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Research Papers

Differences in Trabecular Microarchitecture and Simplified Boundary Conditions Limit the Accuracy of Quantitative Computed Tomography-Based Finite Element Models of Vertebral Failure

[+] Author and Article Information
Amira I. Hussein

Department of Mechanical Engineering,
Boston University,
110 Cummington Mall,
Boston, MA 02215
e-mail: amirah@bu.edu

Daniel T. Louzeiro, Ginu U. Unnikrishnan, Elise F. Morgan

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215

1Corresponding author.

Manuscript received August 17, 2017; final manuscript received November 20, 2017; published online January 12, 2018. Editor: Beth A. Winkelstein.

J Biomech Eng 140(2), 021004 (Jan 12, 2018) (11 pages) Paper No: BIO-17-1370; doi: 10.1115/1.4038609 History: Received August 17, 2017; Revised November 20, 2017

Vertebral fractures are common in the elderly, but efforts to reduce their incidence have been hampered by incomplete understanding of the failure processes that are involved. This study's goal was to elucidate failure processes in the lumbar vertebra and to assess the accuracy of quantitative computed tomography (QCT)-based finite element (FE) simulations of these processes. Following QCT scanning, spine segments (n = 27) consisting of L1 with adjacent intervertebral disks and neighboring endplates of T12 and L2 were compressed axially in a stepwise manner. A microcomputed tomography scan was performed at each loading step. The resulting time-lapse series of images was analyzed using digital volume correlation (DVC) to quantify deformations throughout the vertebral body. While some diversity among vertebrae was observed on how these deformations progressed, common features were large strains that developed progressively in the superior third and, concomitantly, in the midtransverse plane, in a manner that was associated with spatial variations in microstructural parameters such as connectivity density. Results of FE simulations corresponded qualitatively to the measured failure patterns when boundary conditions were derived from DVC displacements at the endplate. However, quantitative correspondence was often poor, particularly when boundary conditions were simplified to uniform compressive loading. These findings suggest that variations in trabecular microstructure are one cause of the differences in failure patterns among vertebrae and that both the lack of incorporation of these variations into QCT-based FE models and the oversimplification of boundary conditions limit the accuracy of these models in simulating vertebral failure.

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Figures

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Fig. 1

Experimental procedure: (a) schematic of the spine segment with top and bottom endplates embedded in PMMA; (b) QCT imaging; (c) mechanical loading within a radiolucent device, and μCT scanning, at each loading step

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Fig. 2

(a) The trabecular microstructure was quantified in each of multiple 5 mm cubes per vertebra (the locations of these cubes in a representative transverse μCT slice are shown at the top left), and each cube was assigned to one of the 27 regions of the vertebral body (top right), defined by dividing the vertebral body in thirds along each anatomic direction (bottom row). The gray shading that depicts the anatomic regions is for visualization only and does not indicate systematic regional differences in densities. (b) The hexahedral regions for DVC analysis were defined by using the first μCT scan to define the surface of the vertebral body and then creating a hexahedral mesh. (c) The QCT-based FE models of the vertebrae were created from the QCT scans by first coarsening the QCT images by a factor of two in each direction, and then, following creating of a mask that defined the outer boundary of the vertebral body, performing a direct voxel-to-element conversion, resulting in 10,000–26,000 cubic elements per model.

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Fig. 3

Distributions of minimum principal strain corresponding to the three observed categories of the progression of deformation: For each category, the minimum principal strain is plotted on the whole vertebra (top row) and midsagittal cut-away views (bottom row) for the load steps marked “a,” “b,” “c,” and “d” on the load–displacement curve. Increment “c” was identified as the yield point.

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Fig. 4

Distributions of maximum shear strain corresponding to the three observed categories of the progression of deformation: For each category, the maximum shear strain is plotted on the whole vertebra (top row) and midsagittal cut-away views (bottom row) for the load steps marked “a,” “b,” “c,” and “d” on the load–displacement curve. Increment “c” was identified as the yield point.

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Fig. 5

Determining the boundary conditions for experimentally matched loading and uniform compression loading: The color map in the top row represents the displacement field measured by DVC (shown only on the surface of the vertebra). Δh is the change in the vertebral height, calculated as described in the text. For experimentally matched loading (bottom left), the displacements (represented as black arrows) at discrete points across the endplates (outlined in black) were obtained from DVC results. For uniform compression loading (bottom left), a uniform displacement of magnitude Δh was applied to the superior endplate, while the inferior endplate was fixed.

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Fig. 6

Distributions of strain and microstructure within and among each of the three transverse planes: (a) minimum principal strain at yield point, (b) maximum shear strain at yield point, (c) bone volume fraction, (d) apparent mineral density, (e) trabecular number, and (f) connectivity density. The color of each of the 27 regions corresponds to the median value over all vertebrae, while the number that labels each region is the interquartile range over all vertebrae with the same units and on the same scale as the median values. *Difference between transverse planes; #Difference between coronal planes.

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Fig. 7

Directionality of the minimum principal strain within one representative vertebra: (a) minimum principal strain versus maximum shear strain (each data point represents one hexahedral region and (b) histogram showing the distribution of the direction of the minimum principal strain for the same vertebra whose strains are shown in (a). A value equal to 0 deg or 180 deg would indicate that the minimum principal strain in that hexahedral regions is aligned with the superior-inferior direction.

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Fig. 8

Comparison of the experimentally measured displacements and strains at the yield point to the FE-computed values, for one vertebra: (a)–(c) measured and FE-computed axial displacements (z-direction), (d)–(f) midsagittal cut-away views of (a)–(c), (g)–(i) measured and FE-computed minimum principal strains, and (j)–(l) midsagittal cut-away views of (g)–(i)

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Fig. 9

Statistical comparison of FE-computed and experimentally measured displacements: (a) FE-computed axial displacements experimentally matched loading and uniform compression loading boundary conditions plotted point-by-point against the corresponding experimentally measured axial displacements throughout one L1 vertebral body; (b) R2 values for each specimen for the type of regression shown in (a) (each pair of points corresponds to one L1 vertebral body); (c) median percent difference between measured and FE-computed displacements for the simulations using experimentally matched loading and uniform compression loading boundary conditions (each pair of points corresponds to one L1 vertebral body: diamond symbols represent vertebrae for which the paired t-tests indicated no difference between experimentally measured and FE-computed displacements, for the given boundary condition)

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