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Sánchez JF, Ramtani S, Boucetta A, Velasco MA, Vaca-González JJ, Duque-Daza CA, Garzón-Alvarado DA. Tumor growth for remodeling process: A 2D approach. J Theor Biol 2024; 585:111781. [PMID: 38432504 DOI: 10.1016/j.jtbi.2024.111781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 02/07/2024] [Accepted: 02/27/2024] [Indexed: 03/05/2024]
Abstract
This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.
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Affiliation(s)
| | - Salah Ramtani
- Laboratoire CSPBAT, equipe LBPS, CNRS (UMR 7244), Universit e Sorbonne Paris Nord, France.
| | - Abdelkader Boucetta
- Laboratoire CSPBAT, equipe LBPS, CNRS (UMR 7244), Universit e Sorbonne Paris Nord, France
| | | | - Juan Jairo Vaca-González
- Escuela de Pregrado - Direccion Académica, Universidad Nacional de Colombia, Sede de La Paz, Colombia.
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2
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Martin BL, Reynolds KJ, Fazzalari NL, Bottema MJ. Modelling the Effects of Growth and Remodelling on the Density and Structure of Cancellous Bone. Bull Math Biol 2024; 86:37. [PMID: 38436708 PMCID: PMC10912124 DOI: 10.1007/s11538-024-01267-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 02/08/2024] [Indexed: 03/05/2024]
Abstract
A two-stage model is proposed for investigating remodelling characteristics in bone over time and distance to the growth plate. The first stage comprises a partial differential equation (PDE) for bone density as a function of time and distance from the growth plate. This stage clarifies the contributions to changes in bone density due to remodelling and growth processes and tracks the rate at which new bone emanates from the growth plate. The second stage consists of simulating the remodelling process to determine remodelling characteristics. Implementing the second stage requires the rate at which bone moves away from the growth plate computed during the first stage. The second stage is also needed to confirm that remodelling characteristics predicted by the first stage may be explained by a realistic model for remodelling and to compute activation frequency. The model is demonstrated on microCT scans of tibia of juvenile female rats in three experimental groups: sham-operated control, oestrogen deprived, and oestrogen deprived followed by treatment. Model predictions for changes in bone density and remodelling characteristics agree with the literature. In addition, the model provides new insight into the role of treatment on the density of new bone emanating from the growth plate and provides quantitative descriptions of changes in remodelling characteristics beyond what has been possible to ascertain by experimentation alone.
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Affiliation(s)
- Brianna L Martin
- Marine Spatial Ecology Laboratory, School of the Environment, The University of Queensland, Level 5, Goddard Building, St. Lucia, QLD, 4072, Australia
| | - Karen J Reynolds
- Medical Device Research Institute, College of Science and Engineering, Flinders University, Tonsley Campus, 1284 South Rd, Clovelly Park, SA, 5042, Australia
| | - Nicola L Fazzalari
- Medical Device Research Institute, College of Science and Engineering, Flinders University, Tonsley Campus, 1284 South Rd, Clovelly Park, SA, 5042, Australia
| | - Murk J Bottema
- Medical Device Research Institute, College of Science and Engineering, Flinders University, Tonsley Campus, 1284 South Rd, Clovelly Park, SA, 5042, Australia.
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3
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Miller CJ, Pickering E, Martelli S, Dall'Ara E, Delisser P, Pivonka P. Cortical bone adaptation response is region specific, but not peak load dependent: insights from μ CT image analysis and mechanostat simulations of the mouse tibia loading model. Biomech Model Mechanobiol 2024; 23:287-304. [PMID: 37851203 PMCID: PMC10901956 DOI: 10.1007/s10237-023-01775-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 09/20/2023] [Indexed: 10/19/2023]
Abstract
The two major aims of the present study were: (i) quantify localised cortical bone adaptation at the surface level using contralateral endpoint imaging data and image analysis techniques, and (ii) investigate whether cortical bone adaptation responses are universal or region specific and dependent on the respective peak load. For this purpose, we re-analyse previously published μ CT data of the mouse tibia loading model that investigated bone adaptation in response to sciatic neurectomy and various peak load magnitudes (F = 0, 2, 4, 6, 8, 10, 12 N). A beam theory-based approach was developed to simulate cortical bone adaptation in different sections of the tibia, using longitudinal strains as the adaptive stimuli. We developed four mechanostat models: universal, surface-based, strain directional-based, and combined surface and strain direction-based. Rates of bone adaptation in these mechanostat models were computed using an optimisation procedure (131,606 total simulations), performed on a single load case (F = 10 N). Subsequently, the models were validated against the remaining six peak loads. Our findings indicate that local bone adaptation responses are quasi-linear and bone region specific. The mechanostat model which accounted for differences in endosteal and periosteal regions and strain directions (i.e. tensile versus compressive) produced the lowest root mean squared error between simulated and experimental data for all loads, with a combined prediction accuracy of 76.6, 55.0 and 80.7% for periosteal, endosteal, and cortical thickness measurements (in the midshaft of the tibia). The largest root mean squared errors were observed in the transitional loads, i.e. F = 2 to 6 N, where inter-animal variability was highest. Finally, while endpoint imaging studies provide great insights into organ level bone adaptation responses, the between animal and loaded versus control limb variability make simulations of local surface-based adaptation responses challenging.
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Affiliation(s)
- Corey J Miller
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane, Australia.
| | - Edmund Pickering
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane, Australia
| | - Saulo Martelli
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane, Australia
| | - Enrico Dall'Ara
- Department of Oncology and Metabolism and Insigneo Institute for In Silico Medicine, University of Sheffield, Sheffield, UK
| | | | - Peter Pivonka
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology (QUT), Brisbane, Australia.
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4
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Sen A, Follet H, Sornay-Rendu E, Rémond Y, George D. Prediction of osteoporotic degradation of tibia human bone at trabecular scale. J Mech Behav Biomed Mater 2023; 139:105650. [PMID: 36657191 DOI: 10.1016/j.jmbbm.2023.105650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Revised: 11/18/2022] [Accepted: 01/01/2023] [Indexed: 01/11/2023]
Abstract
A theoretical numerical model is proposed to predict patient dependent osteoporotic bone degradation. The model parameters are identified through a particle swarm optimization algorithm and based on individual patient high resolution peripherical quantitative computer tomography (HRpQCT) scan data. The degradation model is based on cellular activity initiated by the elastic strain energy developed in the bone microstructure through patient's body weight. The macro (organ scale) and meso (trabecular scale) scale analyses are carried out and predicted bone volume fraction and microstructure evolution are compared with in-vivo experimental bone degradation for four elderly women over a period of 10 years. A significant correlation (r > 0.9) is observed between the model predictions and in-vivo experiments in all cases with an average deviation error of 1.46%. The model can easily be extended to other patients and provide good predictions for different population categories such as ethnicity, gender, age, etc.
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Affiliation(s)
- Ahmet Sen
- University of Strasbourg, CNRS, ICUBE Laboratory, Strasbourg, France
| | - Hélène Follet
- University Claude Bernard Lyon 1, INSERM, LYOS UMR 1033, 69008, Lyon, France.
| | - Elisabeth Sornay-Rendu
- University Claude Bernard Lyon 1, INSERM, LYOS UMR 1033, 69008, Lyon, France; Edouard Heriot Hospital, Hospices Civils of Lyon, 69437, Lyon, France
| | - Yves Rémond
- University of Strasbourg, CNRS, ICUBE Laboratory, Strasbourg, France
| | - Daniel George
- University of Strasbourg, CNRS, ICUBE Laboratory, Strasbourg, France.
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5
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Development of Osteopenia During Distal Radius Fracture Recovery. JOURNAL OF HAND SURGERY GLOBAL ONLINE 2022; 4:315-319. [DOI: 10.1016/j.jhsg.2022.09.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 09/01/2022] [Indexed: 11/20/2022] Open
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6
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Ledoux C, Boaretti D, Sachan A, Müller R, Collins CJ. Clinical Data for Parametrization of In Silico Bone Models Incorporating Cell-Cytokine Dynamics: A Systematic Review of Literature. Front Bioeng Biotechnol 2022; 10:901720. [PMID: 35910035 PMCID: PMC9335409 DOI: 10.3389/fbioe.2022.901720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/13/2022] [Indexed: 11/13/2022] Open
Abstract
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.
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Affiliation(s)
- Charles Ledoux
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
| | | | - Akanksha Sachan
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India
| | - Ralph Müller
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
| | - Caitlyn J. Collins
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
- Department for Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VI,United States
- *Correspondence: Caitlyn J. Collins,
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7
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Poorhemati H, Komarova SV. Mathematical modeling of the role of bone turnover in pH regulation in bone interstitial fluid. Comput Biol Chem 2021; 94:107564. [PMID: 34455167 DOI: 10.1016/j.compbiolchem.2021.107564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 07/20/2021] [Accepted: 08/15/2021] [Indexed: 11/26/2022]
Abstract
BACKGROUND AND AIMS Bone turnover is strongly affected by pH of surrounding fluid, and in turn plays a role in maintaining systemic pH, however the quantitative contribution of bone processes to pH regulation is not known. Our goal was to develop a mathematical model describing pH regulation in the interstitial fluid and to examine the contribution of hydroxyapatite dissolution and precipitation to pH regulation. MATERIALS AND METHODS We modeled twelve reversible equilibrium reactions of sixteen calcium, phosphate, hydrogen and carbonate species in the interstitial fluid and examined the buffering capacity and range. The effect of hydroxyapatite dissolution and precipitation was modeled by assuming that the calcium, phosphate and hydroxide contained in the bone volume adjacent to the interstitial fluid is instantaneously added to or removed from the interstitial fluid. RESULTS The carbonate buffer was found to dominate electrochemical buffering system of the bone interstitial fluid. Nevertheless, the phosphate added during dissolution of bone hydroxyapatite significantly improved the interstitial fluid buffering capacity. In contrast, hydroxyapatite precipitation had limited effect on the interstitial fluid pH regulation. CONCLUSION This study provides mechanistic insights into the physicochemical processes underlying the known role of bone turnover processes in regulation of body pH homeostasis.
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Affiliation(s)
- Hossein Poorhemati
- Department of Biological and Biomedical Engineering, McGill University, Montreal, QC, Canada; Shriners Hospital for Children - Canada, Montreal, QC, Canada.
| | - Svetlana V Komarova
- Department of Biological and Biomedical Engineering, McGill University, Montreal, QC, Canada; Shriners Hospital for Children - Canada, Montreal, QC, Canada; Faculty of Dentistry, McGill University, Montreal, QC, Canada.
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8
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Miller CJ, Trichilo S, Pickering E, Martelli S, Delisser P, Meakin LB, Pivonka P. Cortical Thickness Adaptive Response to Mechanical Loading Depends on Periosteal Position and Varies Linearly With Loading Magnitude. Front Bioeng Biotechnol 2021; 9:671606. [PMID: 34222215 PMCID: PMC8249932 DOI: 10.3389/fbioe.2021.671606] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 05/21/2021] [Indexed: 11/13/2022] Open
Abstract
The aim of the current study was to quantify the local effect of mechanical loading on cortical bone formation response at the periosteal surface using previously obtained μCT data from a mouse tibia mechanical loading study. A novel image analysis algorithm was developed to quantify local cortical thickness changes (ΔCt.Th) along the periosteal surface due to different peak loads (0N ≤ F ≤ 12N) applied to right-neurectomised mature female C57BL/6 mice. Furthermore, beam analysis was performed to analyse the local strain distribution including regions of tensile, compressive, and low strain magnitudes. Student’s paired t-test showed that ΔCt.Th in the proximal (25%), proximal/middle (37%), and middle (50%) cross-sections (along the z-axis of tibia) is strongly associated with the peak applied loads. These changes are significant in a majority of periosteal positions, in particular those experiencing high compressive or tensile strains. No association between F and ΔCt.Th was found in regions around the neutral axis. For the most distal cross-section (75%), the association of loading magnitude and ΔCt.Th was not as pronounced as the more proximal cross-sections. Also, bone formation responses along the periosteum did not occur in regions of highest compressive and tensile strains predicted by beam theory. This could be due to complex experimental loading conditions which were not explicitly accounted for in the mechanical analysis. Our results show that the bone formation response depends on the load magnitude and the periosteal position. Bone resorption due to the neurectomy of the loaded tibia occurs throughout the entire cross-sectional region for all investigated cortical sections 25, 37, 50, and 75%. For peak applied loads higher than 4 N, compressive and tensile regions show bone formation; however, regions around the neutral axis show constant resorption. The 50% cross-section showed the most regular ΔCt.Th response with increased loading when compared to 25 and 37% cross-sections. Relative thickness gains of approximately 70, 60, and 55% were observed for F = 12 N in the 25, 37, and 50% cross-sections. ΔCt.Th at selected points of the periosteum follow a linear response with increased peak load; no lazy zone was observed at these positions.
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Affiliation(s)
- Corey J Miller
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
| | - Silvia Trichilo
- St. Vincent's Department of Surgery, University of Melbourne, Melbourne, VIC, Australia
| | - Edmund Pickering
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
| | - Saulo Martelli
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
| | - Peter Delisser
- School of Veterinary Sciences, University of Bristol, Bristol, United Kingdom
| | - Lee B Meakin
- School of Veterinary Sciences, University of Bristol, Bristol, United Kingdom
| | - Peter Pivonka
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
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9
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A General Mechano-Pharmaco-Biological Model for Bone Remodeling Including Cortisol Variation. MATHEMATICS 2021. [DOI: 10.3390/math9121401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
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.
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10
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Cheong VS, Kadirkamanathan V, Dall'Ara E. The Role of the Loading Condition in Predictions of Bone Adaptation in a Mouse Tibial Loading Model. Front Bioeng Biotechnol 2021; 9:676867. [PMID: 34178966 PMCID: PMC8225949 DOI: 10.3389/fbioe.2021.676867] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2021] [Accepted: 05/10/2021] [Indexed: 11/13/2022] Open
Abstract
The in vivo mouse tibial loading model is used to evaluate the effectiveness of mechanical loading treatment against skeletal diseases. Although studies have correlated bone adaptation with the induced mechanical stimulus, predictions of bone remodeling remained poor, and the interaction between external and physiological loading in engendering bone changes have not been determined. The aim of this study was to determine the effect of passive mechanical loading on the strain distribution in the mouse tibia and its predictions of bone adaptation. Longitudinal micro-computed tomography (micro-CT) imaging was performed over 2 weeks of cyclic loading from weeks 18 to 22 of age, to quantify the shape change, remodeling, and changes in densitometric properties. Micro-CT based finite element analysis coupled with an optimization algorithm for bone remodeling was used to predict bone adaptation under physiological loads, nominal 12N axial load and combined nominal 12N axial load superimposed to the physiological load. The results showed that despite large differences in the strain energy density magnitudes and distributions across the tibial length, the overall accuracy of the model and the spatial match were similar for all evaluated loading conditions. Predictions of densitometric properties were most similar to the experimental data for combined loading, followed closely by physiological loading conditions, despite no significant difference between these two predicted groups. However, all predicted densitometric properties were significantly different for the 12N and the combined loading conditions. The results suggest that computational modeling of bone's adaptive response to passive mechanical loading should include the contribution of daily physiological load.
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Affiliation(s)
- Vee San Cheong
- Insigneo Institute for in Silico Medicine, University of Sheffield, Sheffield, United Kingdom.,Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, United Kingdom
| | - Visakan Kadirkamanathan
- Insigneo Institute for in Silico Medicine, University of Sheffield, Sheffield, United Kingdom.,Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, United Kingdom
| | - Enrico Dall'Ara
- Insigneo Institute for in Silico Medicine, University of Sheffield, Sheffield, United Kingdom.,Department of Oncology and Metabolism, University of Sheffield, Sheffield, United Kingdom
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11
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Load adaptation through bone remodeling: a mechanobiological model coupled with the finite element method. Biomech Model Mechanobiol 2021; 20:1495-1507. [PMID: 33900492 DOI: 10.1007/s10237-021-01458-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Accepted: 04/05/2021] [Indexed: 10/21/2022]
Abstract
This work proposes a novel tissue-scale mechanobiological model of bone remodeling to study bone's adaptation to distinct loading conditions. The devised algorithm describes the mechanosensitivity of bone and its impact on bone cells' functioning through distinct signaling factors. In this study, remodeling is mechanically ruled by variations of the strain energy density (SED) of bone, which is determined by performing a linear elastostatic analysis combined with the finite element method. Depending on the SED levels and on a set of biological signaling factors ([Formula: see text] parameters), osteoclasts and osteoblasts can be mechanically triggered. To reproduce this phenomenon, this work proposes a new set of [Formula: see text] parameters. The combined response of osteoclasts and osteoblasts will then affect bone's apparent density, which is correlated with other mechanical properties of bone, through a phenomenological law. Thus, this novel model proposes a constant interplay between the mechanical and biological components of the process. The spatiotemporal simulation used to validate this new approach is a benchmark example composed by two distinct phases: (1) pre-orientation and (2) load adaptation. On both of them, bone is able to adapt its morphology according to the loading condition, achieving the required trabecular distribution to withstand the applied loads. Moreover, the equilibrium morphology reflects the orientation of the load. These preliminary results support the new approach proposed in this study.
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12
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Miszkiewicz JJ, Valentin F, Vrahnas C, Sims NA, Vongsvivut J, Tobin MJ, Clark G. Bone loss markers in the earliest Pacific Islanders. Sci Rep 2021; 11:3981. [PMID: 33597553 PMCID: PMC7889909 DOI: 10.1038/s41598-021-83264-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 01/25/2021] [Indexed: 11/09/2022] Open
Abstract
Kingdom of Tonga in Polynesia is one of the most obese nations where metabolic conditions, sedentary lifestyles, and poor quality diet are widespread. These factors can lead to poor musculoskeletal health. However, whether metabolic abnormalities such as osteoporosis occurred in archaeological populations of Tonga is unknown. We employed a microscopic investigation of femur samples to establish whether bone loss afflicted humans in this Pacific region approximately 3000 years ago. Histology, laser confocal microscopy, and synchrotron Fourier-transform infrared microspectroscopy were used to measure bone vascular canal densities, bone porosity, and carbonate and phosphate content of bone composition in eight samples extracted from adult Talasiu males and females dated to 2650 BP. Compared to males, samples from females had fewer vascular canals, lower carbonate and phosphate content, and higher bone porosity. Although both sexes showed evidence of trabecularised cortical bone, it was more widespread in females (35.5%) than males (15.8%). Our data suggest experiences of advanced bone resorption, possibly as a result of osteoporosis. This provides first evidence for microscopic bone loss in a sample of archaeological humans from a Pacific population widely afflicted by metabolic conditions today.
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Affiliation(s)
- Justyna J Miszkiewicz
- School of Archaeology and Anthropology, Australian National University, 44 Linnaeus Way, Canberra, ACT, 2601, Australia.
| | - Frédérique Valentin
- CNRS, UMR 7041, ArScAn, Ethnologie préhistorique, Maison René-Ginouvès, Archéologie et Ethnologie, 21 Allée de l'Université, 92023, Nanterre Cedex, France.,Archaeology and Natural History, School of Culture History and Language, College of Asia and the Pacific, Australian National University, Canberra, ACT, 2601, Australia
| | - Christina Vrahnas
- Bone Biology and Disease Unit, St. Vincent's Institute of Medical Research, 9 Princes Street, Fitzroy, Melbourne, VIC, 3065, Australia.,Department of Medicine, St. Vincent's Hospital, The University of Melbourne, Melbourne, VIC, 3065, Australia.,MRC Protein Phosphorylation and Ubiquitylation Unit, James Black Centre, University of Dundee, Dundee, DD1 5EH, UK
| | - Natalie A Sims
- Department of Medicine, St. Vincent's Hospital, The University of Melbourne, Melbourne, VIC, 3065, Australia.,MRC Protein Phosphorylation and Ubiquitylation Unit, James Black Centre, University of Dundee, Dundee, DD1 5EH, UK
| | - Jitraporn Vongsvivut
- Infrared Microspectroscopy Beamline, ANSTO - Australian Synchrotron, 800 Blackburn Road, Clayton, VIC, 3168, Australia
| | - Mark J Tobin
- Infrared Microspectroscopy Beamline, ANSTO - Australian Synchrotron, 800 Blackburn Road, Clayton, VIC, 3168, Australia
| | - Geoffrey Clark
- Archaeology and Natural History, School of Culture History and Language, College of Asia and the Pacific, Australian National University, Canberra, ACT, 2601, Australia
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13
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Peyroteo MMA, Belinha J, Natal Jorge RM. A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method. Comput Biol Med 2020; 129:104170. [PMID: 33352308 DOI: 10.1016/j.compbiomed.2020.104170] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Revised: 12/03/2020] [Accepted: 12/04/2020] [Indexed: 11/18/2022]
Abstract
Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach - the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.
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Affiliation(s)
- M M A Peyroteo
- INEGI, Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal.
| | - J Belinha
- School of Engineering, Polytechnic of Porto (ISEP), Mechanical Engineering Department, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal.
| | - R M Natal Jorge
- Faculty of Engineering of the University of Porto, Mechanical Engineering Department, FEUP, Rua Dr. Roberto Frias, S/N, 4200-465, Porto, Portugal.
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14
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Ait Oumghar I, Barkaoui A, Chabrand P. Toward a Mathematical Modeling of Diseases' Impact on Bone Remodeling: Technical Review. Front Bioeng Biotechnol 2020; 8:584198. [PMID: 33224935 PMCID: PMC7667152 DOI: 10.3389/fbioe.2020.584198] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 09/30/2020] [Indexed: 12/18/2022] Open
Abstract
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.
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Affiliation(s)
- Imane Ait Oumghar
- Laboratoire des Energies Renouvelables et Matériaux Avancés (LERMA), Université Internationale de Rabat, Rabat-Sala El Jadida, Morocco.,Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France
| | - Abdelwahed Barkaoui
- Laboratoire des Energies Renouvelables et Matériaux Avancés (LERMA), Université Internationale de Rabat, Rabat-Sala El Jadida, Morocco
| | - Patrick Chabrand
- Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France
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15
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Lerebours C, Weinkamer R, Roschger A, Buenzli PR. Mineral density differences between femoral cortical bone and trabecular bone are not explained by turnover rate alone. Bone Rep 2020; 13:100731. [PMID: 33392366 PMCID: PMC7772649 DOI: 10.1016/j.bonr.2020.100731] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Revised: 10/12/2020] [Accepted: 10/25/2020] [Indexed: 11/24/2022] Open
Abstract
Bone mineral density distributions (BMDDs) are a measurable property of bone tissues that depends strongly on bone remodelling and mineralisation processes. These processes can vary significantly in health and disease and across skeletal sites, so there is high interest in analysing these processes from experimental BMDDs. Here, we propose a rigorous hypothesis-testing approach based on a mathematical model of mineral heterogeneity in bone due to remodelling and mineralisation, to help explain differences observed between the BMDD of human femoral cortical bone and the BMDD of human trabecular bone. Recent BMDD measurements show that femoral cortical bone possesses a higher bone mineral density, but a similar mineral heterogeneity around the mean compared to trabecular bone. By combining this data with the mathematical model, we are able to test whether this difference in BMDD can be explained by (i) differences in turnover rate; (ii) differences in osteoclast resorption behaviour; and (iii) differences in mineralisation kinetics between the two bone types. We find that accounting only for differences in turnover rate is inconsistent with the fact that both BMDDs have a similar spread around the mean, and that accounting for differences in osteoclast resorption behaviour leads to biologically inconsistent bone remodelling patterns. We conclude that the kinetics of mineral accumulation in bone matrix must therefore be different in femoral cortical bone and trabecular bone. Although both cortical and trabecular bone are made up of lamellar bone, the different mineralisation kinetics in the two types of bone point towards more profound structural differences than usually assumed.
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Affiliation(s)
- Chloé Lerebours
- School of Mathematical Sciences, Monash University, Clayton, Australia
| | - Richard Weinkamer
- Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Potsdam, Germany
| | - Andreas Roschger
- Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Potsdam, Germany.,Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, Salzburg, Austria
| | - Pascal R Buenzli
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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16
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Cheong VS, Roberts BC, Kadirkamanathan V, Dall'Ara E. Bone remodelling in the mouse tibia is spatio-temporally modulated by oestrogen deficiency and external mechanical loading: A combined in vivo/in silico study. Acta Biomater 2020; 116:302-317. [PMID: 32911105 DOI: 10.1016/j.actbio.2020.09.011] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Revised: 08/19/2020] [Accepted: 09/01/2020] [Indexed: 12/17/2022]
Abstract
Osteoporosis disrupts the healthy remodelling process in bone and affects its mechanical properties. Mechanical loading has been shown to be effective in stimulating bone formation to mitigate initial bone loss. However, no study has investigated the effects of repeated mechanical loading, with a pause of one week in between, in the mouse tibia with oestrogen deficiency. This study uses a combined experimental and computational approach, through longitudinal monitoring with micro-computed tomography, to evaluate the effects of loading on bone adaptation in the tibiae of ovariectomised (OVX) C57BL/6 mice from 14 to 22 weeks of age. Micro-FE models coupled with bone adaptation algorithms were used to estimate changes in local tissue strains due to OVX and mechanical loading, and to quantify the relationship between local strain and remodelling. The first in vivo mechanical loading increased apposition, by 50-150%, while resorption decreased by 50-60%. Both endosteal and periosteal resorption increased despite the second mechanical loading, and periosteal resorption was up to 70% higher than that after the first loading. This was found to correlate with an initial decrease in average strain energy density after the first loading, which was lower and more localised after the second loading. Predictions of bone adaptation showed that between 50 and 90% of the load-induced bone apposition is linearly strain driven at the organ-level, but resorption is more biologically driven at the local level. The results imply that a systematic increase in peak load or loading rate may be required to achieve a similar bone adaptation rate in specific regions of interests.
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17
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A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach. Biomech Model Mechanobiol 2020; 19:2499-2523. [PMID: 32623542 DOI: 10.1007/s10237-020-01353-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 05/29/2020] [Indexed: 12/26/2022]
Abstract
Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.
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18
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Martelli S, Beck B, Saxby D, Lloyd D, Pivonka P, Taylor M. Modelling Human Locomotion to Inform Exercise Prescription for Osteoporosis. Curr Osteoporos Rep 2020; 18:301-311. [PMID: 32335858 PMCID: PMC7250953 DOI: 10.1007/s11914-020-00592-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
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.
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Affiliation(s)
- Saulo Martelli
- Medical Device Research Institute, College of Science and Engineering, Flinders University, Tonsley, SA, 5042, Australia.
| | - Belinda Beck
- School of Allied Health Sciences, Griffith University, Gold Coast, QLD, Australia
| | - David Saxby
- School of Allied Health Sciences, Griffith University, Gold Coast, QLD, Australia
- Griffith Centre of Biomedical and Rehabilitation Engineering (GCORE), Menzies Health Institute Queensland, Griffith University, Gold Coast, QLD, Australia
| | - David Lloyd
- School of Allied Health Sciences, Griffith University, Gold Coast, QLD, Australia
- Griffith Centre of Biomedical and Rehabilitation Engineering (GCORE), Menzies Health Institute Queensland, Griffith University, Gold Coast, QLD, Australia
| | - Peter Pivonka
- School of Chemistry, Physics and Mechanical Engineering Queensland University of Technology, Brisbane, Australia
| | - Mark Taylor
- Medical Device Research Institute, College of Science and Engineering, Flinders University, Tonsley, SA, 5042, Australia
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Mattazio RR, Noritomi PY, Silveira ZC. An In Silico Model for the Prediction of Changes in Mineral Density in Cortical Bone Remodeling. J Biomech Eng 2020; 142:2737111. [PMID: 31233121 DOI: 10.1115/1.4044094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Indexed: 11/08/2022]
Abstract
An in silico model for the estimation of volumetric bone mineral density (vBMD) changes at a cortical bone site subjected to mechanobiological bone remodeling is proposed in this manuscript. Mechanisms of cell differentiation, receptor-ligand binding, mechanical signaling, and resorption or deposition of bone matrix were considered, therefore providing a comprehensive description of mechanobiological bone remodeling in the bone microenvironment and enabling the analysis of temporal evolution of disease or therapy scenarios. The proposed model is composed by five modules, namely, bone cells populations, mechanobiology, volume fractions and porosity, mineral density, and structural stiffness. The model is an extension of other models found in the literature because equations for the obtaining of cortical vBMD and the binding of parathyroid hormone (PTH) to parathyroid hormone 1 receptor are included. The proposed model showed a satisfactory agreement with the solutions of other in silico models found in the literature. Simulations of walking and running exercise routines were performed for the evaluation of model capability regarding the control of the numerical error and prediction of vBMD. The computational method used to solve the case study controlled the relative numerical error by less than 1 × 10-7 for approximately 1.7 × 106 time steps. The predicted values correlate with the concept of increasing BMD by vigorous physical activity; however, they contrast with the specific effect of physical activities on cortical vBMD.
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Affiliation(s)
- Rafael R Mattazio
- São Carlos School of Engineering, University of São Paulo, 400 Trabalhador São-carlense Avenue, São Carlos, SP 13566-590, Brazil
| | - Pedro Y Noritomi
- Three-dimensional Technologies, Information Technology Center Renato Archer, 143.6 Km Dom Pedro I Highway (SP-65), Campinas, SP 13069-901, Brazil
| | - Zilda C Silveira
- São Carlos School of Engineering, University of São Paulo, 400 Trabalhador São-carlense Avenue, São Carlos, SP 13566-590, Brazil
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20
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Alcântara ACS, Assis I, Prada D, Mehle K, Schwan S, Costa-Paiva L, Skaf MS, Wrobel LC, Sollero P. Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey. MATERIALS (BASEL, SWITZERLAND) 2019; 13:E106. [PMID: 31878356 PMCID: PMC6981613 DOI: 10.3390/ma13010106] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/16/2019] [Accepted: 12/17/2019] [Indexed: 12/26/2022]
Abstract
This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.
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Affiliation(s)
- Amadeus C. S. Alcântara
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
| | - Israel Assis
- Department of Integrated Systems, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil;
| | - Daniel Prada
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
| | - Konrad Mehle
- Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, 06217 Merseburg, Germany;
| | - Stefan Schwan
- Fraunhofer Institute for Microstructure of Materials and Systems IMWS, 06120 Halle/Saale, Germany;
| | - Lúcia Costa-Paiva
- Department of Obstetrics and Gynecology, School of Medical Sciences, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-887, Brazil;
| | - Munir S. Skaf
- Institute of Chemistry and Center for Computing in Engineering and Sciences, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil;
| | - Luiz C. Wrobel
- Institute of Materials and Manufacturing, Brunel University London, Uxbridge UB8 3PH, UK;
- Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
| | - Paulo Sollero
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
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21
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BARKAOUI ABDELWAHED, KAHLA RABEBBEN, MERZOUKI TAREK, HAMBLI RIDHA. NUMERICAL SIMULATION OF APPARENT DENSITY EVOLUTION OF TRABECULAR BONE UNDER FATIGUE LOADING: EFFECT OF BONE INITIAL PROPERTIES. J MECH MED BIOL 2019. [DOI: 10.1142/s0219519419500416] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Bone remodeling is a physiological phenomenon coupling resorption and formation processes that are mainly mediated by osteoclasts and osteoblasts, in response to mechanical stimuli transduced by osteocytes to biochemical signals activating the bone multicellular unit. Under normal loading conditions, bone resorption and formation are balanced by a homeostasis process. When bone is subjected to overstress, microdamaging occurs, which induces a modification of the structural integrity and microarchitecture. This has drawn significant attention to the mechanical properties of bone. In this context, the current study has been carried out with the aim of numerically investigating the impact of the mechanical properties on the remodeling process of the trabecular bone under cyclic loading, highlighting the effects of different values of the mineral density and the Young’s modulus. This was performed using a mechanobiological model, coupling mechanical and biological approaches, allowing to numerically simulate the effect of the selected parameters for a 20-year-period of cyclic loading for 2D and 3D models of a human femur head. The current work is an explorative numerical study, and the obtained results revealed the changes in the overall stiffness of the bone according to the mechanical properties.
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Affiliation(s)
- ABDELWAHED BARKAOUI
- Laboratoire des Energies Renouvelables et, Matériaux Avancés (LERMA), Ecole Supérieure de, l’Ingénierie de l’Energie, Université Internationale, de Rabat, Rocade Rabat-Salé, 11100, Rabat-Sala El Jadida, Maroc
| | - RABEB BEN KAHLA
- Laboratoire de Systèmes et de Mécanique, Appliquée (Lasmap-EPT), Ecole Polytechnique de Tunis, Université de Carthage, 2078 La Marsa, Tunisie
| | - TAREK MERZOUKI
- Laboratoire Ingénierie des Systèmes de Versailles, Université de Versailles St Quentin en Yvelines, 10 avenue de l’Europe, 78140 Velizy, France
| | - RIDHA HAMBLI
- Laboratoire Prisme, EA4229, Ecole d’Ingénieurs, Polytech Orléans, Université d’Orléans, 8 Rue Léonard de Vinci, 45072 Orléans, France
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22
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Computational model of the dual action of PTH - Application to a rat model of osteoporosis. J Theor Biol 2019; 473:67-79. [PMID: 31009612 DOI: 10.1016/j.jtbi.2019.04.020] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Revised: 04/18/2019] [Accepted: 04/19/2019] [Indexed: 11/22/2022]
Abstract
This paper presents a pharmacokinetic/pharmacodynamic (PK/PD) model of the action of PTH(1-34) on bone modelling and remodelling, developed for quantitatively investigating the dose- and administration pattern-dependency of the bone tissue response to this drug. Firstly, a PK model of PTH(1-34) was developed, accounting for administration via subcutaneous injections. Subsequently, the PK model was coupled to a (mechanistic) bone cell population model of bone modelling and remodelling, taking into account the effects of PTH(1-34) on the differentiation of lining cells into active osteoblasts, on the apoptosis of active osteoblasts, and on proliferation of osteoblast precursors, as well as on the key regulatory pathways of bone cell activities. Numerical simulations show that the coupled PK/PD model is able to distinguish between continuous and intermittent administration patterns of PTH(1-34), in terms of yielding both catabolic bone responses (if drug administration is carried out continuously) and anabolic bone responses (if drug administration is carried out intermittently). The model also features a non-linear relation between bone gain and drug dose (as known from experiments); doubling the dose from 80 μg/kg/day to 160 μg/kg/day induced a 1.3-fold increase of the bone volume-to-total volume ratio. Furthermore, the model presented in this paper confirmed that bone modelling represents an essential mechanism of the anabolic response of bone to PTH(1-34) administration in rat models, and that the large amount of bone formation observed in such models cannot be explained via remodelling alone.
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23
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Paul GR, Malhotra A, Müller R. Mechanical Stimuli in the Local In Vivo Environment in Bone: Computational Approaches Linking Organ-Scale Loads to Cellular Signals. Curr Osteoporos Rep 2018; 16:395-403. [PMID: 29915967 PMCID: PMC6579731 DOI: 10.1007/s11914-018-0448-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
PURPOSE OF REVIEW Connecting organ-scale loads to cellular signals in their local in vivo environment is a current challenge in the field of bone (re)modelling. Understanding this critical missing link would greatly improve our ability to anticipate mechanotransduction during different modes of stimuli and the resultant cellular responses. This review characterises computational approaches that could enable coupling links across the multiple scales of bone. RECENT FINDINGS Current approaches using strain and fluid shear stress concepts have begun to link organ-scale loads to cellular signals; however, these approaches fail to capture localised micro-structural heterogeneities. Furthermore, models that incorporate downstream communication from osteocytes to osteoclasts, bone-lining cells and osteoblasts, will help improve the understanding of (re)modelling activities. Incorporating this potentially key information in the local in vivo environment will aid in developing multiscale models of mechanotransduction that can predict or help describe resultant biological events related to bone (re)modelling. Progress towards multiscale determination of the cell mechanical environment from organ-scale loads remains elusive. Construction of organ-, tissue- and cell-scale computational models that include localised environmental variation, strain amplification and intercellular communication mechanisms will ultimately help couple the hierarchal levels of bone.
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Affiliation(s)
- Graeme R Paul
- Institute for Biomechanics, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093, Zürich, Switzerland
| | - Angad Malhotra
- Institute for Biomechanics, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093, Zürich, Switzerland
| | - Ralph Müller
- Institute for Biomechanics, ETH Zurich, Leopold-Ruzicka-Weg 4, 8093, Zürich, Switzerland.
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24
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Osteoblasts infill irregular pores under curvature and porosity controls: a hypothesis-testing analysis of cell behaviours. Biomech Model Mechanobiol 2018; 17:1357-1371. [DOI: 10.1007/s10237-018-1031-x] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Accepted: 05/12/2018] [Indexed: 01/11/2023]
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25
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Pastrama MI, Scheiner S, Pivonka P, Hellmich C. A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation. Bone 2018; 107:208-221. [PMID: 29170108 DOI: 10.1016/j.bone.2017.11.009] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 10/30/2017] [Accepted: 11/14/2017] [Indexed: 10/18/2022]
Abstract
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.
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Affiliation(s)
- Maria-Ioana Pastrama
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria; KU Leuven, Department of Movement Sciences, Human Movement Biomechanics Research Group, Tervuursevest 101, 3001 Leuven, Belgium
| | - Stefan Scheiner
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria.
| | - Peter Pivonka
- School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, 2 George St, Brisbane 4000, QLD, Australia; St. Vincent's Department of Surgery, The University of Melbourne, Clinical Science Building, 29 Regent Street, VIC 3065, Australia
| | - Christian Hellmich
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria
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26
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Martin M, Lemaire T, Haïat G, Pivonka P, Sansalone V. A thermodynamically consistent model of bone rotary remodeling: a 2D study. Comput Methods Biomech Biomed Engin 2017; 20:127-128. [PMID: 29088616 DOI: 10.1080/10255842.2017.1382894] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- M Martin
- a Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208, CNRS , Université Paris-Est , Créteil , France
| | - T Lemaire
- a Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208, CNRS , Université Paris-Est , Créteil , France
| | - G Haïat
- a Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208, CNRS , Université Paris-Est , Créteil , France
| | - P Pivonka
- b School of Chemistry, Physics and Mechanical Engineering , Queensland University of Technology , Australia
| | - V Sansalone
- a Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208, CNRS , Université Paris-Est , Créteil , France
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Abstract
Biomedical research and clinical practice are struggling to cope with the growing complexity that the progress of health care involves. The most challenging diseases, those with the largest socioeconomic impact (cardiovascular conditions; musculoskeletal conditions; cancer; metabolic, immunity, and neurodegenerative conditions), are all characterized by a complex genotype-phenotype interaction and by a "systemic" nature that poses a challenge to the traditional reductionist approach. In 2005 a small group of researchers discussed how the vision of computational physiology promoted by the Physiome Project could be translated into clinical practice and formally proposed the term Virtual Physiological Human. Our knowledge about these diseases is fragmentary, as it is associated with molecular and cellular processes on the one hand and with tissue and organ phenotype changes (related to clinical symptoms of disease conditions) on the other. The problem could be solved if we could capture all these fragments of knowledge into predictive models and then compose them into hypermodels that help us tame the complexity that such systemic behavior involves. In 2005 this was simply not possible-the necessary methods and technologies were not available. Now, 10 years later, it seems the right time to reflect on the original vision, the results achieved so far, and what remains to be done.
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Affiliation(s)
- Marco Viceconti
- Department of Mechanical Engineering and Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield S1 3JD, United Kingdom;
| | - Peter Hunter
- Auckland Bioengineering Institute, University of Auckland, Auckland 1142, New Zealand
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28
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Lerebours C, Buenzli PR. Towards a cell-based mechanostat theory of bone: the need to account for osteocyte desensitisation and osteocyte replacement. J Biomech 2016; 49:2600-2606. [DOI: 10.1016/j.jbiomech.2016.05.012] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2015] [Revised: 04/13/2016] [Accepted: 05/15/2016] [Indexed: 10/21/2022]
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Yu JS, Bagheri N. Multi-class and multi-scale models of complex biological phenomena. Curr Opin Biotechnol 2016; 39:167-173. [PMID: 27115496 DOI: 10.1016/j.copbio.2016.04.002] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Revised: 03/28/2016] [Accepted: 04/01/2016] [Indexed: 02/06/2023]
Abstract
Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.
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Affiliation(s)
- Jessica S Yu
- Chemical & Biological Engineering, Northwestern University, Evanston, IL, United States
| | - Neda Bagheri
- Chemical & Biological Engineering, Northwestern University, Evanston, IL, United States.
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Governing Equations of Tissue Modelling and Remodelling: A Unified Generalised Description of Surface and Bulk Balance. PLoS One 2016; 11:e0152582. [PMID: 27043309 PMCID: PMC4820236 DOI: 10.1371/journal.pone.0152582] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2015] [Accepted: 03/14/2016] [Indexed: 11/19/2022] Open
Abstract
Several biological tissues undergo changes in their geometry and in their bulk material properties by modelling and remodelling processes. Modelling synthesises tissue in some regions and removes tissue in others. Remodelling overwrites old tissue material properties with newly formed, immature tissue properties. As a result, tissues are made up of different “patches”, i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries. In this paper, generalised equations governing the spatio-temporal evolution of such tissues are developed within the continuum model. These equations take into account nonconservative, discontinuous surface mass balance due to creation and destruction of material at moving interfaces, and bulk balance due to tissue maturation. These equations make it possible to model patchy tissue states and their evolution without explicitly maintaining a record of when/where resorption and formation processes occurred. The time evolution of spatially averaged tissue properties is derived systematically by integration. These spatially-averaged equations cannot be written in closed form as they retain traces that tissue destruction is localised at tissue boundaries. The formalism developed in this paper is applied to bone tissues, which exhibit strong material heterogeneities due to their slow mineralisation and remodelling processes. Evolution equations are proposed in particular for osteocyte density and bone mineral density. Effective average equations for bone mineral density (BMD) and tissue mineral density (TMD) are derived using a mean-field approximation. The error made by this approximation when remodelling patchy tissue is investigated. The specific signatures of the time evolution of BMD or TMD during remodelling events are exhibited. These signatures may provide a way to detect remodelling events at lower, unseen spatial resolutions from microCT scans.
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