Tensile properties of human spinal dura mater and pericranium

Autologous pericranium is a promising dural graft material. An optimal graft should exhibit similar mechanical properties to the native dura, but the mechanical properties of human pericranium have not been characterized, and studies of the biomechanical performance of human spinal dura are limited. The primary aim of this study was to measure the tensile structural and material properties of the pericranium, in the longitudinal and circumferential directions, and of the dura in each spinal region (cervical, thoracic and lumbar) and in three directions (longitudinal anterior and posterior, and circumferential). The secondary aim was to determine corresponding constitutive stress–strain equations using a one-term Ogden model. A total of 146 specimens were tested from 7 cadavers. Linear regression models assessed the effect of tissue type, region, and orientation on the structural and material properties. Pericranium was isotropic, while spinal dura was anisotropic with higher stiffness and strength in the longitudinal than the circumferential direction. Pericranium had lower strength and modulus than spinal dura across all regions in the longitudinal direction but was stronger and stiffer than dura in the circumferential direction. Spinal dura and pericranium had similar strain at peak force, toe, and yield, across all regions and directions. Human pericranium exhibits isotropic mechanical behavior that lies between that of the longitudinal and circumferential spinal dura. Further studies are required to determine if pericranium grafts behave like native dura under in vivo loading conditions. The Ogden parameters reported may be used for computational modeling of the central nervous system. Graphical abstract

Data describing the structural and material properties of human central nervous system tissues are required to develop accurate numerical and computational models of brain and spinal cord trauma [33] and to investigate cerebrospinal fluid system dynamics and physiology [34][35][36][37][38]. While finite element (FE) models may omit spinal dura or represent it as a linear elastic material [39][40][41][42][43][44][45][46][47], human and animal dura mater have a nonlinear stress-strain response that is characteristic of collagenous soft tissues [48,49]. Few FE models have incorporated nonlinear elastic material properties for spinal dura [33,50,51], likely in part due to a lack of empirically derived nonlinear stress-strain constitutive models for human spinal dura; spinal dura remains under-investigated compared to cranial dura [52]. Mechanical characterization of human cranial dura has suggested that the stress-strain response σ(ε) is best approximated by a one-term Ogden hyperelastic model: where G 0 is the instantaneous shear modulus [40]. An accurate characterization of the parameters G 0 and α is therefore important to improve the constitutive equations of human spinal dura and pericranium for use in computational models.
The primary aim of this study was to characterize the tensile mechanical and material properties of human pericranium and spinal dura (cervical, thoracic, and lumbar) in the longitudinal and circumferential directions. This data was used to identify the regions of spinal dura with tensile properties that are most comparable to pericranium, and to determine the constitutive equations for each tissue region and direction.

Methods
Institutional Human Research Ethics Committee approval was granted for this study (Reference No. H-2018-261). Sample preparation and mechanical testing protocols were adapted from those described previously for porcine dura and pericranium specimens [53].
Cyanoacrylate adhesive (Loctite, Henkel, Düsseldorf, Germany) fixed 7 × 10 mm sandpaper rectangles to the dried distal ends of each sample to prevent slippage during tensile loading [54]. The average sample thickness was calculated from three-micrometer measurements (293-330-30, Mitutoyo, Sakado, Japan; resolution 1 μm, accuracy ±2 μm) at the center and at each end of the unloaded sample. Samples were stored on PBS-soaked gauze in a sealed container at 4°C for 1 -4 h until testing was performed in a temperature-controlled room (22°C). Table 1 Donor demographics, specimen designation, number of samples, and mean thickness, for each region and direction

Mechanical testing
Samples were fixed within the test space of a uniaxial materials testing machine (5543, Instron, High Wycombe, UK) using pneumatic side-action grips (5 bar). A 50 N load cell (2530-50N, Instron, High Wycombe, UK; linearity ±0.25%) and a linear variable differential transformer (73-10-10, Instron, High Wycombe, UK; resolution 0.001 mm, accuracy 0.25%) recorded axial force and actuator position, respectively, at 10 Hz. The load cell was zeroed with the sample suspended from the upper clamp to account for the weight of the specimen, prior to attaching the lower clamp. Samples were then pre-loaded to 0.05 N and Vernier calipers (500-196-30, Mitutoyo, Sakado, Japan; resolution 0.01 mm) were used to measure the width at the mid-span. For preconditioning [55], each sample underwent three cycles of sub-yield tensile loading at 1.6 mm/ min. A pilot study (Supplementary Material A) determined the ideal number of load-unload cycles, and showed that yield point was specific to the anatomical region of the sample. Three preconditioning strain limits (approximately the middle of the linear region) were identified: 10% for thoracic and lumbar dura; 15% for pericranium; and, 20% for cervical dura. Following preconditioning, samples were loaded in tension at 1.6 mm/min until failure occurred. Sample hydration was maintained throughout via a continuous flow of room-temperature phosphate-buffered saline (22°C).

Data analysis
Data analysis was performed using custom Matlab code (R2015a, Mathworks, Massachusetts, USA). Raw data were filtered with a second-order, two-way Butterworth low-pass filter (cut-off frequency of 10 Hz). Engineering stress σ ¼ F wt À Á and engineering strain ε ¼ d l À Á were derived from the displacement d, the load F, the width of the sample w, its initial length l, and its thickness, t. The peak stress and the linear region of the stress-strain curve were automatically detected [53], from which the strain at peak, elastic modulus (slope of the linear region), and strains at the lower (toe) and upper (yield) bounds of the linear region were determined (Supplementary Material B). Structural properties (peak force, extension at peak, stiffness, extension at toe/yield) were similarly extracted. A one-term was fitted to the filtered stress-strain curves ( Supplementary Fig. S2). The model accommodated the low stiffness nonlinear region (toe region) and the higher stiffness linear region which provided the parameters of the fit (α and G 0 , the shear modulus). The yield region of the specimen response was excluded because its exponential form is not accommodated by the Ogden model.
For each structural and material property (ten outcomes in total), linear regression models with cluster-robust standard errors were used to assess if the property differed due to region (cervical, thoracic, and lumbar spinal dura, or pericranium) and/or orientation (C, L, LA, or LP), using SPSS v26 (IBM, Illinois, USA). Multiple samples were obtained from the same region of some donors, so clusterrobust standard errors accounted for non-independent observations. Sequential Bonferroni-adjusted post hoc analyses provided p values for all region-orientation comparisons. A threshold of significance of 0.05 was chosen to reject the hypothesis that a spinal region-orientation was similar to pericranium.

Results
A total of 112 spinal dura samples from 5 donors and 42 pericranium samples from 5 donors were tested (Table 1). Of these, eight samples were excluded from the study because failure occurred near the grip edge. No sample failed during preconditioning. Spinal dura from the cervical region was thicker than lumbar (p < 0.01), but similar to thoracic (p = 0.28), dura. Pericranium was thinner than dura from any region (p < 0.001). Large standard deviations indicated non-  * indicates a significant difference with P-L and P-C. C circumferential, L longitudinal, A anterior, P posterior uniformity of tissue thickness and differences between regions were not significant.
The pericranium and longitudinal spinal dura samples from each region typically displayed J-shaped stress-strain curves consistent with other collagenous biological soft tissues, comprising a toe region, quasi-linear elastic region, yield, and abrupt failure characterized by a sharp stress reduction (Fig. 1). In contrast, the circumferential spinal dura samples exhibited prolonged plastic deformation without abrupt failure. Pericranium was isotropic, with no observed differences in material or structural properties between circumferential and longitudinal samples (Figs. 1D, 2, and 3).
For all spinal regions, in the longitudinal orientation, spinal dura demonstrated greater stiffness, tangent modulus, peak force, and peak stress than pericranium, while in the circumferential orientation these parameters were all significantly lower for spinal dura than for pericranium ( Table  2 and Fig. 2). Pericranium had comparable extension and strain, at yield and peak stress, to LP spinal dura from all spinal regions (except yield strain for Ce-LP), and to LA for cervical and lumbar dura ( Table 2 and Fig. 3). Thoracic LP and cervical LA dura were similar to pericranium for all extension and strain outcomes.
Toe and linear regions of stress-strain curves were fit to a one-term Ogden model. The G 0 and α parameters for the Ogden models from each tissue region and orientation are provided (Table 3). Lu lumbar, Th thoracic, Ce cervical, P pericranium, C circumferential, L longitudinal, A anterior, P posterior

Discussion
Because of their biological and biomechanical performance, autologous membranes are commonly used in duraplasty procedures [15, 21-23, 31, 56]. For example, periosteum has reported benefits of non-immunogenicity, nontoxicity, ability to be sutured watertight, rapid biological/tissue integration, low cost, and low risk of infection in human studies [1,24,25,28,29,31]. Pericranium has been identified as a promising autologous cranio-spinal dura graft material [24,25]. This study characterized and compared the mechanical and material properties of human pericranium and spinal dura tissue. Tensile mechanical tests were performed on human cadaveric spinal dura, and pericranium, in the longitudinal and circumferential directions.
Pericranium was isotropic and exhibited similar extension and strain at yield and failure to longitudinal dura tissue, but the ultimate stress and tangent modulus were significantly lower than that of longitudinal dura. Anisotropic behavior of human spinal dura was observed, with peak stress and modulus consistently largest in the longitudinal direction. This behavior has been described for lumbar spinal dura [57,58] and attributed to the alignment of collagen fibers in the longitudinal direction [58]. For lumbar dura (donor age 39-86 years, mixed anterior/posterior), Runza et al. The latter were similar to that obtained for lumbar dura in the current study (Fig. 2D), and the former were similar for the Elastic moduli reported in Zarzur et al. (1996) are not provided herein because of an apparent error in the Modulus of Elasticity equation provided in that paper, and therefore uncertainty in the results c Properties could not be calculated/measured due to low tensile strength longitudinal posterior orientation but smaller in the longitudinal anterior and circumferential orientations (Fig. 2B). Tencer et al. [59] reported longitudinal (mixed anterior/posterior) apparent modulus similar to that observed for thoracic posterior and cervical posterior regions, but higher than that observed in lumbar region, in the current study. The trend was similar for the peak stress. Previous reports of strain at peak force for the longitudinal orientation range from 20 to 62% [57,58] compared to 27 ± 6% in the current study. Substantial variation in strain at peak force for the circumferential orientation (83 ± 54%) was observed in the current study, consistent with previous reports [57][58][59], and may be due to local differences in tissue microstructure [58]. There is limited reported data with which to compare the pericranium mechanical properties. The ultimate strength of pericranium in this study (9.41 (C) to 9.76 (L) MPa) was higher than that reported for periosteum in the nasal region (3.66-4.04 MPa) [60]. Similarly, the tangent modulus of pericranium in this study (62.0 (C)-69.2 (L) MPa) was greater than that of mandibular periosteum (8.0-16.4 MPa) [61], which may be due to the different region of harvest, as well as different testing protocols.
The stiffness, modulus, peak force, and peak stress of pericranium were greater than that of circumferential spinal dura and lower than that of longitudinal dura. However, strains in the linear region and at peak were mostly similar for pericranium and all regions and orientations of spinal dura. A similar study comparing porcine pericranium and spinal dura reported similar stiffness and peak stress, but different linear region and peak strains, between these tissues [53].
The lower strength of pericranium, than longitudinal spinal dura, may limit its ability to protect the dural sac as a graft material post surgery. However, its lower stiffness may be beneficial for cranial decompression following traumatic brain injury. For instance, in order to close the cranial dura after decompressive craniectomy, pericranium is preferred by neurosurgeons over rigid allografts or synthetic dural substitutes because of its ability to stretch and allow the brain to herniate [62]. The relatively low stiffness of pericranium may also be advantageous in the case of traumatic spinal cord injury with oedemic-related cord-dura contact, where duraplasty may be indicated in some patients to decompress the spinal cord [4,63]. However, the potential influence of dural graft material properties on local CSF dynamics is unknown [35]. The structural and material properties of pericranium were more similar to spinal dura than most of the synthetic biomaterials used for duraplasty [64][65][66]. The strength (9.41 (C) to 9.76 (L) MPa) was higher than that of Tutopatch® bovine pericardium (3.51 MPa) and its modulus (62.0-69.2 MPa) was higher than that of Gore-Tex® Expanded Cardiovascular Patch (18.26 MPa) [64]. The current study also suggests the strain response of pericranium is also more compatible with spinal dura. For example, a linear region corresponding to 40-60% of strain is reported for Durepair® and 0.5-1.5% for Gore-Tex® Expanded Cardiovascular Patch [64] while in the current study the strain at yield was 24.2-25.7% for pericranium and 20.3-31.4% for spinal dura.
While some manufactured materials that have been used as dural grafts have some mechanical similitude to native dura [64,66], none have the combination of strength, modulus, and strain at peak force measured in the current study for spinal dura and pericranium (Table 4). In addition, some synthetic grafts have demonstrated an increased risk of infection compared to autologous pericranium grafts [24] and have exhibited limited tissue integration [67,68]. In some studies, nonautologous dural grafts have been associated with complications such as hemorrhage, bacteria and virus transmission, Creutzfeldt-Jakob disease transmission, immune response, slower healing, or graft dissolution [19,25,[69][70][71][72].
The hyperelastic Ogden model parameters provided for the elastic regions of the pericranium and spinal dura stress-strain data may be used to improve future numerical analyses that model human spinal dura and pericranium. In part due to a lack of appropriate data, most reported computational models of the spine apply simple linear elastic properties to the dura [34][35][36][37][38][39][40][41][42][43][44][45][46][47]. As is typical in the application of Ogden models to hyperelastic collagenous tissue, the exponential form of the model does not account for the yield region in which sequential failure of collagen fibers occurs [48,73,74], thus the derived material models are limited to simulating mechanics below the damage threshold. Values for G 0 were more distributed than α, as evidenced by relatively large standard deviations.
Some limitations accompany this study. There were relatively wide distributions for some outcomes (particularly extension and strain at toe/yield); however, this is not unique to this study, for example, similar variability of the shear modulus (G 0 ) has been reported for human cranial dura [40], and animal spinal [48,73,75] and cranial dura [39,74]. This spread of data may be partly attributed to specimen-specific factors such as age, health conditions, physiology, and cause of death; for instance, the tensile properties of human cranial dura (elastic modulus, tensile strength and maximum strain) are inversely related to donor age [76]. Other extrinsic factors such as tissue storage and preparation conditions may also affect the mechanical properties [77]. Dura is a composite material with heterogeneous and site-specific microstructural arrangements and variable geometry [58] which contributes to variation in mechanical behavior. The overall effect of these intrinsic and extrinsic factors could be somewhat mitigated by increasing the number of donors, collecting samples from every region of interest in each donor, and increasing the number of samples tested from each region.
The experimental procedures were developed to minimize damage to the tissues during sample preparation, and to prevent sample slippage during testing. A combination of sandpaper, cyanoacrylate adhesive, and pneumatic grips was used to minimize the risk of slippage [48,54,74]. In addition, rectangular, rather than dumbbell-shaped, samples were used to reduce the damage to the tissue during preparation. Such rectangular geometry is known to underestimate the stress due to stress concentration at the grip [78]. The largest span possible was used to increase the specimen length-to-width ratio and minimize the stress concentration effect, and to maintain a uniform stress far away from the gripped ends [78]. The span length and width were limited by the circumference of the spinal dura and the continuity of defect-free zones (i.e. absence of nerve roots or damage during tissue harvest), respectively. Only eight samples were discarded because failure occurred near the grip; however, digital image correlation could be used to improve slip detection and mid-span strain measurements.
This study describes the uniaxial tensile mechanical response of human pericranium and spinal dura. Pericranium exhibited isotropic mechanical behavior, and demonstrated similar strains at the boundaries of the linear region, and at peak force, to the anisotropic spinal dura from all spinal regions. Pericranium (in both tested directions) had lower strength and stiffness than spinal dura in the longitudinal orientation, but had higher strength and stiffness than spinal dura in the circumferential direction. Taken together, these findings suggest that pericranium may have suitable extensibility when used as a spinal dural graft material, but further investigations are required to assess its protective ability during physiological loading.

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.
Author contributions CFJ, RDQ and SC designed the study and harvested specimens. SC performed the experimental testing with oversight of RDQ and CFJ. SC, RDQ and CFJ interpreted experimental data. RDQ carried out the statistical analysis of data. SC wrote the initial manuscript, and RDQ and CFJ substantially revised the manuscript. All authors gave approval for publication of the final version.

Compliance with ethical standards
Conflict of interest The authors declare no competing interests.
Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons. org/licenses/by/4.0/.