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Colabella L, Naili S, Le Cann S, Haiat G. Effect of collagen fibril orientation on the anisotropic properties of peri-implant bone. Biomech Model Mechanobiol 2024; 23:879-891. [PMID: 38300439 DOI: 10.1007/s10237-023-01811-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 12/22/2023] [Indexed: 02/02/2024]
Abstract
In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.
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Affiliation(s)
- Lucas Colabella
- CNRS, Univ Paris Est Creteil, Univ Gustave Eiffel, UMR 8208, F-94010, Creteil, France
- INTEMA, CONICET, Av. Cristóbal Colón 10850, B7606BWV, Mar del Plata, Argentina
| | - Salah Naili
- Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, F-94010, Creteil, France
| | - Sophie Le Cann
- CNRS, Univ Paris Est Creteil, Univ Gustave Eiffel, UMR 8208, F-94010, Creteil, France
| | - Guillaume Haiat
- CNRS, Univ Paris Est Creteil, Univ Gustave Eiffel, UMR 8208, F-94010, Creteil, France.
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2
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Prada DM, Galvis AF, Miller J, Foster JM, Zavaglia C. Multiscale stiffness characterisation of both healthy and osteoporotic bone tissue using subject-specific data. J Mech Behav Biomed Mater 2022; 135:105431. [DOI: 10.1016/j.jmbbm.2022.105431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Revised: 08/22/2022] [Accepted: 08/26/2022] [Indexed: 10/31/2022]
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3
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Post JN, Loerakker S, Merks R, Carlier A. Implementing computational modeling in tissue engineering: where disciplines meet. Tissue Eng Part A 2022; 28:542-554. [PMID: 35345902 DOI: 10.1089/ten.tea.2021.0215] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.
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Affiliation(s)
- Janine Nicole Post
- University of Twente, 3230, Tissue Regeneration, Enschede, Overijssel, Netherlands;
| | - Sandra Loerakker
- Eindhoven University of Technology, 3169, Department of Biomedical Engineering, Eindhoven, Noord-Brabant, Netherlands.,Eindhoven University of Technology, 3169, Institute for Complex Molecular Systems, Eindhoven, Noord-Brabant, Netherlands;
| | - Roeland Merks
- Leiden University, 4496, Institute for Biology Leiden and Mathematical Institute, Leiden, Zuid-Holland, Netherlands;
| | - Aurélie Carlier
- Maastricht University, 5211, MERLN Institute for Technology-Inspired Regenerative Medicine, Universiteitssingel 40, 6229 ER Maastricht, Maastricht, Netherlands, 6200 MD;
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Abstract
PURPOSE OF REVIEW We re-evaluated clinical applications of image-to-FE models to understand if clinical advantages are already evident, which proposals are promising, and which questions are still open. RECENT FINDINGS CT-to-FE is useful in longitudinal treatment evaluation and groups discrimination. In metastatic lesions, CT-to-FE strength alone accurately predicts impending femoral fractures. In osteoporosis, strength from CT-to-FE or DXA-to-FE predicts incident fractures similarly to DXA-aBMD. Coupling loads and strength (possibly in dynamic models) may improve prediction. One promising MRI-to-FE workflow may now be tested on clinical data. Evidence of artificial intelligence usefulness is appearing. CT-to-FE is already clinical in opportunistic CT screening for osteoporosis, and risk of metastasis-related impending fractures. Short-term keys to improve image-to-FE in osteoporosis may be coupling FE with fall risk estimates, pool FE results with other parameters through robust artificial intelligence approaches, and increase reproducibility and cross-validation of models. Modeling bone modifications over time and bone fracture mechanics are still open issues.
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Affiliation(s)
- Enrico Schileo
- Bioengineering and Computing Laboratory, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy.
| | - Fulvia Taddei
- Bioengineering and Computing Laboratory, IRCCS Istituto Ortopedico Rizzoli, Bologna, Italy
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5
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García-Aznar JM, Nasello G, Hervas-Raluy S, Pérez MÁ, Gómez-Benito MJ. Multiscale modeling of bone tissue mechanobiology. Bone 2021; 151:116032. [PMID: 34118446 DOI: 10.1016/j.bone.2021.116032] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 04/25/2021] [Accepted: 06/02/2021] [Indexed: 02/07/2023]
Abstract
Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.
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Affiliation(s)
- José Manuel García-Aznar
- Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, Zaragoza, Spain.
| | - Gabriele Nasello
- Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, Zaragoza, Spain; Biomechanics Section, KU Leuven, Leuven, Belgium
| | - Silvia Hervas-Raluy
- Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, Zaragoza, Spain
| | - María Ángeles Pérez
- Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, Zaragoza, Spain
| | - María José Gómez-Benito
- Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, Zaragoza, Spain
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6
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Gubaua JE, Dicati GWO, Mercuri EGF, Pereira JT. Simulation of bone remodeling around a femoral prosthesis using a model that accounts for biological and mechanical interactions. Med Eng Phys 2020; 84:126-135. [PMID: 32977909 DOI: 10.1016/j.medengphy.2020.08.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 08/10/2020] [Accepted: 08/15/2020] [Indexed: 11/28/2022]
Abstract
The present study focuses on a model for three-dimensional bone remodeling of the human femur that considers cellular dynamics to determine the volume fraction of new bone. The model considers the interaction among responsive osteoblasts, active osteoblasts, and osteoclasts, as well as signaling molecules and parathyroid hormone (PTH). The stimulus of the model has a systemic origin due to the PTH effect, and a local origin due to the action of cytokines, growth factors, and mechanical stimuli near the site of the bone cells. The present work considers that the mechanical stimulus that activates cellular activity is obtained from stresses acting on the bone tissue and the number of daily loading cycles. In addition to simulating the bone modeling process in an intact femur, the numerical model is used to simulate bone adaptation in relation to the stress shielding phenomenon after the implantation of a femoral prosthesis. The results showed that the simulations provide a distribution of bone density that is similar to a radiograph and, in addition, allows the visualization of osteoblast and osteoclast dynamics in bone adaptation response after prosthesis implantation.
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Affiliation(s)
- José Eduardo Gubaua
- Postgraduate Program in Mechanical Engineering, Federal University of Paraná, Paraná, Brazil.
| | - Gabriela Wessling Oening Dicati
- Postgraduate Program in Mechanical Engineering, Federal University of Paraná, Paraná, Brazil; Mechanical Engineering Department, Federal Technological University of Paraná, Campus Pato Branco, Paraná, Brazil
| | | | - Jucélio Tomás Pereira
- Postgraduate Program in Mechanical Engineering, Federal University of Paraná, Paraná, Brazil; Mechanical Engineering Department, Federal University of Paraná, Paraná, Brazil
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7
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A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach. Biomech Model Mechanobiol 2020; 19:2499-2523. [PMID: 32623542 DOI: 10.1007/s10237-020-01353-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 05/29/2020] [Indexed: 12/26/2022]
Abstract
Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.
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8
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Alcântara ACS, Assis I, Prada D, Mehle K, Schwan S, Costa-Paiva L, Skaf MS, Wrobel LC, Sollero P. Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey. MATERIALS (BASEL, SWITZERLAND) 2019; 13:E106. [PMID: 31878356 PMCID: PMC6981613 DOI: 10.3390/ma13010106] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/16/2019] [Accepted: 12/17/2019] [Indexed: 12/26/2022]
Abstract
This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.
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Affiliation(s)
- Amadeus C. S. Alcântara
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
| | - Israel Assis
- Department of Integrated Systems, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil;
| | - Daniel Prada
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
| | - Konrad Mehle
- Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, 06217 Merseburg, Germany;
| | - Stefan Schwan
- Fraunhofer Institute for Microstructure of Materials and Systems IMWS, 06120 Halle/Saale, Germany;
| | - Lúcia Costa-Paiva
- Department of Obstetrics and Gynecology, School of Medical Sciences, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-887, Brazil;
| | - Munir S. Skaf
- Institute of Chemistry and Center for Computing in Engineering and Sciences, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil;
| | - Luiz C. Wrobel
- Institute of Materials and Manufacturing, Brunel University London, Uxbridge UB8 3PH, UK;
- Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
| | - Paulo Sollero
- Department of Computational Mechanics, School of Mechanical Engineering, University of Campinas—UNICAMP, Campinas, Sao Paulo 13083-860, Brazil; (A.C.S.A.); (D.P.)
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9
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Abstract
Multiscale analysis has become an attractive technique to predict the behaviour of materials whose microstructure strongly changes spatially or among samples, with that microstructure controlling the local constitutive behaviour. This is the case, for example, of most biological tissues—such as bone. Multiscale approaches not only allow, not only to better characterise the local behaviour, but also to predict the field-variable distributions (e.g., strains, stresses) at both scales (macro and micro) simultaneously. However, multiscale analysis usually lacks sufficient experimental feedback to demonstrate its validity. In this paper an experimental and numerical micromechanics analysis is developed with application to cortical bone. Displacement and strain fields are obtained across the microstructure by means of digital image correlation (DIC). The other mechanical variables are computed following the micromechanics theory. Special emphasis is given to the differences found in the different field variables between the micro- and macro-structures, which points out the need for this multiscale approach in cortical bone tissue. The obtained results are used to establish the basis of a multiscale methodology with application to the analysis of bone tissue mechanics at different spatial scales.
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10
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Guimera AM, Shanley DP, Proctor CJ. Modelling the role of redox-related mechanisms in musculoskeletal ageing. Free Radic Biol Med 2019; 132:11-18. [PMID: 30219703 DOI: 10.1016/j.freeradbiomed.2018.09.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Revised: 09/07/2018] [Accepted: 09/12/2018] [Indexed: 02/06/2023]
Abstract
The decline in the musculoskeletal system with age is driven at the cellular level by random molecular damage. Cells possess mechanisms to repair or remove damage and many of the pathways involved in this response are regulated by redox signals. However, with ageing there is an increase in oxidative stress which can lead to chronic inflammation and disruption of redox signalling pathways. The complexity of the processes involved has led to the use of computational modelling to help increase our understanding of the system, test hypotheses and make testable predictions. This paper will give a brief background of the biological systems that have been modelled, an introduction to computational modelling, a review of models that involve redox-related mechanisms that are applicable to musculoskeletal ageing, and finally a discussion of the future potential for modelling in this field.
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Affiliation(s)
- Alvaro Martinez Guimera
- Institute for Cell and Molecular Biosciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne NE4 5PL, UK
| | - Daryl P Shanley
- Institute for Cell and Molecular Biosciences, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne NE4 5PL, UK
| | - Carole J Proctor
- Institute of Cellular Medicine, Newcastle University, Campus for Ageing and Vitality, Newcastle upon Tyne NE4 5PL, UK.
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11
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Solitro GF, Mainnemare F, Amirouche F, Mehta A. A novel technique with reduced computed tomography exposure to predict vertebral compression fracture: a finite element study based on rat vertebrae. Med Biol Eng Comput 2018; 57:795-805. [PMID: 30402789 DOI: 10.1007/s11517-018-1918-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Accepted: 10/21/2018] [Indexed: 10/27/2022]
Abstract
Vertebral compression fractures are a significant clinical issue with an annual incidence of approximately 750,000 cases in the USA alone. Mechanical properties of vertebrae are successfully evaluated through finite element (FE) models based on vertebrae CT. However, clinical drawbacks associated to radiation transmission encouraged to explore the possibility to use selected or reduced portions of the vertebra. The objective of our study was to develop a new procedure to predict vertebral compression fracture from sub-volumes. We reconstructed rat vertebras from micro-CT of thoracic and lumbar groups. Each vertebra was partitioned into three sub-volumes of different axial thickness. FE simulating compression tests were performed on each model to evaluate their failure load and stiffness. Using a power function, a high correlation was found for stiffness and strength. The sub-volume with three fifths thickness had a failure load of 180.7 ± 19.2 N for thoracic and of 209.5 ± 27.4 N for the lumbar vertebra. These values were not significantly different from the values found for the entire vertebra (p > 0.05). Based on our findings, failure loads and stiffnesses obtained with reduced CT scans can be successfully used to predict full vertebral failure. This sub-region analysis and power relationship suggests that one can limit radiation exposure to patients when bone characterization is needed. Graphical abstract Estimated mechanical properties in relation to the extent of the computed tomography reconstruction.
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Affiliation(s)
- Giovanni F Solitro
- Department of Orthopaedics, University of Illinois at Chicago, 835 S. Wolcott Avenue, Room E270, Chicago, IL, 60612, USA.,Department of Orthopaedic Surgery, Louisiana State University Health Science Center of Shreveport, 1501 Kings Hwy, Room 3-317, Shreveport, LA, 71104, USA
| | - Florian Mainnemare
- Department of Mechanical Engineering, ENS Cachan, Université Paris-Saclay, 61 Avenue du Président Wilson, 94235, Cachan, France
| | - Farid Amirouche
- Department of Orthopaedics, University of Illinois at Chicago, 835 S. Wolcott Avenue, Room E270, Chicago, IL, 60612, USA.
| | - Ankit Mehta
- Department of Neurosurgery, University of Illinois at Chicago, 912 S Wood St, Chicago, IL, USA
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12
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Pastrama MI, Scheiner S, Pivonka P, Hellmich C. A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation. Bone 2018; 107:208-221. [PMID: 29170108 DOI: 10.1016/j.bone.2017.11.009] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 10/30/2017] [Accepted: 11/14/2017] [Indexed: 10/18/2022]
Abstract
While bone tissue is a hierarchically organized material, mathematical formulations of bone remodeling are often defined on the level of a millimeter-sized representative volume element (RVE), "smeared" over all types of bone microstructures seen at lower observation scales. Thus, there is no explicit consideration of the fact that the biological cells and biochemical factors driving bone remodeling are actually located in differently sized pore spaces: active osteoblasts and osteoclasts can be found in the vascular pores, whereas the lacunar pores host osteocytes - bone cells originating from former osteoblasts which were then "buried" in newly deposited extracellular bone matrix. We here propose a mathematical description which considers size and shape of the pore spaces where the biological and biochemical events take place. In particular, a previously published systems biology formulation, accounting for biochemical regulatory mechanisms such as the rank-rankl-opg pathway, is cast into a multiscale framework coupled to a poromicromechanical model. The latter gives access to the vascular and lacunar pore pressures arising from macroscopic loading. Extensive experimental data on the biological consequences of this loading strongly suggest that the aforementioned pore pressures, together with the loading frequency, are essential drivers of bone remodeling. The novel approach presented here allows for satisfactory simulation of the evolution of bone tissue under various loading conditions, and for different species; including scenarios such as mechanical dis- and overuse of murine and human bone, or in osteocyte-free bone.
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Affiliation(s)
- Maria-Ioana Pastrama
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria; KU Leuven, Department of Movement Sciences, Human Movement Biomechanics Research Group, Tervuursevest 101, 3001 Leuven, Belgium
| | - Stefan Scheiner
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria.
| | - Peter Pivonka
- School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, 2 George St, Brisbane 4000, QLD, Australia; St. Vincent's Department of Surgery, The University of Melbourne, Clinical Science Building, 29 Regent Street, VIC 3065, Australia
| | - Christian Hellmich
- Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, Vienna A-1040, Austria
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13
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Hitchens PL, Pivonka P, Malekipour F, Whitton RC. Mathematical modelling of bone adaptation of the metacarpal subchondral bone in racehorses. Biomech Model Mechanobiol 2018; 17:877-890. [PMID: 29344755 DOI: 10.1007/s10237-017-0998-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Accepted: 12/23/2017] [Indexed: 02/02/2023]
Abstract
In Thoroughbred racehorses, fractures of the distal limb are commonly catastrophic. Most of these fractures occur due to the accumulation of fatigue damage from repetitive loading, as evidenced by microdamage at the predilection sites for fracture. Adaptation of the bone in response to training loads is important for fatigue resistance. In order to better understand the mechanism of subchondral bone adaptation to its loading environment, we utilised a square root function defining the relationship between bone volume fraction [Formula: see text] and specific surface [Formula: see text] of the subchondral bone of the lateral condyles of the third metacarpal bone (MCIII) of the racehorse, and using this equation, developed a mathematical model of subchondral bone that adapts to loading conditions observed in vivo. The model is expressed as an ordinary differential equation incorporating a formation rate that is dependent on strain energy density. The loading conditions applied to a selected subchondral region, i.e. volume of interest, were estimated based on joint contact forces sustained by racehorses in training. For each of the initial conditions of [Formula: see text] we found no difference between subsequent homoeostatic [Formula: see text] at any given loading condition, but the time to reach equilibrium differed by initial [Formula: see text] and loading condition. We found that the observed values for [Formula: see text] from the mathematical model output were a good approximation to the existing data for racehorses in training or at rest. This model provides the basis for understanding the effect of changes to training strategies that may reduce the risk of racehorse injury.
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Affiliation(s)
- Peta L Hitchens
- Equine Centre, Melbourne Veterinary School, Faculty of Veterinary and Agricultural Sciences, University of Melbourne, Werribee, VIC, 3030, Australia.
| | - Peter Pivonka
- School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD, 4000, Australia
| | - Fatemeh Malekipour
- Department of Biomedical Engineering, University of Melbourne, Parkville, VIC, 3010, Australia
| | - R Chris Whitton
- Equine Centre, Melbourne Veterinary School, Faculty of Veterinary and Agricultural Sciences, University of Melbourne, Werribee, VIC, 3030, Australia
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Szlazak K, Vass V, Hasslinger P, Jaroszewicz J, Dejaco A, Idaszek J, Scheiner S, Hellmich C, Swieszkowski W. X-ray physics-based CT-to-composition conversion applied to a tissue engineering scaffold, enabling multiscale simulation of its elastic behavior. MATERIALS SCIENCE & ENGINEERING. C, MATERIALS FOR BIOLOGICAL APPLICATIONS 2017; 95:389-396. [PMID: 30573263 DOI: 10.1016/j.msec.2017.11.044] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2017] [Revised: 09/05/2017] [Accepted: 11/29/2017] [Indexed: 12/13/2022]
Abstract
Nowadays, the assessment of the mechanical competence of tissue engineering scaffolds based on computer simulations is a well-accepted technology. Typically, such simulations are performed by means of the Finite Element (FE) method, with the underlying structural model being created based on micro-computed tomography (microCT). Here, this analysis modality is applied to a new, ternary composite, consisting of PHBV, i.e. poly(3-hydroxybutyrate-co-3-hydroxyvalerate), PLGA, i.e. poly(lactic-co-glycolide), as well as of TCP, i.e. tricalcium phosphate hydrate. The studied scaffold structure is made up by fibers of this new composite material, manufactured by means of the rapid prototyping method. The data collected from microCT is utilized for adequately defining the mechanical properties of the FE model. In particular, the three-dimensional field of grey values is interpreted in terms of the underlying field of attenuation coefficients, taking into account the photon energy employed in microCT imaging, eventually allowing for calculation of the three-dimensionally distributed, voxel-specific composition of the studied material. For the sake of keeping the FE simulations as efficient as possible, groups of voxels are combined into one finite element; the grey value of the latter is obtained by volume averaging. Employing a two-step micromechanical homogenization scheme, the experimentally accessible stiffness of the three constituents (PHBV, PLGA, and TCP) is then, finite element by finite element, upscaled to the composition-dependent stiffness of the composite material. The plausibility and adequacy of the FE model is demonstrated by simulating the effects of uniaxial compression on the scaffold structure, in terms of resulting stress and strain fields, highlighting the importance of the fiber junctions (as they are the mechanically most stressed regions), and that neglecting the material heterogeneity would lead to a potentially significant underestimation of stresses and strains. Finally, a comparison is made of the employed analysis modality of microCT data with a previously pursued, simplified analysis strategy, highlighting the conceptual superiority of the former, and pointing out the application limits of the latter.
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Affiliation(s)
- Karol Szlazak
- Faculty of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland
| | - Viktoria Vass
- Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Vienna, Austria
| | - Patricia Hasslinger
- Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Vienna, Austria
| | - Jakub Jaroszewicz
- Faculty of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland
| | - Alexander Dejaco
- Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Vienna, Austria
| | - Joanna Idaszek
- Faculty of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland
| | - Stefan Scheiner
- Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Vienna, Austria.
| | - Christian Hellmich
- Institute for Mechanics of Materials and Structures, TU Wien - Vienna University of Technology, Vienna, Austria
| | - Wojciech Swieszkowski
- Faculty of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland
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15
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Abstract
Biomedical research and clinical practice are struggling to cope with the growing complexity that the progress of health care involves. The most challenging diseases, those with the largest socioeconomic impact (cardiovascular conditions; musculoskeletal conditions; cancer; metabolic, immunity, and neurodegenerative conditions), are all characterized by a complex genotype-phenotype interaction and by a "systemic" nature that poses a challenge to the traditional reductionist approach. In 2005 a small group of researchers discussed how the vision of computational physiology promoted by the Physiome Project could be translated into clinical practice and formally proposed the term Virtual Physiological Human. Our knowledge about these diseases is fragmentary, as it is associated with molecular and cellular processes on the one hand and with tissue and organ phenotype changes (related to clinical symptoms of disease conditions) on the other. The problem could be solved if we could capture all these fragments of knowledge into predictive models and then compose them into hypermodels that help us tame the complexity that such systemic behavior involves. In 2005 this was simply not possible-the necessary methods and technologies were not available. Now, 10 years later, it seems the right time to reflect on the original vision, the results achieved so far, and what remains to be done.
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Affiliation(s)
- Marco Viceconti
- Department of Mechanical Engineering and Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield S1 3JD, United Kingdom;
| | - Peter Hunter
- Auckland Bioengineering Institute, University of Auckland, Auckland 1142, New Zealand
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16
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Systems modelling ageing: from single senescent cells to simple multi-cellular models. Essays Biochem 2017; 61:369-377. [PMID: 28698310 PMCID: PMC5869859 DOI: 10.1042/ebc20160087] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Revised: 05/25/2017] [Accepted: 05/25/2017] [Indexed: 01/10/2023]
Abstract
Systems modelling has been successfully used to investigate several key molecular mechanisms of ageing. Modelling frameworks to allow integration of models and methods to enhance confidence in models are now well established. In this article, we discuss these issues and work through the process of building an integrated model for cellular senescence as a single cell and in a simple tissue context.
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17
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Kim YK, Kameo Y, Tanaka S, Adachi T. Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation. Biomech Model Mechanobiol 2017; 16:1697-1708. [DOI: 10.1007/s10237-017-0914-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Accepted: 04/26/2017] [Indexed: 11/29/2022]
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18
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Bhattacharya P, Viceconti M. Multiscale modeling methods in biomechanics. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2017; 9:e1375. [PMID: 28102563 PMCID: PMC5412936 DOI: 10.1002/wsbm.1375] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Revised: 11/09/2016] [Accepted: 11/17/2016] [Indexed: 01/08/2023]
Abstract
More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Pinaki Bhattacharya
- Department of Mechanical Engineering and INSIGNEO Institute for in silico MedicineUniversity of SheffieldSheffieldUK
| | - Marco Viceconti
- Department of Mechanical Engineering and INSIGNEO Institute for in silico MedicineUniversity of SheffieldSheffieldUK
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19
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Haj-Ali R, Massarwa E, Aboudi J, Galbusera F, Wolfram U, Wilke HJ. A new multiscale micromechanical model of vertebral trabecular bones. Biomech Model Mechanobiol 2016; 16:933-946. [PMID: 27913902 DOI: 10.1007/s10237-016-0862-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2016] [Accepted: 11/23/2016] [Indexed: 10/20/2022]
Abstract
A new three-dimensional (3D) multiscale micromechanical model has been suggested as adept at predicting the overall linear anisotropic mechanical properties of a vertebral trabecular bone (VTB) highly porous microstructure. A nested 3D modeling analysis framework spanning the multiscale nature of the VTB is presented herein. This hierarchical analysis framework employs the following micromechanical methods: the 3D parametric high-fidelity generalized method of cells (HFGMC) as well as the 3D sublaminate model. At the nanoscale level, the 3D HFGMC method is applied to obtain the effective elastic properties of a representative unit cell (RUC) representing the mineral collagen fibrils composite. Next at the submicron scale level, the 3D sublaminate model is used to generate the effective elastic properties of a repeated stack of multilayered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron scale level, the 3D HFGMC method is used again on a RUC of the highly porous VTB microstructure. The VTB-RUC geometries are taken from microcomputed tomography scans of VTB samples harvested from different vertebrae of human cadavers [Formula: see text]. The predicted anisotropic overall elastic properties for native VTBs are, then, examined as a function of age and sex. The predicted results of the VTBs longitudinal Young's modulus are compared to reported values found in the literature. The proposed 3D nested modeling analysis framework provides a good agreement with reported values of Young's modulus of single trabeculae as well as for VTB-RUC in the literature.
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Affiliation(s)
- Rami Haj-Ali
- Faculty of Engineering, Tel-Aviv University, 6997801, Tel Aviv, Israel.
| | - Eyass Massarwa
- Faculty of Engineering, Tel-Aviv University, 6997801, Tel Aviv, Israel
| | - Jacob Aboudi
- Faculty of Engineering, Tel-Aviv University, 6997801, Tel Aviv, Israel
| | - Fabio Galbusera
- Department of Spine Surgery III, IRCCS Istituto Ortopedico Galeazzi, Milan, Italy
| | - Uwe Wolfram
- Mechanical, Process and Energy Engineering, Heriot-Watt University, Edinburgh, UK
| | - Hans-Joachim Wilke
- Institute for Orthopedic Research and Biomechanics, Ulm University, Helmholtzstrasse. 14, 89081, Ulm, Germany
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20
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Advanced computational workflow for the multi-scale modeling of the bone metabolic processes. Med Biol Eng Comput 2016; 55:923-933. [DOI: 10.1007/s11517-016-1572-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Accepted: 09/11/2016] [Indexed: 01/11/2023]
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21
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A multiscale modeling framework for studying the mechanobiology of sarcopenic obesity. Biomech Model Mechanobiol 2016; 16:275-295. [DOI: 10.1007/s10237-016-0816-z] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2016] [Accepted: 08/08/2016] [Indexed: 01/08/2023]
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22
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Rosa N, Simoes R, Magalhães FD, Marques AT. From mechanical stimulus to bone formation: A review. Med Eng Phys 2016; 37:719-28. [PMID: 26117332 DOI: 10.1016/j.medengphy.2015.05.015] [Citation(s) in RCA: 80] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2014] [Revised: 05/12/2015] [Accepted: 05/31/2015] [Indexed: 02/07/2023]
Abstract
Bone is a remarkable tissue that can respond to external stimuli. The importance of mechanical forces on the mass and structural development of bone has long been accepted. This adaptation behaviour is very complex and involves multidisciplinary concepts, and significant progress has recently been made in understanding this process. In this review, we describe the state of the art studies in this area and highlight current insights while simultaneously clarifying some basic yet essential topics related to the origin of mechanical stimulus in bone, the biomechanisms associated with mechanotransduction, the nature of physiological bone stimuli and the test systems most commonly used to study the mechanical stimulation of bone.
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Affiliation(s)
- Natacha Rosa
- DEMec, Faculty of Engineering, University of Porto, Rua Roberto Frias, 4200-465 Porto, Portugal.
| | - Ricardo Simoes
- Polytechnic Institute of Cávado and Ave, School of Technology, Campus do IPCA, 4750-810 Barcelos, Portugal; Institute for Polymers and Composites IPC/I3N, University of Minho, Campus de Azurem, 4800-058 Guimarães, Portugal
| | - Fernão D Magalhães
- LEPABE - Faculdade de Engenharia, Universidade do Porto, Rua Roberto Frias, 4200-465 Porto, Portugal
| | - Antonio Torres Marques
- DEMec, Faculty of Engineering, University of Porto, Rua Roberto Frias, 4200-465 Porto, Portugal
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23
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Badilatti SD, Kuhn GA, Ferguson SJ, Müller R. Computational modelling of bone augmentation in the spine. J Orthop Translat 2015; 3:185-196. [PMID: 30035057 PMCID: PMC5986996 DOI: 10.1016/j.jot.2015.09.003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/20/2015] [Revised: 08/31/2015] [Accepted: 09/10/2015] [Indexed: 11/19/2022] Open
Abstract
Computational models are gaining importance not only for basic science, but also for the analysis of clinical interventions and to support clinicians prior to intervention. Vertebroplasty has been used to stabilise compression fractures in the spine for years, yet there are still diverging ideas on the ideal deposition location, volume, and augmentation material. In particular, little is known about the long-term effects of the intervention on the surrounding biological tissue. This review aims to investigate computational efforts made in the field of vertebroplasty, from the augmentation procedure to strength prediction and long-term in silico bone biology in augmented human vertebrae. While there is ample work on simulating the augmentation procedure and strength prediction, simulations predicting long-term effects are lacking. Recent developments in bone remodelling simulations have the potential to show adaptation to cement augmentation and, thus, close this gap.
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Affiliation(s)
| | - Gisela A Kuhn
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
| | | | - Ralph Müller
- Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
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24
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Abstract
Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to “feel” the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al. (Bone 46(4):1075–1081, 2010) strongly suggest that the lacunar pores are likely to experience, during typical physiological load cycles, not only fluid transport, but also undrained conditions. The latter entail the buildup of lacunar pore pressures, which we here quantify by means of a thorough multiscale modeling approach. In particular, the proposed model is based on classical poroelasticity theory, and able to account for multiple pore spaces. First, the model reveals distinct nonlinear dependencies of the resulting lacunar (and vascular) pore pressures on the underlying bone composition, highlighting the importance of a rigorous multiscale approach for appropriate computation of the aforementioned pore pressures. Then, the derived equations are evaluated for macroscopic (uniaxial as well as hydrostatic) mechanical loading of physiological magnitude. The resulting model-predicted pore pressures agree very well with the pressures that have been revealed, by means of in vitro studies, to be of adequate magnitude for modulating the responses of biological cells, including osteocytes. This underlines that osteocytes may respond to many types of loading stimuli at the same time, in particular so to fluid flow and hydrostatic pressure.
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