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Giorgio I, dell'Isola F, Andreaus U, Misra A. An orthotropic continuum model with substructure evolution for describing bone remodeling: an interpretation of the primary mechanism behind Wolff's law. Biomech Model Mechanobiol 2023; 22:2135-2152. [PMID: 37542620 PMCID: PMC10613191 DOI: 10.1007/s10237-023-01755-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2023] [Accepted: 07/16/2023] [Indexed: 08/07/2023]
Abstract
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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Affiliation(s)
- Ivan Giorgio
- Department of Civil, Construction-Architectural and Environmental Engineering (DICEAA), University of L'Aquila, 1, P.zza Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy.
- International Research Center for the Mathematics and Mechanics of Complex Systems (M &MoCS), University of L'Aquila, 1, P.zza Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy.
| | - Francesco dell'Isola
- Department of Civil, Construction-Architectural and Environmental Engineering (DICEAA), University of L'Aquila, 1, P.zza Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy
- International Research Center for the Mathematics and Mechanics of Complex Systems (M &MoCS), University of L'Aquila, 1, P.zza Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy
- Faculty of Mechanical and Industrial Engineering, Warsaw University of Technology, ul. Narbutta 85, Warsaw, 02-524, Poland
- CNRS Fellow, ENS Paris-Saclay, 4, avenue des Sciences, Gif-sur-Yvette, 91190, France
| | - Ugo Andreaus
- Department of Structural and Geotechnical Engineering (DISG), Università di Roma La Sapienza, 18, Via Eudossiana, Rome, 00184, Italy
| | - Anil Misra
- International Research Center for the Mathematics and Mechanics of Complex Systems (M &MoCS), University of L'Aquila, 1, P.zza Ernesto Pontieri, Monteluco di Roio, L'Aquila, 67100, Italy
- Civil, Environmental and Architectural Engineering Department (CEAE), The University of Kansas, 1530 W. 15th Street, Learned Hall, Lawrence, 66045-7609, Kansas, USA
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Abstract
Speckles are introduced in the ultrasound data due to constructive and destructive interference of the probing signals that are used for capturing the characteristics of the tissue being imaged. There are a plethora of models discussed in the literature to improve the contrast and resolution of the ultrasound images by despeckling them. There is a class of models that assumes that the noise is multiplicative in its original form, and transforming the model to a log domain makes it an additive one. Nevertheless, such a transformation duly oversimplifies the scenario and does not capture the inherent properties of the data-correlated nature of speckles. Therefore, it results in poor reconstruction. This problem is addressed to a considerable extent in the subsequent works by adopting various models to address the data-correlated nature of the noise and its distributions. This work introduces a weberized non-local total bounded variational model based on the noise distribution built on the Retinex theory. This perceptually inspired model apparently restores and improves the contrast of the images without compromising much on the details inherently present in the data. The numerical implementation of the model is carried out using the Bregman formulation to improve the convergence rate and reduce the parameter sensitivity. The experimental results are highlighted and compared to demonstrate the efficiency of the model.
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Affiliation(s)
- I. P. Febin
- Department of Mathematical and computational sciences, National Institute of Technology Karnataka, Surathkal, Mangalore, 575025 India
| | - P. Jidesh
- Department of Mathematical and computational sciences, National Institute of Technology Karnataka, Surathkal, Mangalore, 575025 India
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