Relating mechanical properties of vertebral trabecular bones to osteoporosis

Abstract

Osteoporosis is an osteometabolic disease, which promotes structural degradation of bone tissue and reduction of mineral density. We reported here a mechanical resistance assay from normal, osteopenic and osteoporotic trabecular vertebral bones of human cadavers. We performed a compressed test on ninety samples, evaluating Young’s modulus and X-ray microtomography to measure bone volume fraction and trabecular thickness. This experimental data are employed for computing the orthotropic macroscopic behavior of vertebral trabecular bones using known analytical formulae that were obtained by Galka et al. (Arch Mech 51: 335-355, 1999) via an asymptotic homogenization model. A geometrical model with a periodic orthogonal plate-like structure is applied. The properties of the bone-trabecular mass are considered linear, homogeneous and orthotropic. Average values for all technical or engineering elastic properties are computed for three important regions of the trabecular bones corresponding to thirty individuals classified as normal, osteopenic or osteoporotic by calcaneus ultrassometry. This study could be useful for a better understanding of the elastic behavior of trabecular bones in human vertebral bodies, allowing an estimation of bone answer under stress in different directions and the risk of fracture associated with osteoporosis.

Highlights

• Describing the elastic behavior of trabecular bones in human vertebral bodies at the micro and macroscopic.

• Allow a better estimation of the stress in different directions and risk of fracture associated with osteoporosis.

• Model request a very low computational cost.

• Offer a better understand the global effective coefficients of samples of trabecular bone, from the model of a periodic unit cell, in the format orthogonal plate-like structure with homogeneous bone mass.

Keywords:

• Trabecular bone
• osteoporosis
• microtomography
• mechanical resistance
• asymptotic homogenization

Acknowledgments

The authors would like to thank the Institute of Orthopedics and Traumatology of the Clinical Hospital (IOT HC USP), São Carlos School of Engineering (EESC – USP), Faculty of Mathematics and Computation of the University of Havana (MATCOM – UH) for the partnership, MyM-IIMAS-UNAM and DGAPA-UNAM (Project PAPIIT-DGAPA-UNAM IA100919), GE Medical Systems Lunar® by loan of the Achilles Insight ultrasonometry equipment and to all people involved in the collection and testing of samples.

Disclosure statement

There is no conflict of interest regarding this paper.

Additional information

Funding

This research was supported by the Coordination for the Improvement of Higher-Level Personnel (CAPES), National Council for Scientific and Technological Development (CNPq) (protocol n. 149100/2010-8) and São Paulo Research Foundation (FAPESP) (protocol n. 2010/51698-0, 2014/02163-7, 2017/011958-1).