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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

Brandolini, N. , Kapur, N. , and Hall, R. M. , 2014, “ Dynamics of Interpedicular Widening in Spinal Burst Fractures: An In Vitro Investigation,” Spine J., 14(9), pp. 2164–2171. [CrossRef] [PubMed]
Hongo, M. , Abe, E. , Shimada, Y. , Murai, H. , Ishikawa, N. , and Sato, K. , 1999, “ Surface Strain Distribution on Thoracic and Lumbar Vertebrae Under Axial Compression: The Role in Burst Fractures,” Spine, 24(12), pp. 1197–1202. [CrossRef] [PubMed]
Whyne, C. M. , Hu, S. S. , and Lotz, J. C. , 2003, “ Burst Fracture in the Metastatically Involved Spine: Development, Validation, and Parametric Analysis of a Three-Dimensional Poroelastic Finite-Element Model,” Spine (Phila Pa 1976), 28(7), pp. 652–660. [PubMed]
Zirbel, S. A. , Stolworthy, D. K. , Howell, L. L. , and Bowden, A. E. , 2013, “ Intervertebral Disc Degeneration Alters Lumbar Spine Segmental Stiffness in All Modes of Loading Under a Compressive Follower Load,” Spine J., 13(9), pp. 1134–1147. [CrossRef] [PubMed]
Jiang, G. , Luo, J. , Pollintine, P. , Dolan, P. , Adams, M. A. , and Eastell, R. , 2010, “ Vertebral Fractures in the Elderly May Not Always Be ‘Osteoporotic’,” Bone, 47(1), pp. 111–116. [CrossRef] [PubMed]
Cristofolini, L. , Brandolini, N. , Danesi, V. , Erani, P. , Viceconti, M. , and Ferguson, S. J. , 2016, “ A Preliminary In Vitro Biomechanical Evaluation of Prophylactic Cement Augmentation of the Thoracolumbar Vertebrae,” J. Mech. Med. Biol., 16(5), p. 1650074. [CrossRef]
White, A. A. , 3rd, and Panjabi, M. M. , 1978, “ The Basic Kinematics of the Human Spine. A Review of Past and Current Knowledge,” Spine (Phila Pa 1976), 3(1), pp. 12–20. [CrossRef] [PubMed]
Brandolini, N. , Cristofolini, L. , and Viceconti, M. , 2014, “ Experimental Methods for the Biomechanical Investigation of the Human Spine: A Review,” J. Mech. Med. Biol., 14(1), p. 1430002. [CrossRef]
Lochmüller, E. M. , Burklein, D. , Kuhn, V. , Glaser, C. , Muller, R. , Gluer, C. C. , and Eckstein, F. , 2002, “ Mechanical Strength of the Thoracolumbar Spine in the Elderly: Prediction From In Situ Dual-Energy X-Ray Absorptiometry, Quantitative Computed Tomography (QCT), Upper and Lower Limb Peripheral QCT, and Quantitative Ultrasound,” Bone, 31(1), pp. 77–84. [CrossRef] [PubMed]
Cristofolini, L. , Brandolini, N. , Danesi, V. , Juszczyk, M. M. , Erani, P. , and Viceconti, M. , 2013, “ Strain Distribution in the Lumbar Vertebrae Under Different Loading Configurations,” Spine J., 13(10), pp. 1281–1292. [CrossRef] [PubMed]
Kayanja, M. M. , Ferrara, L. A. , and Lieberman, I. H. , 2004, “ Distribution of Anterior Cortical Shear Strain After a Thoracic Wedge Compression Fracture,” Spine J., 4(1), pp. 76–87. [CrossRef] [PubMed]
Ananthakrishnan, D. , Berven, S. , Deviren, V. , Cheng, K. , Lotz, J. C. , Xu, Z. , and Puttlitz, C. M. , 2005, “ The Effect on Anterior Column Loading Due to Different Vertebral Augmentation Techniques,” Clin. Biomech. (Bristol, Avon), 20(1), pp. 25–31. [CrossRef] [PubMed]
Lu, Y. , Maquer, G. , Museyko, O. , Puschel, K. , Engelke, K. , Zysset, P. , Morlock, M. , and Huber, G. , 2014, “ Finite Element Analyses of Human Vertebral Bodies Embedded in Polymethylmethalcrylate or Loaded Via the Hyperelastic Intervertebral Disc Models Provide Equivalent Predictions of Experimental Strength,” J. Biomech., 47(10), pp. 2512–2516. [CrossRef] [PubMed]
Oakland, R. J. , Furtado, N. R. , Wilcox, R. K. , Timothy, J. , and Hall, R. M. , 2009, “ Preliminary Biomechanical Evaluation of Prophylactic Vertebral Reinforcement Adjacent to Vertebroplasty Under Cyclic Loading,” Spine J., 9(2), pp. 174–181. [CrossRef] [PubMed]
Bürklein, D. , Lochmüller, E. M. , Kuhn, V. , Grimm, J. , Barkmann, R. , Müller, R. , and Eckstein, F. , 2001, “ Correlation of Thoracic and Lumbar Vertebral Failure Loads With In Situ vs. Ex Situ Dual Energy X-Ray Absorptiometry,” J. Biomech., 34(5), pp. 579–587. [CrossRef] [PubMed]
Moro, M. , Hecker, A. T. , Bouxsein, M. L. , and Myers, E. R. , 1995, “ Failure Load of Thoracic Vertebrae Correlates With Lumbar Bone Mineral Density Measured by DXA,” Calcif. Tissue Int., 56(3), pp. 206–209. [CrossRef] [PubMed]
Andresen, R. , Werner, H. , and Schober, H. , 1998, “ Contribution of the Cortical Shell of Vertebrae to Mechanical Behaviour of the Lumbar Vertebrae With Implications for Predicting Fracture Risk,” Br. J. Radiol., 71(847), pp. 759–765. [CrossRef] [PubMed]
Chevalier, Y. , Pahr, D. , Charlebois, M. , Heini, P. , Schneider, E. , and Zysset, P. , 2008, “ Cement Distribution, Volume, and Compliance in Vertebroplasty: Some Answers From an Anatomy-Based Nonlinear Finite Element Study,” Spine (Phila Pa 1976), 33(16), pp. 1722–1730. [CrossRef] [PubMed]
Aquarius, R. , van der Zijden, A. M. , Homminga, J. , Verdonschot, N. , and Tanck, E. , 2013, “ Does Bone Cement in Percutaneous Vertebroplasty Act as a Stress Riser?,” Spine (Phila Pa 1976), 38(24), pp. 2092–2097. [CrossRef] [PubMed]
Belkoff, S. M. , Mathis, J. M. , Fenton, D. C. , Scribner, R. M. , Reiley, M. E. , and Talmadge, K. , 2001, “ An Ex Vivo Biomechanical Evaluation of an Inflatable Bone Tamp Used in the Treatment of Compression Fracture,” Spine (Phila Pa 1976), 26(2), pp. 151–156. [CrossRef] [PubMed]
Heini, P. F. , Berlemann, U. , Kaufmann, M. , Lippuner, K. , Fankhauser, C. , and van Landuyt, P. , 2001, “ Augmentation of Mechanical Properties in Osteoporotic Vertebral Bones—A Biomechanical Investigation of Vertebroplasty Efficacy With Different Bone Cements,” Eur. Spine J., 10(2), pp. 164–171. [CrossRef] [PubMed]
Higgins, K. B. , Harten, R. D. , Langrana, N. A. , and Reiter, M. F. , 2003, “ Biomechanical Effects of Unipedicular Vertebroplasty on Intact Vertebrae,” Spine (Phila Pa 1976), 28(14), pp. 1540–1547. [PubMed]
Ikeuchi, M. , Yamamoto, H. , Shibata, T. , and Otani, M. , 2001, “ Mechanical Augmentation of the Vertebral Body by Calcium Phosphate Cement Injection,” J. Orthop. Sci., 6(1), pp. 39–45. [CrossRef] [PubMed]
Buckley, J. M. , Cheng, L. , Loo, K. , Slyfield, C. , and Xu, Z. , 2007, “ Quantitative Computed Tomography-Based Predictions of Vertebral Strength in Anterior Bending,” Spine, 32(9), pp. 1019–1027. [CrossRef] [PubMed]
Buckley, J. M. , Kuo, C. C. , Cheng, L. C. , Loo, K. , Motherway, J. , Slyfield, C. , Deviren, V. , and Ames, C. , 2009, “ Relative Strength of Thoracic Vertebrae in Axial Compression Versus Flexion,” Spine J., 9(6), pp. 478–485. [CrossRef] [PubMed]
Edmondston, S. J. , Singer, K. P. , Day, R. E. , Price, R. I. , and Breidahl, P. D. , 1997, “ Ex Vivo Estimation of Thoracolumbar Vertebral Body Compressive Strength: The Relative Contributions of Bone Densitometry and Vertebral Morphometry,” Osteoporosis Int., 7(2), pp. 142–148. [CrossRef]
Furtado, N. , Oakland, R. J. , Wilcox, R. K. , and Hall, R. M. , 2007, “ A Biomechanical Investigation of Vertebroplasty in Osteoporotic Compression Fractures and in Prophylactic Vertebral Reinforcement,” Spine, 32(17), pp. E480–E487. [CrossRef] [PubMed]
Imai, K. , Ohnishi, I. , Bessho, M. , and Nakamura, K. , 2006, “ Nonlinear Finite Element Model Predicts Vertebral Bone Strength and Fracture Site,” Spine (Phila Pa 1976), 31(16), pp. 1789–1794. [CrossRef] [PubMed]
Perilli, E. , Briggs, A. M. , Kantor, S. , Codrington, J. , Wark, J. D. , Parkinson, I. H. , and Fazzalari, N. L. , 2012, “ Failure Strength of Human Vertebrae: Prediction Using Bone Mineral Density Measured by DXA and Bone Volume by Micro-CT,” Bone, 50(6), pp. 1416–1425. [CrossRef] [PubMed]
Fields, A. J. , Eswaran, S. K. , Jekir, M. G. , and Keaveny, T. M. , 2009, “ Role of Trabecular Microarchitecture in Whole-Vertebral Body Biomechanical Behavior,” J. Bone Miner. Res., 24(9), pp. 1523–1530. [CrossRef] [PubMed]
Dall'Ara, E. , Schmidt, R. , Pahr, D. , Varga, P. , Chevalier, Y. , Patsch, J. , Kainberger, F. , and Zysset, P. , 2010, “ A Nonlinear Finite Element Model Validation Study Based on a Novel Experimental Technique for Inducing Anterior Wedge-Shape Fractures in Human Vertebral Bodies In Vitro,” J. Biomech., 43(12), pp. 2374–2380. [CrossRef] [PubMed]
Ebbesen, E. N. , Thomsen, J. S. , Beck-Nielsen, H. , Nepper-Rasmussen, H. J. , and Mosekilde, L. , 1999, “ Lumbar Vertebral Body Compressive Strength Evaluated by Dual-Energy X-Ray Absorptiometry, Quantitative Computed Tomography, and Ashing,” Bone, 25(6), pp. 713–724. [CrossRef] [PubMed]
Yerby, S. A. , Bay, B. K. , Toh, E. , McLain, R. F. , and Drews, M. J. , 1998, “ The Effect of Boundary Conditions on Experimentally Measured Trabecular Strain in the Thoracic Spine,” J. Biomech., 31(10), pp. 891–897. [CrossRef] [PubMed]
Hussein, A. I. , Mason, Z. D. , and Morgan, E. F. , 2013, “ Presence of Intervertebral Discs Alters Observed Stiffness and Failure Mechanisms in the Vertebra,” J. Biomech., 46(10), pp. 1683–1688. [CrossRef] [PubMed]
Eswaran, S. K. , Gupta, A. , Adams, M. F. , and Keaveny, T. M. , 2006, “ Cortical and Trabecular Load Sharing in the Human Vertebral Body,” J. Bone Miner. Res., 21(2), pp. 307–314. [CrossRef] [PubMed]
Danesi, V. , Zani, L. , Scheele, A. , Berra, F. , and Cristofolini, L. , 2014, “ Reproducible Reference Frame for In Vitro Testing of the Human Vertebrae,” J. Biomech., 47(1), pp. 313–318. [CrossRef] [PubMed]
Cristofolini, L. , Conti, G. , Juszczyk, M. , Cremonini, S. , Van Sint Jan, S. , and Viceconti, M. , 2010, “ Structural Behaviour and Strain Distribution of the Long Bones of the Human Lower Limbs,” J. Biomech., 43(5), pp. 826–835. [CrossRef] [PubMed]
Bergmann, G. , 2008, “ Charité Universitaetsmedizin Berlin ‘OrthoLoad’,” epub, accessed Sept. 10, 2015, www.orthoload.de
Gay, R. E. , and Brault, J. S. , 2008, “ Evidence-Informed Management of Chronic Low Back Pain With Traction Therapy,” Spine J., 8(1), pp. 234–242. [CrossRef] [PubMed]
Edwards, W. T. , 1991, “ Biomechanics of Posterior Lumbar Fixation—Analysis of Testing Methodologies,” Spine (Phila Pa 1976), 16(10), pp. 1224–1232. [CrossRef] [PubMed]
Koh, I. , Marini, G. , Widmer, R. P. , Brandolini, N. , Helgason, B. , and Ferguson, S. J. , 2016, “ In Silico Investigation of Vertebroplasty as a Stand-Alone Treatment for Vertebral Burst Fractures,” Clin. Biomech. (Bristol, Avon), 34, pp. 53–61. [CrossRef] [PubMed]
Liebschner, M. A. , Kopperdahl, D. L. , Rosenberg, W. S. , and Keaveny, T. M. , 2003, “ Finite Element Modeling of the Human Thoracolumbar Spine,” Spine (Phila Pa 1976), 28(6), pp. 559–565. [PubMed]
Kopperdahl, D. L. , Pearlman, J. L. , and Keaveny, T. M. , 2000, “ Biomechanical Consequences of an Isolated Overload on the Human Vertebral Body,” J. Orthop. Res., 18(5), pp. 685–690. [CrossRef] [PubMed]
Cristofolini, L. , Juszczyk, M. , Taddei, F. , and Viceconti, M. , 2009, “ Strain Distribution in the Proximal Human Femoral Metaphysis,” Proc. Inst. Mech. Eng., Part H, 223(3), pp. 273–288. [CrossRef]
Lanyon, I. E. , 1980, “ Bone Remodelling, Mechanical Stress, and Osteoporosis,” Osteoporosis, H. F. De Luca , ed., University Park Press, Baltimore, MD, pp. 129–138.
Bayraktar, H. H. , Morgan, E. F. , Niebur, G. L. , Morris, G. E. , Wong, E. K. , and Keaveny, T. M. , 2004, “ Comparison of the Elastic and Yield Properties of Human Femoral Trabecular and Cortical Bone Tissue,” J. Biomech., 37(1), pp. 27–35. [CrossRef] [PubMed]
Taddei, F. , Cristofolini, L. , Martelli, S. , Gill, H. S. , and Viceconti, M. , 2006, “ Subject-Specific Finite Element Models of Long Bones: An In Vitro Evaluation of the Overall Accuracy,” J. Biomech., 39(13), pp. 2457–2467. [CrossRef] [PubMed]
Ross, S. M. , 2003, “ Peirce's Criterion for the Elimination of Suspect Experimental Data,” J. Eng. Technol., 20(2), pp. 38–41.
Fahim, D. K. , Sun, K. , Tawackoli, W. , Mendel, E. , Rhines, L. D. , Burton, A. W. , Kim, D. H. , Ehni, B. L. , and Liebschner, M. A. , 2011, “ Premature Adjacent Vertebral Fracture After Vertebroplasty: A Biomechanical Study,” Neurosurgery, 69(3), pp. 733–744. [CrossRef] [PubMed]
Cristofolini, L. , 2015, “ In Vitro Evidence of the Structural Optimization of the Human Skeletal Bones,” J. Biomech., 48(5), pp. 787–796. [CrossRef] [PubMed]
Adams, M. A. , Dolan, P. , and McNally, D. S. , 2009, “ The Internal Mechanical Functioning of Intervertebral Discs and Articular Cartilage, and Its Relevance to Matrix Biology,” Matrix Biol., 28(7), pp. 384–389. [CrossRef] [PubMed]
Kyere, K. A. , Than, K. D. , Wang, A. C. , Rahman, S. U. , Valdivia-Valdivia, J. M. , La Marca, F. , and Park, P. , 2012, “ Schmorl's Nodes,” Eur. Spine J., 21(11), pp. 2115–2121. [CrossRef] [PubMed]
Shah, J. , Hampson, W. , and Jayson, M. , 1978, “ The Distribution of Surface Strain in the Cadaveric Lumbar Spine,” J. Bone Jt. Surg. Br., 60-B(2), pp. 246–251.
Alkalay, R. N. , and Harrigan, T. P. , 2016, “ Mechanical Assessment of the Effects of Metastatic Lytic Defect on the Structural Response of Human Thoracolumbar Spine,” J. Orthop. Res. (in press).
Kilincer, C. , Inceoglu, S. , Sohn, M. J. , Ferrara, L. A. , Bakirci, N. , and Benzel, E. C. , 2007, “ Load Sharing Within a Human Thoracic Vertebral Body: An In Vitro Biomechanical Study,” Turk. Neurosurg., 17(3), pp. 167–177. [PubMed]
McLain, R. F. , Yerby, S. A. , and Moseley, T. A. , 2002, “ Comparative Morphometry of L4 Vertebrae: Comparison of Large Animal Models for the Human Lumbar Spine,” Spine (Phila Pa 1976), 27(8), pp. E200–206. [CrossRef] [PubMed]
Panjabi, M. M. , Goel, V. , Oxland, T. , Takata, K. , Duranceau, J. , Krag, M. , and Price, M. , 1992, “ Human Lumbar Vertebrae—Quantitative Three-Dimensional Anatomy,” Spine (Phila Pa 1976), 17(3), pp. 299–306. [CrossRef] [PubMed]
Panjabi, M. M. , Takata, K. , Goel, V. , Federico, D. , Oxland, T. , Duranceau, J. , and Krag, M. , 1991, “ Thoracic Human Vertebrae—Quantitative Three-Dimensional Anatomy,” Spine (Phila Pa 1976), 16(8), pp. 888–901. [CrossRef] [PubMed]
Pollintine, P. , Dolan, P. , Tobias, J. H. , and Adams, M. A. , 2004, “ Intervertebral Disc Degeneration Can Lead to ‘Stress-Shielding’ of the Anterior Vertebral Body: A Cause of Osteoporotic Vertebral Fracture?,” Spine (Phila Pa 1976), 29(7), pp. 774–782. [CrossRef] [PubMed]
Hansson, T. , Roos, B. , and Nachemson, A. , 1980, “ The Bone Mineral Content and Ultimate Compressive Strength of Lumbar Vertebrae,” Spine (Phila Pa 1976), 5(1), pp. 46–55. [CrossRef] [PubMed]
Hulme, P. A. , Boyd, S. K. , and Ferguson, S. J. , 2007, “ Regional Variation in Vertebral Bone Morphology and Its Contribution to Vertebral Fracture Strength,” Bone, 41(6), pp. 946–957. [CrossRef] [PubMed]
Hussein, A. I. , Barbone, P. E. , and Morgan, E. F. , 2012, “ Digital Volume Correlation for Study of the Mechanics of Whole Bones,” Procedia IUTAM, 4, pp. 116–125. [CrossRef] [PubMed]
Roberts, B. C. , Perilli, E. , and Reynolds, K. J. , 2014, “ Application of the Digital Volume Correlation Technique for the Measurement of Displacement and Strain Fields in Bone: A Literature Review,” J. Biomech., 47(5), pp. 923–934. [CrossRef] [PubMed]
Freddi, A. , Olmi, G. , and Cristofolini, L. , 2015, Experimental Stress Analysis for Materials and Structures: Stress Analysis Models for Developing Design Methodologies, Springer, Cham, Switzerland.
Palanca, M. , Tozzi, G. , Cristofolini, L. , Viceconti, M. , and Dall'Ara, E. , 2015, “ Three-Dimensional Local Measurements of Bone Strain and Displacement: Comparison of Three Digital Volume Correlation Approaches,” ASME J. Biomech. Eng., 137(7), p. 071006. [CrossRef]

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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