New Aspects of the Trabecular Bone Remodeling Regulatory Model—Two Postulates Based on Shape Optimization Studies

Nowak, Michał

doi:10.1007/978-3-030-50464-9_6

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…Numerous authors interpret the remodeling of bone tissue as a complex optimization problem in which the local properties of mass and stiffness are regarded as conflicting objectives that must be balanced. From this perspective, once again, the variational tools provide a powerful arsenal at our disposal to obtain the optimized substructure underlying the bone tissue (see, as general reference Bendsoe and Sigmund 2003 ; Eschenauer and Olhoff 2001 , and as a more specific application to the bone Nowak 2010 , 2020 ).…”

Section: Introductionmentioning

confidence: 99%

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law

Giorgio,

dell’Isola,

Andreaus

et al. 2023

Biomech Model Mechanobiol

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We propose a variational approach that employs a generalized principle of virtual work to estimate both the mechanical response and the changes in living bone tissue during the remodeling process. This approach provides an explanation for the adaptive regulation of the bone substructure in the context of orthotropic material symmetry. We specifically focus upon the crucial gradual adjustment of bone tissue as a structural material that adapts its mechanical features, such as materials stiffnesses and microstructure, in response to the evolving loading conditions. We postulate that the evolution process relies on a feedback mechanism involving multiple stimulus signals. The mechanical and remodeling behavior of bone tissue is clearly a complex process that is difficult to describe within the framework of classical continuum theories. For this reason, a generalized continuum elastic theory is employed as a proper mathematical context for an adequate description of the examined phenomenon. To simplify the investigation, we considered a two-dimensional problem. Numerical simulations have been performed to illustrate bone evolution in a few significant cases: the bending of a rectangular cantilever plate and a three-point flexure test. The results are encouraging because they can replicate the optimization process observed in bone remodeling. The proposed model provides a likely distribution of stiffnesses and accurately represents the arrangement of trabeculae macroscopically described by the orthotropic symmetry directions, as supported by experimental evidence from the trajectorial theory.

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Section: Introductionmentioning

confidence: 99%

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law

Giorgio,

dell’Isola,

Andreaus

et al. 2023

Biomech Model Mechanobiol

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The Efficient Trabecular Bone Remodeling Numerical Tool Enabling Multiple Load Case Simulation

Polak

Nowak

2022

Advanced Structured Materials

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A bone remodeling approach encoding the effect of damage and a diffusive bio-mechanical stimulus

Addessi,

D’Annibale,

Placidi

et al. 2024

Continuum Mech. Thermodyn.

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The paper focuses on the effect of damage on the bone remodeling process. This is a crucial, although complex, aspect. A one-dimensional continuous deformable body is employed to model living bone tissue. The model incorporates the bone functional adaptation through an evolution law for an effective elastic modulus driven by mechanical feedback via a mechano-transduction diffusive signal. This type of information transduction, i.e., diffusion, is essential for the model to take into account remodeling in the case of minor injury or pathology-affected regions where there is no signal production. In addition, the model is able to also take into account potential tissue damage that may evolve over time according to a suitable evolution law. To illustrate the capability of the model to describe the mentioned complex coupled phenomena, numerical tests have been performed encompassing high external loads causing the onset of damage and cyclic loading for healing. The numerical simulations carried out via finite-element analyses yield insights into the mechanisms of bone remodeling, with the final goal of aiding clinical decisions and implant designs for bone health and repair. Overall, a key aspect of the paper is to highlight the feasibility of modeling the evolution in bone elasticity arising from the combined effect of damage and remodeling.

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New Aspects of the Trabecular Bone Remodeling Regulatory Model—Two Postulates Based on Shape Optimization Studies

Cited by 3 publications

References 15 publications

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law

An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff’s law

The Efficient Trabecular Bone Remodeling Numerical Tool Enabling Multiple Load Case Simulation

A bone remodeling approach encoding the effect of damage and a diffusive bio-mechanical stimulus

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