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Technical Brief

Effect of the In Vitro Boundary Conditions on the Surface Strain Experienced by the Vertebral Body in the Elastic Regime

[+] Author and Article Information
Valentina Danesi

Department of Industrial Engineering,
Alma Mater Studiorum—Università di Bologna,
Bologna 40136, Italy

Paolo Erani

Medical Technology Laboratory,
Rizzoli Orthopaedic Institute,
Bologna 40136, Italy

Nicola Brandolini

Medical Technology Laboratory,
Rizzoli Orthopaedic Institute,
Bologna 40136, Italy;
School of Mechanical Engineering,
University of Leeds,
Woodhouse Lane,
Leeds LS2 9JT, UK

Mateusz M. Juszczyk

Department of Industrial Engineering,
Alma Mater Studiorum—Università di Bologna,
Bologna 40136, Italy;
Medical Technology Laboratory,
Rizzoli Orthopaedic Institute,
Bologna 40136, Italy

Luca Cristofolini

Department of Industrial Engineering,
Alma Mater Studiorum—Università di Bologna,
Viale Risorgimento, 2,
Bologna 40136, Italy
e-mail: luca.cristofolini@unibo.it

1Corresponding author.

Manuscript received March 17, 2016; final manuscript received July 21, 2016; published online August 23, 2016. Assoc. Editor: Pasquale Vena.

J Biomech Eng 138(10), 104503 (Aug 23, 2016) (9 pages) Paper No: BIO-16-1104; doi: 10.1115/1.4034383 History: Received March 17, 2016; Revised July 21, 2016

The vertebral strength and strain can be assessed in vitro by both using isolated vertebrae and sets of three adjacent vertebrae (the central one is loaded through the disks). Our goal was to elucidate if testing single-vertebra-specimens in the elastic regime provides different surface strains to three-vertebrae-segments. Twelve three-vertebrae sets were extracted from thoracolumbar human spines. To measure the principal strains, the central vertebra of each segment was prepared with eight strain-gauges. The sets were tested mechanically, allowing comparison of the surface strains between the two boundary conditions: first when the same vertebra was loaded through the disks (three-vertebrae-segment) and then with the endplates embedded in cement (single-vertebra). They were all subjected to four nondestructive tests (compression, traction, torsion clockwise, and counterclockwise). The magnitude of principal strains differed significantly between the two boundary conditions. For axial loading, the largest principal strains (along vertebral axis) were significantly higher when the same vertebra was tested isolated compared to the three-vertebrae-segment. Conversely, circumferential strains decreased significantly in the single vertebrae compared to the three-vertebrae-segment, with some variations exceeding 100% of the strain magnitude, including changes from tension to compression. For torsion, the differences between boundary conditions were smaller. This study shows that, in the elastic regime, when the vertebra is loaded through a cement pot, the surface strains differ from when it is loaded through the disks. Therefore, when single vertebrae are tested, surface strain should be taken with caution.

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References

Figures

Grahic Jump Location
Fig. 1

Two different boundary conditions were applied to the same vertebrae: (a) three-adjacent-vertebrae (the central vertebra was loaded through its adjacent intervertebral disks); (b) single-vertebra (the same central vertebra of three-adjacent-vertebrae specimen was loaded through its endplates embedded in bone cement). (c) Schematic of a vertebra showing the position of the eight triaxial strain-gauges. The anterior (A) right (R) and left (L) sides are indicated. The strain-gauges were equally spaced around the vertebral body, at midheight. The actual position of the strain-gauges was sometimes adjusted by up to 4 mm from the theoretical location due to small defects of the bone surface (pores, ridges, or grooves). One grid of each strain-gauge was aligned parallel to the craniocaudal axis.

Grahic Jump Location
Fig. 2

Axial-compression. The principal strain magnitude (ε1, ε2) in the single-vertebra is expressed as a fraction of the three-adjacent-vertebrae condition (average and SD: 100% indicates no difference between the two conditions; greater than 100% means that the single-vertebra experienced an increase of strain compared to the three-adjacent-vertebrae; a negative value indicates a change of sign). The variation of principal direction Δθp=θpSINGLE−VERTEBRA−θpTHREE−VERTEBRAE is the difference between the three-adjacent-vertebrae and the single-vertebra (median and SD: 0 deg indicates no variation; a positive sign indicates a clockwise difference from the three-adjacent-vertebrae to the single-vertebra).(The detailed strain distribution in absolute terms for the two boundary conditions is reported as Supplementary material, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection).

Grahic Jump Location
Fig. 3

Axial-traction. The principal strain magnitude (ε1, ε2) in the single-vertebra is expressed as a fraction of the three-adjacent-vertebrae condition (average and SD: 100% indicates no difference between the two conditions; greater than 100% means that the single-vertebra experienced an increase of strain compared to the three-adjacent-vertebrae; a negative value indicates a change of sign). The variation of principal direction Δθp=θpSINGLE−VERTEBRA−θpTHREE−VERTEBRAE is the difference between the three-adjacent-vertebrae and the single-vertebra (median and SD: 0 deg indicates no variation; a positive sign indicates a clockwise difference from the three-adjacent-vertebrae to the single-vertebra). (The detailed strain distribution in absolute terms for the two boundary conditions is reported as Supplementary material, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection).

Grahic Jump Location
Fig. 4

Torsion. The principal strain magnitude (ε1, ε2) in the single-vertebra is expressed as a fraction of the three-adjacent-vertebrae condition (average and SD: 100% indicates no difference between the two conditions; greater than 100% means that the single-vertebra experienced an increase of strain compared to the three-adjacent-vertebrae). The variation of principal direction Δθp=θpSINGLE−VERTEBRA−θpTHREE−VERTEBRAE is the difference between the three-adjacent-vertebrae and the single-vertebra (median and SD: 0 deg indicates no variation; a positive sign indicates a clockwise difference from the three-adjacent-vertebrae to the single-vertebra). (The detailed strain distribution in absolute terms for the two boundary conditions is reported as Supplementary material, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection).

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