Spinal cord and meningeal mechanics: viscoelastic characterization and computational modeling

Abstract

Suffering a spinal cord injury (SCI) can be physically, emotionally, and financially devastating. With the complex loading environment typically seen in SCI events, finite element (FE) computational models provide an important economical and ethical option for investigating the mechanical etiology of SCI, evaluating prevention techniques, and assessing clinical treatments. To this end, numerous research groups have developed FE models of the spinal cord using various degrees of material and structural sophistication. However, the level of model complexity that is necessary to achieve accurate predictions of SCI has not been explicitly investigated as few studies have reported applicable tissue behavior. What are reported in the literature as "spinal cord mechanical properties" are most commonly based on ex-vivo tests of the spinal-cord-pia-arachnoid construct (SCPC). The pia and arachnoid maters are fibrous meningeal tissues that closely envelope the spinal cord, and together are referred to as the pia-arachnoid-complex (PAC). Currently available data demonstrate the PAC's importance in the overall SCPC stiffness and shape restoration following compression. However, only one previous study has reported mechanical properties of isolated spinal PAC, and therefore, conclusions about its contribution to SCPC mechanics are largely unknown. Additionally, it has been shown that SCPC material properties begin to degrade within 90 minutes of death. Considering the experimental difficulties and ethical concerns associated with in-vivo mechanical testing of the SCPC, determining the relationship between in-vivo and ex-vivo viscoelastic properties would allow researchers to more accurately analyze existing ex-vivo data. Therefore, the overarching goal of this work is to address the current gaps in knowledge regarding spinal cord and meningeal tissue mechanics and incorporate the developed material models into a FE model. Comparisons of ex-vivo and in-vivo porcine SCPC non-linear viscoelastic behavior revealed significantly different acute behaviors where the ex-vivo condition exhibited a higher stress response but also relaxed quicker and to a greater extent than the in-vivo condition. Although it only made up less than 6% of the ovine SCPC volume, the PAC was found to significantly affect the non-linear viscoelastic behavior of the SCPC which supports the conclusion that it plays an important protective mechanical role. Examining the fitting and predictive accuracy of linear, quasi-linear, and non-linear viscoelastic formulations to SCPC, cord, and PAC stress-strain data, non-linear formulations are recommended to model the SCPC and cord response to arbitrary loading conditions while the QLV is recommended for the PAC. This work provides researchers with novel insights into the complex mechanical behavior of the spinal cord and PAC. The experimental results represent an important addition to the limited literature on in-vivo versus ex-vivo neural tissue viscoelastic properties; they are also the first to quantify the non-linear elastic behavior of spinal PAC and the non-linear viscoelastic properties of the isolated spinal cord. Finally, the computational portion of this work provides a detailed report of the effects of viscoelastic formulation complexity on FE model prediction accuracy and computational time allowing researchers interested in modeling SCI to make informed decisions about the balance of accuracy and efficiency necessary for their specific modeling efforts.