The measurements were performed in a French tertiary care center from May to July 2019. We used 4 Mtw Awinda XSens^® (weight 16 g, dimensions 47 mm × 30 mm × 13 mm, sensitivity ± 2000 deg/s and ± 160 m/s²) (XSens^® Technologies, Enschede, the Netherlands). All signals were acquired at 100 Hz with the Awinda Recording and Docking Station.

Participants were in a 10 m² room. Four sensors were strapped with Velcro on the right and left wrist (the lower limit of the wrist strap was at the radial stylus level), on the forehead (the lower limit of the strap was 2 cm above the eyebrows and on the lower back (lumbosacral level) (Figure 1A). During each recording session, the participant performed 11 arm movements (analytic and functional) that were chosen to reflect shoulder clinical examination (Table 1).

Participants were asked to face a large height-adjustable target on the wall in front of them at eye level during each arm movement to standardize the position of the head among participants. They were instructed to complete each analytic arm movement for about 10 s. To help the participants, the observer counted out loud.

For the first part of the experiment, participants were seated on a fixed stool, arms alongside the body, straight back, feet flat on the floor (Supplementary Appendix Figures SA1A,B). First, they performed bilateral maximal arm elevation (ascending and lowering phase), elbows in extension, in sagittal, scapular and frontal planes, successively, (Supplementary Appendix Figure SA1C). Then, they performed functional movement [simulation of 2 activities of daily living (ADL)]: low back washing (Supplementary Appendix Figure SA1D) and hair combing (Supplementary Appendix Figure SA1E) successively. These 2 ADL have been frequently investigated in studies assessing shoulder motion (Sheikhzadeh et al., 2008; Rundquist et al., 2009). They are frequent movements contributing to autonomy and they involve combined movements at the glenohumeral joint: scapular plane arm elevation and lateral rotation for hair combing, extension and medial rotation for low back washing. For hair combing, the instruction was to raise the hand in front of the face, then pass it above the head and finally to go down to the nape of the neck. For low back washing, the instruction was to touch the lower back (above the sensor) with the back of the hand. The participants were instructed to avoid touching the lower back sensor. Functional movements were performed with both arms alternately, right arm first.

For the second part of the experiment, participants were standing and performed unilateral maximal arm elevation (ascending and lowering phase) in sagittal and scapular plane, successively (Supplementary Appendix Figure SA1F). Participants performed each arm elevation with both arms alternately, right arm first.

For analytic arm movement, no instruction was given about the position of the hand (i.e., the rotation of the humerus).

Before recording, participants practiced the motion at least once. During analytic arm movement, the observer visually checked the plane of the movement by using the projection of a light beam (attached by Velcro on the wrist cuff) on marks on the wall. The observer checked the good quality of each movement performed. If a movement was considered incorrect (incomplete movement, wrong speed, or wrong arm elevation plane), it was repeated. The arm elevations and functional movements assessed in the current study were part of a longer protocol containing 6 other arm movements. The whole protocol lasted about 30 min; the first part, presented in the current study, lasted about 20 min.

To assess the intra-(recording) session repeatability, each arm movement was performed 3 times successively (3 trials) with a rest time of 3 s between each trial. Participants had a rest time of 10 s between each different movement (Figure 2). To assess inter-session reliability, each participant performed the whole experimental procedure (i.e., recording session), 2 with observer A (JBD) and 1 with observer B (DVR) (observers A and B are physiotherapists experienced in shoulder assessment and the use of IMUs). The trial-observer was randomized. The participant had 3–7 days’ rest between each recording session.

The position of the participant (seated or standing) was not considered in the present study.

The Xsens MVN studio software (MVN Studio, Xsens, the Netherlands) was used for data capture. The measurements were performed at 100 Hz and synchronized over the 4 sensors. The following time series were measured by the sensors:

• Sensor free linear accelerations in the sensor frames ( R right , R left , R head and R back ).

Free accelerations are defined as the accelerations measured by the sensor minus the effect of gravity. In the current study, all presented accelerations were free accelerations. The accelerations and angular velocities were measured raw by the sensors, and the orientation was estimated with a Kalman filter (Xsens Kalman Filter, XKF). A subject frame R subject , such that the x axis is orthogonal to the frontal plane and the z axis is vertical, was obtained from the subject’s resting position (Figure 1): the vertical (z) axis is already provided by the Xsens software, and the y axis is obtained from the orientations of the forehead and lower back sensors, from which the vertical component has been removed. After frame transformation, the orientations take the form of a rotation matrix time series that characterizes the orientation of the sensor frames R right , R left , R head and R back with regard to the subject frame R subject . The orientations are displayed in Supplementary Appendix Figure SA2A.

From these inputs, the following 4 quantities were computed:

• Left/right wrist linear acceleration a ^left(t)/a ^right(t): the 3D free linear accelerations in the sensor’s frames. Assuming that the sensor was rigidly attached, this quantity can be assimilated with the acceleration of the body part it was attached to. For a sensor “s” (“left” or “right”), the acceleration consists of the linear accelerations projected on the 3 axes of the sensor frame a x s ( t ) , a y s ( t ) and a z s ( t ) :

The different angles introduced in this paragraph are displayed in Supplementary Appendix Figure SA2B, and all the presented quantities are displayed during a movement as time series in Figure 3. In accordance with previous research, all the resulting time series were pre-processed with a fourth-order Butterworth filter with cutoff frequency of 10 Hz (Zhou et al., 2008).

Because each recorded time series consisted of three successive trials of the same movements, the signals presented in the previous subsection needed to be segmented to isolate the distinct trials. This time series segmentation task was performed with a 4 step pipeline:

• The manual segmentation of all the time series for 20% of the subjects.

The decision random forest was trained with the sklearn.ensemble.RandomForestClassifier algorithm, along with n = 40 estimators. The resulting model achieved 94% accuracy on the training dataset. The Ruptures package gathers a wide panel of multivariate time series segmentation methods along with the possibility to implement personalized loss functions, therefore allowing custom conditions on the resulting segmentation. Figure 4 displays the signals for a scapular arm elevation, the estimated motion probability signal and the resulting segmentation.

The present study required comparing jerk metrics between the ascending phase and lowering phase of an arm elevation, which depends upon a mid-elevation timestep. Our approach for estimating the timestep of mid-elevation was based on a local symmetry criterion of the elevation angles θ _E (t). For each candidate timestep, we computed a local symmetry loss L _sym (t) (3), which quantified how symmetric the signal was on the interval [t − w, t + w] (with w, the window size, set to 100 timesteps). The timestep of mid-elevation was chosen to minimize the symmetry loss. Figure 4 displays the symmetry loss of candidate timesteps as well as the resulting mid-elevation timestep. L sym s t = 1 w ∑ i = 1 w θ E s t − i − θ E s t + i 2 L sym t = L sym right t 2 + L sym left t 2 (3)

Given the trajectory of a point, r ( t ) ∈ R 3 , between the starting timestep t _init and the ending timestep t _end, the jerk quantity is defined as follows (Flash and Hogan, 1985): Jerk Function = ∫ t init t end ‖ ∂ 3 r ∂ t 3 t ‖ 2 d t (4)

The previous expression is introduced as a function of the position, and the sensors provided the local free acceleration (i.e., the second-order derivative of the position as a discrete time series).

Considering the novelty of the comparisons of jerk metrics between different conditions of active analytic and functional arm movements, we were not able to perform a power analysis. Based on previous studies of jerk metrics the sample size of 30 participants appears to be appropriate (Pan et al., 2020; Chen et al., 2021). This sample size is also suitable for a reliability study (Fermanian, 1984).

R was used for the statistical analysis, along with the packages “psych” and “irr.” The variables of interest for each subject were the jerk metrics for each arm elevation trial (right or left arm or both arms together, for ascending or lowering phase or both phases together) and the jerk metrics for each functional movement (right or left arm). Intra-session trial-to-trial repeatability and inter-session intra- and inter-observer reliability were assessed with the intraclass correlation coefficient (ICC) based on the two-way random effects ANOVA for a single measurement [ICC (3,1) for intrasession and ICC (2,1) for intersession] (Shrout and Fleiss, 1979). The repeatibility/reliability was determined with the following criteria: < 0.40 = poor; 0.40–0.59 = fair; 0.60–074 = good; > 0.74 = excellent.

In addition, the precision of the measurements was assessed using the standard error of measurement (SEM) and the 95% minimal detectable change (MDC) (Atkinson and Nevill, 1998; de Vet et al., 2006).

For unbiased comparison tests for the recorded population, only one data point per subject was included in the statistical analysis. The 3 recording sessions performed by each subject and the 3 trials of each movement lead to 9 values for each studied jerk metrics. We considered the median of these values.

We compared the following jerks using the jerk ratios:

• The right jerk against the left jerk during arm elevation for all arm elevations, with r _{(Left)/(Right)}.

Functional movements were excluded from comparisons of jerk metrics between ascending and lowering phases of the movement because we could not determine with accuracy the mid point of the motion (i.e., the moment of the transition between ascending and descending phases). Functional movements were also excluded from comparisons of jerk metrics between the 3 planes of arm elevation because those movements involve several planes of elevation.

The position of the participant (seated or standing) were not taken into account in the present study. The jerk quantities of the Forehead sensor and the Lower back sensor were not computed and not included in the present analysis. The comparisons involved a Wilcoxon mean comparison test (p ≤ 0.05). All presented p-values were corrected with the Bonferroni correction method.

A convenience sample of 30 right-handed asymptomatic volunteers was included between May and July 2019 [17 men (57%), mean (SD) age 31.9 (11.4) years, mean BMI 22.7 (3.1) kg.m²]. The participants belonged to the professional or student circle of the authors and were asked to join the study by personal communication. All subject provided written informed consent. The entire procedure (3 tests) was performed over a mean of 14.5 (6.4) days. Because of an experimental error, one of the measurements was performed at 40 Hz, so only the measurements for 29 of 30 participants were used for the study. The distribution of the participants’ jerk metrics is illustrated in Supplementary Appendix Figures SA3–A5.

For intra-session trial-to-trial repeatability, the ICC ranged from 0.55 to 0.93 for analytic arm elevation and 0.89 to 0.95 for functional movements. For inter-session intra-observer reliability, the ICC ranged from 0.19 to 0.76 for analytic arm elevation and from 0.44 to 0.65 for functional movements. For inter-session inter-observer reliability, the ICC ranged from 0.19 to 0.78 for analytic arm elevation and from 0.64 to 0.89 for functional movements (Table 2). Overall, for inter-session reliability, the smallest ICC (0.19) was for the lowering (eccentric) phase of arm elevation and the highest ICC (0.89) was for hair combing. On the whole, the SEM ranged from 0.07 m s⁻² (MDC = 0.19 m s⁻²) to 1.38 m s⁻² (MDC = 3.83 m s⁻²) (Tables 2, 3). The jerk mean values ranged from 0.56 m s⁻² to 5.61 m s⁻².

The intra-session trial-to-trial repeatability of the jerk metrics was good to excellent for analytic arm movements (except for jerk during the ascending phase of left arm elevation in the sagittal plane) and excellent for functional movements (simulation of ADL: hair combing and low back washing), which shows that the smoothness of successive movements was repeatable. The inter-session reliability was poor to excellent for analytic arm elevation and fair to excellent for functional movements. SEM and MDC remained small nevertheless, they can be considered high regarding the mean jerk values. The repeatability and reliability of functional movements can be linked to the nature of the movements. ADL are by definition goal-directed and everyday movements. Movement repetition improves movement direction and speed and favors control of the trajectory (Mawase et al., 2018). A study that assessed the reliability of jerk metrics for 11 everyday tasks in asymptomatic participants showed excellent inter-session intra-observer reliability for 81% of the tasks (Engdahl and Gates, 2019). Two other studies showed good (Takada et al., 2006) to excellent (Germanotta et al., 2015) inter-session intra-observer reliability of jerk metrics in asymptomatic subjects and in patients with Friedreich’s ataxia, respectively. Nevertheless, the RoM assessed was restricted: chewing jaw movements (Takada et al., 2006), reaching and manipulation tasks (Engdahl and Gates, 2019), and planar reaching movement (Germanotta et al., 2015). Overall, in the current study, intra-observer reliability was not superior to inter-observer reliability. The differences in jerk metrics found between 2 sessions may be explained more by the inherent intra-subject variability than observer-dependent factors. Some of the inter-session variability in jerk metrics could be explained by variations in physiologic tremor. This action tremor present in every healthy subject has a frequency of 8–12 Hz in young adults and varies with physiologic states such as muscular fatigue or emotional state (McAuley and Marsden, 2000). We could not exclude that the physiologic state of the participants varied between the 2 sessions.

The results of the current study favor the use of jerk metrics for clinical examination and research of arm movements provided that movements are usual and factors of intra-subject variability are controlled.

The current study showed that arm movements performed with the right dominant arm were smoother than with the left arm during all arm movements: bilateral, unilateral analytic, and functional. This result agrees with our first hypothesis.

Handedness defined as side preference and efficiency depends on practice and experience, which improve motor learning (Serrien et al., 2006; Nielsen and Cohen, 2008; Mawase et al., 2018). Long-term preferential use may result in changes in muscle fiber composition and activity (Diederichsen et al., 2007). Preferential use improves both quantitative (muscle strength and endurance) and qualitative (coordination and level of coactivation of muscles, coordination of muscles and joints etc.) muscle parameters (Demura et al., 2010). Nevertheless, several studies of differences in muscle activity between the arms had controversial results (Adam et al., 1998; Diederichsen et al., 2007). Greater muscular strength resulting from preferential use of the dominant arm (Crosby and Wehbé, 1994; Incel et al., 2002) could ease the motor control and the smoothness of the movement.

Jerk metrics well describe differences between dominant and non-dominant sides. In case of unilateral shoulder pathology (the most common case), comparing both arms using jerk metrics can help to better define the objective of treatment.

Our results showed increased jerk metrics for arm lowering versus arm ascending during bilateral and unilateral arm elevation in all planes of movement, which indicates that the eccentric phase of the movement is less smooth than the concentric phase. This result is consistent with our second hypothesis.

Eccentric contractions are associated with a slowing down effect, supported by the recruitment of viscoelastic structures and the residual lasting force from the stretching of the active muscle or fibers (Hessel et al., 2017). Such contractions involve decreased recruitment of motor units and discharge rate, whereas the slowing down requires fine motor control (Enoka, 1996; Fang et al., 2001; Ebaugh and Spinelli, 2010; Duchateau and Baudry, 2014). The lower electromyography activity during eccentric contractions may induce less control of the variation of velocity that could explain the increased jerk metrics (Hoppeler, 2016; Hody et al., 2019).

Jerk metrics differ according to the mode of muscle contraction. Most of shoulder musculoskeletal pathologies (i.e., gleno-humeral osteoarthritis, rotator cuff disease) involve shoulder muscles weakness that makes the lowering phase easier to perform than the ascending one (Hody et al., 2019). Measuring the jerk metrics for both phases can help to monitor progress in patients.

According to our hypothesis, elevation was smoother in the sagittal and scapular planes than the frontal plane (for both unilateral and bilateral elevation). Several studies found higher humero-thoracic and scapulo-thoracic muscle activity during arm elevation in the frontal plane than the scapular and sagittal planes, which showed the lowest muscle activity (Castillo-Lozano et al., 2014; Ishigaki et al., 2015). In the frontal plane, owing to the convexity of the thorax, the rotation and linear displacement of the scapula cannot ensure optimal bony and muscular alignment (Johnston, 1937; Ludewig et al., 2009).

In opposition to our hypothesis, arm elevation was smoother in the sagittal than scapular plane during bilateral and left unilateral arm elevation. In the scapular plane, muscle rotational forces are balanced to keep the axis of the humerus and scapula aligned (Johnston, 1937; Kapandji, 1980; Ludewig et al., 2009). The increase in saccades for arm movements in the scapular versus sagittal plane may be related to fine muscle performance to keep the humeral head centered and remaining in the same plane during arm elevation (Suprak et al., 2006; Diederichsen et al., 2007). Visual feedback may play a role in the smoothness of movement. Movements in the sagittal plane are most visible to participants when they are asked to look straight ahead, and visual feedback during arm movements is known to be an important source of information for guiding movements (Sarlegna et al., 2004). Jerk metrics were not significantly lower in the sagittal than scapular plane during right arm elevation. This result may be related to both hand dominance and habits (the scapular plane is used for many unilateral daily activities, including hair combing) (Sheikhzadeh et al., 2008).

Jerk metrics differ according to the plane of arm elevation. We found that the sagittal plane was the most favorable to motor control, so it should be preferred to the scapular plane to begin rehabilitation of arm elevation. Nevertheless, the preferential plane of arm movement could vary according to the musculoskeletal or neuro-muscular disorder (Ludewig et al., 2009; Roren et al., 2012, 2013).

To our knowledge, this is the first study to quantify and compare jerk metrics during different conditions of a selection of arm movements (maximal active arm elevation and functional movements) based on conventional clinical examination of the shoulder. These movements explore the greatest shoulder RoM; nevertheless, the assessment of jerk metrics for analytic glenohumeral axial rotations is lacking and we have no information about the other joints of the upper limb that contribute to the arm movements. The data pipeline used in this paper (including segmentation) is fully automated, mathematically based and empirically stable but remains to be validated with a larger database. We assessed the intra-session repeatability and inter-session reliability of jerk metrics. Our measures remain to be validated by comparing them to standard optoelectronic measurements. The limited sample size, the homogeneity of the population (right-handed, health professionals or students, asymptomatic and relatively young) and the lack of randomization of the successive movements limit the representativeness of our results. The movements were not performed freely, their duration was imposed and the functional movements were constrained for the sake of standardization. This pilot study brings new information that need to be completed by larger studies including participants with musculoskeletal disorders.