Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Perrin, Eléonore; Bou‐Saïd, Benyebka; Massi, Francesco

doi:10.1016/j.jmbbm.2018.12.015

Cited by 15 publications

(7 citation statements)

References 49 publications

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“…Therefore, this model might be useful if spatial discretisation is not needed in the analysis. Furthermore, the cells themselves are complex systems and some multiscale models either do not include them (Estermann and Scheiner, 2018;Perrin et al, 2019) or study only single cell characteristics across finer levels, such as cell shape or motility with a resolution of 50-100 nm (Borau et al, 2014;McGarry and Prendergast, 2004). Finally, some models use a semi-concurrent method that is a combination of both concurrent and hierarchical methods (Andrade and Tu, 2009;Kouznetsova et al, 2002;Marques et al, 2020;Silani et al, 2014;Talebi et al, 2014).…”

Section: Multiscale Modelling Of Bonementioning

confidence: 99%

Perspectives on in silico bone mechanobio

Boaretti¹,

Wehrle²,

Bansod³

et al. 2022

eCM

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Bone mechanobiology is the study of the physical, biological and mechanical processes that continuously affect the multiscale multicellular system of the bone from the organ to the molecular scale. Current knowledge derives from experimental studies, which are often limited to gathering qualitative data in a cross-sectional manner, up to a restricted number of time points. Moreover, the simultaneous collection of information about 3D bone microarchitecture, cell activity as well as protein distribution and level is still a challenge. In silico models can expand qualitative information with hypothetical quantitative systems, which allow quantification, testing and comparison to existing quantifiable experimental data. An overview of multiscale, multiphysics, agent-based and hybrid techniques and their applications to bone mechanobiology is provided in the present review. The study analysed how mechanical signals, cells and proteins can be modelled in silico to represent bone remodelling and adaptation. Hybrid modelling of bone mechanobiology could combine the methods used in multiscale, multiphysics and agent-based models into a single model, leading to a unified and comprehensive understanding of bone mechanobiology. Numerical simulations of in vivo multicellular systems aided in hypothesis testing of such in silico models. Recently, in silico trials have been used to illustrate the mechanobiology of cells and signalling pathways in clinical biopsies and animal bones, including the effects of drugs on single cells and signalling pathways up to the organ level. This improved understanding may lead to the identification of novel therapies for degenerative diseases such as osteoporosis.

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Section: Multiscale Modelling Of Bonementioning

confidence: 99%

Perspectives on in silico bone mechanobio

Boaretti¹,

Wehrle²,

Bansod³

et al. 2022

eCM

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“…When devising a multiscale poroelastic cortical bone model, ref. [144] found that the fluid flow influences the stiffness of bone. A constitutive equation accounting for the pressure both in the material pores 10C 1 and over interconnected fluid compartments 10C 2 within a porous solid is studied in [235]; in bone, 10C 1 may refer to the collagen-water-hydroxyapatite-lattice lengthscale, see Section 13, and 10C 2 may refer to the bone marrow-filled intertrabecular pores, see Section 13.…”

Section: Definition 4 (Porous Material)mentioning

confidence: 99%

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

et al. 2019

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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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“…Apart from the use of the theory of elasticity to describe remodeling—by using Wolff law, modified similar relations as well as introducing multiscale models (Matsuura et al, 2003 ; Li et al, 2007 ; Coelho et al, 2009 ; Perrin et al, 2019 )—the influence of interstitial fluid on bone remodeling plays a crucial role, often highlighted in literature with respect to processes occurring at cellular level (Fornells et al, 2007 ; You et al, 2008 ). The complex network of lacunae-canaliculi channels in the bone tissue (Li et al, 1987 ; Grimm and Williams 1997 ; Nauman et al, 1999 ; Lim and Hong 2000 ; Beno et al 2006 ) permits interstitial fluid flow through micro-porosities (Piekarski and Munro 1977 ; Weinbaum et al, 1994 ; Cowin et al, 1995 ).…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Esposito

Minutolo

Gargiulo

et al. 2022

Biomech Model Mechanobiol

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Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

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Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Cited by 15 publications

References 49 publications

Perspectives on in silico bone mechanobio

Perspectives on in silico bone mechanobio

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

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