Diffusion model to describe osteogenesis within a porous titanium scaffold

Schmitt, Mark R.; Allena, Rachèle; Schouman, Thomas; Frasca, Sophie; Collombet, Jean-Marc; Holy, Xavier; Rouch, Philippe

doi:10.1080/10255842.2014.998207

Cited by 19 publications

(22 citation statements)

References 44 publications

(57 reference statements)

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“…However, in case the bite force is considered strong, the strength of reconstruction could be increased by combination use with a reconstruction plate and screws, clinically. It appears that titanium scaffold combines mechanical stability and osteoconductivity [31,32].…”

Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 98%

Development of a biointegrated mandibular reconstruction device consisting of bone compatible titanium fiber mesh scaffold

et al. 2016

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Section: A C C E P T E D Accepted Manuscriptmentioning

confidence: 98%

Development of a biointegrated mandibular reconstruction device consisting of bone compatible titanium fiber mesh scaffold

et al. 2016

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“…Taking into account the exact anisotropic directions of the cortical bone microstructure will allow one to rigorously describe the damage model. This constitutes a fundamental element to describe the overall remodeling process, including the evolution in time of the anisotropic directions [Placidi et al 2004], and more specifically the interplay between the biological and the mechanical processes involved [Frame et al 2017;Schmitt et al 2016Schmitt et al ]. et al 1994, the canals are previously ink-soaked and then developed by successive polishing.…”

Section: Discussionmentioning

confidence: 99%

“…The external sources used here to calculate the mechanobiological stimulus are: (i) the mechanical energy accounting for the mechanical loads sustained by the bone cells and triggering bone density evolution, (ii) the concentration of nutriments (oxygen and glucose) expressed as a function of the developed hydrostatic pressure, and (iii) the cells activity triggered by specific levels of oxygen and glucose concentration due to the applied mechanical load. The cells recruiting and migration is described via two diffusion equations [Allena and Maini 2014;Schmitt et al 2015; and the bone density variation in time is calculated by the rates of bone synthesis and resorption respectively, depending on the positiveness of the defined coupled mechanobiological stimulus [George et al 2017a].…”

Section: Introductionmentioning

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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“…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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Diffusion model to describe osteogenesis within a porous titanium scaffold

Cited by 19 publications

References 44 publications

Development of a biointegrated mandibular reconstruction device consisting of bone compatible titanium fiber mesh scaffold

Development of a biointegrated mandibular reconstruction device consisting of bone compatible titanium fiber mesh scaffold

Untitled

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

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