Concurrent synchronization and covariation in upper extremity joint angles during a reciprocal aiming task

Concurrent synchronization and covariation in upper extremity joint angles during a reciprocal aiming task | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Concurrent synchronization and covariation in upper extremity joint angles during a reciprocal aiming task Marijn S.J. Hafkamp, Tim A. Valk, Raoul M. Bongers This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9455901/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 15 You are reading this latest preprint version Abstract The ecological-dynamical approach holds that movement is self-organized, implying a circular causality between the kinematics of the end-effector and the coordination of degrees of freedom (DOF) into synergies. Yet, how this circular causality manifests itself in redundant effector systems remains underexplored. Therefore, we investigated concurrently the coordination dynamics of the end-effector and the upper extremity joint angles –as DOF–during a reciprocal aiming task with varying target widths and distances. Results revealed that different joint angles were differently related to the end-effector. A continuous relative phase analysis showed that the three joint angles with the largest range of motion synchronized with the end-effector, suggesting a strong dynamical coupling between the levels. At the same time, all joint angles exhibited variability that was not shared with the end-effector. A detrended fluctuation analyses revealed signatures of fractality as well as drift in this residual variability, suggesting distinct dynamical regimes at the DOF level. Moreover, the angular drift occurred predominantly along the uncontrolled manifold, leaving the end-effector unaffected. We conclude that the DOF of a redundant system are not only coordinated into synergies to stabilize the end-effector, but also to keep the system flexible. Biological sciences/Neuroscience Physical sciences/Physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction In human movement, the many available degrees of freedom (DOF, e.g., muscles, joint angles) of the movement apparatus are typically organized into stable coordinative structures [ 1 – 3 ]. Within the ecological-dynamical approach, these structures are known as synergies : temporary assemblies of DOF that are constrained to act as functional units [ 4 – 7 ]. Such synergies are understood to be self-organizing, meaning that the kinematic outcome of the movement and the underlying coordination of the DOF –respectively the macro- and microscopic level of organization– are linked through circular causality. When aiming to a target, for instance, there is reciprocity between the kinematics of the end-effector and the coordination of the joint angles in the upper extremity [ 8 ]. The end-effector trajectory emerges from the coordination of the joint angles, while the joint angle coordination is simultaneously constrained by the trajectory of the end-effector. Yet, how this circular causality manifests itself in such redundant effector systems –which have more DOF than necessary to perform the task– remains underexplored [ 9 , 10 ]. The present study therefore investigated concurrently the coordination dynamics of the upper extremity joint angles and the end-effector during a reciprocal aiming task [ 11 , 12 ], to capture the circular causality that characterizes self-organization in movement systems. A seminal account of self-organization in movement is provided by the Haken–Kelso–Bunz (HKB) model of rhythmic interlimb coordination [ 13 ]. In this model, two rhythmically moving limbs are treated as a pair of self-sustaining oscillators with a non-linear coupling function. Their coordination can be captured macroscopically by a potential function with only two attractor states: in-phase (0°) and anti-phase (180°). At low movement frequencies, both attractors are stable and relative phase variability is minimal. As the movement frequency increases, however, the anti-phase attractor loses stability, leading the system to switch to the more stable in-phase coordination [ 14 , 15 ]. Thus, the state of the attractor depends on the rhythmic frequency of the oscillators, while the oscillators’ rhythmicity is constrained by the attractor state. This reciprocity illustrates the model’s circular causality between the macro- and microscopic level of organization. Soon after its introduction, the coupled-oscillator model became a general operational paradigm for studying self-organization in movement [ 16 – 18 ]. By integrating system modeling with empirical work, the paradigm uncovered some of the core principles of coordination dynamics. Notably, it demonstrated that the stability of a macroscopic attractor depends not only on the two oscillator’s frequencies, but also on the symmetry between the rhythmic components. When the oscillators differ in their eigenfrequency, the faster oscillator takes the lead and the stability of their (anti-phase) coordination declines immediately [ 19 , 20 ]. Similarly, when two oscillators are coupled asymmetrically, their synchrony is disrupted and their coordinative stability decreases as well [ 21 ]. The fundamental insight gained from these models is that coordinative stability on a macroscopic level hinges upon the capacity of system components on a microscopic level (i.e., DOF) to establish stable phase relationships. Consequently, synergy came to be associated with the sychronization of DOF [ 7 , 9 , 17 ], here defined as an in-phase/anti-phase coupling. However, for tasks in which an end-effector needs to be positioned in space, synchronization is not the only route to coordinative stability. Because the movement system is inherently redundant (or abundant [ 22 ]) for most tasks, multiple configurations of the system’s DOF can produce the same outcome at the macroscopic level. Therefore, stability at this level can also emerge from mutual compensations (i.e., covariation) between the system’s DOF [ 3 , 22 , 23 ]. For instance, the same hand movement can be brought about by extending the elbow while keeping the shoulder fixed, or by rotating the shoulder while holding the elbow steady. In goal-directed movement, this covariation in joint angles ensures that the target can be reached in multiple ways using different patterns of coordination, which is fundamental to the system’s flexibility. The idea of motor abundance has been linked to the concept of the uncontrolled manifold [ 23 , 24 ]: a subset of DOF configurations that yield the same movement outcome, such as all joint angle combinations that keep the effector on a target. In line with this idea, synergy has been re-interpreted [ 3 ] as a grouping of DOF that covaries within an uncontrolled manifold, as a way to stabilize a movement while preserving its flexibility. In the ecological-dynamical approach, the two models of synergy –HKB and UCM– are often used interchangeably [ 10 ]. Synchronization and covariation have even been described as complementary features of one and the same synergy concept, each contributing to coordinative stability in their own way [ 5 ]. For goal-directed movement, however, the models yield different predictions about the system’s coordination dynamics. Coupled oscillator models, on the one hand, suggest that the DOF of a redundant system must be synchronized for the end-effector trajectory to be stable. Studies on the coordination dynamics of reciprocal aiming have shown that the end-effector can behave as a self-sustaining oscillator, suggesting a limit cycle attractor at the macroscopic level [ 12 , 25 ]. To preserve the stability of this attractor, its dynamics must somehow be reflected in the back-and-forth movement of the joint angles at the microscopic level, implying synchronicity as a basis for their coordination. The UCM model, on the other hand, suggests a weaker synchronization between the macro- and microscopic level of system organization. Studies of discrete [ 26 , 27 ] and reciprocal [ 8 ] aiming have shown that the joint angles of the upper extremity covary to stabilize the trajectory of the end-effector. This suggests that the angles are free to deviate from the end-effector dynamics, because they can (co)vary along an uncontrolled manifold. At the same time, there must be some synchronization between the levels, for the joint angles ultimately drive the end-effector motion. Using a cross-recurrent quantification analysis (CRQA), Valk and colleagues [ 8 ] explored this ambiguity. CRQA is a non-linear analysis that quantifies how patterns of motion in one time series (e.g., in the end-effector) recur in another time series (e.g. in a joint angle) at different temporal offsets, without specifying the dynamics of either signal. They found that only three out of the nine upper extremity joint angles –the shoulder plane of elevation (SPE), the shoulder exo-endorotation (SEE) and the elbow flexion-extension (EFE)– had a strong dynamical coupling to the end-effector, while six other angles –the shoulder elevation (SEL), elbow pronation-supination (EPS), wrist-flexion extension (WFE), wrist abduction-adduction (WAA), finger flexion-extension (FFE) and the finger abduction-adduction (FAA)– were only weakly coupled. This suggests that not all joint angles synchronise similarly with the end-effector and that some angles display dynamical regimes that are not observed at the end-effector level. Yet, neither a CRQA nor a UCM captures a system’s dynamics, leaving unresolved how circular causality manifests itself in redundant systems. Therefore, the current study examined the coordination dynamics of the upper extremity joint angles and the end-effector during a reciprocal aiming paradigm [ 11 , 12 ]. In this task, participants made back-and-forth aiming movements between two targets, while target distance and target width were both manipulated. First, we investigated the degree of synchronization between the joint angles and the end-effector. Following up on the work of Valk et al. [ 8 ], we conducted a relative phase analysis and hypothesized that only the three ‘coupled’ joint angles – the SPE, SEE and EFE – would be locked into in-phase or anti-phase relationships with the end-effector. Second, we investigated the deviations from synchrony in the joint angles movements, the so-called ‘residual variability’. Since we had no a priori hypotheses regarding the dynamical regimes at the joint angle level, we conducted our analyses in an exploratory fashion, focusing on the temporal evolution of the considered DOF. Results Originally, this study was designed to compare aiming conditions of varying target distance (5, 10, 20 and 30 cm) and target width (index of difficulty 3.5 - 6.0 with increments of 0.5). Our aim here, however, was to compare the coordination dynamics of the joint angles with the end-effector. Accordingly, our analyses focused on within trial effects. For comparisons between aiming trial conditions, we refer the reader to Valk et al. [8]. Synchronicity between joint angles and end-effector Phase plane portraits In Figure 1 we reconstructed the normalized phase plane portraits of the end-effector ( 1A ) and the joint angles ( 1B ) of the upper extremity for a representative participant in an exemplary condition (index of difficulty 5.0, distance 20 cm). As illustrated in these portraits, three of the nine joint angles (SPE, SEE and EFE, in red) displayed limit-cycle dynamics that was comparable to that of the end-effector (established by continuous relative phase analysis, see below). The six remaining joint angles (SEL, EPS, WFE, WAA, FFE, FAA, in blue) were much more variable in their dynamics, some of them exhibiting no apparent structure. Figure 1 Continuous relative phase analysis To examine the synchronization between the joint angles and the end-effector, we computed the continuous relative phase (CRP) [28] with tightened normalization procedures [29] between the corresponding time series. In Figure 2 we showed the distribution of the CRP for each joint angle, for the same participant and trial condition as in Fig. 1 . The polar histograms reveal that the CRP fluctuated around 0° or 180° for most angles, most notably for the SPE, SEE and EFE angles. This suggests high degrees of synchronization with the end-effector. At the same time, the CRP fluctuated strongly for angles such as the wrist abduction-adduction (WAA, between 0° or 180°) and the finger abduction-adduction (FAA, between 90° and 270°). This suggested lower degrees of synchronization. Figure 2 To assess the degree of synchronization for each joint angle, we computed the phase locking value (PLV) for all CRP time series across participants and conditions. The PLV was defined such that in-phase and anti-phase synchronization would both correspond to a coefficient of 1, while a random distribution of CRP values (i.e., no synchronization) corresponded to a coefficient of 0. As shown in Figure 3 , the PLV of the SPE, SEE and EFE (in red) was close to 1 in all conditions, indicating a very high degree of synchronization. In the other six angles (in blue), the PLV was substantially lower, ranging from 0.5 to 1.0. This demonstrated a weak synchronization between these joint angles and the end-effector, pointing at deviations from the macroscopic dynamics. Following analyses further investigated these deviations. Figure 3 Deviations from synchronicity Residual variability in the joint angles To further assess the deviations of joint angles from macroscopic dynamics, we separated the variability in the joint angles that deviated from the end-effector dynamics from that which was shared with the end-effector. To do this, we conducted a first order regression analysis on the normalized angular time series of each joint angle, with the normalized end-effector trajectory as a predictor. This resulted in residual variability time series per trial, which we illustrated in Figure 4 for the same participant and condition as presented in Fig. 1 and 2 . As can be observed, the residual variability was small for the joint angles that strongly synchronized with the end-effector (SPE, SEE and EFE, residual variability depicted in red), but much larger for the other joint angles (in blue). In the latter case, it displayed (1) distinct spatiotemporal structures and (2) a strong extent of relative drift in the joint angle over time. The next two sections systematically study both phenomena. Figure 4 Detrended fluctuation analysis To examine the spatiotemporal structure of the residual joint angle variability, we conducted a detrended fluctuation analysis (DFA) on all residual time series. DFA quantifies long range correlations in a time series by measuring how fluctuations scale across timescales, potentially signifying a fractal structure in the variability. This means it assesses whether patterns of variability repeat themselves across timescales. The output of DFA is a scaling exponent a, ranging roughly from 0 to 2. An a of 0.5 generally indicates randomness in the time series (white noise), whereas an a of 1.0 points at fractality (pink noise). A residual time series that expresses pink noise signifies that smaller, shorter fluctuations are embedded in larger, longer fluctuations. An a of 1.5 indicates non-stationarity or drift in the time series, also called Brownian noise. As shown in Figure 5 , the DFA on the residual joint angle variability resulted in a-values between 1.0 and 1.5 in all angles, across all conditions. This indicated that the residual variability was not random, but structured. More particularly, it exhibited a mixture of fractality and drift, as already anticipated in Fig. 4 . The indication of fractality was the strongest in the elbow flexion extension angle, while the suggestion of drift was the clearest for the wrist flexion extension angle. Figure 5 Drift analysis To obtain a linear approximation of the drift, we fitted a first-order regression to the normalized angular time series, with time as a predictor and slope as our measure of drift. Fig. 4 already showed these slope lines in the illustrated time series, demonstrating that the range and directionality of the drift (i.e., positive or negative drift) varied across the joint angles. In Figure 6 we presented the distribution of the drift slopes across participants for all joint angles in all aiming conditions. As can be appreciated from this graph, all angles exhibited drift, even though the drift was larger for the non-synchronous angles (in blue). However, as shown in Table 1 , the average range of motion (ROM) of these joint angles was also substantially lower than the ROM of the synchronous joint angles (in red). This means that the contribution of the non-synchronous joint angles to the upper extremity movement was smaller and the freedom to ‘wander off from their trajectory’ without destabilizing the end-effector , larger. Figure 6 Table 1: The mean (standard deviation) range of motion of the joint angles in degrees, averaged per target size condition across all participants and all ID conditions. Dist. SPE SEE EFE SEL EPS WFE WAA FFE FAA 5 cm 9.1 (3.6) 10.8 (4.3) 10.0 (3.2) 4.7 (1.9) 6.0 (3.0) 5.8 (3.4) 3.6 (2.0) 2.1 (1.5) 3.2 (1.8) 10 cm 17.3 (5.1) 20.2 (6.0) 20.3 (4.3) 8.2 (3.2) 9.4 (3.8) 8.0 (4.3) 4.5 (1.8) 2.7 (2.2) 3.9 (2.2) 20 cm 32.7 (8.1) 37.8 (10.0) 40.0 (5.8) 13.0 (3.9) 15.0 (6.3) 11.7 (6.3) 5.9 (2.3) 3.5 (2.8) 4.8 (2.3) 30 cm 44.5 (10.2) 53.2 (13.4) 56.8 (7.7) 16.5 (4.2) 20.6 (8.7) 16.1 (8.6) 7.7 (3.0) 4.4 (3.8) 5.8 (2.8) Projection length analysis That joint angles exhibited drift while the end-effector dynamics remained stationary suggests that the drift occurred within the uncontrolled manifold [23] – the subspace in joint angle space that encompasses all joint angle configurations that stabilize the end-effector on a certain position. To investigate whether this was indeed the case, we projected the joint angle configurations of different cycles within a condition on the uncontrolled manifold as well as on the range space. The range space is a subspace orthogonal to the manifold, including all joint angle configurations that lead to deviations of the end-effector from a certain position. We computed the projections for four instants of the cycle of motion: at the two moments of reversal at the physical target (indicated as 0 and 180 degrees of the cycle) and two moments mid-half-cycle (indicated as 90 and 270 degrees of the cycle). Using the joint angle configuration of the first cycle as reference, projection lengths for all four cycle moments increased when joint angle configurations were projected on the uncontrolled manifold, but not when projected onto the range space ( Figure 7 ). This indicated that the drift observed in the joint angles was gradual and could be collectively described as drift along a subset of configurations that stabilizes end-effector behavior. Discussion In this contribution we examined how circular causality, a key feature of self-organization, manifests itself in a redundant movement system. We investigated the coordination dynamics of upper extremity joint angles –as microscopy– and the end-effector –as macroscopy– during a reciprocal aiming paradigm. Our results revealed that the dynamical relationship between joint angles and end-effector was not the same for all joint angles. Those joint angles with the largest range of motion synchronized with the end-effector, suggesting that dynamical coupling between macro- and microscopy is an important component of circular causality. At the same time, the joint angles exhibited variability that was not shared with the end-effector. We found indications of fractality and drift at the joint angle level, neither of which affected the stability of the end-effector dynamics. This seems to indicate that the joint angles were not only coordinated to stabilize the end-effector, but also to keep the movement system flexible. In what follows, we will first discuss these results in more detail, before interpreting them in light of the ecological-dynamical concept of synergy. In an earlier contribution exploiting the current data, Valk and colleagues [8] used a cross-recurrent quantification analysis to show that the shoulder plane of elevation angle, the shoulder exo-endorotation angle, the elbow flexion-extension angle and the end-effector were strongly coupled to one another. Here, we followed up on this finding with a continuous relative phase analysis, which demonstrated that this coupling comprised stable in-phase or anti-phase relationships. This indicated a high degree of synchronization between the macro- and microscopic level of organization, at least for some of the angles. Rather than preceding or following the end-effector, a subset of the joint angles moved simultaneously with the tip of the finger, effectively driving its macroscopic limit-cycle dynamics [12,25]. The other six joint angles, in particular those of the finger and wrist, were much more variable in their phase progression. Note that this CRP variability persisted even when we controlled for drift and for variations in the amplitude. Using the tightened normalization procedures of de Poel et al. [29], we detrended and normalized each half cycle, but the phase locking values of the wrist and finger angles remained low. This demonstrated substantial ‘residual’ variability in the angular time series, the structure of which we examined using a detrended fluctuation analysis (DFA). Although all joint angles exhibited residual variability, the non-synchronous joint angles exhibited more fluctuations that were not shared with the end-effector than the synchronous angles, as expected. The DFA on the residual variability revealed two intriguing properties. In the first place, it showed indications of fractality, meaning that smaller, shorter fluctuations were embedded in larger, longer fluctuations. This finding is interesting, because it suggests a dynamical patterns on top of the macroscopic dynamics. It shows that the variations in the joint angle motion on a faster timescale than the back-and-forth movement were not random, but (at least partially) deterministic. In fact, they were correlated with one another on a timescale that was longer than that of the main cycle of motion. In motor control literature, such long range correlations have been linked to properties of flexibility and adaptability [29,34]. They were first found in locomotion patterns [35,36], but have also been demonstrated in other rhythmic movements such as rowing [37,38] and manual tapping [39,40]. The embedding of fluctuations of different time scales prevents a rhythm from becoming rigid, in the sense that every cycle of motion is the same. At the same time, fractality channels variability, since fluctuations are not random but correlated. As such, it is a “compromise between order and disorder”, keeping the movement system adaptive, without degenerating into randomness or inflexibility [31,34]. Secondly, the DFA revealed indications of Brownian noise, suggesting drift in the joint angle time series. Follow up analyses showed that most of the drift occurred within the uncontrolled manifold, implying covariation (see Valk et al. [8] for a broader discussion of the UCM). Combined with the finding that the drift was the largest in the joint angles with the smallest range of motion, this suggests that the angles only drifted if they had the freedom to do so without damaging the end-effector motion. That the joint angles used this freedom is intriguing. As to its functional role, we can only speculate. Possibly, participants fatigued over the course of a trial, causing them to slowly lower their elbow during the trial. Further examination of the upper extremity postures, however, did not reveal such a systematic lowering of the elbow joint over cycles of motion. Alternatively, participants may have drifted towards a posture that was most comfortable for producing the aiming movement, or they may have explored different ways to perform the task to warrant adaptability. Although the effect was subtle and the preferred posture probably unique for every individual, the tendency to drift along the UCM was significant for most participants. It shows that a singular focus on neither a relative phase nor a pattern of covariation is sufficient to capture the richness of coordination in redundant systems. Equally important is showing how participants move along the manifold, either gradually or in discrete steps [41]. What do these findings tell us about synergy, a concept that is as old as the discipline of movement science itself [1-3,7,9]? Within the ecological–dynamical approach, synergy is understood as an emergent structure of coordination with circular causality between its levels of organization [4,6]. Using the example of reciprocal aiming, we showed that this circular causality exhibits at least two critical features when applied to a redundant movement system. To begin with, the DOF are coordinated to stabilize the kinematic outcome on the movement. Notably, this stabilization involves synchronization as well as covariation. Synchronization ‘drives’ the end-effector trajectory and occurs between the joint angles with the largest range of motion. Covariation ‘preserves’ the end-effector trajectory and ensures that it maintains its dynamics between the targets. This interpretation aligns roughly with the understanding of synergy as promoted by Riley et al. [5]. In this view, synchronization serves to reduce the system’s dimensionality, so that a macroscopic organization emerges from the many DOF in the movement apparatus. And covariation preserves the integrity of that organization, so that it is robust against minor perturbations. This way, synchronization and covariation are actually two sides of the same coin – both bringing stability to movement. In redundant systems, however, stability is not the only feature of circular causality. The DOF are also coordinated to preserve the system’s flexibility . Even during stable rhythmic movement, the system component’s trajectories vary from cycle to cycle, creating distinct dynamical regimes at the microscopic level of organization. In the case of reciprocal aiming, the variability in the joint angles exhibited fractality as well as non-stationarity. Small fluctuations in the angular movement (at a timescale faster than reciprocal cycle of motion) were embedded in larger fluctuations, and some of the joint angles slowly wandered off in space without affecting the stability of the end-effector dynamics. This variability keeps the system adaptive, such that it can respond adequately to changes in the circumstances. But it also allows the system to transform to a more comfortable or effective configuration, like an upper extremity posture that is optimal for sustaining the back-and-forth movement. Flexibility has been attributed to synergy before, most distinctly within the uncontrolled manifold approach [3]. But how this flexibility is reflected in the stable coordination dynamics of a redundant effector system has remained obscured. The UCM method has been designed to study the static stabilization of a performance variable and is thus ill-posed to reveal dynamical properties of flexibility in movement (see also Grover et al. [42]). Our results suggest that flexibility manifests itself in fractality and unboundedness of the degrees of freedom, and thus in the temporal structure of their variability. Variations in movement from repetition to repetition are not random, but deterministic. Rather than being noise around an attractor, they prepare the system to adapt to changing circumstances or help the system move toward other configurations. As such, variability is intrinsic to the coordination, even during stable episodes of movement. This is, at its core, what self-organization in redundant movement systems implies. The emergence of a coordinative structure –a synergy– that is stable and ready to withstand perturbations, but also variable and ready to adapt to the environment. Methods Ethics statement The experimental protocol was carried out in accordance with the Declaration of Helsinki and approved by the local ethics committee of the Department of Human Movement Sciences at the University Medical Center Groningen. Before the start of the experiment, we informed participants about the goal of the study, after which all participants signed informed consent. Participants In total, we recruited twenty right-handed participants. Two participants were excluded because of failed data acquisition during the measurements. The remaining eighteen participants had an age of 20.8 ± 1.9 years (M ± SD). They had no neurological conditions or other health issues and they all had normal or corrected-to-normal sight. Experimental task Participants made reciprocal aiming movements (i.e., back-and-forth in an anterior-posterior direction in front of them) between two targets, according to a continuous Fitts’ paradigm [11,12] ( Figure 8 ). We manipulated both target distance and index of difficulty (ID; a logarithmic function of target distance and target width), by varying the target width relative to the target distance. In total, the experiment comprised 24 unique conditions (trials), combining 4 target sizes (5, 10, 20 and 30 cm) with 6 ID’s (3.5; 4.0; 4.5; 5.0; 5.5; 6.0). These conditions were presented to participants in a randomized order. In each trial, the targets were presented on a laminated sheet of paper (A3 size, portrait orientation) that was attached to the table in front of the participants. To avoid drifting of the end-effector in the frontal plane, all targets had a width of 1 cm in this plane. Participants made the pointing movements with a stylus that was attached to their index finger, leaving no trace to the paper. The stylus was attached such that it prohibited movement in the interphalangeal joints while allowing free movement of the metacarpophalangeal joint. Figure 8. Experimental procedure In each trial, participants made forty reciprocal movements (cycles) between the targets. Participants always started a trial with the tip of the stylus in the middle of the target that was closest to them. They were instructed to take the same starting posture across conditions – an instruction that was repeated before the start of every new trial. To check whether participants followed the instruction, we compared the standard deviation of the starting joint angle configurations across IDs within a target distance with the standard deviation of starting joint angle configurations recorded in previous studies in which a similar starting posture was ensured by means of an elbow placer [43,44]. This comparison showed that participants followed the instruction. During the trial, participants had to move the tip of the stylus as fast and accurate as possible. Experimenters observed whether this instruction was followed and motivated participants to move as fast as possible while adhering to accuracy demands. Participants were instructed to keep the tip of the stylus at the sheet of paper at all times. Data acquisition To capture the participants’ movements in three dimensions, we attached five rigid bodies to the right side of the body and one to the sternum. Each rigid body was triangular in shape and contained three light-emitting diodes. One rigid body, with a length of 4 cm, was attached to the stylus; four others were attached to segments of the participant’s right arm and shoulder. Two rigid bodies, with a length of 6 cm, were attached to the sternum and the upper arm just below the insertion of the deltoid; three others, with a length of 4 cm, were attached to the dorsal side of the hand, the dorsal side of the upper arm just proximal of the ulnar and radial styloids, and the flat part of the acromion. We captured the movements of the LEDs using two Optotrak 3020 units (Waterloo, Ontario, Canada) that were synchronized and sampled at 100 Hz. Using a pointer device, we digitized eighteen bony landmarks and the tip of the stylus to relate the LED motion to the movement of the participant’s arm. To prohibit movement of the trunk while allowing free movement of the shoulder joint, we gently strapped participants against the extended back of the chair using an elastic bandage. We determined the end-effector trajectory from the motion of the three Optotrak LEDs attached to the stylus, using rigid body transformations. For further analyses, we exclusively used the forward-backward movement of the end-effector in the transversal plane. The trajectories of the nine joint angles we computed using the motion of the relevant Optotrak LEDs and the segment orientations derived from the digitized bony landmarks. Following ISB guidelines [45], we acquired the following joint angles: the shoulder plane of elevation (SPE), shoulder elevation (SEL), shoulder exorotation-endorotation (SEE), elbow flexion-extension (EFE), elbow pronation-supination (EPS), wrist flexion-extension (WFE), wrist abduction-adduction (WAA), finger flexion-extension (FFE), and the finger abduction-adduction (FAA). Data analysis The time series of the end-effector and the nine joint angles were filtered using a 4th order low-pass Butterworth filter with a cut off frequency of 5 Hz. To reconstruct the coordination dynamics at both levels, we created phase plane portraits of the end-effector and all joint angles. We normalized the (angular) position and (angular) velocity time series to their mean and standard deviation and plotted the latter against the former in to create phase planes. Continuous relative phase analysis To examine the synchronization between the joint angles and the end-effector, we computed the continuous relative phase between the corresponding time series. We cut all time series into half cycles, demarcated by the reversal points of the end-effector signal. Following the procedure of de Poel et al. [29], we then centered, detrended and normalized each half cycle relative to the standard deviation of that cycle, so as to avoid distortion of drift or amplitude. Subsequently, we transformed the half cycles of the end-effector and the joint angles to analytic signals using the Hilbert transform and used that to compute the phase angles in degrees [28]. After concatenating all half cycles, the continuous relative phase was then acquired by subtracting the phase angle of the joint angle from the end-effector. For interpretation, we plotted the CRP distributions per joint angle in polar histograms. Moreover, we computed the phase locking value per CRP time series to quantify the degree of synchronization. To define both in-phase and anti-phase as synchronization, we first doubled the CRP values, after which we took the complex phase vectors to represent each CRP value on the unit cycle. We then averaged all complex vectors on the unit cycle to compute the PLV. A PLV of 1 indicated maximum synchronization (in-phase/anti-phase), while a PLV of 0 indicated a random distribution of CRP values. Detrended fluctuation analysis To investigate the variability that deviated from the end-effector, we conducted a first order regression analysis on the normalized time series of the joint angles, with the normalized end-effector time series as a predictor. This resulted in a component of shared variability and a component of residual variability. We then analyzed the residual variability using a detrended fluctuation analysis (DFA), following standard procudures for periodic movement data [e.g. 37,38]. DFA quantifies long range correlations in a time series by measuring how fluctuations scale across timescales. As a first step, we integrated the residual variability time series. Subsequently, we divided it into windows of increasing length, from n=10 to n = N/4 with 20 scales in total. We then detrended each window and calculated its root mean square (RMS). As a last step, we derived a scaling exponent a from the slope of the log–log relationship between the RMS and the window size. The scaling exponent may range from 0 to 2. An α-value of 0.5 indicates the absence of correlations (white noise), α > 0.5 indicates that large values are more likely to be followed by large values, and α < 0.5 indicates that large values are more likely to be followed by small values and vice versa. Then, α-values of 1.0 and 1.5 correspond to pink noise and Brownian noise, respectively. Drift analysis To assess the drift in the time series of the joint angles, we first normalized the angular time series to z-scores by dividing them by their standard deviation. Thereafter, we fitted a first order regression on the normalized time series with time as a predictor, taking the slope of the regression model as our drift coefficient (z/sec). An inspection of the drift distribution revealed that both positive and negative drift values were present. Projection length analysis To compute the projection lengths onto the uncontrolled manifold of joint angle configurations, we used an adapted version of motor equivalence analysis [8,46-48] . To achieve these projections, first, a Jacobian matrix that describes how changes in joint angles relate to changes in end-effector position was constructed. Using linear regression procedures [49], for each condition, a Jacobian matrix was constructed for four cycle moments (at movement reversals at the target, and two mid-half-cycle moments during the movement in between two targets) using the joint configurations at those moments from all cycles within that condition. The null space of such a Jacobian matrix reflects the uncontrolled manifold containing all joint angle configurations that lead to a stable end-effector position, whereas the range space of this Jacobian matrix contains all joint angle configurations that lead to changes in end-effector position. To be able to project joint angle configurations onto both these spaces, joint deviation vectors (JDVs) were computed by subtracting the joint angle configuration of the first cycle (used as reference) from the joint angle configurations of subsequent cycles. Subsequently, these JDVs were projected onto both the uncontrolled manifold and the range space of the Jacobian to assess the evolution of projection lengths along these spaces across the different cycles of the various conditions (see Valk et al. [8] for details of the formulae used). Declarations Data availability statement The raw data supporting the conclusions of this article will be made available upon request. Acknowledgements We would like to thank all participants who volunteered in this study. Author contributions M.S.J.H., T.A.V. and R.M.B. conceived this study. T.A.V. and R.M.B. designed the original experiment. T.A.V. conducted the experiment. M.S.J.H and T.A.V. wrote the programs to run the data analysis. M.S.J.H., T.A.V., R.M.B. interpreted the results. M.S.J.H., T.A.V. and R.M.B. wrote the manuscript and approved the final version of the paper. Funding Declaration This project did not receive any funding. Additional information Competing interests We declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. References Bernstein, N. A. The Co-ordination and Regulation of Movements . Oxford: Pergamon Press (1967). Turvey, M. T. Coordination. Am. Psychol. , 45 (8), 938–953 (1990). Latash, M. L., Scholz, J. P., & Schöner, G. Toward a New Theory of Motor Synergies. Motor Control , 11 (3), 276–308 (2007). Turvey, M. T. Action and perception at the level of synergies. Hum. Mov. Sci. , 26 (4), 657–697 (2007). Riley, M. A., Richardson, M. J., Shockley, K., & Ramenzoni, V. C. Interpersonal Synergies. Front. Psychol ., 2 (2011). Kelso, J. A. S. Synergies: Atoms of Brain and Behavior. in Progress in Motor Control (ed. Sternad, D.) 83–91. Springer US (2009). Kelso, J. A. S. On the coordination dynamics of (animate) moving bodies. JPhys Complexity , 3 (3), 031001 (2022). Valk, T. A., Mouton, L. J., Otten, E., & Bongers, R. M. Synergies reciprocally relate end-effector and joint-angles in rhythmic pointing movements. Sci. Rep , 9 (1) (2019b). Kelso, J. A. S. Unifying Large- and Small-Scale Theories of Coordination. Entropy , 23 (5), 537 (2021b). Bongers, R. M., Hafkamp, M. S. J., Mehta, A., & Valk, T. A. Turvey’s Coordinative Structures Appraised. Ecol. Psychol. , 37 (4), 340–352 (2025). Fitts, P. M. The information capacity of the human motor system in controlling the amplitude of movement. J. Exp. Psychol ., 47 (6), 381–391 (1954). Mottet, D., & Bootsma, R. J. The dynamics of goal-directed rhythmical aiming. Biol. Cybern ., 80 (4), 235–245 (1999). Haken, H., Kelso, J. A. S., & Bunz, H. A theoretical model of phase transitions in human hand movements. Biol. Cybern. , 51 (5), 347–356 (1985). Kelso, J. A. S. Phase transitions and critical behavior in human bimanual coordination. Am. J. Physiol. Regul. Integr. Comp. Physiol. , 246 (6) (1984). Kelso, J. A. S., Scholz, J. P., & Schöner, G. Nonequilibrium phase transitions in coordinated biological motion: Critical fluctuations. Phys. Lett. A., 118 (6), 279–284 (1986). Beek, P. J., Peper, C. E., & Stegeman, D. F. Dynamical models of movement coordination. Hum. Mov. Sci. , 14 (4–5), 573–608 (1995). Kelso, J. A. S. The Haken–Kelso–Bunz (HKB) model: From matter to movement to mind. Biol. Cybern. , 115 (4), 305–322 (2021a). Schmidt, R. C., & Richardson, M. J. Dynamics of Interpersonal Coordination. In A. Fuchs & V. K. Jirsa (Eds.), Coordination: Neural, Behavioral and Social Dynamics (281–308). Springer Berlin Heidelberg (2008). Schmidt, R. C., & Turvey, M. T. Phase-entrainment dynamics of visually coupled rhythmic movements. Biol. Cybern. , 70 (4), 369–376 (1994). Schmidt, R. C., Christianson, N., Carello, C., & Baron, R. Effects of Social and Physical Variables on Between-Person Visual Coordination. Ecol. Psychol ., 6 (3), 159–183 (1994). De Poel, H. J. Anisotropy and Antagonism in the Coupling of Two Oscillators: Concepts and Applications for Between-Person Coordination. Front. Psychol ., 7 (2016). Latash, M. L. The bliss (not the problem) of motor abundance (not redundancy). Exp. Brain Res ., 217 (1), 1–5 (2012). Scholz, J. P., & Schöner, G. The uncontrolled manifold concept: Identifying control variables for a functional task. Exp. Brain Res. , 126 (3), 289–306 (1999). Schöner, G. Recent developments and problems in human movement science and their conceptual implications. Ecol. Psychol. , 7 (4), 291–314 (1995). Bongers, R. M., Fernandez, L., & Bootsma, R. J. Linear and logarithmic speed–accuracy trade-offs in reciprocal aiming result from task-specific parameterization of an invariant underlying dynamics. J. Exp. Psychol. Hum. Percept. Perform ., 35 (5), 1443–1457 (2009). Domkin, D., Laczko, J., Djupsjöbacka, M., Jaric, S., & Latash, M. L. Joint angle variability in 3D bimanual pointing: Uncontrolled manifold analysis. Exp. Brain Res. , 163 (1), 44–57 (2005). Golenia, L., Schoemaker, M. M., Otten, E., Tuitert, I., & Bongers, R. M. The development of consistency and flexibility in manual pointing during middle childhood. Dev. Psychobiol . 60 (5), 511–519 (2018). Lamb, P. F., & Stöckl, M. On the use of continuous relative phase: Review of current approaches and outline for a new standard. Clin. Biomech ., 29 (5), 484–493 (2014). De Poel, H. J., Roerdink, M., Peper, C. (Lieke) E., & Beek, P. J. A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures. Brain Sci ., 10 (10), 724 (2020). Riley, M. A., & Turvey, M. T. Variability and Determinism in Motor Behavior. J. Mot. Behav ., 34 (2), 99–125 (2002). Stergiou, N., Harbourne, R. T., & Cavanaugh, J. T. Optimal Movement Variability: A New Theoretical Perspective for Neurologic Physical Therapy. J. Neurol. Phys. Ther ., 30 (3), 120–129 (2006). Stergiou, N., & Decker, L. M.. Human movement variability, nonlinear dynamics, and pathology: Is there a connection? Hum. Mov. Sci., 30 (5), 869–888 (2011). Delignieres, D., & Marmelat, V. Fractal Fluctuations and Complexity: Current Debates and Future Challenges. Crit. Rev. Biom. Eng ., 40 (6), 485–500 (2012). Cavanaugh, J. T., Kelty-Stephen, D. G., & Stergiou, N. Multifractality, Interactivity, and the Adaptive Capacity of the Human Movement System: A Perspective for Advancing the Conceptual Basis of Neurologic Physical Therapy. J. Neurol. Phys. Ther ., 41 (4), 245–251 (2017). Hausdorff, M., Purdon, L., Ladin, Z., Wei, Y., & Goldberger, A. L. Fractal dynamics of human gait: Stability of long-range correlations in stride interval fluctuations. XXXXxx (1996). Hausdorff, J. M., Mitchell, S. L., Firtion, R., Peng, C. K., Cudkowicz, M. E., Wei, J. Y., & Goldberger, A. L. Altered fractal dynamics of gait: Reduced stride-interval correlations with aging and Huntington’s disease . J. Appl. Physiol ., 82 (1), 262–269 (1997). Den Hartigh, R. J. R., Cox, R. F. A., Gernigon, C., Van Yperen, N. W., & Van Geert, P. L. C. Pink Noise in Rowing Ergometer Performance and the Role of Skill Level. Motor Control , 19(4), 355–369 (2015). Den Hartigh, R. J. R., Marmelat, V., & Cox, R. F. A. Multiscale coordination between athletes: Complexity matching in ergometer rowing. Hum. Mov. Sci ., 57 , 434–441 (2018). Coey, C. A., Hassebrock, J., Kloos, H., & Richardson, M. J. The complexities of keeping the beat: Dynamical structure in the nested behaviors of finger tapping. Attent. Percept. Psychophys ., 77 (4), 1423–1439 (2015). Coey, C. A., Washburn, A., Hassebrock, J., & Richardson, M. J. Complexity matching effects in bimanual and interpersonal syncopated finger tapping. Neurosc. Lett ., 616 , 204–210 (2016). Sternad, D. It’s not (only) the mean that matters: Variability, noise and exploration in skill learning. Curr. Opin. Behav. Sci ., 20 , 183–195 (2018). Grover, F. M., Andrade, V., Carver, N. S., Bonnette, S., Riley, M. A., & Silva, P. L. A Dynamical Approach to the Uncontrolled Manifold: Predicting Performance Error During Steady-State Isometric Force Production. Motor Control , 26 (4), 536–557 (2022). Valk, T. A., Mouton, L. J. & Bongers, R. M. Joint-Angle Coordination Patterns Ensure Stabilization of a Body-Plus-Tool System in Point-to-Point Movements with a Rod. Front. Psychol. 7 (2016). Valk, T. A., Mouton, L. J., Otten, E. & Bongers, R. M. Fixed muscle synergies and their potential to improve the intuitive control of myoelectric assistive technology for upper extremities. J . Neuroeng. Rehabil . 16 , 6 (2019). Wu, G. et al. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion—Part II: shoulder, elbow, wrist and hand. J. Biomech. 38 , 981–992 (2005). Mattos, D. J. S., Latash, M. L., Park, E., Kuhl, J., & Scholz, J. P. Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence. J. Neurophysiol ., 106 (3), 1424–1436 (2011). Scholz, J. P., Schöner, G., Hsu, W. L., Jeka, J. J., Horak, F., & Martin, V. Motor equivalent control of the center of mass in response to support surface perturbations. Exp. Brain Res. , 180 (1), 163–179 (2007). Scholz, J. P., Dwight-Higgin, T., Lynch, J. E., Tseng, Y. W., Martin, V., & Schöner, G. Motor equivalence and self-motion induced by different movement speeds. Exp. Brain Res ., 209 (3), 319–332 (2011). Tuitert, I., Valk, T. A., Otten, E., Golenia, L., & Bongers, R. M. Comparing Different Methods to Create a Linear Model for Uncontrolled Manifold Analysis. Motor Control , 23 (2), 189–204 (2019). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 12 May, 2026 Reviews received at journal 11 May, 2026 Reviews received at journal 11 May, 2026 Reviews received at journal 08 May, 2026 Reviewers agreed at journal 02 May, 2026 Reviews received at journal 02 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers invited by journal 29 Apr, 2026 Editor invited by journal 28 Apr, 2026 Editor assigned by journal 24 Apr, 2026 Submission checks completed at journal 24 Apr, 2026 First submitted to journal 18 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9455901","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":634385855,"identity":"c22e6d70-9fc9-4bf3-9465-aba87b202d18","order_by":0,"name":"Marijn S.J. Hafkamp","email":"data:image/png;base64,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","orcid":"","institution":"Tilburg University","correspondingAuthor":true,"prefix":"","firstName":"Marijn","middleName":"S.J.","lastName":"Hafkamp","suffix":""},{"id":634385857,"identity":"18f296c8-37e3-401e-9a81-905d2d121df7","order_by":1,"name":"Tim A. Valk","email":"","orcid":"","institution":"University of Groningen","correspondingAuthor":false,"prefix":"","firstName":"Tim","middleName":"A.","lastName":"Valk","suffix":""},{"id":634385859,"identity":"4fa4af3c-e239-4a4c-85aa-4a1a0ca0d425","order_by":2,"name":"Raoul M. Bongers","email":"","orcid":"","institution":"University of Groningen","correspondingAuthor":false,"prefix":"","firstName":"Raoul","middleName":"M.","lastName":"Bongers","suffix":""}],"badges":[],"createdAt":"2026-04-18 10:23:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9455901/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9455901/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108851089,"identity":"77e82356-3c5b-46eb-a722-4d9d3bcdb0b5","added_by":"auto","created_at":"2026-05-09 05:49:33","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":210418,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized phase plane portraits of the end-effector (left) and the nine joint angles (right) for a representative participant (5) in an exemplary condition (distance 20 cm, ID 5.0). In a phase plane the (angular) velocity is plotted against the (angular) position. The graphs in red correspond to the joint angles that are synchronized with the end-effector, while the graphs in blue correspond to the angles that synchronized less with the end-effector.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/252006cb33a773486b847023.png"},{"id":108976690,"identity":"8751169c-6273-4444-97cc-59597a939232","added_by":"auto","created_at":"2026-05-11 11:28:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":59427,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the continuous relative phase (in degrees) of all joint angles for a representative participant (5) in an exemplary condition (distance 20 cm, ID 5.0). The graphs in red correspond to the joint angles that are synchronized with the end-effector, while the graphs in blue correspond to the angles that synchronized less with that effector. For reasons of visibility, the r-axis varies in scale. Circles indicate the proportional frequency in steps of 0.25 on a scale of 0 to 1.00.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/4639980fc6f25a56016449ae.png"},{"id":108978001,"identity":"accceae4-74f1-4f11-a365-b323d5b7e29b","added_by":"auto","created_at":"2026-05-11 11:33:39","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1654373,"visible":true,"origin":"","legend":"\u003cp\u003eDistributions of the phase locking value (PLV) across all participants of the nine joint angle across all ID (horizontal axis) and target distance (vertical axis) conditions. Synchronized joint angles are represented in red, while non-synchronized joint angles are represented in blue.\u003c/p\u003e","description":"","filename":"image3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/5959681eeeda8b290bec52e7.jpg"},{"id":108851087,"identity":"701dc5f3-8a93-405b-a426-f6d35272a850","added_by":"auto","created_at":"2026-05-09 05:49:33","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":340778,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized time series (depicted in gray) of the end-effector (left) and the joint angles (right) for a representative participant (5) in an exemplary condition (distance 20 cm, ID 5.0). In the same plots, the residual variability for the joint angles that strongly synchronize with the end-effector (depicted in red) and that does not synchronize with the end-effector (depicted in blue) is presented. The trend line in each graph corresponds to the average linear drift in the joint angle over time.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/6548f2d6af037490aa53de23.png"},{"id":108977081,"identity":"e8037159-0ac7-4bbf-a87c-fb01f71248ba","added_by":"auto","created_at":"2026-05-11 11:30:18","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1694590,"visible":true,"origin":"","legend":"\u003cp\u003eDistributions of the alpha-value (DFA) across participants of the nine joint angle across all ID (horizontal axis) and target distance (vertical axis) conditions. Synchronized joint angles are represented in red, while non-synchronized joint angles are represented in blue. Lines indicate alpha values of 1.0 and 1.5, between which most of the data is located. See text for interpretation.\u003c/p\u003e","description":"","filename":"image5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/acd043cd9341865716f06afd.jpg"},{"id":108976863,"identity":"5552fc3d-8556-4d63-b7e1-35476f4fe4a5","added_by":"auto","created_at":"2026-05-11 11:29:14","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1549179,"visible":true,"origin":"","legend":"\u003cp\u003eDistributions of the drift coefficients of the nine joint angle across all ID (horizontal axis) and target distance (vertical axis) conditions. Synchronized joint angles are represented in red, while non-synchronized joint angles are represented in blue.\u003c/p\u003e","description":"","filename":"image6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/d938cc4688eec43d53cebcde.jpg"},{"id":108976899,"identity":"355a9439-4ada-47c6-a6b4-8760a279f8ea","added_by":"auto","created_at":"2026-05-11 11:29:28","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":600749,"visible":true,"origin":"","legend":"\u003cp\u003eProjection lengths of joint angle configurations onto both the uncontrolled manifold (in green) and the range space (orthogonal to this manifold, in purple), for four movements during the movement cycle between the two targets. 0 and 180 degrees indicate the moment of movement reversal while 90 and 270 degrees indicate the mid-half-cycle moments. Boxplots display the range of projection lengths across all conditions at cycle n, using mean projection length across participants per condition as input data for these boxplots.\u003c/p\u003e","description":"","filename":"image7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/c367839b39ae5582ef9b7907.jpeg"},{"id":108851092,"identity":"5e503bfa-bc7d-4a50-801a-02b13dfce61f","added_by":"auto","created_at":"2026-05-09 05:49:34","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":22168,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental set-up, as seen from above. Note that the distance between targets and width of the targets (in the forward-backward direction with respect to the participants heading) was adjusted across conditions. Dashed lines illustrate the end-effector trajectory for one cycle of pointing movements. Figure copied with permission from Valk et al [8].\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/516ac741e8f96ff5c2634df3.png"},{"id":108979943,"identity":"24888b17-e08e-437c-a979-e2deed2da76f","added_by":"auto","created_at":"2026-05-11 12:02:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6506695,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9455901/v1/b18887af-2cd5-44d0-aec3-46cb12eda927.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Concurrent synchronization and covariation in upper extremity joint angles during a reciprocal aiming task","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn human movement, the many available degrees of freedom (DOF, e.g., muscles, joint angles) of the movement apparatus are typically organized into stable coordinative structures [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Within the ecological-dynamical approach, these structures are known as \u003cem\u003esynergies\u003c/em\u003e: temporary assemblies of DOF that are constrained to act as functional units [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Such synergies are understood to be self-organizing, meaning that the kinematic outcome of the movement and the underlying coordination of the DOF \u0026ndash;respectively the macro- and microscopic level of organization\u0026ndash; are linked through circular causality. When aiming to a target, for instance, there is reciprocity between the kinematics of the end-effector and the coordination of the joint angles in the upper extremity [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The end-effector trajectory emerges from the coordination of the joint angles, while the joint angle coordination is simultaneously constrained by the trajectory of the end-effector. Yet, how this circular causality manifests itself in such redundant effector systems \u0026ndash;which have more DOF than necessary to perform the task\u0026ndash; remains underexplored [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The present study therefore investigated concurrently the coordination dynamics of the upper extremity joint angles and the end-effector during a reciprocal aiming task [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], to capture the circular causality that characterizes self-organization in movement systems.\u003c/p\u003e \u003cp\u003eA seminal account of self-organization in movement is provided by the Haken\u0026ndash;Kelso\u0026ndash;Bunz (HKB) model of rhythmic interlimb coordination [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. In this model, two rhythmically moving limbs are treated as a pair of self-sustaining oscillators with a non-linear coupling function. Their coordination can be captured macroscopically by a potential function with only two attractor states: in-phase (0\u0026deg;) and anti-phase (180\u0026deg;). At low movement frequencies, both attractors are stable and relative phase variability is minimal. As the movement frequency increases, however, the anti-phase attractor loses stability, leading the system to switch to the more stable in-phase coordination [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Thus, the state of the attractor depends on the rhythmic frequency of the oscillators, while the oscillators\u0026rsquo; rhythmicity is constrained by the attractor state. This reciprocity illustrates the model\u0026rsquo;s circular causality between the macro- and microscopic level of organization.\u003c/p\u003e \u003cp\u003eSoon after its introduction, the coupled-oscillator model became a general operational paradigm for studying self-organization in movement [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. By integrating system modeling with empirical work, the paradigm uncovered some of the core principles of coordination dynamics. Notably, it demonstrated that the stability of a macroscopic attractor depends not only on the two oscillator\u0026rsquo;s frequencies, but also on the symmetry between the rhythmic components. When the oscillators differ in their eigenfrequency, the faster oscillator takes the lead and the stability of their (anti-phase) coordination declines immediately [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Similarly, when two oscillators are coupled asymmetrically, their synchrony is disrupted and their coordinative stability decreases as well [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The fundamental insight gained from these models is that coordinative stability on a macroscopic level hinges upon the capacity of system components on a microscopic level (i.e., DOF) to establish stable phase relationships. Consequently, synergy came to be associated with the sychronization of DOF [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], here defined as an in-phase/anti-phase coupling.\u003c/p\u003e \u003cp\u003eHowever, for tasks in which an end-effector needs to be positioned in space, synchronization is not the only route to coordinative stability. Because the movement system is inherently redundant (or abundant [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]) for most tasks, multiple configurations of the system\u0026rsquo;s DOF can produce the same outcome at the macroscopic level. Therefore, stability at this level can also emerge from mutual compensations (i.e., covariation) between the system\u0026rsquo;s DOF [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. For instance, the same hand movement can be brought about by extending the elbow while keeping the shoulder fixed, or by rotating the shoulder while holding the elbow steady. In goal-directed movement, this covariation in joint angles ensures that the target can be reached in multiple ways using different patterns of coordination, which is fundamental to the system\u0026rsquo;s flexibility. The idea of motor abundance has been linked to the concept of the uncontrolled manifold [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]: a subset of DOF configurations that yield the same movement outcome, such as all joint angle combinations that keep the effector on a target. In line with this idea, synergy has been re-interpreted [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] as a grouping of DOF that covaries within an uncontrolled manifold, as a way to stabilize a movement while preserving its flexibility.\u003c/p\u003e \u003cp\u003eIn the ecological-dynamical approach, the two models of synergy \u0026ndash;HKB and UCM\u0026ndash; are often used interchangeably [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Synchronization and covariation have even been described as complementary features of one and the same synergy concept, each contributing to coordinative stability in their own way [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. For goal-directed movement, however, the models yield different predictions about the system\u0026rsquo;s coordination dynamics. Coupled oscillator models, on the one hand, suggest that the DOF of a redundant system must be synchronized for the end-effector trajectory to be stable. Studies on the coordination dynamics of reciprocal aiming have shown that the end-effector can behave as a self-sustaining oscillator, suggesting a limit cycle attractor at the macroscopic level [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. To preserve the stability of this attractor, its dynamics must somehow be reflected in the back-and-forth movement of the joint angles at the microscopic level, implying synchronicity as a basis for their coordination.\u003c/p\u003e \u003cp\u003eThe UCM model, on the other hand, suggests a weaker synchronization between the macro- and microscopic level of system organization. Studies of discrete [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and reciprocal [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] aiming have shown that the joint angles of the upper extremity covary to stabilize the trajectory of the end-effector. This suggests that the angles are free to deviate from the end-effector dynamics, because they can (co)vary along an uncontrolled manifold. At the same time, there must be \u003cem\u003esome\u003c/em\u003e synchronization between the levels, for the joint angles ultimately drive the end-effector motion. Using a cross-recurrent quantification analysis (CRQA), Valk and colleagues [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] explored this ambiguity. CRQA is a non-linear analysis that quantifies how patterns of motion in one time series (e.g., in the end-effector) recur in another time series (e.g. in a joint angle) at different temporal offsets, without specifying the dynamics of either signal. They found that only three out of the nine upper extremity joint angles \u0026ndash;the shoulder plane of elevation (SPE), the shoulder exo-endorotation (SEE) and the elbow flexion-extension (EFE)\u0026ndash; had a strong dynamical coupling to the end-effector, while six other angles \u0026ndash;the shoulder elevation (SEL), elbow pronation-supination (EPS), wrist-flexion extension (WFE), wrist abduction-adduction (WAA), finger flexion-extension (FFE) and the finger abduction-adduction (FAA)\u0026ndash; were only weakly coupled. This suggests that not all joint angles synchronise similarly with the end-effector and that some angles display dynamical regimes that are not observed at the end-effector level. Yet, neither a CRQA nor a UCM captures a system\u0026rsquo;s dynamics, leaving unresolved how circular causality manifests itself in redundant systems.\u003c/p\u003e \u003cp\u003eTherefore, the current study examined the coordination dynamics of the upper extremity joint angles and the end-effector during a reciprocal aiming paradigm [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In this task, participants made back-and-forth aiming movements between two targets, while target distance and target width were both manipulated. First, we investigated the degree of synchronization between the joint angles and the end-effector. Following up on the work of Valk et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], we conducted a relative phase analysis and hypothesized that only the three \u0026lsquo;coupled\u0026rsquo; joint angles \u0026ndash; the SPE, SEE and EFE \u0026ndash; would be locked into in-phase or anti-phase relationships with the end-effector. Second, we investigated the deviations from synchrony in the joint angles movements, the so-called \u0026lsquo;residual variability\u0026rsquo;. Since we had no a priori hypotheses regarding the dynamical regimes at the joint angle level, we conducted our analyses in an exploratory fashion, focusing on the temporal evolution of the considered DOF.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eOriginally, this study was designed to compare aiming conditions of varying target distance (5, 10, 20 and 30 cm) and target width (index of difficulty 3.5 - 6.0 with increments of 0.5). Our aim here, however, was to compare the coordination dynamics of the joint angles with the end-effector. Accordingly, our analyses focused on \u003cem\u003ewithin trial\u0026nbsp;\u003c/em\u003eeffects. For comparisons between aiming trial conditions, we refer the reader to Valk et al.\u003csup\u003e\u0026nbsp;\u003c/sup\u003e[8].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSynchronicity between joint angles and end-effector \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003ePhase plane portraits\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn \u003cstrong\u003eFigure 1\u0026nbsp;\u003c/strong\u003ewe reconstructed the normalized phase plane portraits of the end-effector (\u003cstrong\u003e1A\u003c/strong\u003e) and the joint angles (\u003cstrong\u003e1B\u003c/strong\u003e) of the upper extremity for a representative participant in an exemplary condition (index of difficulty 5.0, distance 20 cm). As illustrated in these portraits, three of the nine joint angles (SPE, SEE and EFE, in red) displayed limit-cycle dynamics that was comparable to that of the end-effector (established by continuous relative phase analysis, see below). The six remaining joint angles (SEL, EPS, WFE, WAA, FFE, FAA, in blue) were much more variable in their dynamics, some of them exhibiting no apparent structure.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 1\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eContinuous relative phase analysis\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo examine the synchronization between the joint angles and the end-effector, we computed the continuous relative phase (CRP)\u0026nbsp;[28]\u003csup\u003e\u0026nbsp;\u003c/sup\u003ewith tightened normalization procedures\u003csup\u003e\u0026nbsp;\u003c/sup\u003e[29] between the corresponding time series. In \u003cstrong\u003eFigure 2\u0026nbsp;\u003c/strong\u003ewe showed the distribution of the CRP for each joint angle, for the same participant and trial condition as in \u003cstrong\u003eFig. 1\u003c/strong\u003e. The polar histograms reveal that the CRP fluctuated around 0\u0026deg; or 180\u0026deg; for most angles, most notably for the SPE, SEE and EFE angles. This suggests high degrees of synchronization with the end-effector. At the same time, the CRP fluctuated strongly for angles such as the wrist abduction-adduction (WAA, between 0\u0026deg; or 180\u0026deg;) and the finger abduction-adduction (FAA, between 90\u0026deg; and 270\u0026deg;). This suggested lower degrees of synchronization.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 2\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo assess the degree of synchronization for each joint angle, we computed the phase locking value (PLV) for all CRP time series across participants and conditions. The PLV was defined such that in-phase and anti-phase synchronization would both correspond to a coefficient of 1, while a random distribution of CRP values (i.e., no synchronization) corresponded to a coefficient of 0. As shown in \u003cstrong\u003eFigure 3\u003c/strong\u003e, the PLV of the SPE, SEE and EFE (in red) was close to 1 in all conditions, indicating a very high degree of synchronization. In the other six angles (in blue), the PLV was substantially lower, ranging from 0.5 to 1.0. This demonstrated a weak synchronization between these joint angles and the end-effector, pointing at deviations from the macroscopic dynamics. Following analyses further investigated these deviations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 3\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeviations from synchronicity\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eResidual variability in the joint angles\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo further assess the deviations of joint angles from macroscopic dynamics, we separated the variability in the joint angles that \u003cem\u003edeviated\u003c/em\u003e from the end-effector dynamics from that which was shared with the end-effector. To do this, we conducted a first order regression analysis on the normalized angular time series of each joint angle, with the normalized end-effector trajectory as a predictor. This resulted in residual variability time series per trial, which we illustrated in \u003cstrong\u003eFigure 4\u003c/strong\u003e for the same participant and condition as presented in \u003cstrong\u003eFig. 1\u003c/strong\u003e and \u003cstrong\u003e2\u003c/strong\u003e. As can be observed, the residual variability was small for the joint angles that strongly synchronized with the end-effector (SPE, SEE and EFE, residual variability depicted in red), but much larger for the other joint angles (in blue). In the latter case, it displayed (1) distinct spatiotemporal structures and (2) a strong extent of relative drift in the joint angle over time. The next two sections systematically study both phenomena.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eFigure 4\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDetrended fluctuation analysis\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo examine the spatiotemporal structure of the residual joint angle variability, we conducted a detrended fluctuation analysis (DFA) on all residual time series. DFA quantifies long range correlations in a time series by measuring how fluctuations scale across timescales, potentially signifying a fractal structure in the variability. This means it assesses whether patterns of variability repeat themselves across timescales. The output of DFA is a scaling exponent a, ranging roughly from 0 to 2. An a of 0.5 generally indicates randomness in the time series (white noise), whereas an a of 1.0 points at fractality (pink noise). A residual time series that expresses pink noise signifies that smaller, shorter fluctuations are embedded in larger, longer fluctuations. An a of 1.5 indicates non-stationarity or drift in the time series, also called Brownian noise. As shown in \u003cstrong\u003eFigure 5\u003c/strong\u003e, the DFA on the residual joint angle variability resulted in a-values between 1.0 and 1.5 in all angles, across all conditions. This indicated that the residual variability was not random, but structured. More particularly, it exhibited a mixture of fractality and drift, as already anticipated in \u003cstrong\u003eFig. 4\u003c/strong\u003e. The indication of fractality was the strongest in the elbow flexion extension angle, while the suggestion of drift was the clearest for the wrist flexion extension angle. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 5\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDrift analysis\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo obtain a linear approximation of the drift, we fitted a first-order regression to the normalized angular time series, with time as a predictor and slope as our measure of drift. \u003cstrong\u003eFig. 4\u003c/strong\u003e already showed these slope lines in the illustrated time series, demonstrating that the range and directionality of the drift (i.e., positive or negative drift) varied across the joint angles. In \u003cstrong\u003eFigure 6\u003c/strong\u003e we presented the distribution of the drift slopes across participants for all joint angles in all aiming conditions. As can be appreciated from this graph, all angles exhibited drift, even though the drift was larger for the non-synchronous angles (in blue). However, as shown in \u003cstrong\u003eTable 1\u003c/strong\u003e, the average range of motion (ROM) of these joint angles was also substantially lower than the ROM of the synchronous joint angles (in red). This means that the contribution of the non-synchronous joint angles to the upper extremity movement was smaller and the freedom to \u0026lsquo;wander off from their trajectory\u0026rsquo; without destabilizing the end-effector\u003cem\u003e,\u003c/em\u003e larger.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 6\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1:\u0026nbsp;\u003c/strong\u003eThe mean (standard deviation) range of motion of the joint angles in degrees, averaged per target size condition across all participants and all ID conditions.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eDist.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eSPE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003eSEE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eEFE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eSEL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eEPS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003eWFE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003eWAA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003eFFE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003eFAA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e5 cm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e9.1 (3.6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e10.8 (4.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e10.0 (3.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e4.7 (1.9)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e6.0 (3.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e5.8 (3.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e3.6 (2.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e2.1 (1.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e3.2 (1.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e10 cm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e17.3 (5.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e20.2 (6.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e20.3 (4.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e8.2 (3.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e9.4 (3.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e8.0 (4.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e4.5 (1.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e2.7 (2.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e3.9 (2.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e20 cm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e32.7 (8.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e37.8 (10.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e40.0 (5.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e13.0 (3.9)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e15.0 (6.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e11.7 (6.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e5.9 (2.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e3.5 (2.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e4.8 (2.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e30 cm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e44.5 (10.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 76px;\"\u003e\n \u003cp\u003e53.2 (13.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e56.8 (7.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e16.5 (4.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e20.6 (8.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e16.1 (8.6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 56px;\"\u003e\n \u003cp\u003e7.7 (3.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e4.4 (3.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 60px;\"\u003e\n \u003cp\u003e5.8 (2.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eProjection length analysis\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThat joint angles exhibited drift while the end-effector dynamics remained stationary suggests that the drift occurred within the uncontrolled manifold [23] \u0026ndash; the subspace in joint angle space that encompasses all joint angle configurations that stabilize the end-effector on a certain position. To investigate whether this was indeed the case, we projected the joint angle configurations of different cycles within a condition on the uncontrolled manifold as well as on the range space. The range space is a subspace orthogonal to the manifold, including all joint angle configurations that lead to deviations of the end-effector from a certain position. We computed the projections for four instants of the cycle of motion: at the two moments of reversal at the physical target (indicated as 0 and 180 degrees of the cycle) and two moments mid-half-cycle (indicated as 90 and 270 degrees of the cycle). Using the joint angle configuration of the first cycle as reference, projection lengths for all four cycle moments increased when joint angle configurations were projected on the uncontrolled manifold, but not when projected onto the range space (\u003cstrong\u003eFigure 7\u003c/strong\u003e). This indicated that the drift observed in the joint angles was gradual and could be collectively described as drift along a subset of configurations that stabilizes end-effector behavior.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this contribution we examined how circular causality, a key feature of self-organization, manifests itself in a redundant movement system. We investigated the coordination dynamics of upper extremity joint angles \u0026ndash;as microscopy\u0026ndash; and the end-effector \u0026ndash;as macroscopy\u0026ndash; during a reciprocal aiming paradigm.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eOur results revealed that the dynamical relationship between joint angles and end-effector was not the same for all joint angles. Those joint angles with the largest range of motion synchronized with the end-effector, suggesting that dynamical coupling between macro- and microscopy is an important component of circular causality. At the same time, the joint angles exhibited variability that was not shared with the end-effector. We found indications of fractality and drift at the joint angle level, neither of which affected the stability of the end-effector dynamics. This seems to indicate that the joint angles were not only coordinated to stabilize the end-effector, but also to keep the movement system flexible. In what follows, we will first discuss these results in more detail, before interpreting them in light of the ecological-dynamical concept of synergy.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn an earlier contribution exploiting the current data, Valk and colleagues [8] used a cross-recurrent quantification analysis to show that the shoulder plane of elevation angle, the shoulder exo-endorotation angle, the elbow flexion-extension angle and the end-effector were strongly coupled to one another. Here, we followed up on this finding with a continuous relative phase analysis, which demonstrated that this coupling comprised stable in-phase or anti-phase relationships. This indicated a high degree of synchronization between the macro- and microscopic level of organization, at least for some of the angles. Rather than preceding or following the end-effector, a subset of the joint angles moved \u003cem\u003esimultaneously\u003c/em\u003e with the tip of the finger, effectively driving its macroscopic limit-cycle dynamics [12,25]. The other six joint angles, in particular those of the finger and wrist, were much more variable in their phase progression. Note that this CRP variability persisted even when we controlled for drift and for variations in the amplitude. Using the tightened normalization procedures of de Poel et al. [29], we detrended and normalized each half cycle, but the phase locking values of the wrist and finger angles remained low. This demonstrated substantial \u0026lsquo;residual\u0026rsquo; variability in the angular time series, the structure of which we examined using a detrended fluctuation analysis (DFA).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAlthough all joint angles exhibited residual variability, the non-synchronous joint angles exhibited more fluctuations that were not shared with the end-effector than the synchronous angles, as expected. The DFA on the residual variability revealed two intriguing properties. In the first place, it showed indications of fractality, meaning that smaller, shorter fluctuations were embedded in larger, longer fluctuations. This finding is interesting, because it suggests a dynamical patterns \u003cem\u003eon top of\u003c/em\u003e the macroscopic dynamics. It shows that the variations in the joint angle motion on a faster timescale than the back-and-forth movement were not random, but (at least partially) deterministic. In fact, they were correlated with one another on a timescale that was longer than that of the main cycle of motion. In motor control literature, such long range correlations have been linked to properties of flexibility and adaptability [29,34]. They were first found in locomotion patterns [35,36], but have also been demonstrated in other rhythmic movements such as rowing\u003csup\u003e\u0026nbsp;\u003c/sup\u003e[37,38] and manual tapping [39,40]. The embedding of fluctuations of different time scales prevents a rhythm from becoming rigid, in the sense that every cycle of motion is the same. At the same time, fractality channels variability, since fluctuations are not random but correlated. As such, it is a \u0026ldquo;compromise between order and disorder\u0026rdquo;, keeping the movement system adaptive, without degenerating into randomness or inflexibility [31,34].\u003c/p\u003e\n\u003cp\u003eSecondly, the DFA revealed indications of Brownian noise, suggesting drift in the joint angle time series. Follow up analyses showed that most of the drift occurred \u003cem\u003ewithin\u003c/em\u003e the uncontrolled manifold, implying covariation (see Valk et al.\u003csup\u003e\u0026nbsp;\u003c/sup\u003e[8] for a broader discussion of the UCM). Combined with the finding that the drift was the largest in the joint angles with the smallest range of motion, this suggests that the angles only drifted if they had the freedom to do so without damaging the end-effector motion. That the joint angles used this freedom is intriguing. As to its functional role, we can only speculate. Possibly, participants fatigued over the course of a trial, causing them to slowly lower their elbow during the trial. Further examination of the upper extremity postures, however, did not reveal such a systematic lowering of the elbow joint over cycles of motion. Alternatively, participants may have drifted towards a posture that was most comfortable for producing the aiming movement, or they may have explored different ways to perform the task to warrant adaptability. Although the effect was subtle and the preferred posture probably unique for every individual, the tendency to drift along the UCM was significant for most participants. It shows that a singular focus on neither a relative phase nor a pattern of covariation is sufficient to capture the richness of coordination in redundant systems. Equally important is showing how participants move along the manifold, either gradually or in discrete steps [41].\u003c/p\u003e\n\u003cp\u003eWhat do these findings tell us about synergy, a concept that is as old as the discipline of movement science itself [1-3,7,9]? Within the ecological\u0026ndash;dynamical approach, synergy is understood as an emergent structure of coordination with circular causality between its levels of organization [4,6]. Using the example of reciprocal aiming, we showed that this circular causality exhibits at least two critical features when applied to a redundant movement system. To begin with, the DOF are coordinated to \u003cem\u003estabilize\u003c/em\u003e the kinematic outcome on the movement. Notably, this stabilization involves synchronization as well as covariation. Synchronization \u0026lsquo;drives\u0026rsquo; the end-effector trajectory and occurs between the joint angles with the largest range of motion. Covariation \u0026lsquo;preserves\u0026rsquo; the end-effector trajectory and ensures that it maintains its dynamics between the targets. This interpretation aligns roughly with the understanding of synergy as promoted by Riley et al. [5]. In this view, synchronization serves to reduce the system\u0026rsquo;s dimensionality, so that a macroscopic organization emerges from the many DOF in the movement apparatus. And covariation preserves the integrity of that organization, so that it is robust against minor perturbations. This way, synchronization and covariation are actually two sides of the same coin \u0026ndash; both bringing stability to movement.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn redundant systems, however, stability is not the only feature of circular causality. The DOF are also coordinated to preserve the system\u0026rsquo;s \u003cem\u003eflexibility\u003c/em\u003e. Even during stable rhythmic movement, the system component\u0026rsquo;s trajectories vary from cycle to cycle, creating distinct dynamical regimes at the microscopic level of organization. In the case of reciprocal aiming, the variability in the joint angles exhibited fractality as well as non-stationarity. Small fluctuations in the angular movement (at a timescale faster than reciprocal cycle of motion) \u0026nbsp;were embedded in larger fluctuations, and some of the joint angles slowly wandered off in space without affecting the stability of the end-effector dynamics. This variability keeps the system adaptive, such that it can respond adequately to changes in the circumstances. But it also allows the system to transform to a more comfortable or effective configuration, like an upper extremity posture that is optimal for sustaining the back-and-forth movement.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFlexibility has been attributed to synergy before, most distinctly within the uncontrolled manifold approach [3]. But how this flexibility is reflected in the stable coordination dynamics of a redundant effector system has remained obscured. The UCM method has been designed to study the static stabilization of a performance variable and is thus ill-posed to reveal dynamical properties of flexibility in movement (see also Grover et al. [42]). Our results suggest that flexibility manifests itself in fractality and unboundedness of the degrees of freedom, and thus in the temporal structure of their variability. Variations in movement from repetition to repetition are not random, but deterministic. Rather than being noise around an attractor, they prepare the system to adapt to changing circumstances or help the system move toward other configurations. As such, variability is intrinsic to the coordination, even during stable episodes of movement. This is, at its core, what self-organization in redundant movement systems implies. The emergence of a coordinative structure \u0026ndash;a synergy\u0026ndash; that is stable and ready to withstand perturbations, but also variable and ready to adapt to the environment.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eEthics statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe experimental protocol was carried out in accordance with the Declaration of Helsinki and approved by the local ethics committee of the Department of Human Movement Sciences at the University Medical Center Groningen. Before the start of the experiment, we informed participants about the goal of the study, after which all participants signed informed consent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eParticipants\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn total, we recruited twenty right-handed participants. Two participants were excluded because of failed data acquisition during the measurements. The remaining eighteen participants had an age of 20.8 \u0026plusmn; 1.9 years (M \u0026plusmn; SD). They had no neurological conditions or other health issues and they all had normal or corrected-to-normal sight.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eExperimental task\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants made reciprocal aiming movements (i.e., back-and-forth in an anterior-posterior direction in front of them) between two targets, according to a continuous Fitts\u0026rsquo; paradigm [11,12] (\u003cstrong\u003eFigure 8\u003c/strong\u003e). We manipulated both target distance and index of difficulty (ID; a logarithmic function of target distance and target width), by varying the target width relative to the target distance. In total, the experiment comprised 24 unique conditions (trials), combining 4 target sizes (5, 10, 20 and 30 cm) with 6 ID\u0026rsquo;s (3.5; 4.0; 4.5; 5.0; 5.5; 6.0). These conditions were presented to participants in a randomized order. In each trial, the targets were presented on a laminated sheet of paper (A3 size, portrait orientation) that was attached to the table in front of the participants. To avoid drifting of the end-effector in the frontal plane, all targets had a width of 1 cm in this plane. Participants made the pointing movements with a stylus that was attached to their index finger, leaving no trace to the paper. The stylus was attached such that it prohibited movement in the interphalangeal joints while allowing free movement of the metacarpophalangeal joint.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 8.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExperimental procedure\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn each trial, participants made forty reciprocal movements (cycles) between the targets. Participants always started a trial with the tip of the stylus in the middle of the target that was closest to them. They were instructed to take the same starting posture across conditions \u0026ndash; an instruction that was repeated before the start of every new trial. To check whether participants followed the instruction, we compared the standard deviation of the starting joint angle configurations across IDs within a target distance with the standard deviation of starting joint angle configurations recorded in previous studies in which a similar starting posture was ensured by means of an elbow placer [43,44]. This comparison showed that participants followed the instruction. During the trial, participants had to move the tip of the stylus as fast and accurate as possible. Experimenters observed whether this instruction was followed and motivated participants to move as fast as possible while adhering to accuracy demands. Participants were instructed to keep the tip of the stylus at the sheet of paper at all times.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eData acquisition\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo capture the participants\u0026rsquo; movements in three dimensions, we attached five rigid bodies to the right side of the body and one to the sternum. Each rigid body was triangular in shape and contained three light-emitting diodes. One rigid body, with a length of 4 cm, was attached to the stylus; four others were attached to segments of the participant\u0026rsquo;s right arm and shoulder. Two rigid bodies, with a length of 6 cm, were attached to the sternum and the upper arm just below the insertion of the deltoid; three others, with a length of 4 cm, were attached to the dorsal side of the hand, the dorsal side of the upper arm just proximal of the ulnar and radial styloids, and the flat part of the acromion. We captured the movements of the LEDs using two Optotrak 3020 units (Waterloo, Ontario, Canada) that were synchronized and sampled at 100 Hz. Using a pointer device, we digitized eighteen bony landmarks and the tip of the stylus to relate the LED motion to the movement of the participant\u0026rsquo;s arm. To prohibit movement of the trunk while allowing free movement of the shoulder joint, we gently strapped participants against the extended back of the chair using an elastic bandage.\u003c/p\u003e\n\n\u003cp\u003eWe determined the end-effector trajectory from the motion of the three Optotrak LEDs attached to the stylus, using rigid body transformations. For further analyses, we exclusively used the forward-backward movement of the end-effector in the transversal plane. The trajectories of the nine joint angles we computed using the motion of the relevant Optotrak LEDs and the segment orientations derived from the digitized bony landmarks. Following ISB guidelines [45], we acquired the following joint angles: the shoulder plane of elevation (SPE), shoulder elevation (SEL), shoulder exorotation-endorotation (SEE), elbow flexion-extension (EFE), elbow pronation-supination (EPS), wrist flexion-extension (WFE), wrist abduction-adduction (WAA), finger flexion-extension (FFE), and the finger abduction-adduction (FAA).\u0026nbsp;\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eData analysis\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe time series of the end-effector and the nine joint angles were filtered using a 4th order low-pass Butterworth filter with a cut off frequency of 5 Hz. To reconstruct the coordination dynamics at both levels, we created phase plane portraits of the end-effector and all joint angles. We normalized the (angular) position and (angular) velocity time series to their mean and standard deviation and plotted the latter against the former in to create phase planes.\u0026nbsp;\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eContinuous relative phase analysis\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo examine the synchronization between the joint angles and the end-effector, we computed the continuous relative phase between the corresponding time series. We cut all time series into half cycles, demarcated by the reversal points of the end-effector signal. Following the procedure of de Poel et al. [29], we then centered, detrended and normalized each half cycle relative to the standard deviation of that cycle, so as to avoid distortion of drift or amplitude. Subsequently, we transformed the half cycles of the end-effector and the joint angles to analytic signals using the Hilbert transform and used that to compute the phase angles in degrees [28]. After concatenating all half cycles, the continuous relative phase was then acquired by subtracting the phase angle of the joint angle from the end-effector. For interpretation, we plotted the CRP distributions per joint angle in polar histograms. Moreover, we computed the phase locking value per CRP time series to quantify the degree of synchronization. To define both in-phase and anti-phase as synchronization, we first doubled the CRP values, after which we took the complex phase vectors to represent each CRP value on the unit cycle. We then averaged all complex vectors on the unit cycle to compute the PLV. A PLV of 1 indicated maximum synchronization (in-phase/anti-phase), while a PLV of 0 indicated a random distribution of CRP values.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDetrended fluctuation analysis\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo investigate the variability that deviated from the end-effector, we conducted a first order regression analysis on the normalized time series of the joint angles, with the normalized end-effector time series as a predictor. This resulted in a component of shared variability and a component of residual variability. We then analyzed the residual variability using a detrended fluctuation analysis (DFA), following standard procudures for periodic movement data [e.g. 37,38]. DFA quantifies long range correlations in a time series by measuring how fluctuations scale across timescales. As a first step, we integrated the residual variability time series. Subsequently, we divided it into windows of increasing length, from n=10 to n = N/4 with 20 scales in total. We then detrended each window and calculated its root mean square (RMS). As a last step, we derived a scaling exponent a from the slope of the log\u0026ndash;log relationship between the RMS and the window size. The scaling exponent may range from 0 to 2. An \u0026alpha;-value of 0.5 indicates the absence of correlations (white noise), \u0026alpha; \u0026gt; 0.5 indicates that large values are more likely to be followed by large values, and \u0026alpha; \u0026lt; 0.5 indicates that large values are more likely to be followed by small values and vice versa. Then, \u0026alpha;-values of 1.0 \u0026nbsp;and 1.5 correspond to pink noise and Brownian noise, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eDrift analysis\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo assess the drift in the time series of the joint angles, we first normalized the angular time series to z-scores by dividing them by their standard deviation. Thereafter, we fitted a first order regression on the normalized time series with time as a predictor, taking the slope of the regression model as our drift coefficient (z/sec). An inspection of the drift distribution revealed that both positive and negative drift values were present.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eProjection length analysis\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo compute the projection lengths onto the uncontrolled manifold of joint angle configurations, we used an adapted version of motor equivalence analysis [8,46-48] . To achieve these projections, first, a Jacobian matrix that describes how changes in joint angles relate to changes in end-effector position was constructed. Using linear regression procedures [49], for each condition, a Jacobian matrix was constructed for four cycle moments (at movement reversals at the target, and two mid-half-cycle moments during the movement in between two targets) using the joint configurations at those moments from all cycles within that condition. The null space of such a Jacobian matrix reflects the uncontrolled manifold containing all joint angle configurations that lead to a stable end-effector position, whereas the range space of this Jacobian matrix contains all joint angle configurations that lead to changes in end-effector position. To be able to project joint angle configurations onto both these spaces, joint deviation vectors (JDVs) were computed by subtracting the joint angle configuration of the first cycle (used as reference) from the joint angle configurations of subsequent cycles. Subsequently, these JDVs were projected onto both the uncontrolled manifold and the range space of the Jacobian to assess the evolution of projection lengths along these spaces across the different cycles of the various conditions (see Valk et al.\u003csup\u003e\u0026nbsp;\u003c/sup\u003e[8] for details of the formulae used).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe raw data supporting the conclusions of this article will be made available upon request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe would like to thank all participants who volunteered in this study.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM.S.J.H., T.A.V. and R.M.B. conceived this study. T.A.V. and R.M.B. designed the original experiment. T.A.V. conducted the experiment. M.S.J.H and T.A.V. wrote the programs to run the data analysis. M.S.J.H., T.A.V., R.M.B. interpreted the results. M.S.J.H., T.A.V. and R.M.B. wrote the manuscript and approved the final version of the paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis project did not receive any funding.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBernstein, N. A. \u003cem\u003eThe Co-ordination and Regulation of Movements\u003c/em\u003e. Oxford: Pergamon Press (1967). \u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eTurvey, M. T. Coordination. \u003cem\u003eAm. Psychol.\u003c/em\u003e, \u003cstrong\u003e45\u003c/strong\u003e(8), 938\u0026ndash;953 (1990).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eLatash, M. L., Scholz, J. P., \u0026amp; Sch\u0026ouml;ner, G. Toward a New Theory of Motor Synergies. \u003cem\u003eMotor Control\u003c/em\u003e, \u003cstrong\u003e11\u003c/strong\u003e(3), 276\u0026ndash;308 (2007).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eTurvey, M. T. Action and perception at the level of synergies. \u003cem\u003eHum. Mov. Sci.\u003c/em\u003e, \u003cstrong\u003e26\u003c/strong\u003e(4), 657\u0026ndash;697 (2007).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eRiley, M. A., Richardson, M. J., Shockley, K., \u0026amp; Ramenzoni, V. C. Interpersonal Synergies. \u003cem\u003eFront. Psychol\u003c/em\u003e., \u003cstrong\u003e2\u003c/strong\u003e (2011). \u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eKelso, J. A. S. Synergies: Atoms of Brain and Behavior. in \u003cem\u003eProgress in Motor Control\u003c/em\u003e (ed. Sternad, D.) 83\u0026ndash;91. Springer US (2009).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eKelso, J. A. S. On the coordination dynamics of (animate) moving bodies. \u003cem\u003eJPhys Complexity\u003c/em\u003e, \u003cstrong\u003e3\u003c/strong\u003e(3), 031001 (2022).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eValk, T. A., Mouton, L. J., Otten, E., \u0026amp; Bongers, R. M. Synergies reciprocally relate end-effector and joint-angles in rhythmic pointing movements. \u003cem\u003eSci. Rep\u003c/em\u003e, \u003cstrong\u003e9\u003c/strong\u003e(1) (2019b).\u003c/li\u003e\n\u003cli\u003e\u003csup\u003e \u003c/sup\u003eKelso, J. A. S. Unifying Large- and Small-Scale Theories of Coordination. \u003cem\u003eEntropy\u003c/em\u003e, \u003cstrong\u003e23\u003c/strong\u003e(5), 537 (2021b).\u003c/li\u003e\n\u003cli\u003eBongers, R. M., Hafkamp, M. S. J., Mehta, A., \u0026amp; Valk, T. A. Turvey\u0026rsquo;s Coordinative Structures Appraised. \u003cem\u003eEcol. Psychol.\u003c/em\u003e, \u003cstrong\u003e37\u003c/strong\u003e(4), 340\u0026ndash;352 (2025). \u003c/li\u003e\n\u003cli\u003eFitts, P. M. The information capacity of the human motor system in controlling the amplitude of movement. \u003cem\u003eJ. Exp. Psychol\u003c/em\u003e., \u003cstrong\u003e47\u003c/strong\u003e(6), 381\u0026ndash;391 (1954). \u003c/li\u003e\n\u003cli\u003eMottet, D., \u0026amp; Bootsma, R. J. The dynamics of goal-directed rhythmical aiming. \u003cem\u003eBiol. Cybern\u003c/em\u003e., \u003cstrong\u003e80\u003c/strong\u003e(4), 235\u0026ndash;245 (1999).\u003c/li\u003e\n\u003cli\u003eHaken, H., Kelso, J. A. S., \u0026amp; Bunz, H. A theoretical model of phase transitions in human hand movements. \u003cem\u003eBiol. Cybern.\u003c/em\u003e, \u003cstrong\u003e51\u003c/strong\u003e(5), 347\u0026ndash;356 (1985).\u003c/li\u003e\n\u003cli\u003eKelso, J. A. S. Phase transitions and critical behavior in human bimanual coordination. \u003cem\u003eAm. J. Physiol. Regul. Integr. Comp. Physiol.\u003c/em\u003e, \u003cstrong\u003e246\u003c/strong\u003e(6) (1984).\u003c/li\u003e\n\u003cli\u003eKelso, J. A. S., Scholz, J. P., \u0026amp; Sch\u0026ouml;ner, G. Nonequilibrium phase transitions in coordinated biological motion: Critical fluctuations. Phys. Lett. A., \u003cstrong\u003e118\u003c/strong\u003e(6), 279\u0026ndash;284 (1986). \u003c/li\u003e\n\u003cli\u003eBeek, P. J., Peper, C. E., \u0026amp; Stegeman, D. F. Dynamical models of movement coordination. \u003cem\u003eHum. Mov. Sci.\u003c/em\u003e, \u003cstrong\u003e14\u003c/strong\u003e(4\u0026ndash;5), 573\u0026ndash;608 (1995). \u003c/li\u003e\n\u003cli\u003eKelso, J. A. S. The Haken\u0026ndash;Kelso\u0026ndash;Bunz (HKB) model: From matter to movement to mind. \u003cem\u003eBiol. Cybern.\u003c/em\u003e, \u003cstrong\u003e115\u003c/strong\u003e(4), 305\u0026ndash;322 (2021a).\u003c/li\u003e\n\u003cli\u003eSchmidt, R. C., \u0026amp; Richardson, M. J. Dynamics of Interpersonal Coordination. In A. Fuchs \u0026amp; V. K. Jirsa (Eds.), \u003cem\u003eCoordination: Neural, Behavioral and Social Dynamics\u003c/em\u003e (281\u0026ndash;308). Springer Berlin Heidelberg (2008).\u003c/li\u003e\n\u003cli\u003eSchmidt, R. C., \u0026amp; Turvey, M. T. Phase-entrainment dynamics of visually coupled rhythmic movements. \u003cem\u003eBiol. Cybern.\u003c/em\u003e, \u003cstrong\u003e70\u003c/strong\u003e(4), 369\u0026ndash;376 (1994). \u003c/li\u003e\n\u003cli\u003eSchmidt, R. C., Christianson, N., Carello, C., \u0026amp; Baron, R. Effects of Social and Physical Variables on Between-Person Visual Coordination. \u003cem\u003eEcol. Psychol\u003c/em\u003e., \u003cstrong\u003e6\u003c/strong\u003e(3), 159\u0026ndash;183 (1994).\u003c/li\u003e\n\u003cli\u003eDe Poel, H. J. Anisotropy and Antagonism in the Coupling of Two Oscillators: Concepts and Applications for Between-Person Coordination. \u003cem\u003eFront. Psychol\u003c/em\u003e., \u003cstrong\u003e7\u003c/strong\u003e (2016). \u003c/li\u003e\n\u003cli\u003eLatash, M. L. The bliss (not the problem) of motor abundance (not redundancy). \u003cem\u003eExp. Brain Res\u003c/em\u003e., \u003cstrong\u003e217\u003c/strong\u003e(1), 1\u0026ndash;5 (2012).\u003c/li\u003e\n\u003cli\u003eScholz, J. P., \u0026amp; Sch\u0026ouml;ner, G. The uncontrolled manifold concept: Identifying control variables for a functional task. \u003cem\u003eExp. Brain Res.\u003c/em\u003e, \u003cstrong\u003e126\u003c/strong\u003e(3), 289\u0026ndash;306 (1999). \u003c/li\u003e\n\u003cli\u003eSch\u0026ouml;ner, G. Recent developments and problems in human movement science and their conceptual implications. \u003cem\u003eEcol. Psychol.\u003c/em\u003e, \u003cstrong\u003e7\u003c/strong\u003e(4), 291\u0026ndash;314 (1995).\u003c/li\u003e\n\u003cli\u003eBongers, R. M., Fernandez, L., \u0026amp; Bootsma, R. J. Linear and logarithmic speed\u0026ndash;accuracy trade-offs in reciprocal aiming result from task-specific parameterization of an invariant underlying dynamics. \u003cem\u003eJ. Exp. Psychol. Hum. Percept. Perform\u003c/em\u003e., \u003cstrong\u003e35\u003c/strong\u003e(5), 1443\u0026ndash;1457 (2009).\u003c/li\u003e\n\u003cli\u003eDomkin, D., Laczko, J., Djupsj\u0026ouml;backa, M., Jaric, S., \u0026amp; Latash, M. L. Joint angle variability in 3D bimanual pointing: Uncontrolled manifold analysis. \u003cem\u003eExp. Brain Res.\u003c/em\u003e, \u003cstrong\u003e163\u003c/strong\u003e(1), 44\u0026ndash;57 (2005).\u003c/li\u003e\n\u003cli\u003eGolenia, L., Schoemaker, M. M., Otten, E., Tuitert, I., \u0026amp; Bongers, R. M. The development of consistency and flexibility in manual pointing during middle childhood. \u003cem\u003eDev. Psychobiol\u003c/em\u003e. \u003cstrong\u003e60\u003c/strong\u003e(5), 511\u0026ndash;519 (2018).\u003c/li\u003e\n\u003cli\u003eLamb, P. F., \u0026amp; St\u0026ouml;ckl, M. On the use of continuous relative phase: Review of current approaches and outline for a new standard. \u003cem\u003eClin. Biomech\u003c/em\u003e., \u003cstrong\u003e29\u003c/strong\u003e(5), 484\u0026ndash;493 (2014).\u003c/li\u003e\n\u003cli\u003eDe Poel, H. J., Roerdink, M., Peper, C. (Lieke) E., \u0026amp; Beek, P. J. A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures. \u003cem\u003eBrain Sci\u003c/em\u003e., \u003cstrong\u003e10\u003c/strong\u003e(10), 724 (2020).\u003c/li\u003e\n\u003cli\u003eRiley, M. A., \u0026amp; Turvey, M. T. Variability and Determinism in Motor Behavior. \u003cem\u003eJ. Mot. Behav\u003c/em\u003e., \u003cstrong\u003e34\u003c/strong\u003e(2), 99\u0026ndash;125 (2002).\u003c/li\u003e\n\u003cli\u003eStergiou, N., Harbourne, R. T., \u0026amp; Cavanaugh, J. T. Optimal Movement Variability: A New Theoretical Perspective for Neurologic Physical Therapy. \u003cem\u003eJ. Neurol. Phys. Ther\u003c/em\u003e., \u003cstrong\u003e30\u003c/strong\u003e(3), 120\u0026ndash;129 (2006).\u003c/li\u003e\n\u003cli\u003eStergiou, N., \u0026amp; Decker, L. M.. Human movement variability, nonlinear dynamics, and pathology: Is there a connection? Hum. Mov. Sci., \u003cstrong\u003e30\u003c/strong\u003e(5), 869\u0026ndash;888 (2011). \u003c/li\u003e\n\u003cli\u003eDelignieres, D., \u0026amp; Marmelat, V. Fractal Fluctuations and Complexity: Current Debates and Future Challenges. \u003cem\u003eCrit. Rev. Biom. Eng\u003c/em\u003e., \u003cstrong\u003e40\u003c/strong\u003e(6), 485\u0026ndash;500 (2012).\u003c/li\u003e\n\u003cli\u003eCavanaugh, J. T., Kelty-Stephen, D. G., \u0026amp; Stergiou, N. Multifractality, Interactivity, and the Adaptive Capacity of the Human Movement System: A Perspective for Advancing the Conceptual Basis of Neurologic Physical Therapy. \u003cem\u003eJ. Neurol. Phys. Ther\u003c/em\u003e., \u003cstrong\u003e41\u003c/strong\u003e(4), 245\u0026ndash;251 (2017).\u003c/li\u003e\n\u003cli\u003eHausdorff, M., Purdon, L., Ladin, Z., Wei, Y., \u0026amp; Goldberger, A. L. Fractal dynamics of human gait: Stability of long-range correlations in stride interval fluctuations. XXXXxx (1996).\u003c/li\u003e\n\u003cli\u003eHausdorff, J. M., Mitchell, S. L., Firtion, R., Peng, C. K., Cudkowicz, M. E., Wei, J. Y., \u0026amp; Goldberger, A. L. Altered fractal dynamics of gait: Reduced stride-interval correlations with aging and Huntington\u0026rsquo;s disease\u003cem\u003e. J. Appl. Physiol\u003c/em\u003e., \u003cstrong\u003e82\u003c/strong\u003e(1), 262\u0026ndash;269 (1997).\u003c/li\u003e\n\u003cli\u003eDen Hartigh, R. J. R., Cox, R. F. A., Gernigon, C., Van Yperen, N. W., \u0026amp; Van Geert, P. L. C. Pink Noise in Rowing Ergometer Performance and the Role of Skill Level. \u003cem\u003eMotor Control\u003c/em\u003e, 19(4), 355\u0026ndash;369 (2015).\u003c/li\u003e\n\u003cli\u003eDen Hartigh, R. J. R., Marmelat, V., \u0026amp; Cox, R. F. A. Multiscale coordination between athletes: Complexity matching in ergometer rowing. \u003cem\u003eHum. Mov. Sci\u003c/em\u003e., \u003cstrong\u003e57\u003c/strong\u003e, 434\u0026ndash;441 (2018).\u003c/li\u003e\n\u003cli\u003eCoey, C. A., Hassebrock, J., Kloos, H., \u0026amp; Richardson, M. J. The complexities of keeping the beat: Dynamical structure in the nested behaviors of finger tapping. \u003cem\u003eAttent. Percept. Psychophys\u003c/em\u003e., \u003cstrong\u003e77\u003c/strong\u003e(4), 1423\u0026ndash;1439 (2015).\u003c/li\u003e\n\u003cli\u003eCoey, C. A., Washburn, A., Hassebrock, J., \u0026amp; Richardson, M. J. Complexity matching effects in bimanual and interpersonal syncopated finger tapping. \u003cem\u003eNeurosc. Lett\u003c/em\u003e., \u003cstrong\u003e616\u003c/strong\u003e, 204\u0026ndash;210 (2016).\u003c/li\u003e\n\u003cli\u003eSternad, D. It\u0026rsquo;s not (only) the mean that matters: Variability, noise and exploration in skill learning. \u003cem\u003eCurr. Opin. Behav. Sci\u003c/em\u003e.,\u003cstrong\u003e 20\u003c/strong\u003e, 183\u0026ndash;195 (2018).\u003c/li\u003e\n\u003cli\u003eGrover, F. M., Andrade, V., Carver, N. S., Bonnette, S., Riley, M. A., \u0026amp; Silva, P. L. A Dynamical Approach to the Uncontrolled Manifold: Predicting Performance Error During Steady-State Isometric Force Production. \u003cem\u003eMotor Control\u003c/em\u003e, \u003cstrong\u003e26\u003c/strong\u003e(4), 536\u0026ndash;557 (2022).\u003c/li\u003e\n\u003cli\u003eValk, T. A., Mouton, L. J. \u0026amp; Bongers, R. M. Joint-Angle Coordination Patterns Ensure Stabilization of a Body-Plus-Tool System in Point-to-Point Movements with a Rod. \u003cem\u003eFront. Psychol.\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e (2016).\u003c/li\u003e\n\u003cli\u003eValk, T. A., Mouton, L. J., Otten, E. \u0026amp; Bongers, R. M. Fixed muscle synergies and their potential to improve the intuitive control of myoelectric assistive technology for upper extremities. J\u003cem\u003e. Neuroeng. Rehabil\u003c/em\u003e. \u003cstrong\u003e16\u003c/strong\u003e, 6 (2019).\u003c/li\u003e\n\u003cli\u003eWu, G. et al. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion\u0026mdash;Part II: shoulder, elbow, wrist and hand. \u003cem\u003eJ. Biomech.\u003c/em\u003e \u003cstrong\u003e38\u003c/strong\u003e, 981\u0026ndash;992 (2005).\u003c/li\u003e\n\u003cli\u003eMattos, D. J. S., Latash, M. L., Park, E., Kuhl, J., \u0026amp; Scholz, J. P. Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence. \u003cem\u003eJ. Neurophysiol\u003c/em\u003e., \u003cstrong\u003e106\u003c/strong\u003e(3), 1424\u0026ndash;1436 (2011).\u003c/li\u003e\n\u003cli\u003eScholz, J. P., Sch\u0026ouml;ner, G., Hsu, W. L., Jeka, J. J., Horak, F., \u0026amp; Martin, V. Motor equivalent control of the center of mass in response to support surface perturbations. \u003cem\u003eExp. Brain Res.\u003c/em\u003e, \u003cstrong\u003e180\u003c/strong\u003e(1), 163\u0026ndash;179 (2007).\u003c/li\u003e\n\u003cli\u003eScholz, J. P., Dwight-Higgin, T., Lynch, J. E., Tseng, Y. W., Martin, V., \u0026amp; Sch\u0026ouml;ner, G. Motor equivalence and self-motion induced by different movement speeds. \u003cem\u003eExp. Brain Res\u003c/em\u003e., \u003cstrong\u003e209\u003c/strong\u003e(3), 319\u0026ndash;332 (2011).\u003c/li\u003e\n\u003cli\u003eTuitert, I., Valk, T. A., Otten, E., Golenia, L., \u0026amp; Bongers, R. M. Comparing Different Methods to Create a Linear Model for Uncontrolled Manifold Analysis. \u003cem\u003eMotor Control\u003c/em\u003e, \u003cstrong\u003e23\u003c/strong\u003e(2), 189\u0026ndash;204 (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9455901/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9455901/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe ecological-dynamical approach holds that movement is self-organized, implying a circular causality between the kinematics of the end-effector and the coordination of degrees of freedom (DOF) into synergies. Yet, how this circular causality manifests itself in redundant effector systems remains underexplored. Therefore, we investigated concurrently the coordination dynamics of the end-effector and the upper extremity joint angles \u0026ndash;as DOF\u0026ndash;during a reciprocal aiming task with varying target widths and distances. Results revealed that different joint angles were differently related to the end-effector. A continuous relative phase analysis showed that the three joint angles with the largest range of motion synchronized with the end-effector, suggesting a strong dynamical coupling between the levels. At the same time, all joint angles exhibited variability that was not shared with the end-effector. A detrended fluctuation analyses revealed signatures of fractality as well as drift in this residual variability, suggesting distinct dynamical regimes at the DOF level. Moreover, the angular drift occurred predominantly along the uncontrolled manifold, leaving the end-effector unaffected. We conclude that the DOF of a redundant system are not only coordinated into synergies to stabilize the end-effector, but also to keep the system flexible.\u003c/p\u003e","manuscriptTitle":"Concurrent synchronization and covariation in upper extremity joint angles during a reciprocal aiming task","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-09 05:49:29","doi":"10.21203/rs.3.rs-9455901/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-12T08:06:20+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T12:13:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T08:03:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-08T15:40:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18315797246389857242986151008518050068","date":"2026-05-03T01:58:12+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T01:26:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"292690621298416684350310896547479679581","date":"2026-05-02T02:15:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"309107918985563649905172157806915371820","date":"2026-04-30T15:18:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"247416956126134355715915777824804815274","date":"2026-04-30T10:17:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"302649954274766547005618903985684977373","date":"2026-04-30T05:20:07+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-30T02:08:14+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-04-28T11:19:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-24T14:21:36+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-24T14:21:30+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-04-18T10:16:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"01ca867a-4c27-4bd4-878f-02cfc06a7521","owner":[],"postedDate":"May 9th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-12T08:06:20+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T12:13:42+00:00","index":63,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T08:03:13+00:00","index":62,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-08T15:40:57+00:00","index":60,"fulltext":""},{"type":"reviewerAgreed","content":"18315797246389857242986151008518050068","date":"2026-05-03T01:58:12+00:00","index":55,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T01:26:13+00:00","index":54,"fulltext":""},{"type":"reviewerAgreed","content":"292690621298416684350310896547479679581","date":"2026-05-02T02:15:21+00:00","index":50,"fulltext":""},{"type":"reviewerAgreed","content":"309107918985563649905172157806915371820","date":"2026-04-30T15:18:32+00:00","index":46,"fulltext":""},{"type":"reviewerAgreed","content":"247416956126134355715915777824804815274","date":"2026-04-30T10:17:00+00:00","index":42,"fulltext":""},{"type":"reviewerAgreed","content":"302649954274766547005618903985684977373","date":"2026-04-30T05:20:07+00:00","index":41,"fulltext":""},{"type":"reviewersInvited","content":"24","date":"2026-04-30T02:08:14+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":67513776,"name":"Biological sciences/Neuroscience"},{"id":67513777,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-12T08:13:14+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-09 05:49:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9455901","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9455901","identity":"rs-9455901","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}