Dependence of Anisotropy of Human Lumbar Vertebral Trabecular Bone on Quantitative Computed Tomography Based Apparent Density

Abstract

Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property–density relationships have presented results for the superior–inferior (SI), or “onaxisâ€‌ direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) densitydependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCTbased apparent density of HVTB and its apparent compressive mechanical properties— elastic modulus (Eapp), yield strength (دƒy), and yield strain (خµy)—in the SI and TR directions for future clinical QCTbased continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, دپCT. Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, دپapp, showed significant correlation with دپCT [دپCT = 1.0568 أ— دپapp, r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (Eapp) and yield strength (دƒy) were linearly related to the دپCT in the axial direction [ESI = 1493.8 أ— (دپCT), r = 0.77, p < 0.01; دƒY,SI = 6.9 أ— (دپCT) − 0.13, r = 0.76, p < 0.01] while a powerlaw relation provided the best fit in the transverse direction [ETR = 3349.1 أ— (دپCT)1.94, r = 0.89, p < 0.01; دƒY,TR = 18.81 أ— (دپCT)1.83, r = 0.83, p < 0.01]. No significant correlation was found between خµy and دپCT in either direction. Eapp and دƒy in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, خµy exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CTbased densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.