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Zou Z, Cheong VS, Fromme P. Bone remodelling prediction using mechanical stimulus with bone connectivity theory in porous implants. J Mech Behav Biomed Mater 2024; 153:106463. [PMID: 38401186 DOI: 10.1016/j.jmbbm.2024.106463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 01/22/2024] [Accepted: 02/13/2024] [Indexed: 02/26/2024]
Abstract
Strain energy density (SED) is considered to be the primary remodelling stimulus influencing the process of bone growth into porous implants. A bone remodelling algorithm incorporating the concept of bone connectivity, that newly formed bone should only grow from existing bone, was developed to provide a more biologically realistic simulation of bone growth. Results showed that the new algorithm prevented the occurrence of unconnected mature bone within porous implants, an unrealistic phenomenon observed using conventional adaptive elasticity theories. The bone connectivity algorithm had minimal effect (0.67% difference) on the final bone density distribution for standard bending and torsional moment cases. For a porous implant model, both algorithms, with and without bone connectivity implementation, reached the same final stiffness, with a difference of less than 0.01%. The bone connectivity algorithm predicted a slower and more gradual bone remodelling process, requiring at least 50% additional time for full remodelling compared to the conventional adaptive elasticity algorithm, which should be accounted for in the planning of rehabilitation strategies. The developed modelling can be employed to improve porous implant designs to achieve better clinical outcomes.
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Affiliation(s)
- Zhenhao Zou
- Department of Mechanical Engineering, University College London, United Kingdom.
| | - Vee San Cheong
- Future Health Technologies Programme, Singapore-ETH Centre, CREATE Campus, Singapore; Insigneo Institute for in silico Medicine, University of Sheffield, United Kingdom; Department of Mechanical Engineering, University of Sheffield, United Kingdom.
| | - Paul Fromme
- Department of Mechanical Engineering, University College London, United Kingdom.
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Sego TJ, Hsu YT, Chu TM, Tovar A. Modeling Progressive Damage Accumulation in Bone Remodeling Explains the Thermodynamic Basis of Bone Resorption by Overloading. Bull Math Biol 2020; 82:134. [PMID: 33037933 DOI: 10.1007/s11538-020-00808-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 09/18/2020] [Indexed: 11/24/2022]
Abstract
Computational modeling of skeletal tissue seeks to predict the structural adaptation of bone in response to mechanical loading. The theory of continuum damage-repair, a mathematical description of structural adaptation based on principles of damage mechanics, continues to be developed and utilized for the prediction of long-term peri-implant outcomes. Despite its technical soundness, CDR does not account for the accumulation of mechanical damage and irreversible deformation. In this work, a nonlinear mathematical model of independent damage accumulation and plastic deformation is developed in terms of the CDR formulation. The proposed model incorporates empirical correlations from uniaxial experiments. Supporting elements of the model are derived, including damage and yielding criteria, corresponding consistency conditions, and the basic, necessary forms for integration during loading. Positivity of mechanical dissipation due to damage is proved, while strain-based, associative plastic flow and linear hardening describe post-yield behavior. Calibration of model parameters to the empirical correlations from which the model was derived is then accomplished. Results of numerical experiments on a point-wise specimen show that damage and plasticity inhibit bone formation by dissipation of energy available to biological processes, leading to material failure that would otherwise be predicted to experience a net gain of bone.
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Affiliation(s)
- T J Sego
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA.
| | - Yung-Ting Hsu
- Department of Periodontics, University of Washington, Seattle, WA, USA
| | - Tien-Min Chu
- Department of Restorative Dentistry, Indiana University, Indianapolis, IN, USA
| | - Andres Tovar
- Department of Mechanical and Energy Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA
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Abstract
Bone tissue is a material with a complex structure and mechanical properties. Diseases or even normal repetitive loads may cause microfractures to appear in the bone structure, leading to a deterioration of its properties. A better understanding of this phenomenon will lead to better predictions of bone fracture or bone-implant performance. In this work, the model proposed by Frémond and Nedjar in 1996 (initially for concrete structures) is numerically analyzed and compared against a bone specific mechanical model proposed by García et al. in 2009. The objective is to evaluate both models implemented with a finite element method. This will allow us to determine if the modified Frémond–Nedjar model is adequate for this purpose. We show that, in one dimension, both models show similar results, reproducing the qualitative behaviour of bone subjected to typical engineering tests. In particular, the Frémond–Nedjar model with the introduced modifications shows good agreement with experimental data. Finally, some two-dimensional results are also provided for the Frémond–Nedjar model to show its behaviour in the simulation of a real tensile test.
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Finite element model of load adaptive remodelling induced by orthodontic forces. Med Eng Phys 2018; 62:63-68. [DOI: 10.1016/j.medengphy.2018.10.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Revised: 09/27/2018] [Accepted: 10/09/2018] [Indexed: 11/21/2022]
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Martínez-Reina J, Ojeda J, Mayo J. On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution. PLoS One 2016; 11:e0148603. [PMID: 26859888 PMCID: PMC4747586 DOI: 10.1371/journal.pone.0148603] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2015] [Accepted: 01/21/2016] [Indexed: 11/28/2022] Open
Abstract
Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.
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Affiliation(s)
- Javier Martínez-Reina
- Department of Mechanical Engineering, Universidad de Sevilla, Sevilla, Spain
- * E-mail:
| | - Joaquín Ojeda
- Department of Mechanical Engineering, Universidad de Sevilla, Sevilla, Spain
| | - Juana Mayo
- Department of Mechanical Engineering, Universidad de Sevilla, Sevilla, Spain
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Mesh management methods in finite element simulations of orthodontic tooth movement. Med Eng Phys 2016; 38:140-7. [DOI: 10.1016/j.medengphy.2015.11.005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2015] [Revised: 09/10/2015] [Accepted: 11/08/2015] [Indexed: 11/18/2022]
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PourAkbar Saffar K, Sudak LJ, Federico S. A biomechanical evaluation of CNT-grown bone. J Biomed Mater Res A 2015; 104:465-75. [PMID: 26440408 DOI: 10.1002/jbm.a.35582] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2015] [Revised: 09/04/2015] [Accepted: 10/01/2015] [Indexed: 11/11/2022]
Abstract
Beside their biochemical properties, the exceptional mechanical characteristics of carbon nanotubes (CNTs) suggested growing a reinforced composite material very similar to natural bone in structure and chemical composition, but significantly stronger and stiffer. This is where biomechanical considerations portray themselves to justify the need for further investigations, in order to verify the applicability of CNTs as scaffolds that may ease bone regeneration and simultaneously raise its mechanical strength and durability. This research, using several modeling approaches, attempts to look at some of the mechanical changes likely to take place in the promised artificial tissue, while considering the relationships between mechanical and living functions of bone, particularly the remodeling process. Results suggest that notwithstanding the significant improvements induced to the mechanical behavior of the artificial tissue, applications of such stiff inclusions as CNTs in reinforcing the material of bone may detrimentally change the thresholds of mechanical stimuli that are essential for the initiation and resumption of the bone remodeling process.
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Affiliation(s)
- Kaveh PourAkbar Saffar
- Department of Mechanical and Manufacturing Engineering, The University of Calgary, 2500 University Dr NW, Calgary, Alberta, T2N 1N4, Canada
| | - Leszek J Sudak
- Department of Mechanical and Manufacturing Engineering, The University of Calgary, 2500 University Dr NW, Calgary, Alberta, T2N 1N4, Canada
| | - Salvatore Federico
- Department of Mechanical and Manufacturing Engineering, The University of Calgary, 2500 University Dr NW, Calgary, Alberta, T2N 1N4, Canada
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Gardiner BS, Wong KKL, Joldes GR, Rich AJ, Tan CW, Burgess AW, Smith DW. Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components. PLoS Comput Biol 2015; 11:e1004544. [PMID: 26452000 PMCID: PMC4599884 DOI: 10.1371/journal.pcbi.1004544] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2015] [Accepted: 09/09/2015] [Indexed: 01/13/2023] Open
Abstract
This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory. Modelling is an important tool in understanding the behaviour of biological tissues. In this paper we advocate a new modelling framework in which cells and tissues are represented by a collection of particles with associated properties. The particles interact with each other and can change their behaviour in response to changes in their environment. We demonstrate how the propose framework can be used to represent the mechanical behaviour of different tissues with much greater flexibility as compared to traditional continuum based methods.
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Affiliation(s)
- Bruce S. Gardiner
- School of Engineering and Information Technology, Murdoch University, Perth, Australia
- * E-mail:
| | - Kelvin K. L. Wong
- Engineering Computational Biology, School of Computer Science and Software Engineering, The University of Western Australia, Perth, Australia
| | - Grand R. Joldes
- Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, Perth, Australia
| | - Addison J. Rich
- Engineering Computational Biology, School of Computer Science and Software Engineering, The University of Western Australia, Perth, Australia
| | - Chin Wee Tan
- Structural Biology Division, The Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- Department of Medical Biology, University of Melbourne, Melbourne, Victoria, Australia
| | - Antony W. Burgess
- Structural Biology Division, The Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- Department of Medical Biology, University of Melbourne, Melbourne, Victoria, Australia
- Department of Surgery, Royal Melbourne Hospital, Melbourne, Victoria, Australia
| | - David W. Smith
- Engineering Computational Biology, School of Computer Science and Software Engineering, The University of Western Australia, Perth, Australia
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Geris L. Regenerative orthopaedics: in vitro, in vivo...in silico. INTERNATIONAL ORTHOPAEDICS 2014; 38:1771-8. [PMID: 24984594 DOI: 10.1007/s00264-014-2419-6] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2014] [Accepted: 06/05/2014] [Indexed: 11/29/2022]
Abstract
In silico, defined in analogy to in vitro and in vivo as those studies that are performed on a computer, is an essential step in problem-solving and product development in classical engineering fields. The use of in silico models is now slowly easing its way into medicine. In silico models are already used in orthopaedics for the planning of complicated surgeries, personalised implant design and the analysis of gait measurements. However, these in silico models often lack the simulation of the response of the biological system over time. In silico models focusing on the response of the biological systems are in full development. This review starts with an introduction into in silico models of orthopaedic processes. Special attention is paid to the classification of models according to their spatiotemporal scale (gene/protein to population) and the information they were built on (data vs hypotheses). Subsequently, the review focuses on the in silico models used in regenerative orthopaedics research. Contributions of in silico models to an enhanced understanding and optimisation of four key elements-cells, carriers, culture and clinics-are illustrated. Finally, a number of challenges are identified, related to the computational aspects but also to the integration of in silico tools into clinical practice.
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Affiliation(s)
- Liesbet Geris
- Biomechanics Research Unit, University of Liège, Liège, Belgium,
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