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 "on-axis" direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent 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 QCT-based apparent density of HVTB and its apparent compressive mechanical properties--elastic modulus (E(app)), yield strength (σ(y)), and yield strain (ε(y))--in the SI and TR directions for future clinical QCT-based 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, ρ(CT). Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρ(app), showed significant correlation with ρ(CT) [ρ(CT) = 1.0568 × ρ(app), r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (E(app)) and yield strength (σ(y)) were linearly related to the ρ(CT) in the axial direction [E(SI) = 1493.8 × (ρ(CT)), r = 0.77, p < 0.01; σ(Y,SI) = 6.9 × (ρ(CT)) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [E(TR) = 3349.1 × (ρ(CT))(1.94), r = 0.89, p < 0.01; σ(Y,TR) = 18.81 × (ρ(CT))(1.83), r = 0.83, p < 0.01]. No significant correlation was found between ε(y) and ρ(CT) in either direction. E(app) and σ(y) 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, ε(y) 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 CT-based 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.

Influence of the shape of the micro-finite element model on the mechanical properties calculated from micro-finite element analysis

“…Elastic modulus obtained in our studies were similar to former experimental compression studies on trabecular bone samples (18,19). Compression tests on vertebral trabecular bone cores have shown that the apparent elastic modulus on axial direction was 189.7 MPa (18), which is simular to the value of 139.96-146.…”

Standardizing compression testing for measuring the stiffness of human bone

“…Six studies used dried specimens in the compression test. 33 , 51 , 135 , 138 , 157 , 158 The majority of studies tested bone specimens in unconfined conditions, but some tested in confined conditions using confinement chambers, 22 , 98 , 159 , 160 a steel annulus, 52 or polytetrafluoroethylene (PTFE) tape. 130 …”

Combined exposure to big endothelin-1 and mechanical loading in bovine sternal cores promotes osteogenesis

“…Potential sources of error in compression testing of trabecular bone include machine compliance, end artifacts and side artifacts [34, 64–66]. Several steps in the mechanical testing procedure were designed to reduce these errors and sources of variance.…”

“…Standard ZETOS specimen dimensions (10 mm diameter, 5 mm height) meet the main goal of maintaining core viability for several weeks [9, 30], and are adequate for continuum assumptions [34, 64–66] as required for equations of Hooke’s Law. The aspect ratio of the bone cores (0.5) although favorable for maintaining viability could increase end artifacts in the measurement of E app because of specimen-platen interface conditions and structural end artifacts [34, 64–66]. The F-δ curves (Figure 2) did not reveal a large “toe” region indicating machine compliance and possible end-artifact errors have been minimized.…”

“…The axial stiffness ( K axial ) of the cores was measured with this quasi-static compression (Figure 2) through the bioreactors’ sapphire pistons using ZETOS [9–13, 30–32, 34]. To ensure contact between the loading piston and bone core, a preload of 10 N was applied before quasi-static testing and the dynamic loading stimulus.…”