Compressive fatigue behavior of human vertebral trabecular bone

https://doi.org/10.1016/j.jbiomech.2005.04.033Get rights and content

Abstract

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.

Introduction

Low mass and deterioration of trabecular architecture are well recognized contributors to bone fragility. In fact, a defined low level of bone density associated with a high probability of experiencing fractures is the criteria to diagnose osteoporosis. The general increase in population life expectancy together with the morbidity, mortality, and economic costs associated with fractures ranks this disease as a major public health concern (Grigoryan et al., 2003, Riggs and Melton, 1995). Amongst the high risk fractures, vertebral fractures are considered as the hallmark of osteoporosis, because of their high prevalence and their frequent asymptomatic origin (Grigoryan et al., 2003). This asymptomatic characteristic suggests that repetitive loading lower than ultimate loads, associated with low bone mass and microarchitectural deterioration, may be causing these fractures (Keaveny et al., 1999, Kopperdahl et al., 2000). While few studies on vertebral trabecular bone investigated the progressive deterioration of the sample's mechanical properties when subjected to compressive cyclic loading (Bowman et al., 1998, Haddock et al., 2004, Michel et al., 1993, Moore and Gibson, 2003a), none examined the relationship between compressive fatigue behavior and bone microarchitecture.

Typically, results obtained from low cycles and high cycles fatigue studies, with various testing protocols, sample preparation and sample origin, showed progressive damage accumulation in the form of a translation of the stress–strain loop on the strain axis and a decrease in the secant modulus with number of cycles (Moore and Gibson, 2003b). A recent study suggested that creep effects are negligible under low cycle fatigue tests (Moore et al., 2004). Results from previous studies (Bowman et al., 1998, Haddock et al., 2004, Michel et al., 1993) show a decrease in fatigue life with an increase of the applied stress, normalized by the initial equilibrium modulus.

Investigation of the relationships between trabecular morphology and mechanical properties has become more accessible in the past years with the development of direct quantitative morphological analysis on 3D reconstructions obtained from microcomputed tomography (microCT) (Hildebrand et al., 1999). This technique allows the non-invasive evaluation of morphological parameters such as volume fraction (BV/TV), trabecular thickness (TbTh), trabecular spacing (TbSp), trabecular number (TbNb) and others. Degree of anisotropy (DA) for instance, is based on the ratio of the highest over the lowest eigenvalue of a second order fabric tensor that quantifies the overall architectural orientation (Harrigan and Mann, 1984). The structural model index (SMI), indicates if trabecular architecture resembles a plate-like or a rod-like structure. In previous quasistatic tests of human trabecular bone, volume fraction and fabric were shown to provide reasonable estimation of elastic constants as well as yield or failure surfaces (Rincón-Kohli, 2003).

Accordingly, the objective of this study was to determine the compressive fatigue behavior of human vertebral trabecular bone as a function of volume fraction and fabric.

Section snippets

Materials & methods

Human thoracic and lumbar vertebrae were obtained from four donors from age 29 to 86 (n=29). The vertebrae were first aligned along a superior–inferior axis and embedded in a 120 mm aluminum cylinder with dental stone. Then, trabecular bone cylinders of 8 mm diameter were extracted from various regions of the vertebral body using a diamond coated coring tool under constant water irrigation and their extremities were cut with a precision band saw, giving 10 mm long samples. The samples were cleaned

Morphological parameters

Tissue density, measured with Archimede's principle, was constant among donors with a mean value of 1.94g/cm±0.07 (mean±SD). Statistical comparison detected no significant differences between donors (p>0.05). The morphological parameters obtained from microcomputed tomography reconstructions showed a very significant variation between donors for volume fraction and SMI (p<0.001), but not for the axial fabric eigenvalue m (p>0.05). As expected, volume fraction and the axial fabric eigenvalue

Discussion

The objective of this study was to quantify the fatigue behaviour of human vertebral trabecular bone along the inferior–superior axis as a function of volume fraction and anisotropy. The fatigue behaviour was characterized by an accumulation of residual strain and a decrease in elastic modulus that lead eventually to an increase in strain rate, energy dissipation and overall failure of the sample. To prevent any environmental artefacts (Bowman et al., 1998, Rimnac et al., 1993), the experiments

Acknowledgements

  • Grant no. 32-52821.97 of the Swiss National Science Foundation,

  • Kuros Biosurgery AG, Zürich,

  • Prof. R. Müller, Swiss Federal Institute of Technology, Zürich (ETHZ),

  • Liliana Rincón-Kohli, Stryker Trauma, Selzach,

  • Gino Crivellari, Marc Jeanneret and Nicolas Favre, workshop of the ICAP, EPFL.

References (23)

  • T. Hildebrand et al.

    Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus

    Journal of Bone and Mineral Research

    (1999)
  • Cited by (78)

    View all citing articles on Scopus
    View full text