1
|
Al-Qudsy L, Hu YW, Xu H, Yang PF. Mineralized Collagen Fibrils: An Essential Component in Determining the Mechanical Behavior of Cortical Bone. ACS Biomater Sci Eng 2023; 9:2203-2219. [PMID: 37075172 DOI: 10.1021/acsbiomaterials.2c01377] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/21/2023]
Abstract
Bone comprises mechanically different materials in a specific hierarchical structure. Mineralized collagen fibrils (MCFs), represented by tropocollagen molecules and hydroxyapatite nanocrystals, are the fundamental unit of bone. The mechanical characterization of MCFs provides the unique adaptive mechanical competence to bone to withstand mechanical load. The structural and mechanical role of MCFs is critical in the deformation mechanisms of bone and the marvelous strength and toughness possessed by bone. However, the role of MCFs in the mechanical behavior of bone across multiple length scales is not fully understood. In the present study, we shed light upon the latest progress regarding bone deformation at multiple hierarchical levels and emphasize the role of MCFs during bone deformation. We propose the concept of hierarchical deformation of bone to describe the interconnected deformation process across multiple length scales of bone under mechanical loading. Furthermore, how the deterioration of bone caused by aging and diseases impairs the hierarchical deformation process of the cortical bone is discussed. The present work expects to provide insights on the characterization of MCFs in the mechanical properties of bone and lays the framework for the understanding of the multiscale deformation mechanics of bone.
Collapse
Affiliation(s)
- Luban Al-Qudsy
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an 710072, China
- Department of Medical Instrumentation Engineering Techniques, Electrical Engineering Technical College, Middle Technical University, 8998+QHJ Baghdad, Iraq
| | - Yi-Wei Hu
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an 710072, China
| | - Huiyun Xu
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an 710072, China
| | - Peng-Fei Yang
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an 710072, China
| |
Collapse
|
2
|
Cosma C, Apostu D, Vilau C, Popan A, Oltean-Dan D, Balc N, Tomoaie G, Benea H. Finite Element Analysis of Different Osseocartilaginous Reconstruction Techniques in Animal Model Knees. MATERIALS (BASEL, SWITZERLAND) 2023; 16:2546. [PMID: 37048840 PMCID: PMC10095518 DOI: 10.3390/ma16072546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Revised: 03/09/2023] [Accepted: 03/14/2023] [Indexed: 06/19/2023]
Abstract
Lesions of the articular cartilage are frequent in all age populations and lead to functional impairment. Multiple surgical techniques have failed to provide an effective method for cartilage repair. The aim of our research was to evaluate the effect of two different compression forces on three types of cartilage repair using finite element analysis (FEA). Initially, an in vivo study was performed on sheep. The in vivo study was prepared as following: Case 0-control group, without cartilage lesion; Case 1-cartilage lesion treated with macro-porous collagen implants; Case 2-cartilage lesion treated with collagen implants impregnated with bone marrow concentrate (BMC); Case 3-cartilage lesion treated with collagen implants impregnated with adipose-derived stem cells (ASC). Using the computed tomography (CT) data, virtual femur-cartilage-tibia joints were created for each Case. The study showed better results in bone changes when using porous collagen implants impregnated with BMC or ASC stem cells for the treatment of osseocartilaginous defects compared with untreated macro-porous implant. After 7 months postoperative, the presence of un-resorbed collagen influences the von Mises stress distribution, total deformation, and displacement on the Z axis. The BMC treatment was superior to ASC cells in bone tissue morphology, resembling the biomechanics of the control group in all FEA simulations.
Collapse
Affiliation(s)
- Cosmin Cosma
- Department of Manufacturing Engineering, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania; (C.C.)
| | - Dragos Apostu
- Department of Orthopedics and Traumatology, Iuliu Haţieganu University of Medicine and Pharmacy, 400132 Cluj-Napoca, Romania
| | - Cristian Vilau
- Department of Material Resistance, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
| | - Alexandru Popan
- Department of Manufacturing Engineering, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania; (C.C.)
| | - Daniel Oltean-Dan
- Department of Orthopedics and Traumatology, Iuliu Haţieganu University of Medicine and Pharmacy, 400132 Cluj-Napoca, Romania
| | - Nicolae Balc
- Department of Manufacturing Engineering, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania; (C.C.)
| | - Gheorghe Tomoaie
- Department of Orthopedics and Traumatology, Iuliu Haţieganu University of Medicine and Pharmacy, 400132 Cluj-Napoca, Romania
- Academy of Romanian Scientists, 050044 Bucharest, Romania
| | - Horea Benea
- Department of Orthopedics and Traumatology, Iuliu Haţieganu University of Medicine and Pharmacy, 400132 Cluj-Napoca, Romania
| |
Collapse
|
3
|
Mouss MEL, Merzouki T, Rekik A, Hambli R. Multiscale approach incorporating tropocollagen scale to assess the effect of molecular age-related modifications on elastic constants of cortical bone based on finite element and homogenization methods. J Mech Behav Biomed Mater 2022; 128:105130. [DOI: 10.1016/j.jmbbm.2022.105130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Revised: 12/15/2021] [Accepted: 02/10/2022] [Indexed: 10/19/2022]
|
4
|
Percolation networks inside 3D model of the mineralized collagen fibril. Sci Rep 2021; 11:11398. [PMID: 34059767 PMCID: PMC8166932 DOI: 10.1038/s41598-021-90916-x] [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: 02/26/2021] [Accepted: 05/19/2021] [Indexed: 01/04/2023] Open
Abstract
Bone is a hierarchical biological material, characterized at the nanoscale by a recurring structure mainly composed of apatite mineral and collagen, i.e. the mineralized collagen fibril (MCF). Although the architecture of the MCF was extensively investigated by experimental and computational studies, it still represents a topic of debate. In this work, we developed a 3D continuum model of the mineral phase in the framework of percolation theory, that describes the transition from isolated to spanning cluster of connected platelets. Using Monte Carlo technique, we computed overall 120 × 106 iterations and investigated the formation of spanning networks of apatite minerals. We computed the percolation probability for different mineral volume fractions characteristic of human bone tissue. The findings highlight that the percolation threshold occurs at lower volume fractions for spanning clusters in the width direction with respect to the critical mineral volume fractions that characterize the percolation transition in the thickness and length directions. The formation of spanning clusters of minerals represents a condition of instability for the MCF, as it could be the onset of a high susceptibility to fracture. The 3D computational model developed in this study provides new, complementary insights to the experimental investigations concerning human MCF.
Collapse
|
5
|
An efficient two-scale 3D FE model of the bone fibril array: comparison of anisotropic elastic properties with analytical methods and micro-sample testing. Biomech Model Mechanobiol 2020; 19:2127-2147. [DOI: 10.1007/s10237-020-01328-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2019] [Accepted: 04/11/2020] [Indexed: 12/14/2022]
|
6
|
Awasthi A, Sharma R, Ghosh R. Monte Carlo type Simulations of Mineralized Collagen Fibril based on Two Scale Asymptotic Homogenization. J Biomech Eng 2019; 141:2720657. [PMID: 30615067 DOI: 10.1115/1.4042439] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2018] [Indexed: 11/08/2022]
Abstract
A multi-scale model for mineralized collagen fibril is proposed by taking into account the uncertainties associated with the geometrical properties of mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli at two hierarchical length scales, namely: microfibril and mineralized collagen fibril. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes. A total 100 realizations for mineralized collagen fibril model with random distribution have been generated using an in-house MATLAB® code and Monte-Carlo type simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (= 10%) and large (= 10%) strain regimes. The stress transformation mechanism has also been explored in microfibril which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for microfibril under small and large strain have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as input for upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the mineralized collagen fibril in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics simulations in the literature with a significant reduction in the computational cost.
Collapse
Affiliation(s)
- Abhilash Awasthi
- MS Scholar, School of Engineering, Indian Institute of Technology Mandi, Kamand - 175005, Mandi, Himachal Pradesh, India
| | - Rajneesh Sharma
- Assistant Professor, School of Engineering, Indian Institute of Technology Mandi, Kamand - 175005, Mandi, Himachal Pradesh, India
| | - Rajesh Ghosh
- Assistant Professor, School of Engineering, Indian Institute of Technology Mandi, Kamand - 175005, Mandi, Himachal Pradesh, India
| |
Collapse
|
7
|
Su FY, Pang S, Ling YTT, Shyu P, Novitskaya E, Seo K, Lambert S, Zarate K, Graeve OA, Jasiuk I, McKittrick J. Deproteinization of Cortical Bone: Effects of Different Treatments. Calcif Tissue Int 2018; 103:554-566. [PMID: 30022228 DOI: 10.1007/s00223-018-0453-x] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/23/2018] [Accepted: 07/05/2018] [Indexed: 01/28/2023]
Abstract
Bone is a biological composite material having collagen and mineral as its main constituents. In order to better understand the arrangement of the mineral phase in bone, porcine cortical bone was deproteinized using different chemical treatments. This study aims to determine the best method to remove the protein constituent while preserving the mineral component. Chemicals used were H2O2, NaOCl, NaOH, and KOH, and the efficacy of deproteinization treatments was determined by thermogravimetric analysis and Raman spectroscopy. The structure of the residual mineral parts was examined using scanning electron microscopy. X-ray diffraction was used to confirm that the mineral component was not altered by the chemical treatments. NaOCl was found to be the most effective method for deproteinization and the mineral phase was self-standing, supporting the hypothesis that bone is an interpenetrating composite. Thermogravimetric analyses and Raman spectroscopy results showed the preservation of mineral crystallinity and presence of residual organic material after all chemical treatments. A defatting step, which has not previously been used in conjunction with deproteinization to isolate the mineral phase, was also used. Finally, Raman spectroscopy demonstrated that the inclusion of a defatting procedure resulted in the removal of some but not all residual protein in the bone.
Collapse
Affiliation(s)
- Frances Y Su
- Materials Science and Engineering Program, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA
| | - Siyuan Pang
- Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL, 61801, USA
| | - Yik Tung Tracy Ling
- Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL, 61801, USA
| | - Peter Shyu
- Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL, 61801, USA
| | - Ekaterina Novitskaya
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA
| | - Kyungah Seo
- Materials Science and Engineering Program, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA
| | - Sofia Lambert
- Centro de Enseñanza Técnica y Superior - Campus Mexicali, Calzada CETYS s/n. Col. Rivera, Mexicali, Baja California, C.P. 21259, Mexico
| | - Kimberlin Zarate
- Hilltop High School, 555 Claire Avenue, Chula Vista, CA, 91910, USA
| | - Olivia A Graeve
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA
| | - Iwona Jasiuk
- Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL, 61801, USA.
- University of Illinois at Urbana-Champaign, 1206 West Green Street, Room 2101C MEL, Urbana, IL, 61801, USA.
| | - Joanna McKittrick
- Materials Science and Engineering Program, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA.
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA.
- University of California, San Diego, 9500 Gilman Dr., EBU II, Room 257, La Jolla, CA, 92093-0411, USA.
| |
Collapse
|
8
|
KRAIEM TESNIM, BARKAOUI ABDELWAHED, MERZOUKI TAREK, CHAFRA MOEZ. CROSS-LINKS MULTISCALE EFFECTS ON BONE ULTRASTRUCTURE BIOMECHANICAL BEHAVIOR. J MECH MED BIOL 2018. [DOI: 10.1142/s0219519418500628] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Bone is a multiscale combination of collagen molecules merged with mineral crystals. Its high rigidity and stability stem amply from its polymeric organic matrix and secondly from the connections established between interdifferent and intradifferent scale components through cross-links. Several studies have shown that the cross-links inhibition results in a reduction in strength of bone but they do not quantify the degree to which these connections contribute to the bone rigidity and toughness. This report is classified among the few works that measure the cross-links multiscale impact on the ultrastructure bone mechanical behavior. This work aims firstly to study the effect of cross-links at the molecule scale and secondly to gather from literature studies results handling with cross-links effects on the other bone ultrastructure scales in order to reveal the multiscale effect of cross-links. This study proves that cross-links increasing number improves the mechanical performance of each scale of bone ultrastructure. On the other hand, cross-links have a multiscale contribution that depends on its rank related to existing cross-links connecting the same geometries and it depends on mechanical characteristics of geometries connected.
Collapse
Affiliation(s)
- TESNIM KRAIEM
- LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie (LR-MAI), Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar 1002, Tunis, Tunisia
| | - ABDELWAHED BARKAOUI
- Laboratoire des Energies Renouvelables et Matériaux Avancés (LERMA), Ecole Supérieure de l’Ingénierie de l’Energie, Université Internationale de Rabat, Rocade RabatSalé, 11100, Rabat-Sala El Jadida, Morocco
| | - TAREK MERZOUKI
- Laboratoire d’Ingénierie des Systèmes de Versailles LISV, Université of Versailles Saint-Quentin 10-12 avenue, de l’Europe, 78140 Vélisy, France
| | - MOEZ CHAFRA
- Laboratoire de Systèmes et de Mécanique Appliquée (LASMAP), Ecole Polytechnique de Tunis, Université de Carthage, 2078, La Marsa, Tunisia
| |
Collapse
|
9
|
Abueidda DW, Sabet FA, Jasiuk IM. Modeling of Stiffness and Strength of Bone at Nanoscale. J Biomech Eng 2017; 139:2613840. [DOI: 10.1115/1.4036314] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Indexed: 11/08/2022]
Abstract
Two distinct geometrical models of bone at the nanoscale (collagen fibril and mineral platelets) are analyzed computationally. In the first model (model I), minerals are periodically distributed in a staggered manner in a collagen matrix while in the second model (model II), minerals form continuous layers outside the collagen fibril. Elastic modulus and strength of bone at the nanoscale, represented by these two models under longitudinal tensile loading, are studied using a finite element (FE) software abaqus. The analysis employs a traction-separation law (cohesive surface modeling) at various interfaces in the models to account for interfacial delaminations. Plane stress, plane strain, and axisymmetric versions of the two models are considered. Model II is found to have a higher stiffness than model I for all cases. For strength, the two models alternate the superiority of performance depending on the inputs and assumptions used. For model II, the axisymmetric case gives higher results than the plane stress and plane strain cases while an opposite trend is observed for model I. For axisymmetric case, model II shows greater strength and stiffness compared to model I. The collagen–mineral arrangement of bone at nanoscale forms a basic building block of bone. Thus, knowledge of its mechanical properties is of high scientific and clinical interests.
Collapse
Affiliation(s)
- Diab W. Abueidda
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Mechanical Engineering Building, 1206 W Green Street, Urbana, IL 61801 e-mail:
| | - Fereshteh A. Sabet
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Mechanical Engineering Building, 1206 W Green Street, Urbana, IL 61801 e-mail:
| | - Iwona M. Jasiuk
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Mechanical Engineering Building, 1206 W Green Street, Urbana, IL 61801 e-mail:
| |
Collapse
|
10
|
Barkaoui A, Tlili B, Vercher-Martínez A, Hambli R. A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2016; 134:69-78. [PMID: 27480733 DOI: 10.1016/j.cmpb.2016.07.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Revised: 05/24/2016] [Accepted: 07/04/2016] [Indexed: 06/06/2023]
Abstract
Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight that intelligent numerical methods are powerful and accurate procedures to deal with the complex multiscale problem in the bone tissue with results in agreement with values found in literature for specific scale levels.
Collapse
Affiliation(s)
- Abdelwahed Barkaoui
- Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie (LR-MAI), 1002 Tunis, Tunisie; Université de Tunis El Manar, Institut Préparatoire aux Etudes d'Ingénieurs d'El Manar, B.P 244, 2092 Tunis, Tunisie.
| | - Brahim Tlili
- Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie (LR-MAI), 1002 Tunis, Tunisie; Université de Tunis El Manar, Institut Préparatoire aux Etudes d'Ingénieurs d'El Manar, B.P 244, 2092 Tunis, Tunisie
| | - Ana Vercher-Martínez
- Depto. de Ingeniería Mecánica y de Materiales, Centro de Investigación de Tecnología de Vehículos-CITV, Universitat Politècnica de València, Camino de Vera, 46022 Valencia, Spain
| | - Ridha Hambli
- PRISME Laboratory, EA4229, University of Orleans Polytech' Orléans, 8, Rue Léonard de Vinci, 45072 Orléans, France
| |
Collapse
|
11
|
Qwamizadeh M, Zhang Z, Zhou K, Zhang YW. Protein viscosity, mineral fraction and staggered architecture cooperatively enable the fastest stress wave decay in load-bearing biological materials. J Mech Behav Biomed Mater 2016; 60:339-355. [DOI: 10.1016/j.jmbbm.2016.02.016] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Revised: 02/03/2016] [Accepted: 02/10/2016] [Indexed: 10/22/2022]
|
12
|
Sabet FA, Raeisi Najafi A, Hamed E, Jasiuk I. Modelling of bone fracture and strength at different length scales: a review. Interface Focus 2016; 6:20150055. [PMID: 26855749 PMCID: PMC4686238 DOI: 10.1098/rsfs.2015.0055] [Citation(s) in RCA: 62] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.
Collapse
Affiliation(s)
| | | | | | - Iwona Jasiuk
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| |
Collapse
|
13
|
Komarova SV, Safranek L, Gopalakrishnan J, Ou MJY, McKee MD, Murshed M, Rauch F, Zuhr E. Mathematical model for bone mineralization. Front Cell Dev Biol 2015; 3:51. [PMID: 26347868 PMCID: PMC4544393 DOI: 10.3389/fcell.2015.00051] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 08/04/2015] [Indexed: 12/23/2022] Open
Abstract
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
Collapse
Affiliation(s)
- Svetlana V Komarova
- Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada
| | - Lee Safranek
- Department of Mathematics, Simon Fraser University Burnaby, BC, Canada
| | - Jay Gopalakrishnan
- The Fariborz Maseeh Department of Mathematics and Statistics, Portland State University Portland, OR, USA
| | | | - Marc D McKee
- Faculty of Dentistry, McGill University Montreal, QC, Canada ; Department of Anatomy and Cell Biology, Faculty of Medicine, McGill University Montreal, QC, Canada
| | - Monzur Murshed
- Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada ; Department of Medicine, Faculty of Medicine, McGill University Montreal, QC, Canada
| | - Frank Rauch
- Shriners Hospital for Children-Canada Montreal, QC, Canada
| | - Erica Zuhr
- Department of Mathematics, High Point University High Point, NC, USA
| |
Collapse
|
14
|
Hambli R, Frikha S, Toumi H, Tavares JMRS. Finite element prediction of fatigue damage growth in cancellous bone. Comput Methods Biomech Biomed Engin 2015; 19:563-70. [DOI: 10.1080/10255842.2015.1048687] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
15
|
Vercher-Martínez A, Giner E, Arango C, Javier Fuenmayor F. Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone. J Mech Behav Biomed Mater 2015; 42:243-56. [DOI: 10.1016/j.jmbbm.2014.11.022] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2014] [Revised: 11/19/2014] [Accepted: 11/22/2014] [Indexed: 01/30/2023]
|
16
|
Barkaoui A, Chamekh A, Merzouki T, Hambli R, Mkaddem A. Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:318-338. [PMID: 24123969 DOI: 10.1002/cnm.2604] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2013] [Revised: 09/09/2013] [Accepted: 09/10/2013] [Indexed: 06/02/2023]
Abstract
The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data.
Collapse
Affiliation(s)
- Abdelwahed Barkaoui
- Université de Savoie, Laboratoire SYMME, BP 80439, Annecy-le-Vieux Cedex F74944, France
| | | | | | | | | |
Collapse
|
17
|
Barkaoui A, Hambli R, Tavares JMR. Effect of material and structural factors on fracture behaviour of mineralised collagen microfibril using finite element simulation. Comput Methods Biomech Biomed Engin 2014; 18:1181-1190. [DOI: 10.1080/10255842.2014.883601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
|
18
|
Baer E, Cassidy JJ, Hiltner A. Hierarchical structure of collagen composite systems: lessons from biology. PURE APPL CHEM 1991. [DOI: 10.1351/pac199163070961] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|