On the rotary remodelling equilibrium of bone

Sansalone, V.; Naı̈li, S.; Carlo, Antonio Di

doi:10.1080/10255842.2011.595181

Cited by 8 publications

(9 citation statements)

References 4 publications

(7 reference statements)

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“…Remodeling equilibrium is achieved when material properties no longer evolve, corresponding to a stationary state of the rotation, i.e.Ṙ = 0. In the case of passive remodeling, it is worth noting that this model predicts the principal axes of the strain and stress tensors to be locally collinear at the remodeling equilibrium [60]. This condition is similar to that inferred by Cowin for trabecular bone [17].…”

Section: P R E P R I N Tsupporting

confidence: 75%

Bone Orthotropic Remodeling as a Thermodynamically-Driven Evolution

Martin

Lemaire

Haïat

et al. 2020

J. Mech. Med. Biol.

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In this paper, we present and discuss a model of bone remodeling set up in the framework of the theory of generalized continuum mechanics which was first introduced by DiCarlo et al. [Sur le remodelage des tissus osseux anisotropes, Comptes Rendus Mécanique 334(11):651–661, 2006]. Bone is described as an orthotropic body experiencing remodeling as a rotation of its microstructure. Thus, the complete kinematic description of a material point is provided by its position in space and a rotation tensor describing the orientation of its microstructure. Material motion is driven by energetic considerations, namely by the application of the Clausius–Duhem inequality to the microstructured material. Within this framework of orthotropic remodeling, some key features of the remodeling equilibrium configurations are deduced in the case of homogeneous strain or stress loading conditions. First, it is shown that remodeling equilibrium configurations correspond to energy extrema. Second, stability of the remodeling equilibrium configurations is assessed in terms of the local convexity of the strain and complementary energy functionals hence recovering some classical energy theorems. Eventually, it is shown that the remodeling equilibrium configurations are not only highly dependent on the loading conditions, but also on the material properties.

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Section: P R E P R I N Tsupporting

confidence: 75%

Bone Orthotropic Remodeling as a Thermodynamically-Driven Evolution

Martin

Lemaire

Haïat

et al. 2020

J. Mech. Med. Biol.

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“…It is worth noting that this model predicts the principal axes of the strain and stress tensors to be locally collinear at the remodeling equilibrium (Sansalone et al 2011). Thus, a physically sound condition for remodeling equilibrium (Cowin 1986) is recovered without any ad hoc assumption.…”

Section: Methodsmentioning

confidence: 92%

A thermodynamically consistent model of bone rotary remodeling: a 2D study

Martin

Lemaire

Haïat

et al. 2017

Computer Methods in Biomechanics and Biomedical Engineering

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“…More physically driven employment of micromorphic continua has been done in previous studies. [35][36][37][38][39] Another possible application of micromorphic continua to bone modeling is the introduction of a scalar field describing the porosity. This kinematic variable is indeed very important as it affects the apparent mass density as well as the amount of internal surface which bone cells can adhere to.…”

Section: Mechanical Formulation Of the Modelmentioning

confidence: 99%

“…In the cases in which more general continuum models are employed, it is not possible to describe the status of the remodeling process using a simple scalar quantity (like mass density or Young's modulus). Instead, the orientation of the trabeculae has to be considered, 81 which can be done either directly (in the case of micropolar continua, see Sansalone et al 35 ) or by introducing a suitably anisotropic behavior. [82][83][84][85] Bone cell populations A different (even though strongly interconnected) line of research has concerned the mathematical description of the concentrations and/or the activity of the different types of bone cells.…”

Section: Growth/resorption Processesmentioning

confidence: 99%

A review of recent developments in mathematical modeling of bone remodeling

Corte

Giorgio

Scerrato

2019

Proc Inst Mech Eng H

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In this article, we summarize the developments in the mathematical modeling of the mechanics of bone and related biological phenomena. We will devote special attention to the results of the last 10–15 years, although we will cover some relevant classical work to better frame the more recent researches. We will propose a division of the literature based on the main aim of the model (mechanical/biomathematical) and the type of biological phenomena considered (stimulus, growth, cell population dynamics). Finally, we will suggest some possible directions for future investigations.

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On the rotary remodelling equilibrium of bone

Cited by 8 publications

References 4 publications

Bone Orthotropic Remodeling as a Thermodynamically-Driven Evolution

Bone Orthotropic Remodeling as a Thermodynamically-Driven Evolution

A thermodynamically consistent model of bone rotary remodeling: a 2D study

A review of recent developments in mathematical modeling of bone remodeling

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