Methodological Considerations in the Kinematic and Kinetic Analysis of Human Movement among Healthy Adolescents: A Scoping Review of Nonlinear Measures in Data Processing

Nonlinear measures have increasingly revealed the quality of human movement and its behaviour over time. Further analyses of human movement in real contexts are crucial for understanding its complex dynamics. The main objective was to identify and summarize the nonlinear measures used in data processing during out-of-laboratory assessments of human movement among healthy adolescents. Summarizing the methodological considerations was the secondary objective. The inclusion criteria were as follows: According to the Population, Concept, and Context (PCC) framework, healthy teenagers between 10 and 19 years old that reported kinetic and/or kinematic nonlinear data-processing measurements related to human movement in non-laboratory settings were included. PRISMA-ScR was used to conduct this review. PubMed, Science Direct, the Web of Science, and Google Scholar were searched. Studies published between the inception of the database and March 2022 were included. In total, 10 of the 2572 articles met the criteria. The nonlinear measures identified included entropy (n = 8), fractal analysis (n = 3), recurrence quantification (n = 2), and the Lyapunov exponent (n = 2). In addition to walking (n = 4) and swimming (n = 2), each of the remaining studies focused on different motor tasks. Entropy measures are preferred when studying the complexity of human movement, especially multiscale entropy, with authors also carefully combining different measures, namely entropy and fractal analysis.


Introduction
Human movement can be described as harmonious musculoskeletal synergies conditioned by a continuous interaction of multiple neural networks, making adequate and efficient motor actions possible [1,2]. Complex motor performances are the consequences of variability and flexibility, which are needed to adapt each individual to chaotic, alwayschanging environments [3]. Motor variability is one of the most common characteristics of human movement, and it is related to typical variations in kinetic and kinematic patterns during the repetition of a task [4][5][6]. It is via variability that healthy biological systems are able to adjust properly in an unpredictable and constantly changing environment [7,8].
The scientific literature reports linear and nonlinear approaches for processing the kinetic and kinematic data of human movement [9]. Although they complement each other, it is known that nonlinear models reveal more of the quality of movement and the behaviour of movement over time [3]. On the other hand, linear models, although useful, seem to be insufficient for describing the characteristics of movement in human systems endowed with complexity, non-linearity, and variability [10].

Criteria Population
Healthy teenagers between 10 and 19 years old [16]. Adolescents were also considered eligible regardless of whether they were in an experimental or control group or when the studies were experimental or quasi-experimental.

Concept
Nonlinear measurements in kinetic and/or kinematic data processing of human movement.

Context
Assess human movement out of the laboratory, i.e., non-laboratory settings; free living, daily living, or real-life environments.
Studies were also eligible if they met the following criteria: -Experimental and epidemiological study designs; -Studies published in English, Portuguese, French and Spanish.
Studies were excluded if they had any of the following characteristics: -Systematic, narrative, or scoping reviews to avoid the duplication of data; -Qualitative method designs.

Information Source
The relevant studies were identified by searching the databases-PubMed, the Web of Science, and Science Direct-from their inception until March 2022. Google Scholar was contemplated as unpublished and grey literature. The reference lists of original research articles and reviews on the topic were manually verified to identify other eligible studies. The search strategy for PubMed was as follows: ((nonlinear measures) OR (nonlinear dynamics) OR (entropy) OR (motor variability)) AND ((adolescents) OR (children)) AND ((kinematic) OR (kinetic)). Two reviewers independently carried out the search.

Selection of Evidence Sources
The selection of evidence sources considered the PCC acronym, purpose, and research questions. Data were extracted by two independent reviewers, and any disagreements between them were resolved via discussions or with a third reviewer.
A pilot test was carried out where all reviewers analysed the same 25 publications (the first 25 titles/abstracts of the PubMed database) [19]. Based on eligibility criteria defined a priori, an analysis of the titles/abstracts was carried out independently by the two reviewers. The researchers started the screening process only when there was a consensus of at least 75% [19].
After the search, all identified records were imported to the Mendeley software (Elsevier), and duplicates were removed. The titles and abstracts were screened by the same two reviewers that categorized the studies as "include" or "exclude". This stage allowed identifying articles for full-text screening.

Data Extraction
Data were extracted regarding the authors, year of publication, study design, characteristics of the participants (n, age, % female, and body mass), study setting, the tasks under study, assessment instruments to capture the human body motion, kinetic and kinematic variables, and nonlinear measures. The corresponding author of one of the included articles was contacted by e-mail to request additional data. Two authors independently extracted the abovementioned data by using a draft charting table adapted from the original JBI template. Any disagreements were resolved with a third author.

Data Presentation
A narrative report was produced to summarize the extracted data around the following outcomes: nonlinear measures, instruments, kinematic and kinetic variables, and tasks and contexts. These results were described in relation to the research question and in the context of the overall study purpose. A tabular form complemented this synthesis of the main findings.

Results
A total of 2572 articles were identified-2571 records via a database search, and one additional article was identified via a hand search of the reference lists. After removing 338 duplicates, 2233 records remained. The screening process of the titles and abstracts led to the removal of 2107 articles, leaving 127 for full-text analyses. Of these, 117 were excluded after full-text analyses since they did not fulfil the inclusion criteria, namely the population (n = 47), concept (n = 35), and context (n = 35). Hence, 10 articles were included in this review. The study selection process is provided in the flowchart ( Figure 1).

Data Extraction
Data were extracted regarding the authors, year of publication, study design, characteristics of the participants (n, age, % female, and body mass), study setting, the tasks under study, assessment instruments to capture the human body motion, kinetic and kinematic variables, and nonlinear measures. The corresponding author of one of the included articles was contacted by e-mail to request additional data. Two authors independently extracted the abovementioned data by using a draft charting table adapted from the original JBI template. Any disagreements were resolved with a third author.

Data Presentation
A narrative report was produced to summarize the extracted data around the following outcomes: nonlinear measures, instruments, kinematic and kinetic variables, and tasks and contexts. These results were described in relation to the research question and in the context of the overall study purpose. A tabular form complemented this synthesis of the main findings.

Results
A total of 2572 articles were identified-2571 records via a database search, and one additional article was identified via a hand search of the reference lists. After removing 338 duplicates, 2233 records remained. The screening process of the titles and abstracts led to the removal of 2107 articles, leaving 127 for full-text analyses. Of these, 117 were excluded after full-text analyses since they did not fulfil the inclusion criteria, namely the population (n = 47), concept (n = 35), and context (n = 35). Hence, 10 articles were included in this review. The study selection process is provided in the flowchart ( Figure 1).  In total, 10 studies enrolled a total of 261 adolescents. The characteristics of the participants are listed in Table 2. The mean sample size was 26.1 participants, ranging from 10 to 42. In total, eight of the ten studies enrolled participants of both sexes: one study involved only male participants [21], and one study enrolled only female participants [22] (Table 2).
The recurrence quantification measures were used in two studies [26,30], namely the recurrence rate, determinism, and averaged diagonal line length.
To assess the local dynamic stability, two studies used the Lyapunov exponent; one used the short Lyapunov exponent (sLe) [26], and the other used the largest Lyapunov exponent (LLyE) [21], with both using Rosenstein's algorithm.
Three studies applied fractal analyses. More specifically, the fractal dimension was assessed in one study [29] to complement the analysis with the SEn; the correlation dimension was also used in one paper [30], and a detrended fluctuation analysis (DFA) was used in one study [23] as the temporal structure measurements.
Forces plates [27] and portable handled dynamometers [22] were used to assess the kinetic data. The muscular activity was assessed using electromyography [22]. When considering the kinematic data, it was noted that the measurement tools varied according to the context in which the adolescents were evaluated. In a school context, the studies used the electronic uniaxial goniometer [22] and two [24,25] or three axial wireless inertial sensors [26]. In the studies carried out in training centres, whether in athletics or kayak, the instruments included force-sensitive switches placed on the foot [23], six axial wireless inertial sensors [21], and a 3D motion capture system [30]. The two studies collecting data in a swimming pool used a speedometer [28,29].

Kinetic and Kinematic Variables
In this regard, the use of different instruments to collect human movement data led to the acquisition of different variables (Table 3). Concerning the kinetic variables, one study quantified the centre-of-pressure (COP) time series during quiet standing and provided normalized COP mean velocities in both the anteroposterior (AP) and mediolateral (ML) directions [27]. The maximal quadriceps torque and the magnitude of the muscle activity using the root mean square analysis were the main outcomes assessed in one study [22].

Discussion
This scoping review summarized the body of literature concerned with the biomechanical data of human movement, and the data were processed and analysed using nonlinear measures, such as innovative tools, to characterize different aspects of motor control performances, namely variability, stability, and the complexity of movement.
The gathered information allows a deeper understanding of how research has been conducted in real contexts among adolescents and which tasks, instruments, kinetic and kinematic variables, and nonlinear measures have been used in this field.
There is a lack of uniformity in the nomenclature used to describe the nonlinear measures in the included studies. This fact makes the interpretation and comparison of the data difficult. Considering that the study of the complexity of daily life tasks is a key point in human movement analyses, and it is crucial to adopt intervention strategies centred on nonlinear approaches, given that the human being's movement is nonlinear, this lack of standardization of concepts may hinder the translation of these findings into human movement knowledge. This is a barrier to the implementation of a practice based on recent evidence, which makes us look at human movement as something that is highly complex, nonlinear, and endowed with variability.

Nonlinear Measures and Tasks
Given the complexity of human movement and since its variability translates into functionality, the analysis of a task using a combination of different nonlinear measures is important, as it will provide information about the different characteristics of movement variability [31]. Among the studies included in the review, the synthesis showed entropy as a measure that is mostly reported in kinetic and kinematic data processing (with an emphasis on MSE), followed by fractal analysis.
Entropy is a probabilistic complexity measure used in physiological signal analysis to quantify a time series' irregularity [32]. While Costa et al. [12] identified the ApE as the most important entropy measure to assess kinetics and kinematics parameters in children and adolescents up to the age of 14, our review identified MSE as the most common measure of entropy reported in the included studies. In comparison with previous entropy measures, such as SEn or ApE (both identified alone in this review), MSE stands out due to the fact that it permits the assessment of complexity at shorter and longer time scales relative to the quantification of the overall complexity of a system [33,34]. It is known that ApE and SEn and their variants assess entropy only on a time scale, which seems to be insufficient for conveniently detailing physiological signals [10]. Thus, the choice of MSE in most of the studies included in our review seems to indicate a growing concern in the use of measures that can better reflect the complexity of movement, even in a more non-controlled environment, such as out-of-laboratory assessments [33].
Regardless of the applicability of the MSE, it is important to note that, in the studies included in this review, SEn and ApE were used when the data were collected in an aquatic environment. The ApE was used to quantify the regularity of fluctuations over the time series data [28], although the authors themselves stated that this measure has not been used previously to assess competitive swimming or any other competitive techniques. The SEn was applied to provide insight into the randomness of the intra-cyclic variations over the time series [29]. Preatoni et al. [35] suggested that these measures can be considered particularly appropriate for the study of sports movements, where variability is likely to have both a deterministic and a stochastic origin. Rathleff et al. [22], on the other hand, reported that SEn was used as an indicator of the complexity of the surface electromyography (sEMG) time series during stair walking movements. Based on the above-mentioned studies, it seems that the term complexity acquired synonyms, such as "randomness" or "regularity", in accordance with the research question of the studies. This single-scale entropy analysis can be used to quantify regularity/predictability/probability/randomness; however, they do not capture the structural richness and wide-range component characterization of a complex system operating across multiple spatial and temporal scales [36].
Regarding the use of entropy measures, fractal analysis is another main nonlinear measure to highlight. While the included studies that used fractal analysis focus on different tasks, such as gait, swimming, and long swing, it seems to share common ground with the comparison of the same fractal characteristics. Since it is known that fractal analysis aims to quantify self-similarity and fractal or multifractal-like behaviours [37], this choice seems fully justified by the fact that it exhibits a statistical probability of self-similarity and, therefore, fractal-type behaviour. In two studies, fractal analyses, specifically fractal dimension and correlation dimension, were combined with entropy or RQA measurements, respectively. The fractal dimension was calculated by using Higuchi's algorithm, and it is a suitable measure for time series data analyses, providing information about the intra-cyclical complexity and the irregularity of the variations in a given series [29]. Bartolomeu et al. [29] showed that swimming exhibits nonlinear properties and that the fractal dimension differs depending on the style of swimming and the level of specialization of the athlete. On the other hand, Vicinanza [30] applied the correlation dimension to calculate the fractal dimension of a time series in gymnastics [38]; moreover, while the participants looped the high bar, the findings showed that the dynamical degrees of freedom of the centre-of-mass in the skilled performance were reduced compared to those of novices, representing a more efficient and predictive technique rather than an exploratory one. Therefore, it seems that this measure can contribute to an improved understanding of the level of complexity of a cyclic movement that a subject develops relative to a specific skill in clinical practice.
Concerning the quantification of the local dynamic stability of complex nonlinear systems, the LLyE, which allows quantifying the rate of trajectory convergence or divergence in an n-dimensional state phase, was the measure applied in walking (NW and TW) [26] and performing paddling [21]. Both studies calculated the LyE using the algorithm of Rosenstein [39], which is the most frequently used algorithm in biomechanical studies [40]. Indeed, a review on gait demonstrated that 79% of the studies among young participants used Rosenstein's method to calculate the LyE [41]. Raffalt et al. [42] described that its effectiveness is highly dependent on the applied times series normalization procedure, which did not happen in this study during the walking analysis [26]. Bisi, Tamburini, and Stagni [26], in order to complement the LyE and entropy measures, also applied the RQA to quantify the pattern regularities on NW and TW by using the calculation of the recurrence rate (its simplest measure) [43], determinism (which reflects the predictability/regularity of a time series) [44], and averaged diagonal line length. Assuming that the temporal gait parameters are nonlinear, nonstationary, and noisy by nature, and the RQA does not rely on assumptions, such as nonlinearity, nonstationarity, and noiselessness, and works well on short-length gait time series [45], this nonlinear measure helps us understand the periodicity and randomness of the gait.

Assessment Instruments and Kinematic and Kinetic Variables
Inertial measurement units (IMUs) were the preferred instruments [21,[24][25][26] used to evaluate the kinematic data during walking or paddling. Moreover, foot switches were used during walking [23] or stair descent walking [22]. The motion capture system was used only when the data collection was carried out in a training centre [30]. Currently, it is known that wearable systems allow physiotherapists and other professionals working with movement to assess human movement in a more robust, rigorous, valid, and reliable manner in a real context [46]. The number of IMUs or their placement was not consistent between the studies; however, in the gait analysis, the right leg and upper/lower back were always analysed. It should be noted that none of these articles presented an explanation for the choice of the right leg for the placement of the IMU. However, it is known that as gait is a symmetrical activity, the use of one sensor only allows us to improve mobility and reduces power consumption [47].
A higher variety of kinematic outcomes was observed, and as expected, the most pointed outcomes were related to spatiotemporal parameters. Some authors propose combining these variables with joint kinematics or temporal parameters. Indeed, the sensor-based movement analysis generates a large volume of kinematic data for the sagittal, transverse and frontal planes, and joints simultaneously [48].
Regarding kinetic data, the studies included in this review analysed the COP mean velocity and maximal quadriceps torque using a force plate [27] and portable handheld dynamometers [22], respectively. The force plate is a gold standard in the kinetic analysis of human movement in several functional tasks, and it is a reference in the comparison of measurements obtained with other instruments and, therefore, is frequently used in scientific research [49][50][51]. However, given the characteristics of the force plates, its use was only possible because the data collection took place at the adolescents' school. These data reinforce the difficulty of collecting kinetic data in a real context, and in fact, only two studies focused on the kinetics of human movement [22,27].
Some limitations should be highlighted. First, the search was limited to four databases. Hence, we cannot exclude the possibility of having missed some of the relevant literature. Second, we deliberately defined a board search strategy to minimize the risk of not identifying key papers. However, it may have restricted the initially identified studies. Moreover, there was significant heterogeneity between studies in the nomenclature used to describe nonlinear measures; therefore, our results must be interpreted cautiously.

Conclusions
This review demonstrated that, in adolescents assessed in a real context, entropy measures are the preferred ones when studying the complexity of human movement, especially when examining multiscale entropy. Over the years, authors have shown care in combining different measures, namely entropy measures and fractal analysis.
The non-laboratory contexts identified were schools and training centres (either on the ground or in aquatic environments). The kinematics of human movement has been the subject of more studies compared to kinetics, with a focus on walking.

Future Directions
Despite the interesting studies included in this review, there are significant gaps in knowledge that remain in the literature on adolescent movement analyses that benefit from additional research. Gait is the most-studied task; however, there is a wide range of tasks, complex in itself, that was not studied in a real context. Exploratory studies assessing tasks, such as reaching, sit-to-stand, and stand-to-sit, which could contribute to an improved understanding and monitoring of motor development in adolescence due to their representativeness in daily life, are clearly needed.
Furthermore, although the world of nonlinear measurements is continuously growing, the definition of the objectives of the studies centred on the standardization of concepts can be presented as a suggestion for future investigations. Well-designed studies with standardised concepts, measures, and assessment protocols are needed for a better translation of knowledge into clinical practice. We also suggest research focusing on the kinetics of human movement.