**1. Introduction**

Hemiplegia, often observed in children a ffected by cerebral palsy, is a neurological disease characterized by the fact that only half of the body is a ffected by the disorder. Modified selective motor control, weakness and spasticity are associated with hemiplegia, conditioning everyday activities including walking [1]. In the late 1980s, Winters et al. introduced a suitable classification of gait in hemiplegia. Based on a kinematics analysis, the authors identified four di fferent gait patterns in the sagittal plane where four categories were discriminated, based on a progressive distal-proximal involvement of the hemiplegic leg [2]. Winters' type I patients present a hypo-activation of dorsi-flexor muscles of the hemiplegic-leg ankle, causing drop foot during swing. Winters' type II subjects are

typified by the persistence of equinism throughout the gait cycle, often related to a hyperextension of the knee during stance phase [2,3]. Winters' type I and II are the forms of hemiplegia most frequently detected in cerebral palsy; thus, many studies have focused on them [3–6].

Surface electromyography (sEMG) is an acknowledged diagnostic technique, typically used to characterize muscular activity by means of a non-invasive approach. Non-invasiveness and easiness of use, associated with the increasing availability of solutions based on sEMG, make this technique particularly valuable for the analysis of those pathologies in which walking is directly affected, as in cerebral palsy. Many studies, including our own, used an sEMG-based approach to identify the gait patterns adopted by hemiplegic children and to compare them with control children [4,6–11]. In particular, two recent studies, performed on numerous strides (hundreds) per patient, reported clear alterations of muscular-recruitment patterns in hemiplegic side: Reduced and less frequent activity during swing and a dearth of activity at loading response of tibialis anterior in type I and II; and a hyper-activation of gastrocnemius around initial contact was identified in type II only [5,6]. Overall, both studies reported significant variability in activation modality of muscles of both hemiplegic leg [5] and contralateral (non-hemiplegic) one [6].

Adaptive variability is typical of human motor development. According to some researchers, the variability in early infant movements is a key aspect of motor development [12]. Moreover, other sEMGbased studies sugges<sup>t</sup> that an initial attempt of adaptation in postural behavior during sitting could be identified in four-month-old infants [13]. Then, all basic motor functions will achieve the first stages of the so-called secondary variability around the age of 18 months. Active trial-and-error experiences, specific to each subject, are typical of this stage. The basic, variable motor skill reached during the phase of primary variability keeps on developing and modifying all through the subject's life, allowing increasingly accurate and organized movements. Consequently, adult subjects master a wide movement repertoire, enabling an e fficient motor solution for each specific circumstance [13]. Overall variability of human motion is associated with variability of muscle activity, quantified by EMG signals. In a preliminary study of the present group of researchers [14], sEMG-signal variability was quantified in relation to motor development, comparing adult and children populations by means of a quantitative index, the coe fficient of variation (CV), previously tested on di fferent EMG signals [14–16]. That study suggested that CV is an easy-to-measure index able to quantify sEMG variability in di fferent experimental conditions and with di fferent clinical purposes: In adult and pediatric populations and for both intra- and inter-subject studies. sEMG variability has been infrequently assessed in hemiplegic children and only by means of computationally expensive techniques, such as statistical gait analysis [4,6]. To the authors' best knowledge, the CV index has never been applied to quantify the variability of muscular recruitment during hemiplegic walking. Moreover, no attempts were reported in literature to provide a direct and quantitative comparison of sEMG-variability values between hemiplegic children and controls.

Thus, the present work is designed to assess the adaptive variability of muscular recruitment during hemiplegic walking and to detect possible changes in sEMG variability of hemiplegic walking compared to controls. The easy-to-measure CV index is chosen to achieve this goal, in order to propose a novel approach able to limit the complexity of computational procedures. The CV value is computed in 34 school-age hemiplegic children identified as type I and II by Winters' classification and in a large number of cycles per subject (hundreds), resulting in around 30,000 strides in total, to guarantee an adequate number of samples for variability characterization. The same index is used to describe sEMG behavior in two further populations, school-age children (34 subjects) and young adults (34 subjects), to compare and interpret results achieved in the hemiplegic population. The manuscript is organized as follows: Section 2 provides a short summary of the main indices available in the literature and used to quantify and analyze the sEMG signal variability in di fferent scenarios, among which the CV is applied in the present study. Section 3 presents material and methods based on which the research was developed, providing details about sEMG processing, test populations and parameters computation. Section 4 presents the experimental results that are discussed in Section 5, along with retrospection on the related state of the art. Finally, Section 6 concludes the manuscript and provides insights for future research developments.

### **2. Indices for sEMG Variability Analysis**

The non-invasive recording of muscle electrical activity during dynamic tasks is greatly supported by sEMG, thanks to a huge collection of algorithms and techniques specifically designed to obtain and interpret the muscle activation patterns. The last ones may appear in patients with altered locomotion, and the use of sEMG in clinical gait analysis helps identifying such a condition. Despite the aforementioned advantages, and the market availability of wireless, lightweight and minimally invasive sEMG measurement equipment, such as the Myon [17] or the Freeemg [18] devices, sEMG has not witnessed a pervasive and widespread adoption in clinical assessment or rehabilitation yet. This is motivated by education barrier, i.e., understanding the features and information associated with electrical signals measured on the body may be not easy or straightforward by clinical operators [19,20]. Additional complexity is determined by the possibility to apply a huge variety of parameters, indices and figures, di fferently defined and computed from the measured sEMG signal samples, according to the specific muscle feature or activation pattern one is interested to observe [21]. For example, root mean square (RMS), median frequency (MF) and mean power frequencies (MPF) based on Fourier Transform [22] have been e ffectively used in applications dealing with the evaluation of muscular fatigue.

It is well recognized that the human motor system exhibits redundancy, so a single motor task may be performed in several di fferent ways, leading to a similar final result [23]. Redundancy of motor repertoire in human subjects reflects the capability of the nervous system to generate di fferent patterns of muscle activation, for the same given movement. Such a capability motivates either intra- and inter-subject variability of muscle activation, which can be captured by suitably designed indices computed on the measured sEMG signal samples. For example, indices proposed for sEMG analysis focused on aspects pertaining to running are mean, standard deviation (SD) and mean CV, as well as CV calculated over the running cycle [24]. The mean sEMG value at the denominator of the CV definition influences the value of such an index: For sensors located in those body areas where muscle activity is very weak or not present at all, the variability may be overestimated [25]. In order to overcome this limit, other metrics have been introduced, such as the variance ratio (VR) applied in gait analysis [26]. In studying intra-individual variability of sEMG in front crawl swimming, Martens et al. [27] introduced several one- and two-dimension metrics: They included both oneand two-dimension CV, VR and the coe fficient of quartile variation (CQV). Corresponding general definitions are reported in Table 1. In particular, the CV of a quantity is defined as the ratio of its standard deviation to its mean, as given in Table 1. Such an index is largely used in many clinical fields, but it is not commonly applied to sEMG signals. In the present work, CV is adopted to quantify the variability of muscle rhythmic activation during walking in three di fferent populations, namely hemiplegic children, healthy school children and young adult. Motivation for choosing the CV is threefold: (i) We aim for applying and testing this index in the evaluation of sEMG variability during walking in hemiplegic children for the first time at our best knowledge; (ii) we aim for checking the suitability of such an easy-to-compute index in reflecting di fferent characteristics between pathological and control children and then between children and young adults, in order to promote the adoption of sEMG in clinical practice: Despite its simplicity, the index is able to satisfactorily discriminate the muscular recruitment during walking exhibited by di fferent populations [14,28]; (iii) CV is a unit-free measure, suitable to compare normally distributed data by directly quantifying the degree of variability relative to the mean of the distributions [28]. The CV index, indeed, is not directly computed on sEMG samples, but it is derived from the standard deviation of the signal, which is by definition a direct measurement of the signal variability. These characteristics seem to make this index more suitable to the aim of the present study, respect to CQV and VR indices. CQV index, indeed, depends on mean and quartiles, which in turn can be influenced by how they are estimated [28]. VR index, requiring a more articulated

computation algorithm, is more indicated for intra-individual variability, being insensitive to mean sEMG amplitude and data smoothing applied to different waveforms [29]. Neither CQV nor VR indices include the standard deviation in their own definition (Table 1).


**Table 1.** Different indices to quantify intra-individual sEMG signal variability (elaborated from [27]).

(\*) Definition of interval depends on the specific study target (e.g., gait analysis, swimming, walking).

As discussed in [30], sEMG-signal amplitude is typically used as a measure of relative force production and it increases with the number, size and firing rate of active motor units. When collecting sEMG, several aspects may affect the measure of sEMG amplitude and frequency, namely the depth of the active motor units, the thickness of the subcutaneous tissues, proximity to the innervation zone and tendons. As such, electrode placement plays a crucial role in sEMG signal quality. Moreover, it is acknowledged that the thickness of the subcutaneous tissue between the surface electrode and active muscles affect the measurement of electromyographic activity. The amount of excess body fat is considered as an internal noise for EMG because it increases the separation between the active muscle fibers and the detection sites [31]. In this work, sEMG signals have been collected from tibialis anterior (TA) and gastrocnemius lateralis (GL) muscles, based on acknowledged guidelines [32,33] for electrodes positioning to maximize the signal-to-noise-ratio. Moreover, obese subjects have been excluded from the study [34]. So, the potentially limiting factor of a small average sEMG value, associated with CV definition, is avoided.

## **3. Material and Methods**
