Multiphysics of bone remodeling: A 2D mesoscale activation simulation

Spingarn, Camille; Wagner, Delphine; Rémond, Yves; George, Daniel

doi:10.3233/bme-171636

Cited by 23 publications

(16 citation statements)

References 21 publications

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“…To our knowledge there is some biological evidence (Arias et al 2018;Bonewald and Johnson 2008;Kühl et al 2000) and, we believe, there is a clear logical basis, of the fact that the biological stimulus is first produced and then diffused before reaching its target cells, i.e., the active cells governing growth and resorption. (see, e.g., George et al (2017); Spingarn et al (2017); Stern and Nicolella (2013);Himeno-Ando et al (2012); Bonucci (2009)). There is evidence, indeed, of the existence of mechanisms which govern the production of 'signaling chemical species', of phenomena of diffusion of these species in the reconstructing tissue and of their adsorption to initiate the activation of osteoclasts and osteoblasts.…”

Section: Introductionmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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In the past years, many attempts have been made in order to model the process of bone remodeling. This process is complex, as it is governed by not yet completely understood biomechanical coupled phenomena. It is well known that bone tissue is able to self-adapt to different environmental demands of both mechanical and biological origin. The mechanical aspects are related to the functional purpose of the bone tissue, i.e., to provide support to the body and protection for the vitally important organs in response to the external loads. The many biological aspects include the process of oxygen and nutrients supply. To describe the biomechanical process of functional adaptation of bone tissue, the approach commonly

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Section: Introductionmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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“…Osteoblasts and osteoclasts are responsible for bone tissue synthesis and cell-mediated resorption, respectively. Both of the two kinds of cells can be active as remodellers only when attaching on the walls of the pores [33,37]. Though the ratio between them depends on different mechanical and biological conditions, their total number is only related with the available inner surface of the pores.…”

Section: Cell Populationmentioning

confidence: 99%

New description of gradual substitution of graft by bone tissue including biomechanical and structural effects, nutrients supply and consumption

Lekszycki

2018

Continuum Mech. Thermodyn.

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A new description of graft substitution by bone tissue is proposed in this work. The studied domain is considered as a continuum model consisting of a mixture of the bone tissue and the graft material. Densities of both components evolve in time as a result of cellular activity and biodegradation. The proposed model focuses on the interaction between the bone cell activity, mechanical stimuli, nutrients supply and scaffold microstructure. Different combinations of degradation rate and stiffness of the graft material were examined by numerical simulation. It follows from the calculations that the degradation rate of the scaffold should be tuned to the synthesis/resorption rate of the tissue, which are dependent among the others on scaffold porosity changes. Simulation results imply potential criteria to choose proper bone substitute material in consideration of degradation rate, initial porosity and mechanical characteristics. KeywordsBone regeneration · Bioresorbable and biodegradable material · Microstructure · Nutrients supply · Numerical simulation List of symbols ε Strain σ Stress W s Strain energy ϕ Porosity E Young's modulus d a , d s Normalized sensor/actor cell densities S Mechanical stimulus S 0 Reference stimulus R Nutrients consumption rate z s , z a Sensor/actor cell activities L Coefficient defining the range of stimulus without cell activity A m0 Degradation rate of bone substitute material s b , r b , r m Synthesis / resorption coefficients Communicated by Francesco dell'Isola.

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“…In [Herman et al 2010], two types of mechanical degradation of the cortical bone are described: one is linked to linear microcracks, which are 10 to 100 µm long, and the other is a set of diffused microcracks, which are 1 to 2 µm long. In [Seref-Ferlengez et al 2015] these two networks are still observed, but the authors suggest that only the linear microcracks influence the evolution of the elastic behavior of the cortical bone and may be involved in the remodeling process.…”

Section: Appendix: Inverse Transformsmentioning

confidence: 99%

Untitled

2018

Math. Mech. Compl. Sys.

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We study a system of N layers with a Kac horizontal interaction of parameter γ > 0 and a Kac vertical interaction of parameter γ 1/2 . We shall prove that the limit free energy functional is the rate function of the large deviations of the Gibbs measure (of a canonical constrained magnetization). The limit free energy functional is achieved as a -limit for γ → 0 for magnetizations with fixed average. Among all such magnetizations there exists a quasiconstant magnetization that minimizes the energy.Communicated by Raffaele Esposito. MSC2010: 82B24. 267 268 MICHELE ALEANDRI AND VENANZIO DI GIULIO between nearest neighbor horizontal lines (say (x, i) and (y, i + 1)) interact via the Kac potential λJ γ 1/2 (x, y), λ > 0; that is, the vertical interaction is much more local than the horizontal one.We study the mesoscopic limit γ → 0. The mesoscopic state of the system is a collection m ≡ {m(r, i) : r ∈ [0, ], i = 1, . . . , N } of measurable functions with values in [−1, 1]. Its statistical properties are then described by a free energy functional F(m). According to the Gibbs theory such a functional is the limit as γ → 0 of −1/β times the log of a constrained partition function where the spin configurations are required to be "close" to the mesoscopic state m (this involves a coarse grain procedure which is specified in Section 2). This is not as in the classical Lebowitz-Penrose [1966;Penrose and Lebowitz 1971] procedure because there are two scales, γ −1 for the horizontal interaction and γ −1/2 for the vertical one. Thus, there could be oscillations on the scale γ −1/2 which do not appear in m because the latter is defined by averages over ≈ γ −1 but which could affect the free energy of m. These oscillations actually do not occur if λ is small; indeed by Theorem 4.1 the optimal profile is quasiconstant on the scale γ −α with α ∈ (0, 1). However, if λ is large enough we can provide an example where such a phenomena occurs.The paper is organized as follows. In Section 2 we introduce the microscopic and mesoscopic models and enunciate the main results. In Section 3 we introduce the coarse graining procedure used to prove the Lebowitz-Penrose limit. In Section 4 we prove a key result, that is, Theorem 4.1, in which we provide a technique to minimize the free energy. This theorem is needed to prove the main results in Section 2. In Section 5 we prove the Lebowitz-Penrose limit for our model. In Section 6 we prove the -limit result. The proofs of Theorem 2.4 and Proposition 3.1 are deferred to Appendix A. In Appendix B, finally, we illustrate the case in which Theorem 2.3 fails for the parameter λ large enough.Similar model have been studied in [Cassandro et al. 2016;Fontes et al. 2014;. A numerical investigation of the mesoscopic limit for lattice gas model was also recently tackled in [Colangeli et al. 2016;.This work is the first step of a research program pointed towards the characterization of the surface tension associated to free energy in the thermodynamic limit. Model and main resultsWe consider an Ising spin ...

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Multiphysics of bone remodeling: A 2D mesoscale activation simulation

Cited by 23 publications

References 21 publications

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

New description of gradual substitution of graft by bone tissue including biomechanical and structural effects, nutrients supply and consumption

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