The mechanical behavior of bovine spinal cord white matter under various strain rate conditions: tensile testing and visco-hyperelastic constitutive modeling

The mechanical behavior of the white matter is important for estimating the damage of the spinal cord during accidents. In this study, we conducted uniaxial tension testing in vitro of bovine spinal cord white matter under extremely high strain rate conditions (up to 100 s^-1). A visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the bovine spinal cord white matter was developed. A set of material constants was obtained using a Levenberg-Marquardt fitting algorithm to match the uniaxial tension experimental data with various strain rates. Our experimental data confirmed that the modulus and tensile strength increased when the strain rate is higher. For the extremely high strain rate condition (100 s^-1), we found that both the modulus and failure stress significantly increased compared with the low strain rate case. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the developed constitutive model will allow researchers to perform more realistic finite element modeling and simulation of spinal cord injury damage under various complicated conditions.

Tensile mechanical analysis of anisotropy and velocity dependence of the spinal cord white matter: a biomechanical study

In spinal cord injuries, external forces from various directions occur at various velocities. Therefore, it is important to physically evaluate whether the spinal cord is susceptible to damage and an increase in internal stress for external forces. We hypothesized that the spinal cord has mechanical features that vary under stress depending on the direction and velocity of injury. However, it is difficult to perform experiment because the spinal cord is very soft. There are no reports on the effects of multiple external forces. In this study, we used bovine spinal cord white matter to test and analyze the anisotropy and velocity dependence of the spinal cord. Tensile-vertical, tensile-parallel, shear-vertical, and shear-parallel tests were performed on the white matter in the fibrous direction (cranial to caudal). Strain rate in the experiment was 0.1, 1, 10, and 100/s. We calculated the Young's modulus of the spinal cord. Results of the tensile and shear tests revealed that stress tended to increase when external forces were applied parallel to the direction of axon fibers, such as in tensile-vertical and shear-vertical tests. However, external forces those tear against the fibrous direction and vertically, such as in tensile-parallel and shear-parallel tests, were less likely to increase stress even with increased velocity. We found that the spinal cord was prone to external forces, especially in the direction of the fibers, and to be under increased stress levels when the velocity of external forces increased. From these results, we confirmed that the spinal cord has velocity dependence and anisotropy. The Institutional Animal Care and Use Committee of Yamaguchi University waived the requirement for ethical approval.

Compression analysis of the gray and white matter of the spinal cord

The spinal cord is composed of gray matter and white matter. It is well known that the properties of these two tissues differ considerably. Spinal diseases often present with symptoms that are caused by spinal cord compression. Understanding the mechanical properties of gray and white matter would allow us to gain a deep understanding of the injuries caused to the spinal cord and provide information on the pathological changes to these distinct tissues in several disorders. Previous studies have reported on the physical properties of gray and white matter, however, these were focused on longitudinal tension tests. Little is known about the differences between gray and white matter in terms of their response to compression. We therefore performed mechanical compression test of the gray and white matter of spinal cords harvested from cows and analyzed the differences between them in response to compression. We conducted compression testing of gray matter and white matter to detect possible differences in the collapse rate. We found that increased compression (especially more than 50% compression) resulted in more severe injuries to both the gray and white matter. The present results on the mechanical differences between gray and white matter in response to compression will be useful when interpreting findings from medical imaging in patients with spinal conditions.

Age-related changes of the spinal cord: A biomechanical study

Although it is known that aging plays an important role in the incidence and progression of cervical spondylotic myelopathy (CSM), the underlying mechanism is unclear. Studies that used fresh bovine cervical spinal cord report the gray matter of the cervical spinal cord as being more rigid and fragile than the white matter. However, there are no reports regarding the association between aging an tensile and Finite Element Method (FEM). Therefore, FEM was used based on the data pertaining to the mechanical features of older bovine cervical spinal cord to explain the pathogenesis of CSM in elderly patients. Tensile tests were conducted for white and gray matter separately in young and old bovine cervical spinal cords, and compared with their respective mechanical features. Based on the data obtained, FEM analysis was further performed, which included static and dynamic factors to describe the internal stress distribution changes of the spinal cord. These results demonstrated that the mechanical strength of young bovine spinal cords is different from that of old bovine spinal cords. The gray matter of the older spinal cord was significantly softer and more resistant to rupture compared with that of younger spinal cords (P<0.05). Among the old, although the gray matter was more fragile than the white matter, it was similar to the white matter in terms of its rigidity (P<0.05). The in vitro data were subjected to three compression patterns. The FEM analysis demonstrated that the stress level rises higher in the old spinal cords in response to similar compression, when compared with young spinal cords. These results demonstrate that in analyzing the response of the spinal cord to compression, the age of patients is an important factor to be considered, in addition to the degree of compression, compression speed and parts of the spinal cord compression factor.

Mechanism of the spinal cord injury and the cervical spondylotic myelopathy: new approach based on the mechanical features of the spinal cord white and gray matter

OBJECT

The authors have previously investigated the mechanical properties of the white and gray matter in the bovine cervical spinal cord, demonstrating that the gray matter is more rigid, although more fragile, than the white matter. In the present study they conducted additional tensile tests on the bovine cervical spinal cord by changing strain levels and strain rates applied to the white and gray matter.

METHODS

Based on their testing, the authors found the following: 1) Stress within the spinal cord relaxes over time. 2) Intracord stress is related to the strain rates or levels. The finite element method was used to compute the stress distribution within the spinal cord under three compressive loading conditions. Results from the computations showed a different stress distribution in the white and gray matter, where the distribution of stress varied with strain rate, compression volume, and the position of compression.

CONCLUSIONS

These differences in mechanical properties between the white and gray matter constitute different mechanisms contributing to the development of tissue damage and clinical symptoms.

Gray matter of the bovine cervical spinal cord is mechanically more rigid and fragile than the white matter

The gray matter of the cervical spinal cord has been thought to be equally or less rigid than the white matter. Based on this assumption, various studies have been conducted on the changes of stress distributions within the spinal cord under mechanical compression, although the mechanical properties of the white and gray matters had not been fully elucidated. The present study measured the mechanical properties of the white and gray matter of bovine spinal cords. For both the white and gray matter, the stress-strain curves had a nonlinear region, followed by a linear region, and then a region where the stresses plateaued before failure. In the nonlinear region, stress was not significantly different between the gray and white matter samples (strain approximately 0-10%), while stress and Young's modulus in the gray matter was significantly higher than the white matter in the linear part of the curve. The gray matter ruptured at lower strains than the white matter. These findings demonstrated the gray matter is more rigid and fragile than the white matter, and the conventional assumption (i.e., the white matter is more rigid than the gray matter) is not correct. We then applied our data to computer simulations using the finite element method, and confirmed that simulations agreed with actual magnetic resonance imaging findings of the spinal cord under compression. In future computer simulations, including finite element method using our data, changes in stress and strain within the cervical spinal cord under compression would be clarified in more detail, and our findings would also help to elucidate the area which can easily receive histologic damage or which could have hemodynamic disorders under mechanical compression, as well as severity and location of biochemical and molecular biological changes.