Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties

Łukasz Cyganik; Marcin Binkowski; Grzegorz Kokot; Tomasz Rusin; Paulina Popik; Filip Bolechała; Roman Nowak; Zygmunt Wróbel; Antoni John

doi:10.1016/j.jmbbm.2014.04.011

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties

J Mech Behav Biomed Mater. 2014 Aug:36:120-34. doi: 10.1016/j.jmbbm.2014.04.011. Epub 2014 Apr 29.

Authors

Łukasz Cyganik¹, Marcin Binkowski², Grzegorz Kokot³, Tomasz Rusin⁴, Paulina Popik¹, Filip Bolechała⁵, Roman Nowak⁶, Zygmunt Wróbel¹, Antoni John³

Affiliations

¹ X-ray Microtomography Lab, Department of Biomedical Computer Systems, Institute of Computer Science, Faculty of Computer and Materials Science, University of Silesia, 75 Pulku Piechoty 1, budynek H, segment C, pok. P7, 41-500 Chorzów, Poland.
² X-ray Microtomography Lab, Department of Biomedical Computer Systems, Institute of Computer Science, Faculty of Computer and Materials Science, University of Silesia, 75 Pulku Piechoty 1, budynek H, segment C, pok. P7, 41-500 Chorzów, Poland. Electronic address: marcin.binkowski@us.edu.pl.
³ Institute of Computational Mechanics and Engineering, Silesian University of Technology, ul. Konarskiego 18A, 44-100 Gliwice, Poland.
⁴ Elhys Sp. z o.o., MTS Systems Corporation Representative in Poland, ul. Naukowa 45, 02-463 Warszawa, Poland.
⁵ Medical College, Jagiellonian University, ul. Grzegórzecka 16, 31-531 Kraków, Poland.
⁶ Medical University of Silesia, School of Medicine with the Division of Dentistry, Chair and Department of Orthopaedics, WSS no. 5, ul. Medyków 1, 41-200 Sosnowiec, Poland.

PMID: 24837330
DOI: 10.1016/j.jmbbm.2014.04.011

Abstract

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Keywords: Bone mineral density; Digital Image Correlation; Micro-computed tomography; Microscale properties; Trabecular bone; Young׳s modulus.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Absorptiometry, Photon / methods*
Aged
Algorithms*
Bone Density / physiology*
Compressive Strength / physiology
Computer Simulation
Elastic Modulus / physiology
Femur Head / diagnostic imaging*
Femur Head / physiology*
Hardness / physiology
Humans
In Vitro Techniques
Models, Biological*
Stress, Mechanical
Tensile Strength / physiology
Weight-Bearing / physiology