Animal experiment protocols were approved by the animal welfare committee at Tongji Hospital affiliated with Tongji University, Shanghai. To avoid potential sex effects, the analyses used female adult Sprague-Dawley rats (260–280 g), aged >10 weeks, at which they are considered to have mature spinal cords (Clarke et al., 2009). To collect accurate constitutive data from mechanical experiments, normal spinal cord tissue specimens were collected in a way that limited damage to the organ. To this end, rats were killed by intraperitoneal injection of a lethal dose of pentobarbitone sodium (100 mg/kg) and permanent cessation of circulation confirmed by cardiac perfusion with ice-cold phosphate-buffered saline (PBS; pH 7.4). A dorsal laminectomy was then performed, and nerve roots were carefully severed. The spinal cord was then cut at the seventh cervical vertebra and the first lumbar vertebra, and harvested thoracic spinal cord segments were immediately soaked in PBS (4°C). The dura mater was carefully removed. Damaged cords were excluded from the study. Notably, we referred to this specimen as “spinal cord and pia-arachnoid complex (SCPC)” (Ramo et al., 2018a; Ramo et al., 2018b). Next, the specimens were oriented with the ventral surface facing up, attached on a slide using cyanoacrylate adhesive, and placed in a 100-mm-diameter culture dish and covered with PBS to prevent dehydration. The culture dish was then positioned under the indenter tip and the specimen equilibrated for 10 min before indentation testing. To limit proteolysis and necrosis, indentation tests were done at room temperature (24°C) within an hour of the death of the rats, as post-mortem time can greatly affect the mechanical properties of biological tissues (Bilston and Thibault, 1995).

A schematic of the setup of indentation load–relaxation tests on SCPC tissues is shown in Figure 1. Mechanical properties were measured ex vivo using a Mach-1 Model V500css device (Biomomentum Inc., Laval, QC, Canada). The technique precisely assessed surface orientation at each position and recorded normal load with a single-axial load cell (1.5 N range and 0.07 mN resolution on the vertical axis). The Mach-1 micromechanical system was made of the tester frame, three motorized stages, one motion controller, one load cell, one load cell amplifier, one computer, and accessories such as testing chambers and fixtures. The load cell amplifier powered the load cell and converted the measured force signal into a digital value that was relayed to a computer. The stage was commanded using a motion controller, which was in turn controlled by the Mach-1 Motion software.

To systematically characterize the mechanical response of the SCPC tissue, indenter size, indentation displacement, and loading velocity were introduced as experimental parameters. With regards to indenter size, spherical indenters with radii of 0.25, 0.50, and 1.00 mm were used in this study. For loading velocity, loads of 0.04, 0.06, 0.08, 0.10, 0.15, and 0.20 mm/s were applied to each indenter. The indentation protocol consisted of a single indent with an indentation amplitude of 0.25 mm (i.e., 8.3% of the specimen thickness), which lay within the recommended range of 10% to minimize boundary effects (Garo et al., 2007). The relaxation time was set to 30 s. Data with a displacement error of >5% were discarded. Data were collected at a 100-Hz sampling frequency.

Indentation locations were chosen at random for each specimen. Test order was randomized for each specimen to minimize order effects. The indentation system was operated in displacement control mode during loading. Specimens did not undergo any other preconditioning before experiments. Indentation was done at a velocity of 0.04–0.20 mm/s at six different random sites for each specimen. Between tests, the specimen was allowed to recover for 100 s. Because of the high dissipative nature of neural tissues (Shulyakov et al., 2011), specimens were discarded after indentation. Repetitive tests were performed on 10 different rats.

Indentation load–relaxation curves consisted of an indentation and a relaxation portion (Figure 2). In the indentation portion, indenters were indented into the tissue at different constant velocities and held during the relaxation portion. Mean peak loads at maximum indentation depth and mean loads at 5, 10, 15, 20, 25, and 30 s during the relaxation phase were calculated to characterize temporal variations.

The elastic modulus (EM) was determined in the form of an indentation method using a spherical indenter. Areas of interest were identified across the surface of each specimen by visual inspection. Indentation load–displacement curves were performed on each region using a Mach-1 Model V500css test device. Indentation parameters were kept constant for each specimen (displacement: 0.25 mm, relaxation time: 30 s). EM at each position was determined by fitting the load–displacement curve with corresponding thickness and an effective Poisson's ratio of 0.5 (Saxena et al., 2012) to an elastic model for indentation as described before (Hayes et al., 1972) (see Eq. 1) using the Mach-1 analysis software (version 6.3, Biomomentum Inc., Laval, QC, Canada). This model is well suited for the mechanical description of specimens bound to flat rigid support (at least 10 times stiffer than the specimen). E M = P H × 1 − v 2 2 a k ( a h , v ) (1) where P = load, H = indentation displacement, ν = Poisson's ratio, a = radius of the contact region, k = correction factor dependent on a/h and ν, and h = specimen thickness.

Statistical analyses and graphical representation were done on SPSS version 20.0 (SPSS, Inc., Chicago, IL, USA) or GraphPad Prism version 7.0 (GraphPad Software Inc., San Diego, CA, USA). Differences between the two groups were compared using a two-tailed Student's t-test. Non-normally distributed data were compared using the Mann–Whitney–Wilcoxon test. Multiple group comparisons used one-way analysis of variance with Tukey's post-hoc test where there was homogeneity of variances or Tamhane post-hoc test where variances were unequal. Exact p-values are reported in Supplementary Tables S1. p ≤ 0.05 indicated statistically significant differences.

From the contact point onward, the load recording was stable (Figure 2). The indentation depth was held at a maximum of 0.25 mm (up to peak load), and the load decreased upon relaxation.

To assess the influence of velocity on the cord, we performed a series of single indents at velocities of 0.04–0.20 mm/s. We then analyzed the viscoelastic behavior of the specimen during the indentation load–relaxation period and recorded average load curves at different rates for the 0.50-mm indenter (Figure 3). The mechanical behavior observed during this study was typical of biological materials, with the initial ramp region showing a nonlinear increase in load with applied displacement (taking the form of a “J”), with the load at first being compliant and rising slowly before gradually steepening until maximum applied indentation depth was reached (Figure 4A). Moreover, the ramping slope of higher rates was greater than that of lower rates. As expected for viscoelastic materials, in all conditions, peak load increased with increasing velocity. Relaxation portion data at various loading rates are shown in Figure 4B. The curve showed that most peak load decay occurred in the initial phase (0–5 s). After approximately 10 s, the load converged gradually toward its static equilibrium value. The degree of load relaxation present was approximately 50–60% of the initial peak load over the 30-s period. The peak loads obtained at rates of 0.04–0.20 mm/s were 1.08 ± 0.11, 1.37 ± 0.18, 1.62 ± 0.24, 1.83 ± 0.26, 2.11 ± 0.20, 2.34 ± 0.29 mN, respectively (Figure 4C). Notably, long-term (equilibrium) load after relaxation varied with the loading rate, with higher-rate tests exhibiting larger equilibrium loads at the end of the relaxation period (Figure 4D). Analysis of decay (percentage) between peak and equilibrium load revealed no significant differences at different velocities (Figure 4E).

Figures 4F–K quantitatively display the average drop values in peak load of the specimens at six equidistant time points at various loading rates. At the first isochrone (5 s) examined tests, the specimens showed a significant decay than the last two time points (25 and 30 s) (p < 0.001, Supplementary Table S1). In comparison with lower rates, higher rates exhibited a larger drop in peak load for the SCPC tissues at the same isochrones, indicating that the tissues responded more quickly.

Next, we repeated the indentation load–relaxation tests with 0.25- and 1.00-mm indenters at each rate (Supplementary Figures S1,2; Supplementary Tables S2,3). Similar response trends were observed across all indentation tests. To demonstrate the usefulness and applicability of the current data, we further repeated the indentation experiments on the larger animal models (i.e., mature ewes) (N = 6). The results between these two species were similar, suggesting the strong velocity-dependent nature of the SCPC tissue (Supplementary Figure S3).

Here, the variance of contact stress area from common compression factors such as fracture fragment, herniated intervertebral disc, and osteophyte was made by altering the spherical tip radius. Representative indentation and relaxation behaviors of SCPC tissues using spherical indenters with radii of 0.25, 0.5, and 1.00 mm at rates of 0.04–0.20 mm/s are shown in Figures 5A–F. Comparison of peak and equilibrium loads among the three indenters at each rate revealed that load depended on indenter size and significantly increased in magnitude with increasing indenter radius at a constant velocity (p ≤ 0.01, Tukey–Kramer multi-comparison test, Figures 5G, H).

Next, we investigated the effect of indenter size on peak load decay in the relaxation portion (Figure 6). For a given velocity (e.g., 0.04 mm/s), larger contact areas exhibited larger drops in peak load at the same isochrones. Turkey's post-hoc tests or Tamhane post-hoc tests within each indenter to test the statistical significance of the drop in peak load at different relaxation time points (Supplementary Table S4) revealed that the contact stress area indeed significantly influenced the drop in peak load.

We first evaluated the mechanical characteristics and spatial heterogeneity of the elastic properties of rat SCPC tissues (Figure 7A). We defined two tissue regions (Devivo, 2012; Noonan et al., 2012), corresponding to the intermediate zone and marginal zone based on the visual appearance of the ventral surface of the specimen. Inevitably, some diversities were observed for the repetitive experiments due to structural heterogeneity. These differences were not statistically significant (Figure 7B). This indicates that normal SCPC tissue stiffness was spatially relatively homogeneous with low variation in elastic values, which is consistent with past findings (Cooper et al., 2020). The stiffness of regions one and two did not differ significantly across specimens (p ≥ 0.05, Supplementary Figure S4, Supplementary Table S5).

To investigate the effect of velocity on EM, we assessed changes in tissue elasticity at 0.04, 0.06, 0.08, 0.10, 0.15, and 0.20 mm/s at an indentation depth of 0.25 mm and averaged mean EM values from 10 force curves, per area. This analysis found that for all three indenters, the EM of the SCPC tissue was significantly depended on indentation velocity and increased in magnitude with increasing indentation velocity (Figures 7C–E, Supplementary Table S6). For the 0.25-mm indenter, at indentation velocities of 0.04–0.20 mm/s, the average EM of SCPC tissue increased from 6,163 to 12,103 Pa, for the 0.50-mm indenter, average EM increased from 5,171 to 10,703 Pa, and for the 1-mm indenter, average EM increased from 4,074 to 8,520 Pa. No inter-animal variability was observed for the EM calculated at each rate (p ≥ 0.05, Supplementary Figure S5, Supplementary Table S7). For all three indenters, similar elastic behavior was observed with increasing indentation velocity, which is consistent with previous observations (Budday et al., 2015).

Statistical comparisons were performed of EM within the same interval (0.02 or 0.05 mm/s). The 0.08–0.10 mm/s group exhibited a significantly lower drop in elastic stiffness than the 0.06–0.08 mm/s group, and the 0.08–0.10 mm/s group exhibited a significantly lower drop in elastic stiffness than the 0.04–0.06 mm/s group (p ≤ 0.05, Figures 7F–H, Supplementary Table S8). Similarly, the 0.15–0.20 mm/s group exhibited a significantly lower drop in elastic stiffness than the 0.10–0.15 mm/s group (p ≤ 0.05, Figures 7F–H, Supplementary Table S8).

Figure 7I shows the effect of indenter size on EM. This analysis found that EM decreased with increasing indenter size. For example, at the rate of 0.04 mm/s and indenter radii of 0.25–1.00 mm, the average EM decreased from 6,163 to 4,074 Pa.