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Research Papers

The Transverse Isotropy of Spinal Cord White Matter Under Dynamic Load

[+] Author and Article Information
Shervin Jannesar

Department of Mechatronic
Systems Engineering,
Simon Fraser University,
250-13450 102 Avenue,
Surrey, BC V3T 0A3, Canada
e-mail: sjannesa@sfu.ca

Ben Nadler

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC, Canada
e-mail: bnadler@uvic.ca

Carolyn J. Sparrey

Department of Mechatronic
Systems Engineering,
Simon Fraser University,
250-13450 102 Avenue,
Surrey, BC V3T 0A3, Canada;
International Collaboration on
Repair Discoveries (ICORD),
Vancouver, BC V5Z 1M9, Canada
e-mail: csparrey@sfu.ca

1Corresponding author.

Manuscript received January 4, 2016; final manuscript received July 8, 2016; published online August 1, 2016. Assoc. Editor: Barclay Morrison.

J Biomech Eng 138(9), 091004 (Aug 01, 2016) (10 pages) Paper No: BIO-16-1006; doi: 10.1115/1.4034171 History: Received January 04, 2016; Revised July 08, 2016

The rostral-caudally aligned fiber-reinforced structure of spinal cord white matter (WM) gives rise to transverse isotropy in the material. Stress and strain patterns generated in the spinal cord parenchyma following spinal cord injury (SCI) are multidirectional and dependent on the mechanism of the injury. Our objective was to develop a WM constitutive model that captures the material transverse isotropy under dynamic loading. The WM mechanical behavior was extracted from the published tensile and compressive experiments. Combinations of isotropic and fiber-reinforcing models were examined in a conditional quasi-linear viscoelastic (QLV) formulation to capture the WM mechanical behavior. The effect of WM transverse isotropy on SCI model outcomes was evaluated by simulating a nonhuman primate (NHP) contusion injury experiment. A second-order reduced polynomial hyperelastic energy potential conditionally combined with a quadratic reinforcing function in a four-term Prony series QLV model best captured the WM mechanical behavior (0.89 < R2 < 0.99). WM isotropic and transversely isotropic material models combined with discrete modeling of the pia mater resulted in peak impact forces that matched the experimental outcomes. The transversely isotropic WM with discrete pia mater resulted in maximum principal strain (MPS) distributions which effectively captured the combination of ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and the rostral/caudal spread of damage observed in in vivo injuries. The results suggest that the WM transverse isotropy could have an important role in correlating tissue damage with mechanical measures and explaining the directional sensitivity of the spinal cord to injury.

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Figures

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Fig. 1

FE simulation of the experimental studies (a) unconfined compression [19] and (b) uniaxial tension [18]. Axonal fibers are assumed parallel to the loading direction in both cases.

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Fig. 2

Generating the FE contusion model (a) C5 cross section of a representing MRI scan of a NHP. Scale bar is 10 mm. (b) Symmetric FE simulation of the unilateral contusion SCI model. (c) Subregional areas in the spinal cord cross section used to analyze the FE model results. (d) Midcoronal section and one element thick slices in the epicenter (i.e., 0 mm) and 1.6 mm, 3.2 mm, and 4.8 mm rostral to the injury, used to investigate strain distribution patterns in the rostro-caudal direction.

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Fig. 3

Compressive stress-relaxation behavior of different WM hyperelastic models for one representative strain rate (5.0 s−1) compared with the experimental data obtained from Sparrey et al. [19]

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Fig. 4

Representative tensile stress-relaxation response for the combinations of reduced polynomial isotropic model and different reinforcing strain energy functions at 0.05 mm/s deformation rate compared with the experimental data obtained from Ichihara et al. [18]

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Fig. 5

FE simulation results versus experimental results for (a) unconfined compression experiments at four strain rates, and (b) tensile experiments at three deformation rates. Fibers are defined in the direction of loading in both simulations. Error bars indicate ± standard deviation.

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Fig. 6

MPS distribution at 6.5 mm contusion impact in GM and WM over a 0.2 mm thick slice at the injury epicenter. Columns stand for (a) model A, (b) model B, (c) model C, and (d) model D. MPS is dimensionless and the scale bar is 2 mm.

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Fig. 7

Regional variations of the peaks of MPSs for individual elements averaged over the elements of each subregion, for five subregions; dorsal and ventral GM, dorsal, ventral, and lateral WM. The Data are shown for four transverse slices at the injury epicenter and spaced 1.6 mm, 3.2 mm, and 4.8 mm rostral. The x-axis labels indicate the different models. Error bars show the standard deviation of the peak MPSs over the elements in each subregion.

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Fig. 8

The distribution of histological damage at the injury epicenter and rostral to the injury resulting from cervical unilateral contusion SCIs in NHPs (adapted from Salegio et al. [4]). Histological sections processed for eriochrome cyanine and neutral red show the spread of the lesion. The four subjects had impact mechanics similar to those modeled in this study. Although there is variation in the histological outcomes for each subject they all show similar characteristics; ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and decreasing severity of damage in tissue section rostral/caudal to the injury epicenter. Numbers on the left refer to the subject numbers from the in vivo study.

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