**2. Materials and Methods**

The focus of the SCI model was to create a lesion that mimics human SCI without clinical impairments. The experimental methods to create the lesion are described in detail in previous publications [4,7], but are presented here briefly. The subjects, six adult Macaca fasicularis monkeys, underwent two surgical procedures. The first to insert a small transmitter (PhysioTel D70, Data Sciences International, St. Paul, MN, USA) with attached fine-wire intramuscular electrode pair into the lower back of the subjects. The electrodes were implanted into the left and right flexor cauda longus and brevis muscles (tail muscles). The EMG signals were measured using the fine-wire electrodes with 10 mm inter-electrode distance, 10 mm exposed wire length, 1000 Hz sampling frequency, and common ground.

Baseline pre-lesion EMG data from the fine-wire electrode pair were collected during voluntary movement of NHPs within their home enclosures for 30 days. The data were collected from Monday to Friday (excluding holidays) for approximately 1 h per day. After 30 days, the subjects underwent a second surgical procedure. A small laminotomy was completed at the L5 vertebral level. An epidural balloon catheter was inserted and advanced approximately 10 cm cranial to the level of the lower thoracic spinal cord. The lesion was created by inflation of the balloon with air. The balloon remained inflated for 60 s and then was deflated. The catheter was then removed, and the surgical incision closed. The lesions initially disrupted the grey and white matter at the site of lesion creation. The histopathological features, that were created by this method are similar to human TSCI [4]. To mimic the time frame between human injury and administration of emergency medical treatment, the subjects remained under anesthesia for one hour. Four subjects that received the experimental combination treatment for 90 days while two subjects did not receive any treatment. Combination treatment consisted of a bolus 0.2 mg/kg bolus of thyrotropin releasing hormone (TRH), followed by a continuous infusion of 0.2 mg/kg per hour for 1 h. These subjects were also treated with 60 mg of selenium and 80 IU of vitamin E daily. TRH is a tripeptide produced by the hypothalamus; selenium and Vitamin E are antioxidants. The combination of these agents may modulate the physiological sequelae of TSCI [40]. This protocol was approved by the Institutional Animal Care and Use Committee (IACUC) at Harvard University and the University of Wisconsin at Madison. As such, EMG data from the tail is analogous to EMG data obtained from the limb of a human being with TSCI EMG data were collected from all six subjects. However, in one subject, the data from one side was not recorded due to a technical error. As such, raw data in this paper represents the experience of three subjects that received the combination therapy, and two subjects who did not receive treatment. Figure 1 illustrates a sample of the recorded raw EMG data.

**Figure 1.** Graphical representation of the raw electromyography (EMG) signal.

In this NHP model, the induced lesion produced a TSCI limited to the upper motor neuron tracts that supply the lower motor neurons of the tail muscles [7]. Lesion of such nature result in a perturbation in the MUs discharge properties; i.e., abnormalities in the inter-discharge interval, firing rate, and floating serial correlation coefficient [14,41]. These abnormalities have been typically characterized in non-physiological experimental conditions such as low force levels and isometric contraction frequency [14,37–39]. In this work, the EMG data were collected when the subjects engage in physiological activities (i.e., locomotion in a cage). The proposed EMG analysis method consists of the following three steps:

	- 1. The EMG signals were decomposed into seven sub-bands, one approximate coefficient (cA6), and six detail coefficients (cD1, ... , cD6).
	- 2. The EMG signal was then reconstructed at each level using inverse discrete wavelet transform, and seven EMG reconstructed signals (A6, D1, ... , D6) were obtained from their coefficients (cA6, cD1, ... , cD1). Table 1 shows the frequency ranges of the seven EMG sub-bands.

$$RP(\%) = \frac{SBP}{TP} \,\, ^\prime \tag{1}$$

where:

*RP:* the relative power of the desired sub-band. *SBP:* the power of the desired sub-band (e.g., A6, D1, ... or D6). *TP:* the total power of all the sub-bands (A6 + D1, ... , + D6).


**Table 1.** The frequency ranges of the seven EMG reconstructed sub-bands.

**Figure 2.** Wavelet analysis; decomposition and reconstruction steps.

The goal was to address the research questions by analyzing specific subsections of the data and testing specific effects. To test the lateralization effect (attributed to limb dominance), only the pre-lesion data were considered for the two sides (left and right). Then, the lesion effect was tested using the data from both pre-and post-lesion periods, and two separate models were fitted one for each side. To test the treatment effect, two separate models (left and right) were fitted using only the post-lesion data. The data in this work is considered a clustered longitudinal dataset with three levels; days are nested in frequency sub-bands, which are in turn nested within subjects (day: is level 1, sub-bands: is level 2, and subject: is level 3). As a result of such hierarchical structure as in Figure 3, the non-independence problem of the observations would arise which requires an appropriate statistical analysis method. A mixed model is a statistical method that was developed particularly to address the non-independence (correlated, or repeated measurements) issue by including the random effect term in its model. The developed mixed models controlled for the within-subject correlation by including a random effect for the subject and the nested sub-bands within each subject, with a variance-covariance structure and restricted maximum likelihood estimation. The models were implemented in the statistical software R using the (lme4) package. The significance level was set to (α = 0.05). The *RP* for any given subject at (day) *i* for (sub-band) *j* nested within (subject) *k* denoted as *RPijk*, is represented in the following equation (see a summary of parameters in Table 2):

 $RP\_{ijk} = \beta\_0 + \beta\_1$ 
 $Day\_{ijk} + \beta\_2$ 
 $EFFECT\_{jk} + \beta\_3$ 
 $EFFECT\_{jk}$ 
 $Day\_{ijk} + \beta\_4$ 
 $Freq\_{jk} + \beta\_5$ 
 $Freq\_{jk}$ 
 $Day\_{ijk} + \beta\_6$ 
 $Freq\_{jk}$ 
 $EFFECT\_{jk} + \beta\_7$ 
 $Freq\_{jk}$ 
 $EFFECT\_{jk}$ 
 $Day\_{ijk} (fixad) + \beta\_6$ 
 $a\_{0k} + a\_{1k}$ 
 $Day\_{ijk} + a\_{0jk} + a\_{1jk}$ 
 $Day\_{ijk} + \varepsilon\_{ijk}$ 
 $(random)\_i$ 


**Table 2.** Parameters used in Equation (2).

**Figure 3.** Data Structure: The data in this work was collected from the left (L) and right (R) side of the tail for five subjects during multiple experiment days (d1, d2, ... , dn) for (pre- and post-lesion period). The data of each day was decomposed into seven frequency sub-bands (D1, D2, D3, ... , A6). Three of the subjects received a combination of treatment (Treatment group); the remaining two subjects did not receive any treatment post-lesion (Control group).

## **3. Results**

The results were presented in the form of answers to the three research questions that were stated in the introduction. They are as follows:

*(1) Is the intramuscular fine-wire electrode pair capable of detecting limb dominance in the subjects prior to lesion?*

To test the symmetry of tail muscle activity on both sides, the *RP* of the EMG signals during the *pre-lesion* period were analyzed using a linear mixed model. The interaction of the frequency sub-band and the side variable in the statistical model demonstrated a significant effect (*p*-value < 0.001). Given that the (side\*frequency) interaction is significant, Tukey's mean comparisons were generated to identify what means differ significantly. These results suggested that side variable had a significant effect on the *RP* value of the D1, D2, D4, and D5 sub-bands. The estimated mean of the *RP* for the D1, D2 and D4 sub-bands of the *left side* were significantly higher than that of the *right side.* On the contrary, the estimated mean of the *RP* for the D5 sub-band on the *left side* was significantly lower than that of the *right side.* The estimated mean for the *RP* across the different frequency sub-bands for both sides is illustrated in Figure 4. Taken together, these results showed that the left and right tail muscles have asymmetry activation.

**Figure 4.** The estimated mean of the relative power (*RP*) of seven reconstructed EMG sub-bands prior to the creation of traumatic spinal cord injury (TSCI) for the left and right side of the tail. Of note for each band, there is a difference in *RP* value when compared to the left and right side of the tail. The D2 sub-band of the left and right side has the maximum RP, and the significant difference between the two sides is at the D1, D2, D4, and D5 sub-bands. The star indicates a significant difference.

*(2) In the post-lesion period, is there a change in the EMG activity attributed to the experimental spinal cord injury and how it could be characterized in terms of RP?*

To answer this question, the effect of the created lesion was analyzed using a linear mixed model. The lesion effect was studied by testing the difference between the EMG characteristics during the *pre-* and *post-lesion* period. The interaction of the frequency sub-band and the lesion variable in the statistical models of both sides demonstrated a significant effect (*p*-value < 0.001). Given that the (lesion\*frequency) interaction was significant, Tuckey's means comparisons were generated to identify which means differ significantly. Figures 5 and 6 summarized the estimated mean of the *RP* values for different frequency sub-bands of the *pre-* and *post-lesion* group for the two sides. On the *left side*, the estimated mean of the *RP* for the D4, D6 and A6 sub-bands was significantly higher in the *post-lesion* period compared to the *pre-lesion* period. On the *right side*, the estimated mean of the *RP* for the

D4, D6, and A6 sub-band was also higher significantly in the *post-lesion* period. On the other hand, the estimated mean of the *RP* for the D1 and D2 sub-bands was significantly lower in the *post-lesion* period compared to *pre-lesion* period. The results suggested that the created lesion had a clear effect on the discharge properties of MUs, and with this technique, changes in discharge properties can be detected even when there is no clinical evidence.

**Figure 5.** The estimated mean of the *RP* of seven reconstructed EMG sub-bands prior and post to the creation of TSCI for the *left side* of the tail. Of note, the *RP* values for the frequency sub-bands (D4, D6, and A6) are significantly higher in the post-lesion period. The star indicates a significant difference.

**Figure 6.** The estimated mean of the *RP* of seven reconstructed EMG sub-bands prior and post the creation of TSCI for the *right side* of the tail. Of note, the *RP* values for the lower frequency sub-bands (D4, D6, and A6) are significantly higher in the post-lesion period, while the higher frequency sub-bands (D1 and D2) are significantly lower in the post-lesion period. The star indicates a significant difference.

*(3) What is the di*ff*erence in the EMG activity between the control and the treatment group in the post-lesion period (Treatment e*ff*ect)?*

The *post-lesion data* were utilized to generate two separate mixed models, one for each side. The potential effect of the treatment was analyzed using the *RP* of the left and the right sides incorporating an analysis which compared the treatment and the control groups. The interaction of frequency sub-band and treatment variables in the models of both sides demonstrated a significant effect (*p*-value < 0.001). Given that the (treatment\*frequency) interaction was significant, Tukey's mean comparisons were generated to identify what means differ significantly. Figures 7 and 8 summarize the estimated mean of the *RP* values for different sub-bands of the control and treatment group for the two sides. On the *left side*, the D1, D2, D3, and D6 sub-bands have a significant difference, while on the *right side* the effect was significant in all the sub-bands except the D2. The results suggested that there is a significant difference in the discharge properties of MUs of the treatment and the control groups during the post-lesion period.

**Figure 7.** The estimated mean of the *RP* of seven reconstructed EMG sub-bands post-lesion for the treatment (Tr) and the control (Ctrl) groups of the *left side*; of note, the *RP* values for the frequency sub-bands (D1, D2, D3, and D6) are significantly different. Subjectively, the distribution of the *RP* in the treatment group is similar to the *RP* distribution in the pre-lesion period for all the subjects. The star indicates a significant difference.

**Figure 8.** The estimated mean of the *RP* of seven reconstructed EMG sub-bands post-lesion for the treatment (Tr) and the control (Ctrl) group of the *right side*; of note, the *RP* values for frequency sub-bands (D1, D3, D4, D5, D6, and A6) are significantly different. Subjectively, the distribution of the *RP* in the treatment group is similar to the *RP* distribution in the pre-lesion period for all the subjects. The star indicates a significant difference.
