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Bregoli C, Biffi CA, Tuissi A, Buccino F. Effect of trabecular architectures on the mechanical response in osteoporotic and healthy human bone. Med Biol Eng Comput 2024:10.1007/s11517-024-03134-8. [PMID: 38822996 DOI: 10.1007/s11517-024-03134-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2023] [Accepted: 05/18/2024] [Indexed: 06/03/2024]
Abstract
Research at the mesoscale bone trabeculae arrangement yields intriguing results that, due to their clinical resolution, can be applied in clinical field, contributing significantly to the diagnosis of bone-related diseases. While the literature offers quantitative morphometric parameters for a thorough characterization of the mesoscale bone network, there is a gap in understanding relationships among them, particularly in the context of various bone pathologies. This research aims to bridge these gaps by offering a quantitative evaluation of the interplay among morphometric parameters and mechanical response at mesoscale in osteoporotic and non-osteoporotic bones. Bone mechanical response, dependent on trabecular arrangement, is defined by apparent stiffness, computationally calculated using the Gibson-Ashby model. Key findings indicate that: (i) in addition to bone density, measured using X-ray absorptiometry, trabecular connectivity density, trabecular spacing and degree of anisotropy are crucial parameters for characterize osteoporosis state; (ii) apparent stiffness values exhibit strong correlations with bone density and connectivity density; (iii) connectivity density and degree of anisotropy result the best predictors of mechanical response. Despite the inherent heterogeneity in bone structure, suggesting the potential benefit of a larger sample size in the future, this approach presents a valuable method to enhance discrimination between osteoporotic and non-osteoporotic samples.
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Affiliation(s)
- Chiara Bregoli
- National Research Council, CNR-ICMTE, Lecco, Italy.
- Mechanical Engineering Department, Politecnico Di Milano, Milano, Italy.
| | | | | | - Federica Buccino
- Mechanical Engineering Department, Politecnico Di Milano, Milano, Italy
- IRCCS Istituto Ortopedico Galeazzi, Milan, Italy
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2
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Buccino F, Zagra L, Longo E, D'Amico L, Banfi G, Berto F, Tromba G, Vergani LM. Osteoporosis and Covid-19: Detected similarities in bone lacunar-level alterations via combined AI and advanced synchrotron testing. MATERIALS & DESIGN 2023; 231:112087. [PMID: 37323219 PMCID: PMC10257887 DOI: 10.1016/j.matdes.2023.112087] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Revised: 05/03/2023] [Accepted: 06/09/2023] [Indexed: 06/17/2023]
Abstract
While advanced imaging strategies have improved the diagnosis of bone-related pathologies, early signs of bone alterations remain difficult to detect. The Covid-19 pandemic has brought attention to the need for a better understanding of bone micro-scale toughening and weakening phenomena. This study used an artificial intelligence-based tool to automatically investigate and validate four clinical hypotheses by examining osteocyte lacunae on a large scale with synchrotron image-guided failure assessment. The findings indicate that trabecular bone features exhibit intrinsic variability related to external loading, micro-scale bone characteristics affect fracture initiation and propagation, osteoporosis signs can be detected at the micro-scale through changes in osteocyte lacunar features, and Covid-19 worsens micro-scale porosities in a statistically significant manner similar to the osteoporotic condition. Incorporating these findings with existing clinical and diagnostic tools could prevent micro-scale damages from progressing into critical fractures.
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Affiliation(s)
- Federica Buccino
- Department of Mechanical Engineering, Politecnico di Milano, 20156, Italy
| | - Luigi Zagra
- I.R.C.C.S Ospedale Galeazzi - Sant'Ambrogio, Milano 20157, Italy
| | - Elena Longo
- Elettra-Sincrotrone Trieste SCpA, Basovizza, Trieste 34149, Italy
| | - Lorenzo D'Amico
- Elettra-Sincrotrone Trieste SCpA, Basovizza, Trieste 34149, Italy
| | - Giuseppe Banfi
- I.R.C.C.S Ospedale Galeazzi - Sant'Ambrogio, Milano 20157, Italy
| | - Filippo Berto
- Università La Sapienza, Rome 00185, Italy
- NTNU, Norway
| | - Giuliana Tromba
- Elettra-Sincrotrone Trieste SCpA, Basovizza, Trieste 34149, Italy
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Mae T, Hasegawa T, Hongo H, Yamamoto T, Zhao S, Li M, Yamazaki Y, Amizuka N. Immunolocalization of Enzymes/Membrane Transporters Related to Bone Mineralization in the Metaphyses of the Long Bones of Parathyroid-Hormone-Administered Mice. MEDICINA (KAUNAS, LITHUANIA) 2023; 59:1179. [PMID: 37374382 DOI: 10.3390/medicina59061179] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Revised: 06/15/2023] [Accepted: 06/16/2023] [Indexed: 06/29/2023]
Abstract
The present study aimed to demonstrate the immunolocalization and/or gene expressions of the enzymes and membrane transporters involved in bone mineralization after the intermittent administration of parathyroid hormone (PTH). The study especially focused on TNALP, ENPP1, and PHOSPHO1, which are involved in matrix vesicle-mediated mineralization, as well as PHEX and the SIBLING family, which regulate mineralization deep inside bone. Six-week-old male mice were subcutaneously injected with 20 μg/kg/day of human PTH (1-34) two times per day (n = 6) or four times per day (n = 6) for two weeks. Additionally, control mice (n = 6) received a vehicle. Consistently with an increase in the volume of the femoral trabeculae, the mineral appositional rate increased after PTH administration. The areas positive for PHOSPHO1, TNALP, and ENPP1 in the femoral metaphyses expanded, and the gene expressions assessed by real-time PCR were elevated in PTH-administered specimens when compared with the findings in control specimens. The immunoreactivity and/or gene expressions of PHEX and the SIBLING family (MEPE, osteopontin, and DMP1) significantly increased after PTH administration. For example, MEPE immunoreactivity was evident in some osteocytes in PTH-administered specimens but was hardly observed in control specimens. In contrast, mRNA encoding cathepsin B was significantly reduced. Therefore, the bone matrix deep inside might be further mineralized by PHEX/SIBLING family after PTH administration. In summary, it is likely that PTH accelerates mineralization to maintain a balance with elevated matrix synthesis, presumably by mediating TNALP/ENPP1 cooperation and stimulating PHEX/SIBLING family expression.
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Affiliation(s)
- Takahito Mae
- Department of Developmental Biology of Hard Tissue, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
- Department of Gerontology, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
| | - Tomoka Hasegawa
- Department of Developmental Biology of Hard Tissue, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
| | - Hiromi Hongo
- Department of Developmental Biology of Hard Tissue, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
| | - Tomomaya Yamamoto
- Department of Developmental Biology of Hard Tissue, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
- Northern Army Medical Unit, Camp Makomanai, Japan Ground Self-Defense Forces, Sapporo 005-8543, Japan
| | - Shen Zhao
- Department of Endodontics and Operative Dentistry, Shanghai Ninth People's Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Minqi Li
- Center of Osteoporosis and Bone Mineral Research, Department of Bone Metabolism, School of Stomatology, Shandong University, Jinan 250012, China
| | - Yutaka Yamazaki
- Department of Gerontology, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
| | - Norio Amizuka
- Department of Developmental Biology of Hard Tissue, Graduate School of Dental Medicine, Faculty of Dental Medicine, Hokkaido University, Sapporo 060-8586, Japan
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Buccino F, Cervellera F, Ghidini M, Marini R, Bagherifard S, Vergani LM. Isolating the Role of Bone Lacunar Morphology on Static and Fatigue Fracture Progression through Numerical Simulations. MATERIALS (BASEL, SWITZERLAND) 2023; 16:1931. [PMID: 36903046 PMCID: PMC10004234 DOI: 10.3390/ma16051931] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Revised: 02/13/2023] [Accepted: 02/23/2023] [Indexed: 06/18/2023]
Abstract
Currently, the onset of bone damage and the interaction of cracks with the surrounding micro-architecture are still black boxes. With the motivation to address this issue, our research targets isolating lacunar morphological and densitometric effects on crack advancement under both static and cyclic loading conditions by implementing static extended finite element models (XFEM) and fatigue analyses. The effect of lacunar pathological alterations on damage initiation and progression is evaluated; the results indicate that high lacunar density considerably reduces the mechanical strength of the specimens, resulting as the most influencing parameter among the studied ones. Lacunar size has a lower effect on mechanical strength, reducing it by 2%. Additionally, specific lacunar alignments play a key role in deviating the crack path, eventually slowing its progression. This could shed some light on evaluating the effects of lacunar alterations on fracture evolution in the presence of pathologies.
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Long-Term Cola Intake Does Not Cause Evident Pathological Alterations in the Femoral Bone Microstructure: An Animal Study in Adult Mice. Nutrients 2023; 15:nu15030583. [PMID: 36771291 PMCID: PMC9920312 DOI: 10.3390/nu15030583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 01/16/2023] [Accepted: 01/19/2023] [Indexed: 01/24/2023] Open
Abstract
Short-term animal experiments and association studies in humans have shown that cola intake may have a detrimental impact on bone mineral density (BMD); however, other bone parameters have not been investigated. This study examined the effects of long-term cola consumption on the femoral bone microstructure using adult mice (n = 32) as an animal model, which were divided into water and cola groups depending on whether they received water or cola along with a standard rodent diet for 6 months. Micro-computed tomography revealed that cola intake did not significantly affect all measured parameters characterizing trabecular bone mass and microarchitecture, as well as cortical microarchitecture and geometry in both sexes, although a slight deterioration of these parameters was noted. Cola consumption also resulted in a slightly, statistically insignificant worsening of bone mechanical properties. In contrast to female mice, males receiving cola had a lower area of primary osteons' vascular canals. Nevertheless, long-term cola intake did not cause evident pathological alterations in the femur of adult mice, possibly due to a balanced diet and no restriction of physical activity. Therefore, the adverse effects of cola consumption on BMD, the only bone parameter studied so far, may be caused by other risk and lifestyle factors.
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Buccino F, Aiazzi I, Casto A, Liu B, Sbarra MC, Ziarelli G, Banfi G, Vergani LM. The synergy of synchrotron imaging and convolutional neural networks towards the detection of human micro-scale bone architecture and damage. J Mech Behav Biomed Mater 2023; 137:105576. [PMID: 36413863 DOI: 10.1016/j.jmbbm.2022.105576] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Revised: 06/20/2022] [Accepted: 11/15/2022] [Indexed: 11/19/2022]
Abstract
The growing health and economic burden of bone fractures, their intricate multiscale features and the existing knowledge gaps in the comprehension of micro-scale bone damage occurrence make fracture diagnosis a challenging issue. In this scenario, deep-learning and artificial intelligence embody the new frontier of healthcare system, by overcoming the subjectivity of clinicians in the analysis of medical images. However, the preliminary attempts in exploiting the power of machine learning algorithms such as neural networks are still limited to bone macro-scale, while there is an evident lack in their application to smaller scales, where damage starts nucleating. Currently, speculations at the micro-scale are only feasible with the aid of high-resolution imaging techniques, that are particularly time consuming in terms of output images analysis. In this context, this works aims at combining the visualization of the micro-crack propagation mechanism with the promising application of convolutional neural networks. The implemented artificial intelligence tool is based for the first time on a large number of human synchrotron images coming from healthy and osteoporotic femoral heads tested under micro-compression. The designed convolutional neural networks are able to automatically detect lacunae and micro-cracks at different compression levels with high accuracy levels; indeed, with the baseline setup, networks achieve more than 0.99 level of accuracy for both cracks and lacunae, and more than 0.87 of the meanIoU adopted as validation metric. This approach is particularly encouraging for the development of powerful recognition system to comprehend bone micro-damage initiation and propagation, paving the way to the application of machine learning studies to bone micromechanics. This could be additionally crucial for future patient specific micro-scale observations to be related to the clinical practice.
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Affiliation(s)
- Federica Buccino
- Department of Mechanical Engineering, Politecnico di Milano, Italy
| | - Irene Aiazzi
- Department of Mechanical Engineering, Politecnico di Milano, Italy
| | - Alessandro Casto
- Department of Mechanical Engineering, Politecnico di Milano, Italy
| | - Bingqi Liu
- Department of Mechanical Engineering, Politecnico di Milano, Italy
| | | | - Giovanni Ziarelli
- Department of Mathematical Engineering, Politecnico di Milano, Italy
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Superiority of MRI for Evaluation of Sacral Insufficiency Fracture. J Clin Med 2022; 11:jcm11174968. [PMID: 36078896 PMCID: PMC9456416 DOI: 10.3390/jcm11174968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Revised: 08/18/2022] [Accepted: 08/19/2022] [Indexed: 11/17/2022] Open
Abstract
Study Design: Retrospective observational study. Background: Sacral insufficiency fractures (SIF) are relatively rare fractures and difficult to diagnose on plain radiographs. The primary objective of the present study was to evaluate the role of lumbar magnetic resonance imaging (MRI) for the diagnosis of SIF. The secondary objective was to identify the classification of SIF by computed tomography (CT). Methods: A total of 77 (Male 11, female 66, mean 80.3 years) people were included in this study. Inclusion criteria for this study were: age ≥ 60 years and no history of high energy trauma. Exclusion criteria were high energy trauma and a current history of malignancy. Differences in the fracture detection and description in the various radiologic procedures were evaluated. Fracture patterns were evaluated with CT. The detection rates of additional pathologies in the MRI of the pelvis and lumbar spine were also recorded. Results: The sensitivities for SIF were 28.5% in radiographs and 94.2% in CT, and all fractures were detected in MRI. MRI showed a more complex fracture pattern compared with CT in 65% of the cases. We observed 71.4% of single SIFs, 9.1% with other spinal fractures, 13.0% with other pelvic fractures, and 7.8% with other fractures. According to the SIF fracture pattern, the H/U type was 40.2%, transverse type was 33.7%, λ/T type was 24.7%, unilateral vertical type was 1.3%, and bilateral vertical type was 0%. Conclusions: an MRI of the lumbar spine including the sacrum with a coronal fat-suppressed T2-weighted image is useful for elderly patients with suddenly increasing low back pain at an early stage. This procedure improves an early SIF detection, recognition of concomitant pathologies, and adequate treatment for the patients.
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Buccino F, Bunt A, Lazell A, Vergani LM. Mechanical Design Optimization of Prosthetic Hand's Fingers: Novel Solutions towards Weight Reduction. MATERIALS 2022; 15:ma15072456. [PMID: 35407787 PMCID: PMC8999927 DOI: 10.3390/ma15072456] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Revised: 03/17/2022] [Accepted: 03/25/2022] [Indexed: 11/16/2022]
Abstract
From the mechanical function of grabbing objects to the emotional aspect of gesturing, the functionality of human hands is fundamental for both physical and social survival. Therefore, the loss of one or both hands represents a devastating issue, exacerbated by long rehabilitation times and psychological treatments. Prosthetic arms represent an effective solution to provide concrete functional and esthetical support. However, commercial hand prostheses still lack an optimal combination of light weight, durability, adequate cosmetic appearance, and affordability. Among these aspects, the priority for upper-limb prosthesis users is weight, a key parameter that influences both the portability and the functionality of the system. The purpose of this work is to optimize the design of the MyHand prosthesis, by redesigning both the proximal and distal finger and thumb in light of finding an optimal balance between weight reduction and adequate stiffness. Starting from elastic–plastic numerical models and experimental tests on obsolete components, analyzed under the worst loading condition, five different design solutions are suggested. An iterative topology optimization process locates the regions where material removal is permitted. From these results, 2 mm geometrical patterns on the top surface of the hand prosthesis appear as the most prominent, preventing object intrusion.
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Affiliation(s)
- Federica Buccino
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy; (F.B.); (A.B.)
| | - Alessandro Bunt
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy; (F.B.); (A.B.)
| | - Alex Lazell
- Hy5, Bygning 18 Raufoss Industripark, 2830 Raufoss, Norway;
| | - Laura Maria Vergani
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy; (F.B.); (A.B.)
- Correspondence: ; Tel.: +39-0223998249
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Buccino F, Martinoia G, Vergani LM. Torsion-Resistant Structures: A Nature Addressed Solution. MATERIALS (BASEL, SWITZERLAND) 2021; 14:5368. [PMID: 34576592 PMCID: PMC8472553 DOI: 10.3390/ma14185368] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Revised: 09/14/2021] [Accepted: 09/15/2021] [Indexed: 01/21/2023]
Abstract
The complexity of torsional load, its three-dimensional nature, its combination with other stresses, and its disruptive impact make torsional failure prevention an ambitious goal. However, even if the problem has been addressed for decades, a deep and organized treatment is still lacking in the actual research landscape. For this reason, this review aims at presenting a methodical approach to address torsional issues starting from a punctual problem definition. Accidents and breaks due to torsion, which often occur in different engineering fields such as mechanical, biomedical, and civil industry are considered and critically compared. More in depth, the limitations of common-designed torsion-resistant structures (i.e., high complexity and increased weight) are highlighted, and emerge as a crucial point for a deeper nature-driven analysis of novel solutions. In this context, an accurate screening of torsion-resistant bio-inspired unit cells is presented, taking inspiration specifically from plants, that are often subjected to the torsional effect of winds. As future insights, the actual state of technology suggests an innovative transposition to the industry: these unit cells could be prominently implied to develop novel metamaterials that could be able to address the torsional issue with a multi-scale and tailored arrangement.
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Affiliation(s)
- Federica Buccino
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy
| | - Giada Martinoia
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy
| | - Laura Maria Vergani
- Department of Mechanical Engineering (DMEC), Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy
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Subchondral Bone Relative Area and Density in Human Osteoarthritic Femoral Heads Assessed with Micro-CT before and after Mechanical Embedding of the Innovative Multi-Spiked Connecting Scaffold for Resurfacing THA Endoprostheses: A Pilot Study. J Clin Med 2021; 10:jcm10132937. [PMID: 34208953 PMCID: PMC8268800 DOI: 10.3390/jcm10132937] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Revised: 06/27/2021] [Accepted: 06/28/2021] [Indexed: 12/19/2022] Open
Abstract
The multi-spiked connecting scaffold (MSC-Scaffold) prototype is the essential innovation in the fixation of components of resurfacing total hip arthroplasty (THRA) endoprostheses in the subchondral trabecular bone. We conducted the computed micro-tomography (micro-CT) assessment of the subchondral trabecular bone microarchitecture before and after the MSC-Scaffold embedding in femoral heads removed during long-stem endoprosthesis total hip arthroplasty (THA) of different bone densities from 4 patients with hip osteoarthritis (OA). The embedding of the MSC-Scaffold in subchondral trabecular bone causes the change in its relative area (BA/TA, bone area/total area ratio) ranged from 18.2% to 24.7% (translating to the calculated density ρB relative change 11.1–14.4%, and the compressive strength S relative change 75.3–122.7%) regardless of its initial density (before the MSC-Scaffold embedding). The densification of the trabecular microarchitecture of subchondral trabecular bone due to the MSC-Scaffold initial embedding gradually decreases with the increasing distance from the apexes of the MSC-Scaffold’s spikes while the spatial extent of this subchondral trabecular bone densification ranged from 1.5 to 2.5 mm (which is about half the height of the MSC-Scaffold’s spikes). It may be suggested, despite the limited number of examined femoral heads, that: (1) the magnitude of the effect of the MSC-Scaffold embedding on subchondral trabecular bone densification may be a factor contributing to the maintenance of the MSC-Scaffold also for decreased initial bone density values, (2) the deeper this effect of the subchondral trabecular bone densification, the better strength of subchondral trabecular bone, and as consequence, the better post-operative embedding of the MSC-Scaffold in the bone should be expected.
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A Damage Model to Trabecular Bone and Similar Materials: Residual Resource, Effective Elasticity Modulus, and Effective Stress under Uniaxial Compression. Symmetry (Basel) 2021. [DOI: 10.3390/sym13061051] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Experimental research of bone strength remains costly and limited for ethical and technical reasons. Therefore, to predict the mechanical state of bone tissue, as well as similar materials, it is desirable to use computer technology and mathematical modeling. Yet, bone tissue as a bio-mechanical object with a hierarchical structure is difficult to analyze for strength and rigidity; therefore, empirical models are often used, the disadvantage of which is their limited application scope. The use of new analytical solutions overcomes the limitations of empirical models and significantly improves the way engineering problems are solved. Aim of the paper: the development of analytical solutions for computer models of the mechanical state of bone and similar materials. Object of research: a model of trabecular bone tissue as a quasi-brittle material under uniaxial compression (or tension). The new ideas of the fracture mechanics, as well as the methods of mathematical modeling and the biomechanics of bone tissues were used in the work. Compression and tension are considered as asymmetric mechanical states of the material. Results: a new nonlinear function that simulates both tension and compression is justified, analytical solutions for determining the effective and apparent elastic modulus are developed, the residual resource function and the damage function are justified, and the dependences of the initial and effective stresses on strain are obtained. Using the energy criterion, it is proven that the effective stress continuously increases both before and after the extremum point on the load-displacement plot. It is noted that the destruction of bone material is more likely at the inflection point of the load-displacement curve. The model adequacy is explained by the use of the energy criterion of material degradation. The results are consistent with the experimental data available in the literature.
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