New directions offered by the dynamical systems ...

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 14, No. 5, pp. 435-462. © 2010 Society for Chaos Theory in Psychology & Life Sciences.

New Directions Offered by the Dynamical Systems Approach to Bimanual Coordination for Therapeutic Intervention and Research in Stroke Rita Sleimen-Malkoun, Université de la Méditerranée et CNRS, Marseille, France Jean Jacques Temprado 1, Université de la Méditerranée et CNRS, Marseille, France Viktor K. Jirsa, Université de la Méditerranée et CNRS, Marseille, France Eric Berton, Université de la Méditerranée et CNRS, Marseille, France Abstract: In the present paper, we review the main concepts of the dynamical systems approach to bimanual coordination and propose applications to therapeutic intervention for functional recovery of coordinated movements in stroke. Further, we describe the behavioral alterations of discrete bimanual coordination resulting from cerebral vascular accident (CVA) lesions and speculate on the possibility of mimicking the mechanisms of CVA lesions via symmetry breaking in dynamic systems. Key Words: stroke; rehabilitation; upper-limb; bilateral arm training; coupling; dynamical systems. INTRODUCTION Healthy people most frequently use bimanual movements in their natural environment and daily living activities (Kilbreath & Heard, 2005). Moreover, despite that they are able to produce a seemingly unlimited number of interlimb coordination patterns, some elementary rules underlie the production of stable and flexible movement synergies (Swinnen, 2002). During the last twenty years, efforts of movement scientists working in the theoretical context of dynamical systems have been devoted to understand the mechanisms and principles underlying the emergence, stabilization, destabilization and changes of coordination patterns. The so-called “synergetic approach” (Haken, 1983) and the paradigm of rhythmic bimanual coordination introduced almost 30 years ago by Kelso and collaborators (e.g. Haken, Kelso, & Bunz, 1985; 1

Correspondence address: Jean Jacques Temprado, UMR 6233 Institut des Sciences du Mouvement. Université de la Méditerranée et CNRS, Faculté des Sciences du Sport - 163 Avenue de Luminy, BP 910 - 13288 Marseille cedex - France. E-mail: [email protected]

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Kelso, 1981, 1984) have provided new grounds to address these issues (e.g. Kelso, 1995, 2009). The dynamic systems approach to coordination patterns has primarily focused on non-disabled individuals so that its possible applications to motor deficits and therapeutic interventions have been scarcely envisaged (see Fonseca, Holt, Saltzman, & Fetters, 2001; Holt, Obusek, & Fonseca, 1996; Holt, Fonseca, LaFiandra, 2000; Schalow, 2002, 2006; Scholz, 1990; van Emmerik & Wagenaar,1996 for notable exceptions). Thus, the question remains of whether the dynamic theory of coordination patterns may provide theoretical foundations and adequate research methods to address the issue of bimanual coordination in stroke patients and to help therapists to improve the efficacy of rehabilitation protocols. This issue is of importance since stroke results in important chronic functional limitation of upper-limb function, including coordination, even after several months of rehabilitation. Consequently, patients’ autonomy and quality of life dramatically decrease. Thus, recovery of the functional use of upper limbs highlights the need of clinicians for neuro-rehabilitation interventions that are theoretically founded and methodologically reliable. The general objective of the present paper is to draw the prospect of how the basic coordination principles established in the undamaged neuromusculo-skeletal system (NMSS) by the dynamic pattern theory might also provide a conceptual and methodological framework for understanding bimanual coordination in stroke patients and its application to stroke rehabilitation. An attractive hypothesis in this respect is that cerebral vascular accident (CVA) modifies the neural coupling scheme and, more generally, the coalition of constraints that shape bimanual coordination. As a consequence, after a unilateral CVA lesion, the neuro-musculo-skeletal system becomes internally constrained in an asymmetrical manner and will give rise to bimanual synergies characterized by specific behavioral signatures of symmetry breaking. We propose that these behavioral signatures could be used as a window into the central nervous system (CNS) alterations after stroke and, in particular, the alterations of interlimb coupling. Consequently, the concepts, methods and tools of self-organizing dynamic system approach might offer new directions for understanding coordination alterations in stroke and then potentially lead to original therapeutic interventions. In the first part of the present paper, we briefly review the main concepts and tools of the dynamical systems approach to bimanual coordination. In particular, we will address the issue of coupling, symmetry breaking, attention and learning, which may be of particular interest for stroke rehabilitation. Since extensive reviews are already available in the literature (e.g. Kelso, 1995, 2009) and because we focus on clinical applications, conceptual rather than mathematical foundations of the dynamic theory of coordination patterns will be presented. Moreover, we restrict the scope of the paper to the behavioral level. In the second part, we envisage how the dynamic systems framework might give rise to specifications and guidelines for therapeutic intervention in the domain of interlimb coordination. Finally, in a third part, we briefly describe the alterations

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of discrete bimanual coordination in stroke and draw parallels with symmetry breaking phenomena captured by dynamical models of movement coordination. Then, we propose new directions for experimental programs investigating the alterations of bimanual coupling in stroke. BIMANUAL COORDINATION DYNAMICS IN THE UNDAMAGED NEURO-MUSCULO-SKELETAL SYSTEM The basic assumption of the synergetic approach to interlimb coordination is that, as in many other nonlinear complex systems, basic coordination patterns arise spontaneously under certain conditions, as the result of self-organization and coupling influences between interacting components at multiple levels of the NMSS. Accordingly, it is assumed that: (a) emerging patterns of coordination can be characterized by a low dimensional order parameter and (b) pattern stability, loss of stability and the transition between existing patterns reflect the underlying coordination dynamics that can be captured formally by an equation of motion of the order parameter. Some of the most promising support for the dynamic systems approach to coordination pattern has been shown in bimanual coordination tasks. Self-organizing Coordination Patterns and Coupling Principles in Cyclic Bimanual Coordination In cyclic bimanual coordination, coupling interactions that occur at multiple levels in the NMSS can be finally captured by the relative phase between limbs. Bimanual coordination is then characterized by two preferred patterns of coordination, corresponding to 0° and 180° of relative phase and the so-called “in-phase” and “anti-phase”, respectively (Kelso, 1984). In the case of finger motion in the horizontal plane, the in-phase pattern involves symmetric motion of the hands in opposite directions, due to the simultaneous activation of homologous muscles, whereas the anti-phase pattern involves motion in the same direction, with simultaneous activity of the antagonist muscles. The in-phase and anti-phase denomination has been applied to a large variety of bimanual movements as those resulting from flexion-extension of the wrists (e.g. Salesse, Ouiller, & Temprado, 2005), pronation-supination of the forearms (e.g. Temprado, Zanone, Monno, & Laurent, 1999), and flexionextension of the elbows (e.g. Lee, Almeida, & Chua, 2002). Whatever the type of movement task, the in-phase pattern proved to be more stable than the antiphase pattern and an unavoidable switch from the latter to the former (i.e. a phase transition) occurs when oscillation frequency increases beyond a given critical threshold. The behavioral picture of this spontaneous dynamics of bimanual coordination has been formalized by Haken, Kelso and Bunz (1985, henceforth, HKB model). Relative phase between limb oscillations is considered an order parameter of the bimanual coordination dynamics, which captures at a behavioral level the inherent properties of the NMSS. In this model, relative phase dynamics is represented by the following equation of motion:

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f = - a sin f - 2b sin 2f + Qe The parameters a and b govern the strength of the coupling. Changes in the ratio b/a mimic the effect of the frequency (i.e. the control parameter): A decrease in the ratio corresponds to an increase in movement frequency. The parameter e represents the presence of noise fluctuations of strength Q, which is supposed to be constant for both the in-phase and anti-phase coordination patterns. Post, Peper, Daffertshofer, and Beek (2000) showed however that noise strength could be different for the in-phase and the anti-phase patterns as the result of different neurophysiological processes involved in the production of each pattern. Intuitively, the bimanual dynamics may be imagined as a potential landscape composed of two valleys of different depths in which an over-damped particle, representing the current coordination state of the system, moves freely following a gravitational force (see Fig. 1). The lower and higher troughs are “located” at 0° (in-phase) and 180° (anti-phase), respectively. Thus, depending on its initial state, the system is attracted to one of the two valleys, where it eventually stabilizes. The relative depths of the two valleys may vary as a function of oscillation frequency, thus modifying the attractive strength of the stable states (Fig. 1).

Fig. 1. The potential function equation developed by Haken et al. (1985) on the interval [-180°, 180°] for different values of b/a. (adapted from Kelso, 1995).

The ratio b/a in Fig. 1 represents the oscillation frequency effect on the potential landscape. As the ratio b/a is decreased (which corresponds to an increase in frequency), the anti-phase pattern becomes less stable. At a specific value of b/a, the local minimum at 180° disappeared entirely, and any small fluctuation kicks the system into the remaining minimum at 0°. Then, the potential landscape becomes monostable. This corresponds to the spontaneous switch from anti-phase to in-phase observed experimentally. According to the HKB model, the attractive properties of relative phase


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are due to a nonlinear coupling between the homologous limbs, specifying their relative positions and velocities. Coupling may be thought of as an informational flow that links the system's components and captures the multiple interactions that the components actually entertain with each other, substantiated through various substrates (neural, musculo-skeletal, vascular, etc.; see also Bingham, Schmidt, Turvey, & Rosenblum, 1991). Neural processes take an important part in this informational coupling. They can be accounted for by bilateral interactions and information flows between the two hemispheres, resulting in neural crosstalk occurring at different levels of the CNS (Banerjee & Jirsa, 2007; Cardoso de Olivera, 2002; Carson, 2005; Carson & Kelso, 2004). The neural crosstalk model is based on the hypothesis that activation of the muscles of one limb may affect muscle activity in the contralateral limb due to bilateral activation processes. This model accounts for asymmetric interactions between limbs thereby predicting the results of numerous behavioral studies in both discrete and rhythmic movement tasks (Banerjee & Jirsa, 2007) and, in particular, phase transitions in cyclic bimanual tasks (Cattaert, Semjen, & Summers, 1999). A deeper understanding of coupling mechanisms rests however on uncovering how behavioral pattern formation, stabilization and changes are rooted in the underlying brain processes (i.e. cortical dynamics). In this perspective, behavioral flexibility can be explained by the fact that neural networks in the CNS work in a metastable dynamic regime. In such regime, a balanced interplay between integrating and segregating influences allows for a context-dependent reshaping of the system’s attractor landscape, inducing flexible shifts between the dynamic modes of brain networks activation. These switches between dynamic states are the basis of the different tendencies of spatiotemporal coupling between limbs observed at a behavioral level. As an illustration, the synergetic phase transitions paradigm provided a methodological strategy through which to discover laws of neural and behavioral pattern generation and their existing connections; see Jantzen & Kelso (2007) for an extensive review. Indeed, systematically destabilizing the system through an appropriate control parameter range lead to different behavioral regimes and provides an entry point for identifying the cortical and sub-cortical structures involved in pattern switching as well as for studying neural mechanism of pattern selection, formation and change (e.g. Meyer-Lindberger, Zieman, Hajac, Cohen, & Berman, 2002). In this respect, research reviewed by Jantzen and Kelso (2007) strongly support the notion that activity across coordination networks is linked to behavioral stability: Depending on how close the brain is to pattern switching, disruption of the neural network may result in destabilizing the actual behavioral pattern and triggering the transition (e.g. MeyerLindberger et al., 2002). More research is needed however to understand the networks involved in terms of localization, connectivity and dynamics in clinical populations. In particular, further work should address the important issue in stroke of how behavior relates to brain damage and how disruptions of the

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functional coupling scheme relate to lesion size and location in the anatomical connectivity (van Delden et al., 2009). Coupling Strength, Symmetry-breaking and the Dynamic Landscape Symmetry breaking in interlimb coordination has been shown to affect the accuracy and stability of coordination, but also more recently the dynamic repertoire in certain instances. Two mechanisms of symmetry breaking have been proposed, both fundamentally different in their nature. Historically reported first by Kelso, Delcolle and Schöner (1990), neuro-mechanical differences between the coordinated limbs, such as the difference in natural frequencies of the coordinated limbs, may lead to a variety of coordinative phenomena, ranging from moderate shifts in relative phase in combination with reduced stability, to “relative coordination” in which the behavior is no longer (or only transiently) attracted to a stable coordination pattern. The symmetry breaking effect plays here the role of a perturbation of the dynamic repertoire of the coordinating system. In contrast, Fuchs and Jirsa (2000) reported a form of symmetry breaking, which rather modulates the available dynamic repertoire and allows the coordinating system to exchange roles of stable and unstable coordinating patterns. This form of symmetry breaking appears to be closer related to functional aspects of the perception-action cycle and cannot be directly related to mechanical oscillator properties as in Kelso et al. (1990). In the following, we present more details on both types of symmetry breaking. Much of the observed range of behaviors can be simulated by adding a single symmetry-breaking term to the original symmetric HKB potential, indicating that most resulted from the same basic coordination principles (Kelso et al., 1990): .

f = Dw - a sin f - 2b sin 2f + Qe The detuning term (Dw) is commonly referred to the eigenfrequency difference between the coordinated limbs. It shifts the location of in-phase and anti-phase attractors in the HKB potential, thereby acting as a control parameter that affects pattern symmetry and stability and may induce transitions between coordination modes (Figure 2). For large values of Dw there is a point at which the potential loses its minima. Consequently, the form of the potential gives rise to relative coordination. The critical detuning value at which relative coordination appears depends in turn on the coupling strength (e.g. the value of b/a ratio). Thus, bimanual de-synchronization results from the combined effects of increased magnitude of (biomechanical) asymmetry between limbs and loss of entrainment due to a decrease in coupling strength (Fig. 2). The symmetry breaking mechanism proposed by Fuchs and Jirsa (2000) is motivated by the observation, first made by Carson, Riek, Smethurst, Párraga, and Byblow (2000), that variation of certain intrinsic constraints may lead to the


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Fig.2. Representation of the potential V(φ) of coordination dynamics with broken symmetry. The increase of the individual eigenfrequencies induces the progressive vanishing of stable fixed points located at φ = 0, ± 180° together with a shifting away from the pure in-phase (0°) and anti-phase patterns (180°).

exchange of the roles played by the coordination patterns. For instance, in Carson et al.’s (2000) study, as a symmetry breaking parameter, σ, is varied during bimanual interlimb coordination, bistability of the coordination patterns anti- and in-phase persists for lower movement frequencies, but the in-phase pattern becomes unstable for greater movement frequencies. This situation reflects the inverted role of the anti- and in-phase coordination pattern, where traditionally the anti-phase coordination pattern loses stability for increasing movement frequencies (see Fuchs & Jirsa, 2000 for a detailed development of the argument). Clearly, in Carson et al.’s (2000) experiment, symmetry-breaking of the dynamical landscape did not result of eigenfrequency detuning, as suggested by the classical model of symmetry breaking in bimanual coordination literature (Kelso, 1995; Park & Turvey, 2008). Indeed, the “Dw” symmetry-breaking parameter biases the dynamics at previously symmetric states towards a particular behavior (one would say that these states “degenerate”), but it never changes the repertoire of behaviors. According to Fuchs and Jirsa (2000), as a result of increasing the value of the symmetry breaking parameter, bimanual coordination patterns (and the potential function) are predicted to remain as they are when σ is equal to 0; when σ is equal to 1, the potential profile of the HKB function is completely “reversed” so that the

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anti-phase pattern becomes the most stable pattern and upon increasing the oscillation frequency may give rise to transitions to the anti-phase pattern (see Fig. 3). This functional symmetry of the perception-action is expressed in the following Fuchs-Jirsa expansion of the HKB equation: .

f = - a (1 - 2s ) sin f - 2b sin 2f + Qe Such symmetry breaking characteristics cannot be understood in the framework of Kelso et al. (1990), and hence reflects a different mechanism. Specifically, Fuchs and Jirsa’s model also simulates that for an intermediate value of σ (σ≈0.5), the in-phase and anti-phase patterns could vanish, leading to a complete absence of coordination and independence of the two limbs.

Fig. 3. HKB potential function from the Fuchs-Jirsa expansion of HKB equation for different values of b/a and the symmetry breaking parameter (σ). One observes notably a complete absence of coordination and independence of the two limbs for an intermediate value of σ (σ≈0.5).

Though the nature of the exact mechanisms underlying such symmetrybreaking phenomena remains unknown, a plausible origin of the Fuch and Jirsa’s parameter “σ” might be found in the neural couplings underlying the coordination dynamics. This hypothesis is not purely speculative and is supported by the results observed in recent studies by our group. Notably, the


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Fuchs-Jirsa model perfectly predicted the observed results in bimanual coordination, even when there was no frequency detuning between limbs that is, which were inexplicable by the local (biomechanical) mechanism via symmetrybreaking Δω (Salesse, et al., 2005; Salesse, Oullier, Jirsa & Temprado, 2010; Temprado, Swinnen, Coutton-Jean, & Salesse, 2007). The exact nature of the underlying disruptions of perception-action cycle giving rise to the complete loss of the 0° and 180° attractors and leading to the absence of coordination deserves however further investigation. Behavioral and the Dynamic Landscape: Attention, Intention and Learning Seminal work on bimanual coordination dynamics aimed to handle the directed aspects of coordination behavior, including intention, attention, and learning (e.g. Temprado et al., 1999; Zanone & Kelso, 1992). In this perspective, it has been assumed that the richness of the repertoire of coordination patterns results from the interplay of intrinsic patterns and behavioral information, which attracts them in the direction of the task to be performed or learned. The argument is that intention, attention or learning must be considered as a behavioral information in the dynamical sense, that is, in relation to its continuous influence on the collective variable dynamics. Accordingly, behavioral information has been modeled as an extrinsic constraints acting on the intrinsic dynamics toward already existing or new tobe-learned attractors in the initial landscape of the intrinsic dynamics. Behavioral information can be formalized, in relation to the intrinsic dynamics of the HKB model, by the following equation (Zanone & Kelso, 1992): V(Y) = - acosf - bcos 2f + N - c inf cos (f - yinf) The required behavioral pattern V(Y) is a function of the intrinsic dynamics and the strength of the required relative phase. This behavioral information breaks the symmetry of the coordination dynamics, in the direction of the required pattern. This extension of the HKB model has led to testable predictions. For example, the situation in which a person is initially prepared in the anti-phase pattern and is required to switch to the more stable in-phase pattern (Scholz & Kelso, 1990). One observed fast switching times, especially at the higher frequency values, due to the reduction in attraction of the anti-phase pattern as the critical point is approached. However, in the opposite case, switching from in-phase to anti-phase is longer since a greater intentional force is needed to push the pattern out of the deeper well at in-phase and into the less pronounced anti-phase well. In case of attention focused on an existing pattern (e.g. in-phase or anti-phase), behavioral information does not compete with the intrinsic tendencies; it just leads to increasing the strength of coupling and then the stability of the targeted existing attractor (Lee, Blandin, & Proteau, 1996; Temprado et al., 1999, Temprado, Monno, Zanone, & Kelso 2002). De Poel,

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Peper, and Beek (2008) found that directing attention to the preferred hand even led to an increase in pattern stability. These findings demonstrated that active intentional and/or attentional control on the part of the participant could delay, or prevent phase transition, increasing the stability of the pattern. In case of learning, behavioral information may be perceptually specified by metronomes or memory (Yamanashi, Kawato, & Suzuki, 1980; Zanone & Kelso, 1992). Although the information is different in both cases, either visual or memorized, similar modifications of the dynamic landscape of bimanual coordination can be found (Schöner et al., 1992). Self-organizing Coordination Patterns and Coupling Principles in Discrete Bimanual Coordination Evidence also exists however that coupling may shape bimanual synergies in discrete bimanual coordination tasks. As an illustration, Schöner (1990) proposed a dynamic model to capture the synchronization and desynchronization tendencies observed in discrete bimanual coordination. It was assumed that relative timing between limbs expresses the underlying coordination activity of the NMSS and also captures the order among the components at the behavioral level. A first step in achieving the model description has been to identify the limbs’ intrinsic dynamics in terms of initial and final postural states, as well as a stable limb trajectory connecting the former and the latter (see Schöner, 1990, p. 260, for a detailed development). The intention to move was captured by including behavioral information, which initially pushed the system and stabilizes the trajectory for approximately a halfcycle of movement without completely specifying movement time. Then, bimanual coordination has been considered as the result of coupling the dynamics of the two limbs in a fashion analogous to the HKB model of rhythmic coordination patterns. The model predicts that depending on the asymmetry between limbs, bimanual coordination may (or not) be dominated by one component and coupling may (or not) be strong enough to lead to synchronization tendency. An analogy is assumed between the anti-phase pattern of rhythmic movement and the patterns characterized by the sequential initiation of discrete movements (i.e. initiation time, IT) and/or the breaking of synchronization of movement time (MT). Schöner’s (1990) model accounted for the experimental conditions in which the two limbs differed individually in their amplitude and movement duration (Kelso, Putnam, & Goodman, 1983; Kelso, Southard, & Goodman, 1979; Marteniuk, MacKenzie, & Baba, 1984; Corcos, 1984). As an illustration of the basic properties of spontaneous temporal coordination in discrete bimanual coordination tasks, Kelso et al. (1979, 1983) used unimanual and bimanual Fitts’ tasks and manipulated the difficulty of the task and consequently, movement time, by varying both width and distance of the target (Fitts, 1954; Fitts & Peterson, 1964). In unimanual conditions, as predicted by Fitts’s law, MT was shorter for the lower index of difficulty (ID). In the bimanual conditions, task difficulty was manipulated either symmetrically (i.e.


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same ID for both hands) or asymmetrically (i.e. a different ID for each hand). Results showed that, when confronted to dissimilar movement task constraints, the fast hand slowed down to move synchronously with the slower hand, which was weakly affected by the faster one. Kelso et al. (1979) also showed a general tendency to a breakdown of synchronization when the intrinsic movements times become too dissimilar, which means that coupling was not strong enough to maintain a synchronized bimanual synergy (see also Corcos, 1984; Fowler, Duck, Mosher, & Mathieson, 1991; Marteniuk & MacKenzie, 1980; Marteniuk et al., 1984). Riek, Tresilian, Mon-Williams, Coppard, and Carson (2003) also observed that increasing asymmetry between limbs also increased sequential initiation of movements: the hand performing the longer amplitude started before the hand performing the shorter amplitude but the two hands arrived on the target simultaneously. A unifying perspective to discrete and continuous movements has been offered by the work of Jirsa and colleagues (Huys, Fernandez, Bootsma, & Jirsa, 2010; Huys, Studenka, Rheaume, Zelaznik & Jirsa, 2008; Jirsa & Kelso, 2005) who used first principles established in dynamic system theory. The excitator model (Jirsa & Kelso 2005) proposes that movements, either discrete or rhythmic, can be described by a flow field in the state space (or equivalently, phase space) that is, the space spanned by the state variables. Generally speaking, the state variables are the variables, which unambiguously identify the dynamic state of a system; for most movements position and velocity suffice. The flow in phase space prescribes the evolution of the time dependent state variables and corresponds to the rate of change of the state variables. Most notably, phase flow topologies are invariants of dynamics, and hence of movement classes: Two dynamic systems with the same flow topology mathematically belong to the same equivalence class and hence can be transformed into each other (at least locally, see Huys et al., 2008). In this sense, the excitator offers a taxonomy of models of movement generation (of the same dimension) at a high level of abstraction and includes previous models of constant phase flow (see Huys et al., 2008), including Schöner’s model (1990). It is noteworthy in the current context, that interlimb couplings are expressed in this approach as modifications of the phase flow patterns for each limb. Jirsa and Kelso (2005) proposed to compute the Euclidean distance, d, between the state vectors of each component as a measure of the coordination. Specifically they have shown that this distance captures the divergence/convergence to the coordination patterns and their in/stability in bimanual rhythmic coordination; but more importantly, in other task contexts involving combinations of discrete and rhythmic tasks, the Euclidean distance, d, continues to be a useful measure regarding the evolution of the movement trajectories and predicts changes of MT. Huys et al. (2009) applied the phase flow pattern approach to the Fitts task and demonstrated that as the index of task difficulty increases, human coordination actually evokes a different timing mechanism for the movement, i.e. the phase flow topology of the movement generating mechanism changes. In

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this sense the description of movement patterns via phase flows offers a powerful theoretical tool to describe and understand dynamic patterns and coordination dynamics. We contend that the theoretical framework proposed by the synergetic approach to coordination patterns (Haken, et al., 1985; Schöner, 1990; Jirsa & Kelso, 2005) might be helpful for elaborating principles of therapeutic interventions dedicated to functional recovery of coordinated behavior in stroke. It could also provide some insight to investigate alterations of coupling processes underlying inter-limb asymmetry in stroke. Applications of the dynamical pattern theory to stroke research and intervention should however go beyond metaphors and jargon to give rise to a theoretically and empirically founded "dynamical paradigm". In the two following sections, we speculate on: (a) how the dynamic systems approach to coordination could be applied in stroke rehabilitation and (b) how research programs in this domain could help clinicians to better understand coupling impairment resulting from CVA lesions. A DYNAMIC SYSTEMS-INSPIRED APPROACH FOR REHABILITATION OF BIMANUAL COORDINATION IN STROKE Individuals who suffer from mono-hemispheric CVA are usually confronted by varying degrees of partial paralysis of one side of the body. Kilbreath and Heard (2005) reported that less than 25% of patients discharged from rehabilitation able to use their affected hand in functional activities thus leading them to great difficulties to perform bimanual tasks, which are over and above their unimanual deficits. Since most of the tasks people perform in their daily environment require the hands to be used predominantly together (Kilbreath & Heard, 2005), bimanual deficits lead to significant decrease in quality-of-life. Several studies have examined reaching behavior in stroke subjects. They reported that stroke subjects’ behavior is characterized by decreased elbow velocity, decreased hand velocity, initial movement direction error, increased off-axis forces against the support surface, segmentation, decreased movement distance and increased trajectory curvature. Moreover, though there are usually two velocities involved in tasks as aiming or reach-and-grasp in healthy adults, it has been shown that the paretic limb usually exhibits a discontinuous movement execution so that multiple velocity changes during a movement cycle are observed as compared with the intact limb (Kamper, McKenna-Cole, Kahn, & Reinkensmeyer, 2002). Motor deficits in the paretic arm constitute a major obstacle to the recovery of the ability to perform bimanual coordinated movements since they introduce an asymmetry between the two hands kinematics. Thus, in the stroke rehabilitation literature, alterations of bimanual coordination are usually considered as the consequence of impairment of the paretic arm. However, theoretically, bimanual asymmetry could be attenuated, at least in part, by coupling interactions between limbs. Thus, the investigation of how


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coordination principles persist or are eventually lost in stroke patients may constitute a promising, though indirect, window into brain-behavior dynamic relationships when various components of the NMSS are (more or less severely) altered. A careful analysis of the literature suggests however that the status of bimanual coordination in stroke rehabilitation remains ambiguous (Cauraugh & Summers, 2005; McCombe Waller & Whitall, 2008; Stewart, Cauraugh, & Summers, 2006; Stoykov & Corcos, 2009). Although the authors most often underlined the importance of bimanual coordination recovery for stroke patients, bilateral arm training has currently been considered (and predominantly used) as a tool for improving performance of the paretic limb in unimanual tasks. Moreover, therapists are essentially concerned with the assessment and training of the basic activities of daily living (BADL), which often require separate movements of the two hands. Consequently, they may consider as a non-sense that “abstract” tasks such as those currently used in bilateral arm training (i.e. BATRACâ, Luft et al., 2004) would be taken as a standard situation for the assessment and rehabilitation of bimanual function in stroke. Consequently, coordination difficulties are most often measured by dexterity index tests and qualitative behavioral assessment during BADL. Unfortunately, these tests do not provide any information about the possible causes for deficient task performance, in particular those resulting from alterations of bimanual coupling. In this respect, the attention of therapists should be drawn on several important points arising from the dynamics systems approach to coordination patterns: (a) assessing the persistence of the basic repertoire of bimanual movements may be considered as a preliminary step indicating specific dysfunctions in the NMSS; (b) gains in bimanual coordination do not automatically arise from progress of unimanual movements; instead, they must be trained as specific synergies, not as the naïve sum of two single limbs; and (c) restoring the default mode of coupling may be indicative of an ongoing re-learning process, which is of potential benefit for stroke patients. Identification of Functional Coordination Variables Assessing bimanual coordination performance and the effectiveness of stroke therapeutic interventions requires the identification of appropriate coordination variables to quantify and qualify the nature of coordination deficits. The dynamic systems approach provides strategies in this respect. Indeed, relative phase and relative timing between limbs, which are the order parameters of coordination dynamics in rhythmic and discrete bimanual tasks (respectively), are good candidates to capture changes in bimanual (and interlimb) coordination accuracy and stability in stroke (e.g. Scholz, 1991; Ustinova, Fung, & Levin, 2006; Wagenaar & van Emmerik, 1996). They provide effective, though easily measurable, quantitative variables to assess the disruption of default modes of coordination and motor gains during rehabilitation sessions. Moreover, coordination variables are related to the working scale of therapists that is, the behavioral level of the coordinated outputs of the whole NMSS. These

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variables can be easily assessed by therapists as (more or less large) deviations from the symmetric and anti-symmetric spatio-temporal relationships (i.e. phase shifts). It is not to say that other kind of variables, as kinematics and kinetics of isolated components, do not deserve to be measured. Indeed, they both constitute useful measures of performance outcome and motor dysfunction. However, these variables do not provide any information about the spatiotemporal relationships between coordinated components, which are often the primary locus for dysfunctions in pathological movement disorders and readaptation during therapeutic interventions. Clinical Importance of Movement Variability Although the importance of variability has been stressed by the dynamic systems approach to bimanual coordination patterns, this information is far from being generally integrated into therapeutic practice (Harbourne & Stergiou, 2009). Classically, variability in behavioral data is a problem since too much within- or between-subject variability hides the underlying dynamics. However, in stroke patients, inter-individual variability is the rule rather than the exception, in particular because of the absence of systematic relationships between CVA lesion and behavioral capabilities. Thus, inherent inter-individual variability is of methodological importance since it necessitates though often with difficulty, the comparison of large groups of patients with common functional characteristics. The issue of intra-individual variability across trials is also of functional importance in stroke rehabilitation. Indeed, although too much variability is an indicator of neuro-behavioral dysfunction, movement variability does not only reflect central and/or peripheral noise (Davids, Glazier, Araújo, & Bartlett, 2003; Stergiou, Harbourne, & Cavanaugh, 2006). For instance, it also provides information about the potential functional adaptability of the stroke patients. In this respect, “optimal” variability can be assessed thanks to the use of nonlinear analysis of times series representing neuro-behavioral outputs to identify a “dynamical disease” (Glass & MacKey, 1988). This issue is out of the scope of the present paper (e.g. see for introduction in the domain of health, Goldberger, 1996; Harbourne & Stergiou, 2009) but attention of physical therapists can be drawn on the fact that intra-individual variability of coordination patterns is a characteristic of stroke patients since dynamic processes underlying movement production are fragile and strongly context and task dependent. Consequently, assessment of intra-individual variability during therapeutic interventions may provide interesting insights into the stability of neurobehavioral coordination patterns as well as indirect information about the strength of coupling between limbs. Such information is different from those given by variability of the individual limbs. Indeed, one must distinguish withinlimb variability and variability of coordination patterns that is, variability of relative phase. The former refers to fluctuations of movement time although the latter captures the fluctuations of the spatiotemporal relationship between the two limbs. Within-limb variability of the trajectory presumably reflects neural


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noise superimposed to the central commands. On the other hand, variability of relative phase strongly depends on the strength of coupling and is relatively independent of the variability of single-limb movements. Indeed, as we have demonstrated elsewhere (Temprado et al., 1999), by virtue of coupling even highly variable single-limb movements may give rise to stable patterns under the reserve that the coupling is strong enough. Consequently, variability of relative phase can be smaller than the sum of the variability of each limb, confirming the relative independence of single limb and coordination pattern fluctuations. Moreover, variability of one limb’s trajectory may be influenced by the movement of the other limb, through coupling strength during bimanual coordination (see Helmuth & Ivry, 1996; Yamanishi et al., 1980). Accordingly, assessment of intra-individual variability of both single-limb trajectories and coordination patterns before and following therapeutic interventions may provide interesting insights into the level of neural noise present in the system as well as indirect information about the strength of coupling between limbs. In stroke patients, one can hypothesize that both within-limb and coordination patterns stability should be (more or less severely) altered as a result of CVA. Thus, if a large enough coupling strength is preserved by CVA or restored by therapeutic intervention, one can predict that: (a) variability single paretic limb movements should be attenuated as a result of coupling with the non-paretic limb. Conversely, variability of the non-paretic limb might increase; (b) variability of spatio-temporal relationship should change as the result of training and/or attentional focus, thereby revealing changes in the strength of underlying interlimb coupling mechanisms. Moreover, intentional or inappropriate scaling of a control parameter may change the stability of the initial coordination pattern, resulting in an unintended spontaneous transition to another pattern or even in a wandering of spatio-temporal relationships between the limbs. These instabilities and unintentional transitions may be indicative of underlying problems and may provide useful information to therapists about the use of task constraints. A “Constraints-led” Approach to Coordination Training in Stroke Rehabilitation Stable bimanual coordination patterns emerge as the result of a coalition of internal (i.e. alterations of brain connectivity and neural dynamics) and external (i.e. task and environmental) constraints. Consequently, adaptation of the external constraints imposed to the patient when performing targeted movement tasks is of fundamental importance in stroke rehabilitation to induce plastic changes at the different levels of the CNS (i.e. changes in internal constraints). The cornerstone of a “dynamical strategy” for therapeutic intervention lies in the identification, appropriate setting and adequate manipulation of task and environmental constraints to facilitate the production of adaptive coordinated behavior. By conjugating: (a) scaling control parameters of the coordination pattern (e.g. movement speed, physical support,…), (b)

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providing behavioral information (e.g. instruction on movement goal, augmented auditory or visual feedback, guiding metronome…) and (c) practicing the a single or multiple coordination task across multiple training sessions, therapists may expect to obtain both short-term and delayed effects on coordinated behavior, as the result of stabilized CNS adaptations. Short-term effects result from transient effects of control parameters and behavioral information. Long-term effects result from repetitive practice in specific conditions. Here, the important message arising from the dynamic system approach is that, for a given coordination pattern, inappropriate scaling of a control parameter (e.g. movement speed) may preclude or, conversely, facilitate the production of an adaptive coordinated behavior. As an illustration, in the so-called bilateral arm training (BAT), introduced during the last 10 years in stroke rehabilitation (e.g., Mudie & Matyas, 1996), participants are trained to perform “default mode” bimanual coupling (either symmetric or asymmetric patterns) to stimulate informational exchanges between both hemispheres and then to improve functional efficiency of the paretic limb. In this perspective, practicing bimanual movements is supposed to induce a stimulation of bilateral neural networks, which are presumably absent in unimanual movement tasks (see McCombe Waller & Whitall, 2008 for details). In some circumstances (e.g. BATRAC device), BAT has been successfully accompanied by auditory cues specifying the required relative phasing between limbs. Such procedure corresponds, in the dynamical framework, to the use of behavioral information to stabilize the intended coordination pattern (Zanone & Kelso, 1992). In the same line of reasoning, Schalow (2002, 2006) proposed the “coordination dynamics therapy”, inspired by both the dynamic systems theory (Kelso, 1995) and the “variability of practice” motor learning principle (Seidler, 2004; Schmidt & Lee, 2005). It consisted of practicing multiple “default mode” of various interlimb coordination patterns (i.e. including but not restricted to bimanual coordination) in order to stimulate self-organizing properties of the altered CNS (Schalow, 2002). An underlying assumption of the coordination dynamics therapy (CDT) was that, by exercising as many phase and frequency relationships as possible, one helps the CNS to reorganize and repair in a more global and integrated fashion. One could also speculate that practicing about the same relative phase relationships, though implemented by various action systems (two arms, arm-leg,…), repeatedly stimulates and stabilizes the activity of specific coordination networks that transcend the components being coordinated (Jantzen & Kelso, 2007). Both these approaches (i.e. BAT and CDT), more or less directly inspired by the dynamic theory of coordination patterns, contrast with the classic intervention strategies in stroke rehabilitation, which are predominantly centered on exercising the paretic arm. Consequently, this may appear confusing first to some therapists who are used to view stroke patients’ rehabilitation as a complex movement system, which can be reduced into smaller, simpler, and thus more tractable movement units. Accordingly, many therapeutic interventions consist of learning consciously to control elementary movement patterns (e.g.


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constraint-induced therapy, Bobath, Brunnstrom), or to inhibit redundant muscle activity or to dissociate basic synergies between hand, arm, shoulder and trunk. The implicit assumption of such rehabilitation protocols is that as soon as the basic aspects of unimanual control are to some degree relearned (restored) and automatized, they can be more easily integrated in more complex bimanual movement patterns. Conversely, the “dynamic strategy” would consist of training more global coordination patterns under multiple levels of tasks constraints. The underlying conceptually founded hypothesis is that, by using repetitive practice of bimanual (or interlimb) coordination patterns, one either exploits (the still persisting) or restores (the weakened or lost) coupling interactions between limbs. Although they are grounded on different theoretical framework and assumptions, the extent to which the different therapeutic interventions strategies are complementary should be further explored. The existence of bimanual coupling is sometimes cited as a justification for using bilateral arm training (Harris-Love, McCombe Waller, & Whitall, 2005; McCombe Waller, 2008), but only few of the available studies were designed to systematically address the issue of bimanual coupling in stroke patients. Indeed, training bimanual coordination implies as a prerequisite that we need to know more about changes in the natural coupling principles of bimanual coordination resulting from CVA lesion. Only when one knows precisely what the constraints are that shape coordination patterns, one can really begin to ask questions, as to how restoration of coupling may take place. To our knowledge, definite evidence does not yet exist about the eventual persistence, loss or weakening of bimanual coupling as a function of the nature, location and severity of CVA lesions. We conclude that the dynamics system approach to coordination patterns may help researchers to address this issue in bimanual coordination. In the following section we present an overview of the existing literature on bimanual coupling in stroke. Then, we present the new directions to further investigate, at the behavioral level, the effects of CVA lesion on bimanual coupling. A DYNAMIC SYSTEMS-INSPIRED APPROACH TO THE CONSEQUENCES OF CVA ON BIMANUAL COUPLING It can be hypothesized that in stroke patients, the stability of coordination patterns should be altered as a result of CVA due to changes in coupling strength and increases in neuromotor noise. Existing data are spare in this respect since researchers were primarily interested in accuracy of bimanual performance rather than in movement variability. However, such hypothesis is not speculative as attested by the increase in variability of both unimanual and bimanual movements observed in few available studies (see the following sections). From a theoretical point of view, such hypothesis is supported by Banerjee and Jirsa’s (2007) dynamical model of the influence of neural connectivity and times delays of information flows on the stability of in-phase and anti-phase coordination patterns. Such model is based on neural crosstalk

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(Carson, 2005; Cardoso de Oliveira, 2002), which give rise to the bimanual functional coupling scheme. According to Banerjee and Jirsa (2007) increase in variability of bimanual coordination patterns can be predicted and explained by, on the one hand, alterations neural connectivity (which roughly mimics underlying changes in coupling strength in the HKB model) and, on the other hand, by an increase in time delays of information circulation and information processing in the nervous system (see Banerjee & Jirsa, 2007, for details). These theoretical predictions remain however to be confirmed by empirical data. A possible strategy to empirically determine whether bimanual coupling persists, is weakened or even lost after CVA lesion consists of assessing “preferred patterns” (i.e. phase and anti-phase) stability, accuracy and, eventually, phase transitions in rhythmic and discrete coordination tasks. Several studies have been carried out to address this issue, though not in the theoretical context of the dynamic pattern theory. In general, they report inter-limb coordination deficits after stroke that is, a decrease in consistency, accuracy, speed, and synchrony of bimanual movements (McCombe Waller & Whitall, 2004; Rose & Winstein, 2005a; Ustinova et al., 2006). Alterations of Bimanual Temporal Coupling in Rhythmic Movement Tasks Stroke patients with severe lesions usually encounter great difficulties to perform cyclic movements. For instance, Garry, van Steenis, and Summers (2005) reported that hemiparetic patients had difficulty to follow a metronome even at a relatively low frequency (1Hz). Consequently, assessment of bimanual coordination dynamics is not practical, in particular with severely impaired patients. Some studies have been carried out with mild impaired stroke patients, which were able to perform cyclic movement tasks (e.g. Lewis & Byblow, 2004; Mc Combe Waller & Whithall, 2004; Rice & Newell, 2004). McCombe Waller and Whitall (2004) studied index-tapping of coordinated movements (3 patients) and found that, as compared to healthy adults, patients were less stable and less accurate both in in-phase and in anti-phase coordination patterns. In continuous temporally symmetric (1:1) and asymmetric (2:1) movement patterns with poststroke individuals, Rice and Newell (2004) showed that the non-paretic limb was constrained to the slower paretic limb frequency and, consequently, was unable to achieve its unimanual natural frequency. Stroke participants were unable to perform the temporally asymmetric task (2:1). Instead, they switched toward a 1:1 frequency ratio and adopted an in-phase pattern. Lewis and Byblow (2004) examined interlimb temporal and spatial coordination in a continuous circle-drawing task in post-stroke hemiparetic individuals. Their results showed that the paretic limb influenced the behavior of the non-paretic limb and no improvements in the hemiparetic limb were elicited with the continuous bimanual task. Ustinova, Fung, & Levin (2006) investigated how the bilateral coordination pattern was regained after external perturbations of either the paretic and non-paretic limbs. Such an experimental strategy was inspired by those investigating relaxation time after a transient perturbation, in the context


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of dynamic systems theory (Kelso, 1995). Participants performed an arm swinging anti-phase coordination task in an upright standing position. Paretic and non-paretic arm oscillation were unexpectedly and transiently perturbed either in the forward or backward phase of the movement. Results showed that the relaxation time toward the initial anti-phase pattern was longer for stroke patients than for control participants (2 cycles versus 1 cycle, respectively). These findings suggested that coupling strength was altered, though weakly, in mildly impaired stroke patients. Assessment of Alterations of Bimanual Temporal Coupling in Discrete Movement Tasks Inconsistent results have been observed in the literature with respect to CVA effects on coupling in bimanual discrete coordination tasks. Some studies did not find kinematic signatures of coupling in either the paretic or non-paretic limb kinematics during bimanual movements. For instance, Platz, Bock, and Prass (2001), using a bilateral pointing task, found no significant difference between a control healthy participants group and a well-recovered hemiparetic group, with respect to bilateral performance and interference. On the other hand, other experiments succeeded in demonstrating the persistence of symmetric coupling after CVA. In a group of moderately impaired patients, Harris-Love et al. (2005) observed symmetric coupling interference on MT, peak velocity (PV), and peak acceleration (PA) of both arm trajectories, as well as on symmetry ratios for each variable (i.e. the value of the paretic arm divided by non-paretic one). Messier, Bourbonnais, Desrosiers, and Roy (2006) reported a similar pattern for elbow joint motion during simultaneous parallel bilateral movements. These results indicated the persistence of a symmetric coupling as usually observed in healthy participants. Finally, several studies showed an increase in asymmetric coupling after CVA. For instance, Dickstein, Hocherman, Amdor, and Pinar (1993), investigating unilateral and bilateral arm movements resulting from elbow-joint mobilization, reported a prolonged movement time for the non-paretic limb during bilateral elbow flexion compared to the unilateral condition. Temporal asymmetrical coupling, in which the paretic limb slowed the non-paretic one, has also been reported in other studies (Garry et al., 2005; Harris-Love et al., 2005; Lewis & Byblow, 2004; Messier et al., 2006; Rose & Winstein, 2005a, 2005b). On the other hand, Cunningham, Philips, Stoykov, and Walter (2002) showed some facilitation of the paretic limb that is a smoother elbow extension velocity profile during bimanual movements. The analysis of the available literature clearly showed inconsistent results with respect to the persistence of bimanual coupling in stroke patients. A parallel can be drawn with the inconsistent results reported in the literature concerning the efficacy of BAT, as a function of degree of severity of impairment resulting from CVA lesion. Several authors concluded that BAT was more effective in less severely impaired or chronic stroke patients (McCombe Waller & Whitall, 2008; but see van Delden et al., 2009 for a

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different point of view). One can hypothesize that, in severely impaired patients, conditions of practice of BAT proposed in most studies were inadequate to stimulate plasticity by means of neural cross-task and, at the behavioral level, bimanual coupling. It could be the case since in the different studies, similar task conditions (i.e. cyclic in-phase and eventually, anti-phase patterns) were proposed, whatever the severity of stroke impairment. Bimanual coordination principles evidenced by the dynamical system approach suggest that behavioral expression of bimanual coupling could depend on task constraints as, for instance, movement speed and the magnitude of asymmetry between limbs. Moreover, since most of stroke patients (i.e. the more severely impaired) are unable to perform cyclic movements, it is necessary to conceptualize how BAT could be proficiently used for discrete movement tasks (i.e. Bilateral Discrete Arm Training, BDAT). These issues deserve to be investigated in a conceptually founded research program carried out on large cohorts of participants. In the following section, we briefly draw the perspectives currently developed in a research program inspired by the dynamic theory of coordination patterns for the study of bimanual coupling in stroke. IMPAIRMENTS OF BIMANUAL COORDINATION IN STROKE: A CONSEQUENCE OF SYMMETRY BREAKING IN THE NEUROMUSCULO-SKELETAL SYSTEM? The above reviewed studies showed that alterations of bimanual coordination patterns in stroke patients can be characterized as a more or less pronounced asymmetry between limbs, which result from functional differences between the paretic and non-paretic limbs. Here we put forward to treat movement impairment due to stroke as a symmetry-breaking phenomenon in the coordination dynamics, which will allow us to make use of the powerful tools of dynamic system theory. According to Schöner’s (1990) model of discrete bimanual coordination, it can be hypothesized that relative timing between limbs express the effects of neuro-mechanical factors that may originate in both biomechanical factors such as neuro-muscular stiffness of the paretic limb (spasticity) and in the weakness of neural coupling between limbs. Thus, the question arises of how the respective effects of each of theses sources of asymmetry can be theoretically addressed and experimentally investigated in discrete bimanual coordination. To address these issues, the behavioral consequences of: (a) changes in temporal asymmetry between limbs (by changes in either muscular or informational task conditions), and (b) changes in the strength of coupling (by attentional focus or providing a metronome) should be further explored in both healthy people and more or less severely impaired stroke patients. Our experimental strategy consists of the comparison of the observed behaviors of both populations in similar experimental paradigms and tasks conditions, though adapted to stroke patients. Kelso et al.’s (1979) experimental paradigm will be used in this respect. In healthy participants, temporal asymmetry between limbs will be progressively scaled by changing either biomechanical (loading) or task-related and informational constraints (i.e.


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Fitts’s ID by modifying amplitude, target size or both; by re-organizing the location of starting points and endpoints, see Sherwood, 1991) applied to the limbs. This approach will allow us to make use of the recent theoretical account by Huys et al. (2010) using phase flows. Neural coupling will be changed by increasing attentional focus directed to the task (Temprado et al., 1999) or to one limb (de Poel et al., 2008). Following the same logic, in stroke patients, bimanual asymmetry will be attenuated by manipulating movement time of the non-paretic arm, while keeping constant the difficulty of the task for the paretic arm. Participants will also be instructed to focus their attention on the bimanual task or to the paretic limb to increase bimanual coupling. According to Schöner’s (1990) model, in healthy people, when increasing temporal asymmetry between limbs, one should observe a progressive de-synchronization of IT and/or MT as well as an abrupt transition from synchronization pattern (in-phase) to a desynchronized one (anti-phase) when temporal asymmetry between limbs goes beyond a critical threshold. Phase transitions should be preceded by an increase in variability of the relative time between limbs. One can also predict that, for a given magnitude of temporal dissimilarity between limbs, if coupling strength is increased (e.g. by attentional focus), one should observe: (a) a better synchronization for larger interlimb temporal asymmetries, and (b) a higher stability of synchronized patterns and less transition for higher magnitude of temporal asymmetry between limbs. We will also explore whether, when starting from dissimilar conditions and rendering them more similar, a transition from de-synchronization to synchronization will be observed. These predictions are in large part deduced from experimental facts (e.g. Fowler et al., 1991; Kelso et al., 1979, 1983; Marteniuk et al., 1984; Riek et al., 2003), but to our knowledge they have never been tested systematically. In doing so, we should be able to establish a reference frame for further analyzing bimanual asymmetries in stroke patients. In particular, an important question is whether and in what conditions compareable behaviors will be observed in stroke patients and healthy people with respect to the effects of temporal asymmetries between limbs be it caused by mechanical, information or attentional factors. For instance, we would determine whether (more or less severely impaired) stroke patients are able to perform synchronized (relatively stable) bimanual patterns when asymmetry between limbs is attenuated by specific manipulations of constraints on either the nonparetic (e.g. progressive loading, manipulation of ID) or the paretic arm (focus of attention, reduction of spasticity). A tendency to re-synchronization when asymmetry is attenuated would correspond to a transition from anti-phase to inphase. Moreover, we anticipate that the particular case of a transient loss of coordination between limbs, characterized by a complete independence of each limb at a given level of dissimilarity between limbs, could be specifically observed in stroke patients. In the extended version of the HKB model of rhythmic coordination, such situation has been simulated thanks to a frequency detuning parameter (Kelso et al., 1990). This parameter acts as a local

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mechanism on individual states thereby resulting in changes in the directional bias of phase transitions (anti-phase to in-phase) and occurrence of phase wrapping (no coordination or relative coordination). In the Fuchs-Jirsa extension of the HKB model, the symmetry breaking parameter acts a global mechanism affecting the entire dynamic repertoire by modulating the stability of all coordination patterns. In Schöner’s model however, increasing temporal asymmetry between limbs is not predicted to give rise to relative coordination but instead, to abrupt transition from synchronized to desynchronized pattern. Thus, if relative coordination was observed, an extension should be added to Schöner’s model in the spirit of Fuchs and Jirsa (2000) and would correspond, in our experimental paradigm, to a transition from de-synchronization to synchronization tendency when temporal asymmetry between limbs is attenuated. It remains to be determined whether it also predicts behavioral dynamics observed in stroke patients. Since neural coupling is presumably altered as a consequence of CVA lesion (attention deficits, time delays in the information exchange, …), the type of symmetry breaking following Fuchs and Jirsa offers itself as a candidate mechanism. The effects of reducing spasticity of the paretic limb on bimanual coordination will also be of particular interest, in this respect, to distinguish the respective effects of neuromuscular factors and neural coupling. For instance, a crucial question is whether entrainment and synchronization can be gained or whether de-synchronization can be delayed after reducing limb spasticity. Finally, one can hypothesize that behavioral expressions of asymmetries and relative coordination caused by CVA lesions would depend on the location in the dominant or non-dominant hemisphere of the lesion, the age of the patient, the constraints of the task, etc. To our knowledge, these predictions have never been empirically tested for discrete movement tasks in both healthy and stroke participants. Further application of the above “symmetry-breaking hypothesis” to stroke rehabilitation could already be envisaged. From a therapeutic point of view, bimanual coupling is considered as functional when it permits to create a “positive entrainment effect” that is, when temporal and/or spatial features of the non-paretic arm trajectory interfere with the paretic arm trajectory thereby improving its performance. In other words, a main expectation in BADT is that the non-paretic limb can “entrain” the impaired limb, and thus, improve its performance. As a result, in two-handed conditions, the paretic limb movement is expected to be faster, more accurate, and smoother then in one-handed one. Such prediction is nevertheless rarely verified in the available studies (see above). However, from the strict point of view of the existence of coupling, no matter the direction of the spatial and temporal interferences (i.e. from the paretic to the non-paretic or from the non-paretic to the paretic). Indeed, even an asymmetric influence of the paretic limb toward the non-paretic indicates the persistence of bimanual coupling. Furthermore, results observed in both healthy (e.g. Kelso et al., 1979, 1983) and stroke participants (Garry et al., 2005; HarrisLove et al., 2005; Lewis & Byblow, 2004; Messier et al., 2006; Rose & Winstein, 2005a, 2005b) rather suggest that a predominant, asymmetric coupling


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effect, from the slower (i.e. paretic) to the faster (i.e. non paretic) limb should be observed. Therapeutic interventions should then consist of training bimanual coordination in conditions in which appropriate manipulations of identified control parameters or behavioral information reduce biomechanical asymmetry between limbs together with increasing the strength of coupling. It could be made, for instance, by: (a) adapting mean movement time, (b) reducing effective asymmetry between limbs (e.g. by loading the arm, reducing spasticity, etc.), (c) changing asymmetry through changes in informational constraints, (d) changing attentional conditions of the task either by instructing participants to allocate more attention to the paretic arm or by re-organizing the starting point and targets locations (see Sherwood, 1991; Riek et al., 2003). CONCLUSION AND PERSPECTIVES In the present paper, we aimed to provide conceptual foundations about how CVA-induced alterations and functional recovery of coordinated behaviors can be understood as the result of complex interactions among multiple constraints arising at the different levels of the NMSS. Using the example of elementary coupling principles in both cyclic and discrete movement tasks, we concretely envisaged a number of implications of this "dynamic systems" view to understand how one might exploit the CNS plasticity and eventually selforganizing properties for recovering more adaptive coordinated movements. By envisaging therapeutic applications to sometimes vague but new ideas arising from the dynamic pattern theory (e.g. self-organization, emergence, informational coupling and symmetry breaking), we showed that it is possible to go beyond metaphor by demonstrating the validity of concepts for both guidelines elaboration and research programs. Several questions remain however, which deserve further investigation. For instance, a weakness in the existing literature is the frequent neglect of the spatial aspects of interlimb coupling. Some authors suggested however that after stroke spatial coupling is more impaired then the temporal one. Accordingly, clinicians often report a more important residual deficit in terms of spatial control (i.e. amplitude and precision) compared to the temporal one (i.e. movement speed). Finally, it appears that bimanual coupling and its recovery should be further studied in order to elaborate firm and theoretically founded guidelines for improving the efficacy of BAT. As a perspective, one can expect that the present reasoning could be extended to the study of more global interlimb coordination training (e.g. arm and leg). Of course, the dynamic theory of coordination patterns will be very helpful in this respect. REFERENCES Banerjee, A., & Jirsa,V. K. (2007). How do neural connectivity and time delays influence bimanual coordination? Biological Cybernetics, 96, 265-278. Bingham, G. P., Schmidt, R. C., Turvey, M. T., Rosenblum, L. D. (1991). Task dynamics and resource dynamics in the assembly of a coordinated rhythmic activity.

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Journal of Experimental Psychology: Human Perception and Performance, 17, 359-381. Cardoso de Oliveira, S. (2002). The neuronal bases of bimanual coordination: Recent neurophysiological evidence and functional models. Acta Psychologica, 110, 139-159. Carson, R. G. (2005). Neural pathways mediating bilateral interactions between the upper limbs. Brain research Reviews, 49, 641-662. Carson, R. G., & Kelso, J. A. S. (2004). Governing coordination: behavioural principles and neural correlates. Experimental Brain Research, 154, 267-274. Carson, R. G., Riek, S., Smethurst, C. J., Párraga, J. F., & Byblow, W. D. (2000). Neuromuscular-skeletal constraints upon the dynamics of unimanual and bimanual coordination. Experimental Brain Research, 131, 196-214. Cattaert, D., Semjen, A., & Summers, J. J. (1999). Simulating a neural cross-talk model for between-hand interference during bimanual circle drawing. Biological Cybernetics, 8, 343-358. Cauraugh, J. H., & Summers, J. J. (2005). Neural plasticity and bilateral movements: A rehabilitation approach for chronic stroke. Progress in Neurobiology, 75, 309320. Corcos, D. M. (1984). Two-handed movement control. Research Quarterly for Exercise and Sport, 55(2), 117-122. Cunningham, C. L., Philips Stoykov, M. E., & Walter, C. B. (2002). Bilateral facilitation of motor control in chronic hemiplegia. Acta Psychologica, 110, 321-337. Davids, K., Glazier, P., Araújo, D., & Bartlett, R. (2003). Movement systems as dynamical systems: the functional role of variability and its implications for sports medicine. Sports Medicine, 33, 245-60. de Poel, H. J., Peper, C. L., & Beek, P. J. (2008). Laterally focused attention modulates asymmetric coupling in rhythmic interlimb coordination. Psychological Research, 72, 123-37. Dickstein, R., Hocherman, S., Amdor G., & Pinar, T. (1993). Reaction and movement times in patients with hemiparesis for unilateral and bilateral elbow flexion. Physical Therapy, 73, 374-380. Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381-391. Fitts, P. M., & Peterson, J. R. (1964). Information capacity of discrete motor responses. Journal of Experimental Psychology, 67, 103-112. Fonseca, R .T., Holt, K. G., Saltzman, E., & Fetters, L. (2001). A dynamical model of locomotion in spastic hemiplegic cerebral palsy: influence of walking speed. Clinical Biomechanics (Bristol, Avon), 16, 793-805. Fowler, B., Duck, T., Mosher, M., & Mathieson, B. (1991). The coordination of bimanual aiming movements: evidence for progressive desynchronization. The Quarterly Journal of Experimental Psychology, 43, 205-221. Fuchs, A., & Jirsa, V. K. (2000). The HKB Model revisited: How varying the degree of symmetry controls dynamics, Human Movement Science, 19, 425-449. Garry, M. E., van Steenis, R. E., & Summers, J. J. (2005). Interlimb coordination following stroke. Human Movement Science, 24, 849-864. Glass, L., & MacKey, M. C. (1988). From clocks to chaos. Princeton University Press. Goldberger, A. L. (1996). Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. The Lancet, 347, 1312-1314.


459

Goodman, D., Kelso, J. A. S., & Southard, D. L. (1979). On the coordination of twohanded movements. Journal of Experimental Psychology: Human Perception and Performance, 5, 229-238. Haken, H. (1983). Synergetics: An introduction (3rd edition). Berlin: Springer-Verlag. Haken, H., Kelso, J. A. S., & Bunz, H. (1985). A theoretical model of phase transition in human hand movements. Biological Cybernetics, 51, 347-356. Harris-Love, M. L., McCombe Waller, S., & Whitall, J. (2005). Exploiting interlimb coupling to improve paretic arm reaching performance in people with chronic stroke. Archives of Physical Medicine and Rehabilitation, 86, 2131-2137. Harbourne, R. T., & Stergiou, N. (2009). Movement variability and the use of nonlinear tools: principles to guide physical therapist practice. Physical Therapy, 89(3), 267-282. Helmuth, L. L., & Ivry, R. B. (1996). When two hands are better than one: Reduced timing variability during bimanual movements. Journal of Experimental Psychology: Human Perception and Performance, 22, 278-293 Heuer, H., Kleinsorge, T., Spijkers, W., & Steglich, W. (2001). Static and phasic crosstalk effects in discrete bimanual reversal movements. Journal of Motor Behavior, 33, 67-85. Holt, K., Fonseca, S. T., & LaFiandra, M. E. (2000). The dynamics of gait in children with spastic hemiplegic cerebral palsy: theoretical and clinical implications. Human Movement Science, 19, 375-405. Holt, K. G., Obusek, J. P., & Fonseca, S. T. (1996). Constraints on disordered locomotion: A dynamic systems perspective on spastic cerebral palsy. Human Movement Science, 15, 177-202. Huys, R., Fernandez, L., Bootsma, R. J., & Jirsa, V. K. (2010). Fitts’ law is not continuous in reciprocal aiming. Proceedings of the Royal Society B, Biological Sciences, 277, 1179-1184. Huys, R., Studenka, B. E., Rheaume, N. L., Zelaznik, H. N., & Jirsa, V. K. (2008). Distinct timing mechanisms produce discrete and continuous movements. PLoS Computational Biology, 4, e1000061.doi:10.1371/journal.pcbi.1000061. Jantzen, K. J., & Kelso J. A. S. (2007). Neural coordination dynamics of human sensorimotor behavior: A review. In Jirsa, V. K., & McIntosh, A.R. (Eds.) Handbook on Brain Connectivity (pp. 421-461). Springer-Verlag. Jirsa, V. K., & Kelso, J. A. S. (2005). The excitator as a minimal model for the coordination dynamics of discrete and rhythmic movement generation. Journal of Motor Behavior, 37, 35-51. Kamper, D. G., McKenna-Cole, A. N., Kahn, L. E, & Reinkensmeyer, D. J. (2002). Alterations in reaching after stroke and their relation to movement direction and impairment severity. Archives of Physical Medicine and Rehabilitation, 83, 702-707. Kelso, J. A. S. (1981). On the oscillatory basis of movement. Bulletin of the Psychonomic Society, 18, 63. Kelso, J. A. S. (1984). Phase transitions and critical behavior in human bimanual coordination. American Journal of Physiology: Regulatory, Integrative and Comparative Physiology, 246, R1000-R1004. Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA: MIT Press. Kelso, J. A. S. (2009). Coordination dynamics. In R.A Meyers (Ed.), Encyclopedia of Complexity and Systems Science (pp. 1537-1564). City: Springer.

460


Kelso, J. A. S., Delcolle, J. D., & Schöner, G. (1990). Action-perception as a pattern formation process. In M. Jeannerod (Ed.), Attention and performance XIII (pp. 139–169). Hillsdale, NJ: Lawrence Erlbaum. Kelso, J. A. S., Holt, K. G., Rubin, P., & Kugler, P. N. (1981). Patterns of human interlimb coordination emerge from the properties of non-linear limit cycle oscillatory processes: Theory and data. Journal of Motor Behavior, 13, 226261. Kelso, J. A. S., Putnam, C. A., & Goodman, D. (1983). On the space-time structure of human interlimb co-ordination. The Quarterly Journal of Experimental Psychology A: Human Experimental Psychology, 35, 347-375. Kelso, J. A. S., Southard, D. L., & Goodman, D. (1979). On the coordination of twohanded movements. Journal of Experimental Psychology: Human Perception and Performance, 5, 229-238. Kilbreath, S. H., & Heard, R. C. (2005). Frequency of hand use in healthy older persons. The Australian journal of physiotherapy, 51, 119-122. Lee, T. D., Almeida, Q. J., & Chua, R. (2002). Spatial constraints in bimanual coordination: influences of effector orientation. Experimental Brain Research, 146, 205-212. Lee, T .D., Blandin, Y., & Proteau, L. (1996). Effects of task instructions and oscillation frequency on bimanual coordination. Psychological Research, 59, 100-106. Lewis, G. N., & Byblow, W. D. (2004). Bimanual coordination dynamics in poststroke hemiparetics. Journal of Motor Behavior, 36, 174-188. Luft, A. R., McCombe Waller, S., Whitall, J., Forrester, L. W., Macko, R., Sorkin, J. D., Schulz, J. B., Goldberg, A. P., & Hanley, D. F. (2004). Repetitive bilateral arm training and motor cortex activation in chronic stroke: A randomized controlled trial. The Journal of the American Medical Association, 292, 18531861. Marteniuk, R. G., & MacKenzie, C. L. (1980). A preliminary theory of two-handed coordinated control. In G. E. Stelmach & J. Requin, (Eds.), Tutorials in motor behavior, (pp. 185-197). Amsterdam: North Holland. Marteniuk, R. G., MacKenzie, C. L., & Baba, D. M. (1984). Bimanual movement control: Information processing and interaction effects. The Quarterly Journal of Experimental Psychology, 36A, 335-365. McCombe Waller, S., & Whitall, J. (2008). Bilateral arm training: why and who benefits? NeuroRehabilitation, 23, 29-41. McCombe Waller, S., & Whitall, J. (2004). Fine motor control in adults with and without chronic hemiparesis: Baseline comparison to nondisabled adults and effects of bilateral arm training. Archives of Physical Medicine and Rehabilitation, 85, 1076-1083. Messier, S., Bourbonnais, D., Desrosiers, J., & Roy, Y. (2006). Kinematic analysis of upper limbs and trunk movement during bilateral movement after stroke. Archives of Physical Medicine and Rehabilitation, 87, 1463-1470. Meyer-Lindenberg A., Ziemann U., Hajak G., Cohen L., & Berman, K. F. (2000). Transitions between dynamical states of differing stability in the human brain. Proceedings of the National Academy of Sciences, USA, 99, 10948-109453. Mudie, M. H., & Matyas, T. A. (1996). Upper extremity retraining following stroke: Effects of bilateral Practice. Neurorehabilitation Neural Repair, 10, 167-184.


461

Park, H., & Turvey, M. T. (2008). Imperfect symmetry and the elementary coordination law. In A. Fuchs & V.K. Jirsa (Eds.), Coordination: Neural, Behavioral and Social Dynamics (pp. 3-25). Berlin: Springer. Platz, T., Bock, S., & Prass, K. (2001). Reduced skilfulness of arm motor behaviour among motor stroke patients with good clinical recovery: Does it indicate reduced automaticity? Can it be improved by unilateral or bilateral training? A kinematic motion analysis study. Neuropsychology, 39(7), 687-698. Post, A. A., Peper, C. E., Daffertshofer, A., & Beek, P. J. (2000). Relative phase dynamics in perturbed interlimb coordination: Stability and stochasticity. Biological Cybernetics, 83, 443-459. Rice, M. S., & Newell, K. M. (2001). Interlimb coupling and left hemiplegia because of right cerebral vascular accident. Occupational Therapy Journal of Research, 21, 12-28. Rice, M. S., & Newell, K. M. (2004). Upper-extremity interlimb coupling in patients with left hemiplegia due to stroke. Archives of Physical Medecine and Rehabilitation, 85, 629-634. Riek, S., Tresilian, J. R., Mon-Williams, M., Coppard, V. L., & Carson, R. G. (2003). Bimanual aiming and overt attention: one law for two hands. Experimental Brain Research, 153, 59-75. Rose, D. K., & Winstein, C. J. (2005a). The co-ordination of bimanual rapid aiming movements following stroke. Clinical Rehabilitation, 19, 452-462. Rose, D. K., & Winstein, C. J. (2005b). Bimanual training after stroke: Are two hands better than one? Topics in Stroke Rehabilitation, 11, 20-30. Salesse, R., Ouiller, O., & Temprado, J. J. (2005). Plane of motion mediates the coalition of constraints in rhythmic bimanual coordination. Journal of Motor Behavior, 37, 454-464. Salesse, R., Ouiller, O., Jirsa, V. K., & Temprado, J. J. (2010). Mirror-symmetry modulates coordination dynamics. Manuscript submitted for publication. Schalow, G. (2002). Stroke recovery induced by coordination dynamic therapy and quantified by the coordination dynamic recording method. Electromyography and Clinical Neurophysiology, 42, 85-104. Schalow, G. (2006). Symmetry diagnoses and treatment in coordination dynamics therapy. Electromyography and Clinical Neurophysiology, 46, 421-431. Scholz, J. P. (1990). Dynamic pattern theory - Some implications for therapeutics. Physical Therapy, 70, 827-843. Scholz, J. P., & Kelso, J. A. S. (1990). Intentional switching between patterns of bimanual coordination depends on the intrinsic dynamics of the patterns. Journal of Motor Behavior, 22, 98-124. Schmidt, R., & Lee, T. (2005). Motor control and learning: A behavioral emphasis (4th edition). Champaign, IL: Human Kinetics. Schöner, G. (1990). A dynamic theory of coordination of discrete movement. Biological Cybernetics, 53, 257-270. Schöner, G., Zanone, P. G., & Kelso, J. A. S. (1992). Learning as change of coordination dynamics: theory and experiment. Journal of Motor Behavior, 24, 29-48. Seidler, R. D. (2004). Multiple motor learning experiences enhance motor adaptability. Journal of Cognitive Neuroscience, 16, 65-73. Sherwood, D. E. (1994). Hand preference, practice order, and spatial assimilations

462


in rapid bimanual movement. Journal of Motor Behavior, 26, 123-143. Sherwood, D. E. (1991). Distance and location assimilation effects in rapid bimanual movement. Research Quarterly for Exercise and Sport, 62, 302-308. Stergiou, N., Harbourne, R., & Cavanaugh, J. (2006). Optimal movement variability: a new theoretical perspective for neurologic physical therapy. Journal of Neurologic Physical Therapy, 30, 120-129. Stewart, K. C., Cauraugh, J. H., & Summers, J. J. (2006). Bilateral movement training and stroke rehabilitation: A systematic review and meta-analysis. Journal of the Neurological Sciences, 244, 89-95. Stoykov, M. E., & Corcos, D. (2009). A review of bilateral training for upper extremity hemiparesis. Occupational Therapy International. 16, 190-203. Swinnen, S.P. (2002). Intermanual coordination: From behavioural principles to neuralnetwork interactions. Nature Reviews Neuroscience, 3, 350-361. Temprado, J. J., Zanone, P. G., Monno, A., & Laurent, M. (1999). Attentional load associated with performing and stabilizing preferred bimanual patterns. Journal of Experimental Psychology: Human Perception and Performance, 25, 1579-1594. Temprado, J. J., Monno, A., Zanone, P. G., & Kelso, J. A. S. (2002). Attentional demands reflect learning-induced alterations of bimanual coordination dynamics. European Journal of Neuroscience, 16, 1390-1394. Temprado, J. J., Swinnen, S. P., Coutton-Jean, C., & Salesse, R. (2007). Symmetry constraints mediate the learning and transfer of bimanual coordination patterns across planes of motion. Journal of Motor Behavior, 39, 115-125. Turvey, M. T., Rosenblum, L. D., Schmidt, R. C., & Kugler, P. N. (1986). Fluctuations and phase symmetry in coordinated rhythmic movements. Journal of Experimental Psychology: Human Perception and Performance, 12, 564-583. Ustinova, K. I., Fung, J., & Levin, M. F. (2006). Disruption of bilateral temporal coordination during arm swinging in patients with hemiparesis. Experimental Brain Research, 169, 194-207. van Delden, A. E. Q, Peper, C. E, Harlaar, J., Daffertshofer, A., Zijp, N. I., et al. (2009). Comparing unilateral and bilateral upper limb training: the ULTRA-stroke program design. BMC Neurology, 9, 57. van Emmerik, R. E., & Wagenaar, R. C. (1996). Effects of walking velocity on relative phase dynamics in the trunk in human walking. Journal of Biomechanics, 29, 1175-1184. Yamanishi, J., Kawato, M., & Suzuki, R. (1980). Two coupled oscillators as a model for the coordinated finger tapping by both hands. Biological Cybernetics, 37, 219225. Zanone, P. G., & Kelso, J. A. S. (1992). Evolution of behavioral attractors with learning: nonequilibrium phase transitions. Journal of Experimental Psychology: Human Perception and Performance, 18, 403-421.