Data Analysis

Analyses were chosen to establish the effects of slope, spinal transection, and self-reinnervation of the LG and Sol muscles on hindlimb kinematics and muscle activity. Data were arranged based on spinal condition (pretransection and posttransection), slope [flat (0°), upslope (10°), and downslope (−10°)], and state of the LG and Sol muscles (CONTROL and SELF-REINNERVATED groups).

Kinematic data was analyzed off-line and processed using the following techniques implemented in several commercially available numerical packages.

Digital videos of the walking sessions were used to determine the quality of kinematic data and choose acceptable trials for processing. Acceptable trials were selected based on the animal taking 20 consecutive plantar weight-bearing steps on the treadmill with minimal head motion. Motion of hindlimb markers in the sagittal plane was divided into individual strides. A stride was defined as toe off to consecutive toe off and was identified by a semiautomated algorithm implemented into MATLAB (The MathWorks, Natick, MA). All subsequent processing of walking cycle marker data was conducted using custom routines implemented in Igor Pro (Wavemetrics, Lake Oswego, OR). Knee and elbow marker positions were triangulated based on femur and tibia bone lengths for the knee marker and humerus and ulna bone lengths for the elbow marker to correct for skin slippage over those joints (Goslow et al. 1973). Hindlimb gait parameters analyzed included hip height, toe height, timing of toe down and toe off, stance length, and anterior and posterior displacements of the toe for each stride (see Fig. 1B and Ollivier-Lanvin et al. 2015). Hip height was defined as the distance between the hip and the surface of the treadmill belt. Stance length was defined as the distance the foot travels from paw contact to paw off. Toe height was defined as the maximum height the toe travels off the treadmill belt during swing. The anterior displacement, measured from the horizontal position of the hip, is the maximum distance the toe travels forward of the hip. The posterior displacement is the furthest distance the toe travels behind the horizontal hip position.

Performance indexes were calculated by dividing the mean of the kinematic parameter (over 20 steps) by its mean baseline value (typically, the value for walking on a flat surface) for each cat, and multiplying by 100 to give the performance index as a percentage of baseline.

Average joint angles (over 20 strides) as a function of phase of walking cycle were calculated for each cat walking on flat, upslope, and downslope treadmill pre- or posttransection. The minimum, maximum, and range of each angle joint (hip, knee, ankle) were extracted from the average of that joint. Those values were compared across slopes using the same type of linear mixed model as for the kinematic parameters with the minimum, maximum, and range of each angle joint as the dependent variables. Statistical significance was set at P < 0.05. Bonferroni analysis was used to reduce multiple comparisons type I error for the post hoc comparisons of the estimated marginal means. Comparisons between groups and conditions were conducted using the same type of linear mixed model as for the kinematic parameters with the angle parameters serving as dependent variables.

Envelopes of muscle activity were calculated by filtering raw voltage records with a high-pass filter (2-pole Butterworth, 15 Hz), followed by full-wave rectification and low-pass filtering (zero-lag, fourth-order Butterworth, 20-Hz cutoff frequency). A muscle burst was defined as the time between muscle contraction onset and offset. These bursts were identified with a semiautomated algorithm based on the generalized likelihood ratio test. The automatically detected onsets/offsets were visually verified and manually corrected using MATLAB scripts.

Cluster analysis of EMG onset vs. EMG offset was performed. The onset and offset times were normalized to the walking cycle duration based on the mean swing onset (represented by 0), stance onset, and stance offset (represented by 1) times for the slope and condition being analyzed. Each normalized burst was plotted as a function of its onset (x-axis) and offset (y-axis) as in Krouchev et al. (2006). Next, following the procedure in Markin et al. (2012), we calculated the “statistical distance” between the centers of the scatter clouds of points representing each individual muscle burst’s onsets and offsets. The scatterplot of burst onsets and offsets was considered as an edge-weighted graph G with the vertices at the centers of the clouds of muscle burst onsets and offsets, and the edges representing the distances between cloud centers. Muscles were then clustered by establishing the minimal spanning tree of graph G in two steps. Muscles with minimal overlap of their onset/offset times were first divided into clusters using the “graphminsspantree” procedure of MATLAB (The MathWorks, Natick, MA). The resulting clusters that contained more than three muscles were then further examined by using the validity index proposed in Jana and Naik (2009). This index calculates the intra- to intercluster distance ratio as individual muscles are joined and is used to establish the cluster divisions that optimize the index.

EMG burst characteristics (duration, onset, offset) of each stride were also calculated to determine if there were condition- or slope-related changes in muscle activation timings.

As further described in Lyle et al. (2016), the baseline force before stretch was subtracted from the raw force profiles before analyses. Stretches that had a sudden or spontaneous force change unrelated to muscle stretch were not further analyzed. To determine whether the force responses of the SELF-REINNERVATED muscles contained a reflexive component, we assessed whether the stiffness of the muscle in response to the full 2-mm ramp stretch (incremental stiffness, i.e., K_e in Fig. 11) was close to the short-range stiffness (K_i), measured over the first 0.2 mm of the ramp (Huyghues-Despointes et al. 2003a). In the absence of the stretch reflex, the incremental stiffness is less than the short-range stiffness due to the yielding, which leads to a ratio of K_e/K_i less than 1 (Huyghues-Despointes et al. 2003a). This yielding occurs in all muscle types but is more pronounced in slow twitch muscles such as the soleus (Malamud et al. 1996).

Muscle force responses to stretch-hold-release perturbations. Top left: depiction of the stretch applied and stiffness measurements calculation. The stiffness ratio (K_e/K_i) was calculated as incremental stiffness (K_e), measured over the ramp of 2-mm amplitude, divided by the short-range stiffness (K_i), measured over the first 0.2 mm. Color graphs show the muscle force responses to stretch-hold-release measured in a terminal experiment following spinalization and locomotor training for SELF-REINNERVATED 2–4 (not obtained for SELF-REINNERVATED 1). The average (over 20 stretches) muscle force response is displayed for ankle extensors of the right [lateral gastrocnemius/soleus (LG/Sol) nerve cut and repair] and left (intact) hindlimbs. Shading around the response lines indicates ±2 SD. Example of a soleus single-stretch response in SELF-REINNERVATED 2 (top right) clearly demonstrates an increase in force during the hold period that is indicative of a stretch reflex response. Note from Table 3 that most values of K_e/K_i were ≥1.0, and all were >0.7. MG, gastrocnemius medialis.

Kinematic parameter indexes (hip height, toe height, etc.) for all cats were compared across slopes at each condition (pre- and posttransection) for both groups using a linear mixed model (SPSS, IBM, Chicago, IL) with slope as a repeated measure factor. The dependent variables used were hip height, stance length, toe height, anterior displacement of the toe, and the posterior displacement of the toe indexes. Statistical significance was set at P < 0.05. Bonferroni correction was used to reduce multiple comparisons type I error for the post hoc comparisons of the estimated marginal means. Comparisons between groups and conditions were conducted using a linear mixed model with slope and condition as repeated measure factors and group as factor. The performance indexes were the dependent variables. Lack of overlap in the estimated marginal means confidence intervals was used to establish significant difference between groups/conditions.

Joint angle parameters were compared across slopes using a linear mixed model with the minimum, maximum, and range of each angle joint as the dependent variables. Statistical significance was set at P < 0.05. Bonferroni analysis was used to reduce multiple comparisons type I error for the post hoc comparisons of the estimated marginal means. Comparisons between groups and conditions were conducted using the same type of linear mixed model as for the kinematic parameters with the angle parameters serving as dependent variables.

Linear mixed models with the EMG burst characteristics as dependent variables and slope as the factor with slope and stride as repeated variables were used to evaluate the effects of slope on burst characteristics in the pre- or postinjury condition for the animals in each group (CONTROL and SELF-REINNERVATED). Linear mixed models with the burst characteristics as dependent variables and condition (pre- or posttransection) as the factor with slope and stride as repeated variables were used to evaluate the changes in burst characteristics from pre- to postinjury at the different slopes. The estimates of the marginal means were used as a measure of the changes, and post hoc pairwise comparisons were used to evaluate if the changes were significant (at P < 0.05).

The K_e/K_i ratios of the left and right hindlimb muscles were compared with the K_e/K_i ratios for the self-reinnervated Sol and gastrocnemius muscles of published experiments (Huyghues-Despointes et al. 2003a; see their Fig. 6, top, initial force <12 N) using nonparametric one-way ANOVA (Kruskal–Wallis, at P < 0.05; R-Studio version 1.1.423). Pairwise comparisons of the average K_e/K_i between our untreated and self-reinnervated muscles and the self-reinnervated muscles of Huyghues-Despointes et al. (2003a) were done using Dwass–Steel–Critchlow–Fligner pairwise comparisons (at P < 0.05).