**1. Introduction**

Traumatic spinal cord injury (TSCI) is a serious neurological condition. Worldwide, there are approximately 180,000 new cases each year [1,2]. The most common causes of TSCI are motor vehicle

collisions, falls, sports-related activities, and interpersonal violence [2,3]. TSCI typically damages the motor, sensory and autonomic fibre tracts. Patients experience a spectrum of clinical abnormalities such as limb paralysis, dysesthesia, as well as bowel and bladder dysfunction [3–5]. The burden of this condition is shared by the person affected, family members, the community, as well as the healthcare system. Long-term survival and quality of life have improved due to enhanced rehabilitation and medical interventions. However, it has not been convincingly demonstrated that current pharmacological treatments have substantially improved spinal cord function.

Conceptually, the understanding of TSCI impairments and recovery can be advanced through animal models [4–9]. Non-human primate models (NHP) are particularly valuable due to the anatomic and physiological similarities between NHP and human beings [6,7]. The tail in NHPs is analogous to a human limb. The tail is integral to performing functional tasks such as standing on hindlimbs as well as reciprocal movements that aid in balance during ambulation [10]. As described later in this paper, the tail exhibits other features analogous to human beings such as limb dominance or preference.

SCI impairments are usually measured by observing behaviours as well as histopathological assessment [11]. Electromyography (EMG) signals confer certain advantages over these other methods. It is particularly useful for assessing TSCI as EMG data collected on a serial basis as this approach facilitates the characterization of motor unit (MU) activation and recruitment [8]. EMG signals can be recorded through multiple channels, permitting the simultaneous assessment of multiple muscle groups. This is particularly helpful in evaluating agonist–antagonist muscle pairs, in which the assessment of muscle co-contractions are associated with central nervous system disorders [4,9].

EMG data can be obtained through surface recording or intramuscular electrodes placed into the muscles. There is limited literature regarding the nature of intramuscular EMG signals after TSCI in animals and humans. The majority of human studies have been based on surface EMG electrodes. As a general construct, TSCI results in a perturbation of the EMG signal. Calancie et al. [12] studied the recovery of volitional activity after acute SCI in human beings utilizing pairs of surface EMG electrodes. This study demonstrated perturbations in some EMG characteristics including abnormalities in recruitment. Lewko [13] utilized surface EMG electrodes and noted disturbed behaviour in spinal cord conductivity with quiet standing. Nout and Rosenzweig among others [8], ref. [9] developed a NHP model of SCI, and the results demonstrated a significant difference in EMG amplitude and temporal patterns between the healthy and the SCI subjects. Also, they noted uncoordinated muscle activity during the post-lesion condition. Wiegner et al. and Shahani et al. studied the recruitment pattern of MUs post-SCI [14] and cortical pathology [15] using needle EMG signals. The results indicate that MUs fire irregularly with low discharge rate post-SCI. Also, the inter-discharge intervals (IDIs) have a positive serial correlation which results from the decreased variability in length of the adjacent intervals. Capogrosso et al. [16] developed a brain-spine interface to modulate the consequences of TSCI in NHP. EMG signals during continuous locomotion were recorded and averaged to calculate the spatiotemporal maps of the motoneuron activation in monkeys. Their results suggested a practical translational pathway for conceptual analysis studies and investigational applications in human with SCI.

The bio-signals such as EMG are non-stationary signals. Furthermore, EMG signals during volitional muscle contraction have a random nature which means the active MUs have an irregular firing rate [17]. Thus, determining the method to select relevant features of the EMG signal becomes challenging. In this context, several signal processing techniques have been tested, with the goal of developing a robust method [18]. To advance this goal, mathematical transformations can be utilized. Specifically, the EMG signal could be represented in different domains; time, frequency, or a time-frequency/wavelet domain. The amplitude and frequency content of the EMG signal help in understanding the physiology and the pathology aspects of muscle activity. The frequency content of the EMG signal mainly has been calculated using the fast Fourier transform (FFT). However, FFT may not be an appropriate choice for some cases such as the dynamic and variant level of contractions [19,20]. To overcome this problem, the wavelet transforms (WT) is applied. The WT is an

efficient mathematical analysis method for temporally nonstationary and spatially nonhomogeneous bio-signals [21]. Also, this approach has proved its ability to represent precise measurements and to extract useful information from non-stationary biomedical signals [22–25]. Decomposition, denoising, and pattern classification are the most common applications of the WT in the EMG field [18,22,26–34]. Phinyomark et al. [30] investigated the usefulness of extracting EMG features from the multi-resolution wavelet decomposition process. The results showed that the reconstructed EMG of the first and second level (detail coefficients) have improved the class separability. Yamada et al. [26] introduced a new EMG decomposition algorithm by adopting the principal component analysis of wavelet coefficients. This method showed a higher decomposition accuracy when compared to conventional wavelet methods. Fang et al. [27] decomposed EMG signals into their constituent single motor units using wavelet spectrum matching, and the results were satisfying.

The intramuscular fine-wire electrode data of this experiment is particularly unique as it is collected both prior and subsequent to a TSCI. The longitudinal nature of the data, however, presents the challenge of limiting the sampling rate of the sensors to allow for long-term monitoring. In addition, free and dynamic movements must be permitted to allow for data collection that reflected the subjects true volitional control as the limb would be naturally used. Thus, conventional decomposition methods of EMG data are not suitable for this problem as these methods rely on higher sampling frequency (around 25 kHz) [35] as well as the need for isometric contractions [36–39].

In this work, the intramuscular fine-wire EMG data have been analyzed using the WT as an EMG decomposition method and relative power (RP) as a metric of the active MUs within each WT sub-band. Specifically, this work will address the following questions:


The collected intramuscular EMG dataset contains information obtained before and after an experimental TSCI, allowing each subject to serve as normal control. Accurate measurement of impairment and recovery in a model of TSCI has significant implications for the identification and development of TSCI therapeutics. With no standardized model for combined pre-lesion, post-lesion, and recovery analysis, WT with multi-resolution data could provide evidence of being able to account for multiple effects in a single model. The extended recording period both before and after TSCI in the NHP model is necessary to replicate TSCI; recovery in humans will be recognized months after injury. Repeated measurements in the NHP model permit the long-term evaluation effects of experimental therapies. It is expected that the developed NHP model and its preliminary results will provide a better understanding of the TSCI and may help with the prediction of recovery in human limbs.
