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Research Papers

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

[+] Author and Article Information
Ameet K. Aiyangar

Laboratory for Mechanical
Systems Engineering (304),
EMPA (Swiss Federal Laboratories for Materials
Science and Technology) Dübendorf,
Überlandstrasse 129,
CH-8600 Dübendorf,
Zürich 8600, Switzerland
Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706
e-mail: ameetaiyangar@gmail.com

Juan Vivanco

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706
Facultad de Ingeniería y Ciencias,
Universidad Adolfo Ibáñez,
Viña del Mar, Chile

Anthony G. Au

VibeDx Diagnostic Corp.,
Edmonton, AB T5J4P6, Canada

Paul A. Anderson

Department of Orthopedics and Rehabilitation,
University of Wisconsin-Madison,
Madison, WI 53705

Everett L. Smith

Department of Population Health Sciences,
University of Wisconsin-Madison,
Madison, WI 53706

Heidi-Lynn Ploeg

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706

1Corresponding author.

Manuscript received September 25, 2013; final manuscript received May 2, 2014; accepted manuscript posted May 14, 2014; published online July 3, 2014. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 136(9), 091003 (Jul 03, 2014) (10 pages) Paper No: BIO-13-1448; doi: 10.1115/1.4027663 History: Received September 25, 2013; Revised May 02, 2014; Accepted May 14, 2014

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 (Eapp), yield strength (σy), and yield strain (εy)—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, ρCT. Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρapp, showed significant correlation with ρCTCT = 1.0568 × ρapp, 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 (σy) were linearly related to the ρCT in the axial direction [ESI = 1493.8 × (ρCT), r = 0.77, p < 0.01; σY,SI = 6.9 × (ρCT) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [ETR = 3349.1 × (ρCT)1.94, r = 0.89, p < 0.01; σY,TR = 18.81 × (ρCT)1.83, r = 0.83, p < 0.01]. No significant correlation was found between εy and ρCT in either direction. Eapp and σy 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, εy 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.

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Figures

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Fig. 1

Sequence of steps for obtaining bone cores for compression testing. (a) Isolated human vertebra with posterior elements removed. (b) Removal of remaining adhered soft tissue from bone. (c) Sagittal slices from one half of vertebra. (d) Transverse slices from second half of vertebra. (e) Coring with a diamond tipped coring bit to obtain cylindrical bone cores. (f) Precision milling with a six-fluted end mill to obtain plano-parallel surfaces on the cores. (g) Sample bone core (center) with sapphire cylinders. Cores were color coded with india ink to separate cores from different slices.

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Fig. 2

Sequence of steps for demarcating each vertebral core based on CT data. (a) CT scan image of cored vertebra. (b1, b2 and c1, c2) 3D bone model of each half of cored vertebra after segmentation in MIMICS 14.0. (d) 3D bone model of intact vertebra before coring (e) Merged bone models of two cored vertebral halves. (f) Coregistration of intact vertebral model and merged, cored vertebral model. (g) Boolean operation to subtract cored vertebral model from intact vertebral model to obtain segmented, 3D models of individual cores.

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Fig. 3

(a) Schematic showing cross section of the Zetos loading unit. The load cell, PZA, and bone chamber are arranged in a series within the system. (b) A closer look at the bone chamber, where the bone specimen is placed between the two sapphire cylinders. Loading end of PZA is comprised of a convex surface to account for nonparallel surface and prevent moment transfer onto the specimen.

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Fig. 4

Representative stress–strain curve from compression testing of vertebral trabecular bone cores. Shaded grey portion of curve (0% < ε < 0.2%) identifies the points used to calculate the apparent elastic modulus. Dashed line indicates use of the 0.2% offset technique for obtaining yield stress and strain.

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Fig. 5

Measured apparent density as a ratio of ash weight over bulk, wet volume (ρapp) versus computed tomography derived density (ρCT)

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Fig. 6

Variation of elastic modulus (E) with CT-derived apparent density (ρCT). SI = superior–inferior or axial direction. TR = transverse direction. The fitted linear regressions for the axial apparent elastic modulus with the physically measured apparent density (ρapp) has been included to illustrate the excellent agreement between correlations of (E) with (ρapp) and (ρCT).

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Fig. 7

Variation of apparent yield strength (σy) with respect to CT-derived apparent density (ρCT). SI = superior–inferior or axial direction. TR = transverse direction.

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Fig. 8

Variation of apparent yield strain (εy) with respect to to CT-derived apparent density (ρCT). SI = superior–inferior or axial direction. TR = transverse direction.

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Fig. 9

Ratio of axial (SI)–to–transverse (TR) elastic moduli (ESI/ETR) and yield stress (σSI/σTR) for the range of density tested. Elastic moduli and yield stress computed from regression equations (3)–(6) in Table 2

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