenesis and angiogenesis in bone regeneration. Therefore, we aimed to prepare a composite scaffold that cou...
Background: Bone healing of fractures is still an open field for research due to its biological complexity. Adequately adapted experimental model is essential for understanding the factors
influencing the biological process of bone healing. Rabbits provide a good animal model for bone healing studies; its bone had Haversian system similar to human....
Bisphosphonates (BP) decrease bone resorption to curb the activity of the osteoclasts. Vitamin E is an antioxidant and its positive effect on the bone would be by preventing oxidative stress. Infiltrative Alendronate and vitamin E administration wasstudied to determine if they favored the formation of bone in bone repair of the postextraction alveo...
An ideal craniofacial bone repair graft shall not only focus on the repair ability but also the regeneration of natural architecture with occlusal loads‐related function restoration. However, such functional bone tissue engineering scaffold has rarely been reported. Herein, a hierarchical 3D graft is proposed for rebuilding craniofacial bone with b...
Timing bone fractures is one of the main tasks of a forensic anthropologist, but still an uncertain diagnostic. In the literature, there are many macroscopic methods to distinguish perimortem from postmortem fractures, based on the distinct structural and mechanical properties of fresh and dry bones. However, this differentiation is still challengi...
Citations
... En este trabajo, persiguiendo el objetivo de estimar los cambios de densidad ósea tras una cirugía de cadera, se parte de un modelo que se basa en el comportamiento de las UBMs. Este modelo ha demostrado dar buenos resultados (Berli et al., 2017(Berli et al., , 2022Franco et al., 2023) y en este trabajo se lo adapta para su utilización en simulaciones de huesos con implantes. ...
... El modelo propuesto se basa en el utilizado en trabajos previos Berli et al. (2017Berli et al. ( , 2022; Franco et al. (2023). En estos trabajos se describe en detalle los diferentes aspectos del modelo por lo que en esta sección solo se mencionan los conceptos más relevantes. ...
Los modelos numéricos para predecir el efecto mecánico de las prótesis de cadera en el hueso humano suelen considerar a este último como un material estático, sin cambios ante la presencia del implante. Esto limita su capacidad predictiva a largo plazo a nivel del tejido, generando dudas sobre el éxito mecánico del diseño de la prótesis. Para un análisis integral del implante y su efecto en el hueso receptor, se necesita un modelo que refleje la adaptación biológica del tejido mediante la remodelación ósea. Aunque algunos estudios han implementado modelos de remodelación, no abordan un análisis tridimensional que incluya una interacción implante-hueso con condiciones de contorno de contacto y un modelo capaz de predecir densidades óseas fisiológicamente posibles. Este trabajo presenta un modelo de remodelación ósea del fémur humano, aplicado al análisis de prótesis de cadera implantadas, con un modelo de contacto entre hueso e implante. Los resultados subrayan la importancia del diseño geométrico del implante en la evolución a largo plazo de la masa ósea.
... The permeability was determined in accordance with the dependence of the permeability on the modulus of elasticity presented in [33 ; 34]. The porosity θ was calculated from the relationship [7]: θ = 1 − VB/VT, где VB/VT -volume fraction of trabecular bone according to experimental data [63]. The outer shell imitated a muscle tissue layer with poroelastic characteristics from [54]. ...
... two variable parameters representing (1) the mechanosensitivity (k) that affects the bone deposition rate (V) and (2) a reduction factor (α) for the mechanical stimulus that varied based on the implantation site ( Fig. 2 [57,62]; and the reduction factor was set at 50% as fitted in our previous work [41]. The material properties of the newly formed tissue and the normalized cell concentration (c) in the granulation tissue were updated after each iteration with a UMAT and UMATHT subroutines respectively. ...
Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold’s architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold’s core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold’s geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes.
... The majority of works agree that the primary mineralisation takes about 5-10 days (Boivin et al. 2009), but discrepancies are found regarding secondary mineralisation time T sec . While some experimental studies state that secondary mineralisation takes place up to several months (Berli et al. 2017), several numerical studies use values of up to 10 years for secondary mineralisation (Martínez-Reina et al. 2008;Bala et al. 2007). Aiming to analyse the mineralisation kinetics, we studied different values for T sec , as seen in left panel of Fig. 5. ...
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, a Ac . f = 4 BMU/year/mm 3 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.
... This disruption primarily impacts two factors crucial to Basic Multicellular Units (BMUs): the activation frequency, closely related with the bone turnover, and the focal bone balance. The cellular intricacies of bone turnover and focal bone balance have been explored in earlier studies [8,9]. As a consequence of the loss of hormonal anti-catabolic action, the frequency of BMU activation increases from premenopausal levels and the remodeling balance tends toward net resorption, resulting in an excessive loss of bone density [10,11]. ...
... A computational model capable of simulating this behaviour for realistic geometries and loads would provide a valuable tool for predicting the evolution of bone mass in women in clinical situations of interest. Recent studies have pursued this goal to obtain a better understanding of the resorption process [8] and achieved validation in three-dimensional models [9], albeit without incorporating menopausal effects. Another aspect not considered in conjunction with these effects is the self-accommodation of bone tissue to the stimuli it undergoes [26]. ...
... The proposed model is based on previous works [8,9]. In this section, we compile a summary of the most relevant equations to understand the model. ...
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.
... of works agree that the primary mineralisation takes about 5-10 days(Boivin et al, 2009), but discrepancies are found regarding secondary mineralisation time T sec . While some experimental studies state that secondary mineralisation takes place up to several months(Berli et al, 2017), several numerical studies use values of up to 10 years for secondary mineralisation(Martínez-Reina et al, 2008;Bala et al, 2007).Aiming to analyse the mineralisation kinetics, westudied different values for T sec , as seen in left panel of Fig. 4. More details about the secondary mineralisation time T sec and the parameters of the mineralisation law M in Eq. (14) can be found in Appendix A. Even though the mineralisation laws are written in terms of the ash factor α, the evolution of mineral fraction over time can be obtained by using Eq. ...
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, a Ac.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 conclusions 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.
... two variable parameters representing (1) the mechanosensitivity (k) that affects the bone deposition rate (V) and (2) a reduction factor (α) for the mechanical stimulus that varied based on the implantation site ( Fig. 2 [57,62]; and the reduction factor was set at 50% as fitted in our previous work [41]. The material properties of the newly formed tissue and the normalized cell concentration (c) in the granulation tissue were updated after each iteration with a UMAT and UMATHT subroutines respectively. ...
Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold's architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold's core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold's geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes.
... The permeability was determined by the dependence of the permeability on the modulus of elasticity presented in [33 ; 34]. The porosity ϕ was calculated from the relationship [7]: ϕ = 1 − VB/VT, where VB/VT is the volume fraction of trabecular bone according to experimental data [63]. The outer shell imitated a muscle tissue layer with poroelastic characteristics from [54]. ...
... , Δεij and Δγij are the increments of normal and shear strains of the automaton i in i-j pair, Gi is the shear modulus of the material of the automaton i, Ki is the bulk modulus, Di = 1−2Gi/Ki. Formulae(7) are written by analogy with the expressions for the components of the stress tensor of an elastic body, diagonal in the first expression and off-diagonal (shear) in the second. Note that the indices i and j in formulas (1)-(5) and below denote the number of the automaton, and ij are the numbers of the automata in the pair for which the interaction is calculated, and not the axes of the coordinate system, as in the usual expressions of the theory of elasticity. ...
Degenerative diseases are one of the main causes of disability in the middle-aged and older population. One of the most common diseases is osteoporosis and osteonecrosis of the femoral head. For the prevention and treatment of osteoporosis, osteopenia, and osteonecrosis, external mechanical stimulation based on ultrasound and shock wave exposure is used, based on local ultrasonic or shock wave exposure in the area of pathology. The effect of external mechanical action is based on mechanobiological principles, the essence of which is that a certain level of pressure (mechanical stress) and deformation leads to the growth and differentiation of various types of biological tissue. To obtain a therapeutic effect, it is necessary to correctly choose the parameters of exposure and the place of its application. Usually, these problems are solved empirically. In this work, the possibility of creating conditions for bone tissue regeneration under external acoustic impact on a healthy hip joint and a joint affected by osteonecrosis was studied numerically. The study was carried out using the method of mobile cellular automata. The results obtained showed the effectiveness of the use of medium- and high-intensity ultrasound exposure for the prevention of osteopenia and osteoporosis. When exposed to ultrasound on a joint with osteonecrosis of the head, the creation of conditions for osteogenesis and chondrogenesis in the affected area is observed only with high-intensity loading. Thus, the hypothesis that low-intensity ultrasound therapy is effective only in combination with other methods of treatment was con-firmed. It was found that shock-wave action of low intensity promotes the division of biological cells and their transfer, thereby creating conditions for the regeneration of bone tissues. This conclusion is consistent with the results of most experimental studies.
... and a decreasing trend in BMD and BV/TV, in the subgroups sacrificed at 6 and 8 weeks. As the values of BS/BV and BS/TV increase, the remodeling rate becomes higher, and the mineral density becomes lower due to the increased formation and presence of osteoid 42 . These parameters are associated with the propensity of tissue to renew and adapt its microstructure by initiating bone modeling and remodeling events. ...
Bisphosphonate (BP) discontinuation has been advised as a measure to prevent the incidence of bisphosphonate-related osteonecrosis of the jaw (BRONJ), however, its efficacy remains controversial. This study aimed to analyze the efficacy of BP discontinuation in reducing BRONJ severity following tooth extraction in a rat model. Thirty-four male Sprague–Dawley rats were divided into two BRONJ model categories: oral administration (PO) of alendronate (1 mg/kg) for 3 and 8 weeks and intraperitoneal (IP) injection of pamidronate (3 mg/kg) and dexamethasone (1 mg/kg) for 20 days. The PO model was divided into five groups (a control group without BPs and four experimental groups with 1-week discontinuation). The IP model was divided into two groups consisting of group I (without discontinuation) and group II (1-week discontinuation). One molar from both sides of the mandible was extracted. After extraction, the PO models were sacrificed at 3 and 5 weeks, and the IP models were sacrificed either immediately or at 2, 4, 6, and 8 weeks. Micro-CT showed non-significant differences among PO groups but significant differences were observed between IP groups. Most bone remodeling parameters within group I of the IP model differed significantly (p-value < 0.05). Histologically, group I showed a significantly higher percentage of necrotic bone than group II (51.93 ± 12.75%, p < 0.05) and a higher number of detached osteoclasts in TRAP staining. With discontinuation of medication for at least 1 week in rats, the effects of BPs on alveolar bone are suppressed and bone turnover and osteoclast functions are restored.
... In contrast to modelling, in remodelling the osteoblasts and osteoclasts always work together in a coordinated way, forming the so-called basic multicellular unit (BMU) [5], [6]. Remodelling is responsible for tissue maintenance, repair and constant internal adaptation to changing loads, an endless process that continues throughout life [7]- [10]. At the same time, remodelling is the process by which homeostasis in blood calcium and other minerals is maintained by hormonal regulation through the constant mineral interchange between bone and blood [4], [11]. ...
... Martin's hypothesis, this process is constantly being activated and the signals coming from osteocytes may only moderate the intensity of the BMU activity [3], contrary to other theories postulating that osteocytes sense mechanical stimuli and initiate remodelling to modify the bone structure accordingly (see Martin [14] and references therein). These load-linked signals control the number of BMUs activated per unit volume and per unit time [7], [10], [15] and, at the same time, regulate the net bone deposited or resorbed by each BMU depending on how the load magnitudes compare to those that under normal daily routines would maintain homeostasis [4]. Inhibitory theory states that BMUs activity rates are higher in cases of disuse and damage, which is experimentally observed [14]. ...
... Taking all this into account, we proposed, in a previous work [7] Therefore, a mathematical scheme of bone remodelling was computationally implemented on a 3D geometrical model of proximal human femur. Inhibitory theory and the proposed resorption strategy developed in [7] were included, which lead to interesting biological connotations of how bone is remodelled and mineral is distributed within a full 3D geometry which, as far as authors are concerned, has not been reported previously in computational studies. ...
Bone mechanical and biological properties are closely linked to its internal tissue composition and mass distribution, which are in turn governed by the purposeful action of the basic multicellular units (BMUs). The orchestrated action of osteoclasts and osteoblasts, the resorbing and forming tissue cells respectively, in BMUs is responsible for tissue maintenance, repair and adaptation to changing load demands through the phenomenon known as remodelling. In this work, a computational mechano-biological model of bone remodelling based on the inhibitory theory and a new scheme of bone resorption introduced previously in a 2D model, is extended to a 3D model of the real external geometry of a femur under normal walking loads. Starting from a uniform apparent density (ratio of tissue local mass to total local volume) distribution, the BMU action can be shown to lead naturally to an internal density distribution similar to that of a real bone, provided that the initial density value is high enough to avoid unrealistic final mass deposition in zones of high energy density and excessive damage. Physiological internal density values are reached throughout the whole 3D geometry, and at the same time a ‘boomerang’-like relationship between apparent and material density (ratio of tissue mass to tissue volume) emerges naturally under the proposed remodelling scheme. It is also shown here that bone-specific surface is a key parameter that determines the intensity of BMU action linked to the mechanical and biological requirements. Finally, by engaging in simulations of bone in disuse, we were able to confirm the appropriate selection of the model parameters. As an example, our results show good agreement with experimental measurements of bone mass on astronauts a fact that strengthens our belief in the insightful nature of our novel 3D computational model.
