The Correlation between Bone Density and Mechanical Variables in Bone Remodelling Models: Insights from a Case Study Corresponding to the Femur of a Healthy Adult

José Luis Calvo-Gallego (), Fernando Gutiérrez-Millán, Joaquín Ojeda, María Ángeles Pérez and Javier Martínez-Reina ()
Additional contact information
José Luis Calvo-Gallego: Departmento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, 41092 Seville, Spain
Fernando Gutiérrez-Millán: Departmento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, 41092 Seville, Spain
Joaquín Ojeda: Departmento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, 41092 Seville, Spain
María Ángeles Pérez: Multiscale in Mechanical and Biological Engineering, Instituto de Investigación en Ingeniería de Aragón (I3A), Instituto de Investigación Sanitaria Aragón (IIS Aragón), University of Zaragoza, 50018 Zaragoza, Spain
Javier Martínez-Reina: Departmento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, 41092 Seville, Spain

Mathematics, 2022, vol. 10, issue 18, 1-29

Abstract: Bone remodelling models (BRM) are often used to estimate the density distribution in bones from the loads they are subjected to. BRM define a relationship between a certain variable measuring the mechanical stimulus at each bone site and either the local density or the local variation of density. This agrees with the Mechanostat Theory, which establishes that overloaded bones increase their density, while disused bones tend to decrease their density. Many variables have been proposed as mechanical stimuli, with stress or strain energy density (SED) being some of the most common. Yet, no compelling reason has been given to justify the choice of any of these variables. This work proposes a set of variables derived from the local stress and strain tensors as candidates for mechanical stimuli; then, this work correlates them to the density in the femur of one individual. The stress and strain tensors were obtained from a FE model and the density was obtained from a CT-scan, both belonging to the same individual. The variables that best correlate with density are the stresses. Strains are quite uniform across the femur and very poorly correlated with density, as is the SED, which is, therefore, not a good variable to measure the mechanical stimulus.

Keywords: bone remodelling; mechanical stimulus; correlation; bone density distribution; strain energy density; absolute maximum principal stress; fluctuation of stresses (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/18/3367/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/18/3367/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:18:p:3367-:d:916603

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().