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Silva R, dos Santos MD, Madureira R, Soares R, Neto R, Vieira ÂA, Gonçalves PAR, Leite PMSM, Vieira L, Viana F. Scratch and Wear Behaviour of Co-Cr-Mo Alloy in Ringer's Lactate Solution. MATERIALS (BASEL, SWITZERLAND) 2023; 16:2923. [PMID: 37049218 PMCID: PMC10096074 DOI: 10.3390/ma16072923] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 03/15/2023] [Accepted: 03/30/2023] [Indexed: 06/19/2023]
Abstract
Cobalt-chromium-molybdenum (Co-Cr-Mo) alloy is a material recommended for biomedical implants; however, to be suitable for this application, it should have good tribological properties, which are related to grain size. This paper investigates the tribological behaviour of a Co-Cr-Mo alloy produced using investment casting, together with electromagnetic stirring, to reduce its grain size. The samples were subjected to wear and scratch tests in simulated body fluid (Ringer's lactate solution). Since a reduction in grain size can influence the behaviour of the material, in terms of resistance and tribological response, four samples with different grain sizes were produced for use in our investigation of the behaviour of the alloy, in which we considered the friction coefficient, wear, and scratch resistance. The experiments were performed using a tribometer, with mean values for the friction coefficient, normal load, and tangential force acquired and recorded by the software. Spheres of Ti-6Al-4V and 316L steel were used as counterface materials. In addition, to elucidate the influence of grain size on the mechanical properties of the alloy, observations were conducted via scanning electron microscopy (SEM) with electron backscatter diffraction (EBSD). The results showed changes in the structure, with a reduction in grain size from 5.51 to 0.79 mm. Using both spheres, the best results for the friction coefficient and wear volume corresponded to the sample with the smallest grain size of 0.79 mm. The friction coefficients obtained were 0.37 and 0.45, using the Ti-6Al-4V and 316L spheres, respectively. These results confirm that the best surface finish for Co-Cr-Mo alloy used as a biomedical implant is one with a smaller grain size, since this results in a lower friction coefficient and low wear.
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Affiliation(s)
- Raimundo Silva
- Department of Materials Engineering, University of the State of Amazonas (UEA), Darcy Vargas, Manaus 69050-020, Brazil
- Department of Metallurgical and Materials Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;
| | - Marcos Dantas dos Santos
- Department of Materials Engineering, University of the State of Amazonas (UEA), Darcy Vargas, Manaus 69050-020, Brazil
| | - Rui Madureira
- LAETA/INEGI—Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - Rui Soares
- LAETA/INEGI—Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - Rui Neto
- LAETA/INEGI—Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
- Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - Ângela Aparecida Vieira
- Department of Materials, Institute of Research and Development (IP&D), University of Paraíba Valley, São José dos Campos 12244-000, Brazil
| | - Polyana Alves Radi Gonçalves
- Department of Materials, Institute of Research and Development (IP&D), University of Paraíba Valley, São José dos Campos 12244-000, Brazil
| | - Priscila Maria Sarmeiro M. Leite
- Department of Materials, Institute of Research and Development (IP&D), University of Paraíba Valley, São José dos Campos 12244-000, Brazil
| | - Lúcia Vieira
- Department of Materials, Institute of Research and Development (IP&D), University of Paraíba Valley, São José dos Campos 12244-000, Brazil
| | - Filomena Viana
- Department of Metallurgical and Materials Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal;
- LAETA/INEGI—Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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Biomechanical comparison between bioabsorbable and medical titanium screws in distal chevron osteotomy of first metatarsal in hallux valgus treatment. J Mech Behav Biomed Mater 2022; 131:105260. [DOI: 10.1016/j.jmbbm.2022.105260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 04/10/2022] [Accepted: 04/29/2022] [Indexed: 11/22/2022]
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da Rocha Ferreira JJ, Machado LFM, Oliveira JM, Ramos JCT. Effect of crown-to-implant ratio and crown height space on marginal bone stress: a finite element analysis. Int J Implant Dent 2021; 7:81. [PMID: 34467461 PMCID: PMC8408299 DOI: 10.1186/s40729-021-00368-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 06/16/2021] [Indexed: 12/14/2022] Open
Abstract
BACKGROUND Crown-to-implant ratio and crown height space, associated with the use of short implants, have been related with marginal bone loss. However, it is unclear which of the two entities would play the most important role on the bone remodelling process. Using a finite element analysis, the present work aims to help clarifying how those two factors contribute for the stress generation at the marginal bone level. A numerical model (reference model), with a crown-to-implant ratio of 4, was double validated and submitted to a numerical calculation. Then, it was modified in two different ways: (a) by decreasing the prosthetic height obtaining crown-to-implant ratios of 3, 2.5 and 2 and (b) by increasing the implants length obtaining a crown-to-implant ratio of 2.08. The new models were also submitted to numerical calculations. RESULTS The reference model showed a marginal bone stress of 96.9 MPa. The increase in the implants' length did not show statistically significant differences in the marginal bone stress (p-value = 0.2364). The decrease in the prosthetic height was accompanied with a statistically significant decrease in the marginal bone stresses (p-value = 2.2e- 16). CONCLUSIONS The results represent a paradigm change as the crown height space appears to be more responsible for marginal bone stress than the high crown-to-implant ratios or the implants' length. New prosthetic designs should be attempted to decrease the stress generated at the marginal bone level.
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Affiliation(s)
| | | | - José Manuel Oliveira
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Oporto, Portugal
| | - João Carlos Tomás Ramos
- Department of Dentistry, Stomatology and Maxillofacial surgery, Faculty of Medicine, University of Coimbra, Av. Bissaya Barreto-Blocos de Celas, 3000-075, Coimbra, Portugal
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Is the 0.2%-Strain-Offset Approach Appropriate for Calculating the Yield Stress of Cortical Bone? Ann Biomed Eng 2021; 49:1747-1760. [PMID: 33479788 DOI: 10.1007/s10439-020-02719-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 12/28/2020] [Indexed: 11/26/2022]
Abstract
The 0.2% strain offset approach is mostly used to calculate the yield stress and serves as an efficient method for cross-lab comparisons of measured material properties. However, it is difficult to accurately determine the yield of the bone. Especially when computational models require accurate material parameters, clarification of the yield point is needed. We tested 24 cortical specimens harvested from six bovine femora in three-point bending mode, and 11 bovine femoral cortical specimens in the tensile mode. The Young's modulus and yield stress for each specimen derived from the specimen-specific finite element (FE) optimization method was regarded as the most ideal constitutive parameter. Then, the strain offset optimization method was used to find the strain offset closest to the ideal yield stress for the 24 specimens. The results showed that the 0 strain offsets underestimated (- 25%) the yield stress in bending and tensile tests, while the 0.2% strain offsets overestimated the yield stress (+ 65%) in three-point bending tests. Instead, the yield stress determined by 0.007 and 0.05% strain offset for bending and tensile loading respectively, can effectively characterize the biomechanical responses of the bone, thereby helping to build an accurate FE model.
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Martinez-Marquez D, Delmar Y, Sun S, Stewart RA. Exploring Macroporosity of Additively Manufactured Titanium Metamaterials for Bone Regeneration with Quality by Design: A Systematic Literature Review. MATERIALS (BASEL, SWITZERLAND) 2020; 13:E4794. [PMID: 33121025 PMCID: PMC7662257 DOI: 10.3390/ma13214794] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Revised: 10/21/2020] [Accepted: 10/23/2020] [Indexed: 12/14/2022]
Abstract
Additive manufacturing facilitates the design of porous metal implants with detailed internal architecture. A rationally designed porous structure can provide to biocompatible titanium alloys biomimetic mechanical and biological properties for bone regeneration. However, increased porosity results in decreased material strength. The porosity and pore sizes that are ideal for porous implants are still controversial in the literature, complicating the justification of a design decision. Recently, metallic porous biomaterials have been proposed for load-bearing applications beyond surface coatings. This recent science lacks standards, but the Quality by Design (QbD) system can assist the design process in a systematic way. This study used the QbD system to explore the Quality Target Product Profile and Ideal Quality Attributes of additively manufactured titanium porous scaffolds for bone regeneration with a biomimetic approach. For this purpose, a total of 807 experimental results extracted from 50 different studies were benchmarked against proposed target values based on bone properties, governmental regulations, and scientific research relevant to bone implants. The scaffold properties such as unit cell geometry, pore size, porosity, compressive strength, and fatigue strength were studied. The results of this study may help future research to effectively direct the design process under the QbD system.
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Affiliation(s)
| | | | | | - Rodney A. Stewart
- School of Engineering and Built Environment, Griffith University, Gold Coast, QLD 4222, Australia; (D.M.-M.); (Y.D.); (S.S.)
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BASHA SHAIKAKBAR, SARKAR DEBASISH. COMPETITIVE LIFE TIME ASSESSMENT OF SrO-ZTA/SrO-ZTA AND CoCrMo/UHMWPE HIP PROSTHESIS BEARINGS. J MECH MED BIOL 2020. [DOI: 10.1142/s0219519420500098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The hip joint envisages the prime load bearing structure among other joints in the human body. Hip joint failure leads to the replacement of the hip joint prosthesis. This research work focuses on the proper selection of bearing couple materials for the hip joint to improve the performance and life. Herein, the stress and deformation of different bearing couple materials are analysed in the perspective of transient dynamic analysis under jogging load cycle. Selective hip joint bearing (femoral head-liner) couples are SS316L on UHMWPE (MoP), CoCrMo on UHMWPE (MoP), Ti6Al4V on SrO-ZTA (MoC), SrO-ZTA on UHMWPE (CoP) and SrO-ZTA on SrO-ZTA (CoC) encountered, respectively. The SrO-ZTA on SrO-ZTA (CoC) bearing couple generates the less Von Mises stress of 180.88 MPa. Load bearing pressure and Archard law predict the wear depth of CoCrMo on UHMWPE (MoP) and SrO-ZTA on SrO-ZTA (CoC) bearing couples are 0.141 mm/year and 0.031 mm/year, respectively. In simultaneous, the theoretical wear volume for CoCrMo on UHMWPE (MoP) and SrO-ZTA on SrO-ZTA (CoC) bearing couples are found as 35.46[Formula: see text]mm3/year and 2.62[Formula: see text]mm3/year, respectively. The wear depth and wear volume are supporting the available clinical retrievals and exist in well acceptable range. Competitive wear analysis data ensures 15 years safe life of SrO-ZTA on SrO-ZTA (CoC) hip prosthesis bearing.
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Affiliation(s)
- SHAIK AKBAR BASHA
- Department of Ceramic Engineering, National Institute of Technology, Rourkela, India
| | - DEBASISH SARKAR
- Department of Ceramic Engineering, National Institute of Technology, Rourkela, India
- HiLASE, Institute of Physics, ASCR, Prague, Czech Republic
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Low-modulus biomedical Ti-30Nb-5Ta-3Zr additively manufactured by Selective Laser Melting and its biocompatibility. MATERIALS SCIENCE & ENGINEERING. C, MATERIALS FOR BIOLOGICAL APPLICATIONS 2019; 97:275-284. [PMID: 30678912 DOI: 10.1016/j.msec.2018.11.077] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Revised: 11/16/2018] [Accepted: 11/29/2018] [Indexed: 11/21/2022]
Abstract
Low Young's modulus titanium alloys, such as Ti-30Nb-5Ta-3Zr (TNTZ) of this study, were promising biocompatible implant materials. In this work, TNTZ samples with relative density of 96.8%-99.2% were additively manufactured by powder-bed based Selective Laser Melting (SLM) through tuning processing parameters, i.e. varying the point distance between 50 and 75 μm, laser exposure time between 135 and 200 μs, and a fixed laser power of 200 W. The microstructure, elastic properties, fatigue properties and machining accuracy of the fabricated samples have been investigated. Lattice structure TNTZ samples with porosity of 77.23% were also fabricated to further reduce the Young's modulus of the TNTZ. According to the Relative Growth Rate (RGR) value, the as-printed TNTZ samples exhibited no cell cytotoxicity, where they showed even better biocompatibility than the comparative, as-printed Ti-6Al-4V samples. The as-printed TNTZ developed by the study demonstrates good biocompatibility, low stress shielding tendency and high mechanical properties.
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Hammond MA, Wallace JM, Allen MR, Siegmund T. Mechanics of linear microcracking in trabecular bone. J Biomech 2018; 83:34-42. [PMID: 30473136 DOI: 10.1016/j.jbiomech.2018.11.018] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2018] [Revised: 10/05/2018] [Accepted: 11/09/2018] [Indexed: 12/20/2022]
Abstract
Microcracking in trabecular bone is responsible both for the mechanical degradation and remodeling of the trabecular bone tissue. Recent results on trabecular bone mechanics have demonstrated that bone tissue microarchitecture, tissue elastic heterogeneity and tissue-level mechanical anisotropy all should be considered to obtain detailed information on the mechanical stress state. The present study investigated the influence of tissue microarchitecture, tissue heterogeneity in elasticity and material separation properties and tissue-level anisotropy on the microcrack formation process. Microscale bone models were executed with the extended finite element method. It was demonstrated that anisotropy and heterogeneity of the bone tissue contribute significantly to bone tissue toughness and the resistance of trabecular bone to microcrack formation. The compressive strain to microcrack initiation was computed to increase by a factor of four from an assumed homogeneous isotropic tissue to an assumed anisotropic heterogenous tissue.
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Affiliation(s)
- Max A Hammond
- Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
| | - Joseph M Wallace
- Department of Biomedical Engineering, Indiana University-Purdue University at Indianapolis, IN, USA
| | - Matthew R Allen
- Department of Biomedical Engineering, Indiana University-Purdue University at Indianapolis, IN, USA; Department of Anatomy and Cell Biology, Indiana University School of Medicine, IN, USA
| | - Thomas Siegmund
- Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.
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Fan R, Liu J, Jia Z, Deng Y, Liu J. Determination of a tissue-level failure evaluation standard for rat femoral cortical bone utilizing a hybrid computational-experimental method. Proc Inst Mech Eng H 2017; 232:80-89. [PMID: 29165039 DOI: 10.1177/0954411917743275] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Macro-level failure in bone structure could be diagnosed by pain or physical examination. However, diagnosing tissue-level failure in a timely manner is challenging due to the difficulty in observing the interior mechanical environment of bone tissue. Because most fractures begin with tissue-level failure in bone tissue caused by continually applied loading, people attempt to monitor the tissue-level failure of bone and provide corresponding measures to prevent fracture. Many tissue-level mechanical parameters of bone could be predicted or measured; however, the value of the parameter may vary among different specimens belonging to a kind of bone structure even at the same age and anatomical site. These variations cause difficulty in representing tissue-level bone failure. Therefore, determining an appropriate tissue-level failure evaluation standard is necessary to represent tissue-level bone failure. In this study, the yield and failure processes of rat femoral cortical bones were primarily simulated through a hybrid computational-experimental method. Subsequently, the tissue-level strains and the ratio between tissue-level failure and yield strains in cortical bones were predicted. The results indicated that certain differences existed in tissue-level strains; however, slight variations in the ratio were observed among different cortical bones. Therefore, the ratio between tissue-level failure and yield strains for a kind of bone structure could be determined. This ratio may then be regarded as an appropriate tissue-level failure evaluation standard to represent the mechanical status of bone tissue.
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Affiliation(s)
- Ruoxun Fan
- 1 Department of Automotive Engineering, Jilin Institute of Chemical Technology, Jilin, P.R. China
| | - Jie Liu
- 1 Department of Automotive Engineering, Jilin Institute of Chemical Technology, Jilin, P.R. China
| | - Zhengbin Jia
- 2 Department of Engineering Mechanics, Jilin University, Changchun, P.R. China
| | - Ying Deng
- 3 School of Public Health, Jilin University, Changchun, P.R. China
| | - Jun Liu
- 4 Hand & Foot Surgery and Reparative & Reconstructive Surgery Center, No. 2 Hospital of Jilin University, Changchun, P.R. China
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Woodside M, Willett TL. Elastic-plastic fracture toughness and rising JR-curve behavior of cortical bone is partially protected from irradiation-sterilization-induced degradation by ribose protectant. J Mech Behav Biomed Mater 2016; 64:53-64. [PMID: 27479894 DOI: 10.1016/j.jmbbm.2016.07.001] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2016] [Revised: 06/24/2016] [Accepted: 07/03/2016] [Indexed: 12/12/2022]
Abstract
OBJECTIVE This study tested the hypothesis that pre-treating cortical bone with ribose would protect the rising fracture resistance curve behavior and crack initiation fracture toughness of both bovine and human cortical bone from the degrading effects of γ-irradiation sterilization. MATERIALS AND METHODS A ribose pre-treatment (1.8 M for bovine, and 1.2 M for human, in PBS at 60 °C for 24 h) was applied to single-edge notched bending fracture specimens prior to sterilization with a 33 kGy dose of γ-irradiation. Fracture resistance curves were generated with a single specimen method using an optical crack length measurement technique. The effect of the treatment on overall fracture resistance behavior, crack initiation fracture toughness, and tearing modulus was compared with non-irradiated and conventionally irradiation sterilized controls. Hydrothermal isometric tension testing was used to examine collagen network connectivity and thermal stability to explore relationships between collagen network quality and fracture resistance. RESULTS The ribose pre-treatment successfully protected the crack growth initiation fracture toughness of bovine and human bone by 32% and 63%, respectively. The rising JR-curve behavior was also partially protected. Furthermore, collagen connectivity and thermal stability followed similar patterns to those displayed by fracture toughness. CONCLUSIONS This paper demonstrates that the fracture toughness of irradiation-sterilized bone tissue can be partially protected with a ribose pre-treatment. This new approach shows potential for the production and clinical application of sterilized allografts with improved mechanical performance and durability.
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Affiliation(s)
- Mitchell Woodside
- Materials Science and Engineering, University of Toronto, Toronto, ON, Canada; Musculoskeletal Research Laboratory, Mount Sinai Hospital - Lunenfeld-Tanenbaum Research Institute, Toronto, ON, Canada
| | - Thomas L Willett
- Materials Science and Engineering, University of Toronto, Toronto, ON, Canada; Musculoskeletal Research Laboratory, Mount Sinai Hospital - Lunenfeld-Tanenbaum Research Institute, Toronto, ON, Canada; Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada; Division of Orthopaedic Surgery, Mount Sinai Hospital, Toronto, ON, Canada; Division of Orthopaedic Surgery, Department of Surgery, University of Toronto, ON, Canada.
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Fyhrie DP, Christiansen BA. Bone Material Properties and Skeletal Fragility. Calcif Tissue Int 2015; 97:213-28. [PMID: 25939648 DOI: 10.1007/s00223-015-9997-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/29/2015] [Accepted: 04/07/2015] [Indexed: 12/27/2022]
Abstract
Deformations of vertebrae and sudden fractures of long bones caused by essentially normal loading are a characteristic problem in osteoporosis. If the loading is normal, then the explanation for and prediction of unexpected bone failure lies in understanding the mechanical properties of the whole bone-which come from its internal and external geometry, the mechanical properties of the hard tissue, and from how well the tissue repairs damage. Modern QCT and MRI imaging systems can measure the geometry of the mineralized tissue quite well in vivo-leaving the mechanical properties of the hard tissue and the ability of bone to repair damage as important unknown factors in predicting fractures. This review explains which material properties must be measured to understand why some bones fail unexpectedly despite our current ability to determine bone geometry and bone mineral content in vivo. Examples of how to measure the important mechanical properties are presented along with some analysis of potential drawbacks of each method. Particular attention is given to methods useful to characterize the loss of bone toughness caused by mechanical fatigue, drug side effects, and damage to the bone matrix.
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Affiliation(s)
- David P Fyhrie
- Department of Orthopaedic Surgery, University of California-Davis Medical Center, 4635 2nd Ave, Suite 2000, Sacramento, CA, 95817, USA,
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12
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Affiliation(s)
- David B Burr
- Department of Anatomy and Cell Biology, Indiana University School of Medicine, and Department of Biomedical Engineering, Indiana University-Purdue University, Indianapolis, IN, USA
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Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach. Biomech Model Mechanobiol 2012; 12:225-41. [DOI: 10.1007/s10237-012-0394-7] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2011] [Accepted: 03/30/2012] [Indexed: 11/27/2022]
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Juszczyk MM, Cristofolini L, Viceconti M. The human proximal femur behaves linearly elastic up to failure under physiological loading conditions. J Biomech 2011; 44:2259-66. [DOI: 10.1016/j.jbiomech.2011.05.038] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2011] [Revised: 05/26/2011] [Accepted: 05/27/2011] [Indexed: 11/26/2022]
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15
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Zimmermann EA, Launey ME, Ritchie RO. The significance of crack-resistance curves to the mixed-mode fracture toughness of human cortical bone. Biomaterials 2010; 31:5297-305. [PMID: 20409579 DOI: 10.1016/j.biomaterials.2010.03.056] [Citation(s) in RCA: 85] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2010] [Accepted: 03/21/2010] [Indexed: 11/29/2022]
Abstract
The majority of fracture mechanics studies on the toughness of bone have been performed under tensile loading. However, it has recently been shown that the toughness of human cortical bone in the transverse (breaking) orientation is actually much lower in shear (mode II) than in tension (mode I); a fact that is physiologically relevant as in vivo bone is invariably loaded multiaxially. Since bone is a material that derives its fracture resistance primarily during crack growth through extrinsic toughening mechanisms, such as crack deflection and bridging, evaluation of its toughness is best achieved through measurements of the crack-resistance or R-curve, which describes the fracture toughness as a function of crack extension. Accordingly, in this study, we attempt to measure for the first time the R-curve fracture toughness of human cortical bone under physiologically relevant mixed-mode loading conditions. We show that the resulting mixed-mode (mode I+II) toughness depends strongly on the crack trajectory and is the result of the competition between the paths of maximum mechanical driving force and "weakest" microstructural resistance.
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Affiliation(s)
- Elizabeth A Zimmermann
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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Siegmund T, Allen MR, Burr DB. Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone? J Theor Biol 2010; 265:202-10. [PMID: 20398678 DOI: 10.1016/j.jtbi.2010.04.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2010] [Revised: 04/06/2010] [Accepted: 04/08/2010] [Indexed: 11/18/2022]
Abstract
Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.
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Affiliation(s)
- Thomas Siegmund
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA.
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Mullins L, Bruzzi M, McHugh P. Calibration of a constitutive model for the post-yield behaviour of cortical bone. J Mech Behav Biomed Mater 2009; 2:460-70. [DOI: 10.1016/j.jmbbm.2008.11.003] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2007] [Revised: 10/19/2008] [Accepted: 11/04/2008] [Indexed: 10/21/2022]
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18
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Abstract
Animal models, in particular mice, offer the possibility of naturally achieving or genetically engineering a skeletal phenotype associated with disease and conducting destructive fracture tests on bone to determine the resulting change in bone's mechanical properties. Several recent developments, including nano- and micro-indentation testing, microtensile and microcompressive testing, and bending tests on notched whole bone specimens, offer the possibility to mechanically probe small animal bone and investigate the effects of aging, therapeutic treatments, disease, and genetic variation. In contrast to traditional strength tests on small animal bones, fracture mechanics tests display smaller variation and therefore offer the possibility of reducing sample sizes. This article provides an analysis of what such tests measure and proposes methods to reduce errors associated with testing smaller than ideal specimens.
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Butcher MT, Espinoza NR, Cirilo SR, Blob RW. In vivo strains in the femur of river cooter turtles (Pseudemys concinna) during terrestrial locomotion: tests of force-platform models of loading mechanics. ACTA ACUST UNITED AC 2008; 211:2397-407. [PMID: 18626073 DOI: 10.1242/jeb.018986] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Previous analyses of ground reaction force (GRF) and kinematic data from river cooter turtles (Pseudemys concinna) during terrestrial walking led to three primary conclusions about the mechanics of limb bone loading in this lineage: (1) the femur was loaded in a combination of axial compression, bending and torsion, similar to previously studied non-avian reptiles, (2) femoral shear stresses were high despite the possession of a reduced tail in turtles that does not drag on the ground and (3) stress-based calculations of femoral safety factors indicated high values in bending and torsion, similar to other reptiles and suggesting that substantial 'overbuilding' of limb bones could be an ancestral feature of tetrapods. Because force-platform analyses produce indirect estimates of bone loading, we sought to validate these conclusions by surgically implanting strain gauges on turtle femora to directly measure in vivo strains during terrestrial walking. Strain analyses verified axial compression and bending as well as high torsion in turtle femora, with peak axial strains comparable to those of other non-avian reptiles at similar walking speeds but higher peak shear strains approaching 2000 microepsilon. Planar strain analyses showed patterns of neutral axis (NA) of femoral bending orientations and shifting generally consistent with our previous force-platform analyses of bone stresses, tending to place the anterior and dorsal aspects of the femur in tension and verifying an unexpected pattern from our force studies that differs from patterns in other non-avian reptiles. Calculated femoral safety factors were 3.8 in torsion and ranged from 4.4 to 6.9 in bending. Although these safety factors in bending were lower than values derived from our stress-based calculations, they are similar to strain-based safety factors calculated for other non-avian reptiles in terrestrial locomotion and are still high compared with safety factors calculated for limb bones of birds and mammals. These findings are consistent with conclusions drawn from our previous models of limb bone stresses in turtles and suggest that not only are turtle limb bones 'overbuilt' in terms of resisting the loads that they experience during locomotion but also, across tetrapod lineages, elevated torsion and high limb bone safety factors may be primitive features of limb bone design.
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Affiliation(s)
- Michael T Butcher
- Department of Biological Sciences, Clemson University, Clemson, SC 29634, USA
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20
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Koester KJ, Ager JW, Ritchie RO. The true toughness of human cortical bone measured with realistically short cracks. NATURE MATERIALS 2008; 7:672-677. [PMID: 18587403 DOI: 10.1038/nmat2221] [Citation(s) in RCA: 247] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2008] [Accepted: 05/19/2008] [Indexed: 05/26/2023]
Abstract
Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for bone.
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Affiliation(s)
- K J Koester
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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21
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Taylor D, Hazenberg JG, Lee TC. Living with cracks: damage and repair in human bone. NATURE MATERIALS 2007; 6:263-8. [PMID: 17401419 DOI: 10.1038/nmat1866] [Citation(s) in RCA: 170] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Our bones are full of cracks, which form and grow as a result of daily loading activities. Bone is the major structural material in our bodies. Although weaker than many engineering materials, it has one trick that keeps it ahead - it can repair itself. Small cracks, which grow under cyclic stresses by the mechanism of fatigue, can be detected and removed before they become long enough to be dangerous. This article reviews the work that has been done to understand how cracks form and grow in bone, and how they can be detected and repaired in a timely manner. This is truly an interdisciplinary research field, requiring the close cooperation of materials scientists, biologists and engineers.
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Affiliation(s)
- David Taylor
- Trinity Centre for Bioengineering, Mechanical Engineering Department, Trinity College, Dublin 2, Ireland.
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22
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Hazenberg JG, Taylor D, Lee TC. The role of osteocytes and bone microstructure in preventing osteoporotic fractures. Osteoporos Int 2007; 18:1-8. [PMID: 16972016 DOI: 10.1007/s00198-006-0222-y] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/30/2006] [Accepted: 08/08/2006] [Indexed: 01/30/2023]
Abstract
The skeleton alters its geometry following trauma, the introduction of artificial defects and of fatigue-induced microcracks. The precise mechanism by which the skeleton adapts remains unclear. Microcracks might directly affect the cell by damaging the osteocyte cell network or causing apoptosis. Bone microstructure may play an important role in these processes by diverting and arresting propagating microcracks and so prevent fracture failure. This paper discusses the effects of microstructure on propagating cracks, how microdamage may act as a stimulus for bone adaptation and its potential effects on bone biochemistry.
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Affiliation(s)
- Jan G Hazenberg
- Department of Anatomy, Royal College of Surgeons in Ireland, St. Stephen's Green, Dublin 2, Ireland.
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23
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Yang QD, Cox BN, Nalla RK, Ritchie RO. Re-evaluating the toughness of human cortical bone. Bone 2006; 38:878-87. [PMID: 16338188 DOI: 10.1016/j.bone.2005.10.014] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/14/2005] [Revised: 10/18/2005] [Accepted: 10/26/2005] [Indexed: 11/16/2022]
Abstract
Data for fracture in human humeral cortical bone are re-analyzed to assess the validity for this material of linear-elastic fracture mechanics (LEFM), which is the standard method of analyzing toughness and one basis for analyzing clinical data relating to bone quality. A nonlinear fracture model, which is based on representing the damage zone in the bone by a cohesive model, is calibrated against a number of sets of test data for normal (not diseased or aged) human cortical bone taken from cadavers. The data consist of load vs. load-point displacement measurements from standard compact-tension fracture tests. Conventional LEFM is unable to account for the shape of the load-displacement curves, but the nonlinear model overcomes this deficiency. Calibration of the nonlinear model against one data curve leads to predictions of the peak load and the displacement to peak load for two other data curves that are, for this limited test set, more accurate than those made using LEFM. Furthermore, prior observations of damage mechanisms in bone are incompatible with the modeling assumption of LEFM that all nonlinearity is confined to a zone much smaller than the specimen and the crack length. The predictions of the cohesive model and the prior observations concur that the length of the nonlinear zone in human cortical bone varies in the range 3-10 mm, which is comparable to or larger than naturally-occurring bones and the specimens used to test them. We infer that LEFM is not an accurate model for cortical bone. The fracture toughness of bone deduced via LEFM from test data will not generally be a material constant, but will take different values for different crack lengths and test configurations. The accuracy of using LEFM or single-parameter fracture toughness for analyzing the significance of data from clinical studies is called into question. The nonlinear cohesive zone model is proposed to be a more accurate model of bone and the traction-displacement or cohesive law is hypothesized to be a material property. The cohesive law contains a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality, e.g., for assessing the efficacy of therapy for osteoporosis.
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Affiliation(s)
- Q D Yang
- Rockwell Scientific Co. LLC, 1049 Camino Dos Rios, Thousand Oaks, CA 91360, USA.
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24
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Boskey AL, Goldberg M, Kulkarni A, Gomez S. Infrared imaging microscopy of bone: illustrations from a mouse model of Fabry disease. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2006; 1758:942-7. [PMID: 16697974 PMCID: PMC1551908 DOI: 10.1016/j.bbamem.2006.02.019] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2006] [Revised: 02/14/2006] [Accepted: 02/16/2006] [Indexed: 10/24/2022]
Abstract
Bone is a complex tissue whose composition and properties vary with age, sex, diet, tissue type, health and disease. In this review, we demonstrate how infrared spectroscopy and infrared spectroscopic imaging can be applied to the study of these variations. A specific example of mice with Fabry disease (a lipid storage disease) is presented in which it is demonstrated that the bones of these young animals, while showing typical spatial variation in mineral content, mineral crystal size, and collagen maturity, do not differ from the bones of age- and sex-matched wild type animals.
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Affiliation(s)
- Adele L Boskey
- Hospital for Special Surgery and Weill Medical College of Cornell University, USA.
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25
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Yeni YN, Kim DG, Dong XN, Turner AS, Les CM, Fyhrie DP. Do sacrificial bonds affect the viscoelastic and fracture properties of bone? Clin Orthop Relat Res 2006; 443:101-8. [PMID: 16462432 DOI: 10.1097/01.blo.0000200239.29931.56] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Sacrificial bonds have been suggested as a toughening mechanism for bone tissue. Ionic bridges formed by divalent calcium ions between collagen molecules have been proposed as candidates for sacrificial bonds. If this mechanism is active at the macroscopic level, we should observe changes in mechanical properties of bone when calcium ions are maintained or removed from the tissue. To test this hypothesis, we measured viscoelastic and monotonic mechanical properties of cortical bone subjected to differing ionic environments. Storage modulus of bone could be changed up to 3.8% by the presence or absence of Na+ or Ca++ in the environment in a reversible fashion when bones were monitored continuously during treatments. A long-term one-time treatment increased the viscoelastic properties of bone soaked in Na+ solutions whereas the viscoelastic properties of bones soaked in Ca++ solutions were maintained. However, the strength and toughness of bone specimens soaked and fractured in treatment solutions were not improved. The presence of Ca++ affected the mechanical behavior of mineralized bone tissue at the macro scale. These effects were reversible, consistent with the original proposal. However, these effects may not necessarily indicate an increase in strength or toughness of the tissue at the macro scale.
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Affiliation(s)
- Yener N Yeni
- Section of Biomechanics, Bone and Joint Center, Department of Orthopaedics and Rehabilitation, Henry Ford Hospital, Detroit, MI 48202, USA.
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26
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Fantner GE, Hassenkam T, Kindt JH, Weaver JC, Birkedal H, Pechenik L, Cutroni JA, Cidade GAG, Stucky GD, Morse DE, Hansma PK. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. NATURE MATERIALS 2005; 4:612-6. [PMID: 16025123 DOI: 10.1038/nmat1428] [Citation(s) in RCA: 515] [Impact Index Per Article: 27.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2004] [Accepted: 05/10/2005] [Indexed: 05/03/2023]
Abstract
Properties of the organic matrix of bone as well as its function in the microstructure could be the key to the remarkable mechanical properties of bone. Previously, it was found that on the molecular level, calcium-mediated sacrificial bonds increased stiffness and enhanced energy dissipation in bone constituent molecules. Here we present evidence for how this sacrificial bond and hidden length mechanism contributes to the mechanical properties of the bone composite, by investigating the nanoscale arrangement of the bone constituents and their interactions. We find evidence that bone consists of mineralized collagen fibrils and a non-fibrillar organic matrix, which acts as a 'glue' that holds the mineralized fibrils together. We believe that this glue may resist the separation of mineralized collagen fibrils. As in the case of the sacrificial bonds in single molecules, the effectiveness of this mechanism increases with the presence of Ca2+ ions.
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Affiliation(s)
- Georg E Fantner
- University of California, Santa Barbara, Department of Physics, California 93106, USA.
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27
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Akkus O, Belaney RM, Das P. Free radical scavenging alleviates the biomechanical impairment of gamma radiation sterilized bone tissue. J Orthop Res 2005; 23:838-45. [PMID: 16022998 DOI: 10.1016/j.orthres.2005.01.007] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Revised: 01/25/2005] [Accepted: 01/25/2005] [Indexed: 02/04/2023]
Abstract
Terminal sterilization of bone allografts by gamma radiation is often essential prior to their clinical use to minimize the risk of infection and disease transmission. While gamma radiation has efficacy superior to other sterilization methods it also impairs the material properties of bone allografts, which may result in premature clinical failure of the allograft. The mechanisms by which gamma radiation sterilization damages bone tissue are not well known although there is evidence that the damage is induced via free radical attack on the collagen. In the light of the existing literature, it was hypothesized that gamma radiation induced biochemical damage to bone's collagen that can be reduced by scavenging for the free radicals generated during the ionizing radiation. It was also hypothesized that this lessening of the extent of biochemical degradation of collagen will be accompanied by alleviation in the extent of biomechanical impairment secondary to gamma radiation sterilization. Standardized tensile test specimens machined from human femoral cortical bone and specimens were assigned to four treatment groups: control, scavenger treated-control, irradiated and scavenger treated-irradiated. Thiourea was selected as the free radical scavenger and it was applied in aqueous form at the concentration of 1.5 M. Monotonic and cyclic mechanical tests were conducted to evaluate the mechanical performance of the treatment groups and the biochemical integrity of collagen molecules were assessed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. The native mechanical properties of bone tissue did not change by thiourea treatment only. The effect of thiourea treatment on mechanical properties of irradiated specimens were such that the post-yield energy, the fracture energy and the fatigue life of thiourea treated-irradiated treatment group were 1.9-fold, 3.3-fold and 4.7-fold greater than those of the irradiated treatment group, respectively. However, the mechanical function of thiourea treated and irradiated specimens was not to the level of unirradiated controls. The damage occurred through the cleavage of the collagen backbone as revealed by SDS PAGE analysis. Irradiated specimens did not exhibit a noteworthy amount of intact alpha-chains whereas those irradiated in the presence of thiourea demonstrated intact alpha-chains. Results demonstrated that free radical damage is an important pathway of damage, caused by cleaving the collagen backbone. Blocking the activity of free radicals using the scavenger thiourea reduces the extent of damage to collagen, helping to maintain the mechanical strength of sterilized tissue. Therefore, free radical scavenger thiourea has the potential to improve the functional life-time of the allograft component following transplantation.
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Affiliation(s)
- Ozan Akkus
- Department of Bioengineering, The University of Toledo, 5035 Nitschke Hall, 2801 W. Bancroft Street, Mail Stop 303, Toledo, OH 43606 3390, USA.
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28
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Imbeni V, Kruzic JJ, Marshall GW, Marshall SJ, Ritchie RO. The dentin-enamel junction and the fracture of human teeth. NATURE MATERIALS 2005; 4:229-232. [PMID: 15711554 DOI: 10.1038/nmat1323] [Citation(s) in RCA: 210] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2004] [Accepted: 12/09/2004] [Indexed: 05/24/2023]
Abstract
The dentin-enamel junction (DEJ), which is the interfacial region between the dentin and outer enamel coating in teeth, is known for its unique biomechanical properties that provide a crack-arrest barrier for flaws formed in the brittle enamel1. In this work, we re-examine how cracks propagate in the proximity of the DEJ, and specifically quantify, using interfacial fracture mechanics, the fracture toughness of the DEJ region. Careful observation of crack penetration through the interface and the new estimate of the DEJ toughness ( approximately 5 to 10 times higher than enamel but approximately 75% lower than dentin) shed new light on the mechanism of crack arrest. We conclude that the critical role of this region, in preventing cracks formed in enamel from traversing the interface and causing catastrophic tooth fractures, is not associated with the crack-arrest capabilities of the interface itself; rather, cracks tend to penetrate the (optical) DEJ and arrest when they enter the tougher mantle dentin adjacent to the interface due to the development of crack-tip shielding from uncracked-ligament bridging.
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Affiliation(s)
- V Imbeni
- Materials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
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29
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Nalla RK, Kruzic JJ, Ritchie RO. On the origin of the toughness of mineralized tissue: microcracking or crack bridging? Bone 2004; 34:790-8. [PMID: 15121010 DOI: 10.1016/j.bone.2004.02.001] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/23/2003] [Revised: 01/27/2004] [Accepted: 02/02/2004] [Indexed: 10/26/2022]
Abstract
Two major mechanisms that could potentially be responsible for toughening in mineralized tissues, such as bone and dentin, have been identified-microcracking and crack bridging. While evidence has been reported for both mechanisms, there has been no consensus thus far on which mechanism plays the dominant role in toughening these materials. In the present study, we seek to present definitive experimental evidence supporting crack bridging, rather than microcracking, as the most significant mechanism of toughening in cortical bone and dentin. In vitro fracture toughness experiments were conducted to measure the variation of the fracture resistance with crack extension [resistance-curve (R-curve) behavior] for both materials with special attention paid to changes in the sample compliance. Because these two toughening mechanisms induce opposite effects on the sample compliance, such experiments allow for the definitive determination of the dominant toughening mechanism, which in the present study was found to be crack bridging for microstructurally large crack sizes. The results of this work are of relevance from the perspective of developing a micromechanistic framework for understanding fracture behavior of mineralized tissue and in predicting failure in vivo.
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Affiliation(s)
- R K Nalla
- Materials Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA
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