Finite memory model of bone healing in analysis of moving interface between mandible tissue and bone substitute material after tooth implant application

Hernandez-Rodriguez, Yunuhen; Lekszycki, Tomasz

doi:10.1007/s00161-021-01024-0

Cited by 3 publications

(2 citation statements)

References 37 publications

(68 reference statements)

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“…Our further investigations showed that the constitutive equation could be successfully applied in modelling the mechanical behaviour of trabecular bone on a macroscale, e.g. bone adaptation to new loads [44][45][46][47], bone ingrowth in special implants utilised in bone healing process [48] or trabecular bone repair with use of granular medium [41,49]. Numerical simulations with an application of our model can be very useful in the prediction of bone behaviour after a surgical intervention, e.g.…”

Section: Discussionmentioning

confidence: 82%

Multi-scale constitutive model of human trabecular bone

Jankowski

Pawlikowski

Domański

2022

Continuum Mech. Thermodyn.

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The present study aims to formulate a new multiscale constitutive model of human trabecular bone. The trabecular bone was modelled as a nonlinear viscoelastic material. The viscoelastic effects of single trabeculae were considered by means of a hereditary integral in which stress depends on time and strain, while the elastic response was described by the hyperelastic Mooney–Rivlin model. The cuboid bone sample was extracted from the femoral head during the hip replacement surgery. The material constants in the constitutive equation were identified based on the stress relaxation test performed on the cuboid sample and the microindentation tests performed on trabeculae using the curve-fitting procedure. The microindentation tests were performed using a spherical tip instead of Vickers or Berkovich tip to minimize plastic effects during trabecular deformation. In order to validate formulated constitutive model, results from a FE simulation of stress relaxation test and uniaxial compression test were compared to the results of the corresponding experiments conducted on a macroscopic bone sample. Good agreement was observed between numerical and experimental results. The viscoelastic behaviour predicted by the proposed constitutive equation corresponds well to the response of human trabecular bone under various types of load conditions. This demonstrates the high ability of our constitutive model to simulate the behaviour of trabecular bone on a micro- and macroscopic scale. Thus, we conclude that the model, which was formulated for a single trabecula, can be successfully applied to simulate mechanical behaviour of the tissue in a macroscale.

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Section: Discussionmentioning

confidence: 82%

Multi-scale constitutive model of human trabecular bone

Jankowski

Pawlikowski

Domański

2022

Continuum Mech. Thermodyn.

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“…The problem of bone adaptation and remodeling has been considered since Wolff’s observations in 1892 that mathematical laws can describe changes in the architecture of bones [ 21 , 22 ]. Many mathematical models have been developed [ 23 , 24 , 25 , 26 , 27 , 28 , 29 ] dependent on various mechanical stimuli inducing bone adaptation. Among them can be mentioned diverse instances based on strain energy density [ 30 , 31 ], tissue damage [ 32 , 33 , 34 ], daily stress stimulus [ 35 ], effective stress [ 36 ], and strain [ 37 ].…”

Section: Introductionmentioning

confidence: 99%

Bone Remodeling Process Based on Hydrostatic and Deviatoric Strain Mechano-Sensing

et al. 2022

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A macroscopic continuum model intended to provide predictions for the remodeling process occurring in bone tissue is proposed. Specifically, we consider a formulation in which two characteristic stiffnesses, namely the bulk and shear moduli, evolve independently to adapt the hydrostatic and deviatoric response of the bone tissue to environmental changes. The formulation is deliberately simplified, aiming at constituting a preliminary step toward a more comprehensive modeling approach. The evolutive process for describing the functional adaptation of the two stiffnesses is proposed based on an energetic argument. Numerical experiments reveal that it is possible to model the bone remodeling process with a different evolution for more than one material parameter, as usually done. Moreover, the results motivate further investigations into the subject.

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