Viscoelasticity of spinal cord and meningeal tissues

Abstract

Compared to the outer dura mater, the mechanical behavior of spinal pia and arachnoid meningeal layers has received very little attention in the literature. This is despite experimental evidence of their importance with respect to the overall spinal cord stiffness and recovery following compression. Accordingly, inclusion of the mechanical contribution of the pia and arachnoid maters would improve the predictive accuracy of finite element models of the spine, especially in the distribution of stresses and strain through the cord’s cross-section. However, to-date, only linearly elastic moduli for what has been previously identified as spinal pia mater is available in the literature. This study is the first to quantitatively compare the viscoelastic behavior of isolated spinal pia-arachnoid-complex, neural tissue of the spinal cord parenchyma, and intact construct of the two. The results show that while it only makes up 5.5% of the overall cross-sectional area, the thin membranes of the innermost meninges significantly affect both the elastic and viscous response of the intact construct. Without the contribution of the pia and arachnoid maters, the spinal cord has very little inherent stiffness and experiences significant relaxation when strained. The ability of the fitted non-linear viscoelastic material models of each condition to predict independent data within experimental variability supports their implementation into future finite element computational studies of the spine.

Statement of Significance

The neural tissue of the spinal cord is surrounded by three fibrous layers called meninges which are important in the behavior of the overall spinal-cord-meningeal construct. While the mechanical properties of the outermost layer have been reported, the pia mater and arachnoid mater have received considerably less attention. This study is the first to directly compare the behavior of the isolated neural tissue of the cord, the isolated pia-arachnoid complex, and the construct of these individual components. The results show that, despite being very thin, the inner meninges significantly affect the elastic and time-dependent response of the spinal cord, which may have important implications for studies of spinal cord injury.

Introduction

Traumatic spinal cord injury (SCI) is typically initiated by high-velocity, dynamic events such as traffic accidents, falls, violence, or sport/recreation injuries [1], [2], [3], [4], [5], [6]. Due to the complex loading environments which occur during SCI, it is difficult to accurately model human injury and/or measure local tissue mechanical forces using in-vivo animal surrogates. In contrast, computational models provide an efficient, economical, and ethical method for investigating SCI mechanical etiology, prevention techniques, and clinical treatments. As tissue deformation and stress have been shown to correlate with injury severity and neurological impairment [6], [7], [8], [9], [10], [11], [12], finite element (FE) computational modeling allows researchers to conduct very controlled SCI simulations and predict the resultant internal tissue response (and associated injury severity) under various conditions [6], [7], [8], [13], [14]. However, it is important to highlight that the predictive value of an FE model is dependent on the implementation of accurate geometric and material models [9], [15], [16], [17], [18].

In the majority of FE models of the spine, the spinal cord itself is typically modeled as one homogenous material [7], [14], [15], [19], [20] or as a construct of gray and white matter regions [6], [8], [9], [10], [13], [16], [17], while explicit modeling of the innermost meningeal layers (the pia and arachnoid maters) is frequently neglected [6], [7], [8], [9], [10], [13], [14], [15], [19], [20]. The material models assigned to the various spinal cord components vary in complexity from linearly elastic [6], [7], [10], [13], [14], [15], [17], [18], [19], [21], [22], [23], [24], [25] to hyperelastic [10], [15], [16], [17], [19], [20] to viscoelastic [8], [9], [18], [21], [22], or some combination thereof. The material models utilized to represent the homogenous spinal cord are often developed using experimental data collected from spinal cord samples with at least the pia mater intact [9], [26], [27], [28], [29], [30]. However, as most published experimental procedures do not include detailed descriptions of dissection techniques beyond removal of the dura mater, it is difficult to determine if the arachnoid mater is also present (and contributing) to the reported results. These results are often reported as the mechanical properties of the gestalt “spinal cord”. For specificity in this work, the three-part construct of the neural and connective tissues will be referred to as the spinal-cord-pia-arachnoid construct (SCPC), with the spinal cord parenchyma referred to as the cord, and the construct of the innermost meninges as the pia-arachnoid complex (PAC).

As shown by the experimental results of Ozawa et al. [31] and Mazuchowski and Thibault [32], the presence of the PAC significantly effects the mechanical response of the SCPC. Specifically, comparisons of the response before and after PAC removal show a significant decrease in the compressive [31] and tensile stiffness [32], as well as shape recovery after compression [31]. However, to the authors’ knowledge, only one study has reported quantitative mechanical properties of isolated spinal PAC [16]. Unfortunately, little detail was provided with respect to the dissection of samples and only a strain-rate dependent linear elastic modulus was reported.

While some groups have included a distinct pia mater in their computational models [17], [18], [21], [22], [23], [24], [25], [33], the lack of appropriate mechanical properties in the literature constrains the predictive fidelity of explicitly modeling this tissue. For example, in a parametric FE study of the effect of material properties on the magnitude and distribution of stress and strain in the cord cross-section, Sparrey et al. concluded that “pia mater characteristics had limited (<4% change) effects on outcomes” [17]. However, the pia mater was modeled as a linearly elastic membrane with the tangent modulus varied from 600 kPa to 3 MPa [17]. While this range includes the modulus reported by Ozawa et al. [31], it does not include the higher stiffness values reported by Kimpara et al. for spinal pia mater [16] and by Jin et al. for cranial pia mater [34]. Indeed, a subsequent study by Sparrey which implemented the 40 MPa linear elastic modulus reported by Kimpara et al. concluded distinct modeling of the pia mater was necessary to match experimental measurements and tissue damage [33]. However, since the experimental results of Kimpara et al. and Jin et al. suggest the pia mater is a viscoelastic material, tangent moduli may not be adequate to describe its behavior under dynamic conditions. Jin et al. has published numerous studies of the viscoelastic response of cranial PAC under a variety of loading conditions [34], [35], [36], [37], [38], but due to differences in ultrastructure [39], [40], [41], [42], application of these properties to spinal PAC is questionable.

Therefore, the goal of this study was to compare the viscoelastic behavior of the isolated PAC, the isolated cord, and the SCPC to determine the mechanical contribution of each component. A novel numerical integration approach [43] was used to develop non-linear viscoelastic material models for each of the three tissues. Each material model was then validated through predictions of an independent (i.e., not included in the original model fits) data set. The results presented herein represent the first known published account to: (1) describe the nonlinear behavior of spinal PAC; (2) characterize the viscoelastic properties of the isolated cord; and (3) publish validated non-linear viscoelastic material models for the PAC and cord. These findings will allow researchers interested in modeling spinal cord injuries to make informed decisions about the balance of accuracy and complexity necessary for their specific modeling endeavors.