Abstract

In coordination dynamics, rate is a nonspecific control parameter that alters the stability of behavioral patterns and leads to spontaneous pattern switching. We used fMRI in conjunction with measures of effective connectivity to investigate the neural basis of behavioral dynamics by examining two coordination patterns known to be differentially stable (synchronization and syncopation) across a range of rates (0.75 to 1.75 Hz). Activity in primary auditory and motor cortices increased linearly with rate, independent of coordination pattern. On the contrary, activity in a premotor–cerebellar circuit varied directly with the stability of the collective variable (relative phase) that specifies coordinated behavioral patterns. Connectivity between premotor and motor cortices was also modulated by the stability of the behavioral pattern indicative of greater reliance on sensorimotor integration as action becomes more variable. By establishing a critical connection between behavioral and large scale brain dynamics, these findings reveal a basic principle for the neural organization underlying coordinated action.

INTRODUCTION

Coordinated action requires neural mechanisms to generate the spatio-temporal order among multiple interacting sensory and motor components and to flexibly adjust ongoing behavioral patterns to meet changing task and environmental conditions. Principles of large-scale brain function suggest that sensorimotor integration and control arise from a complementary tendency for functional segregation of specialized neural processing areas and global integration across brain regions to form large-scale neural circuits (e.g., Jirsa & McIntosh, 2007; Kelso & Tognoli, 2007; Bressler & Kelso, 2001; Varela, Lachaux, Rodriguez, & Martinerie, 2001; Kelso, 1995). In contrast to extensive research investigating the specialized role of distinct sensory and motor-related regions, much less work has been aimed at uncovering guiding principles for large-scale neural organization during complex, coordinated action. Moreover, in cognitive neuroscience research, it is commonplace to choose certain behavioral variables in an attempt to find their neural correlates—with the implicit hope that these are variables the brain dynamics really cares about. Here we employ an established sensorimotor coordination paradigm in the context of a functional magnetic resonance imaging (fMRI) study to uncover the neural correlates of key theoretically motivated measures of coordination, namely, the stability of collective variables that specify behavioral patterns. In addition, we employ measures of connectivity as a means to determine how parametric changes in sensorimotor coordination are reflected in the integration across large-scale cortical networks.

Basic forms of sensorimotor coordination have proven a fruitful entry point to uncover the coordination dynamics of pattern formation and change at both behavioral and brain levels of analysis (Van Mourik, Daffertshofer, & Beek, 2006; Carson & Kelso, 2004; Jirsa & Kelso, 2004; Schaal, Sternad, Osu, & Kawato, 2004; Bardy, Oullier, Bootsma, & Stoffregen, 2002; Mayville, Jantzen, Fuchs, Steinberg, & Kelso, 2002; Meyer-Lindenberg, Ziemann, Hajak, Cohen, & Berman, 2002; Swinnen, 2002; Cavallari, Cerri, & Baldissera, 2001; Fuchs et al., 2000; Jirsa, Fuchs, & Kelso, 1998; Buchanan, Kelso, & De Guzman, 1997; Beek, Peper, & Stegeman, 1995; Byblow, Chua, & Goodman, 1995; Kelso et al., 1992; Kelso, Delcolle, & Schoner, 1990; Schmidt, Carello, & Turvey, 1990; Kelso, 1984). Coordination dynamics uses the concepts of self-organization and the language and tools of dynamical systems theory to quantify coordinated actions and to understand how they adapt and change (Kelso, 1995). The approach focuses on the stability of behavioral patterns and how new patterns may emerge due to dynamic instabilities when environmental and cognitive factors change. In a number of cases (e.g., Kelso, 1984, 1995; Kelso et al., 1990; Haken, Kelso, & Bunz, 1985), the relative phase between interacting components has been identified as a key order parameter (Haken, 1983) or coordination variable that characterizes the interaction between component parts, thereby providing a macroscopic measure of the system's collective behavior. The dynamics (multistability, instability, transitions, etc.) of intrinsic and learned behavioral patterns is typically investigated using a nonspecific control parameter such as coordination rate. Under parametric manipulations of rate, measures of relative phase stability (e.g., variability, relaxation times following small perturbations, switching times) index behavioral pattern formation and anticipate adaptive switching between patterns (Haken, 1996; Kelso, 1995; Schoner & Kelso, 1988; Kelso et al., 1987). A simple example of adaptive pattern switching is the paradigmatic case of bimanual coordination in which spontaneous transitions occur from antiphase to in-phase coordination as movement speed is increased (analogous, perhaps, to naturally occurring gait transitions). As environmental conditions are systematically altered, patterns of coordinated behavior and brain activity become unstable and switch spontaneously to a new pattern that better fits the circumstances (Mayville, Bressler, Fuchs, & Kelso, 1999; Wallenstein, Kelso, & Bressler, 1995; Kelso et al., 1992). The key concept behind such switching behavior is dynamic stability and its loss, both of which have been precisely quantified and checked against theoretical predictions (Haken, 1996; Kelso, 1995; Schoner & Kelso, 1988; Kelso et al., 1987).

The theoretical framework of coordination dynamics (Jantzen & Kelso, 2007; Jirsa & Kelso, 2004; Tschacher & Dauwalder, 2003; Kelso, 1995) offers a natural partitioning of complex systems into coordination variables or order parameters that characterize behavioral patterns and control parameters which, when varied systematically, alter pattern stability and lead the system through phase transitions. An intriguing possibility pursued here is whether behavioral pattern generation by a complex system like the brain can be understood using a similar framework. Specifically, is the neural organization of behavior, as coordination dynamics predicts, sensitive to pattern stability? If so, to what extent is the neural circuitry for implementing control parameters distinct from (or overlapping with) the neural circuitry that generates and maintains behavioral patterns? Such questions are important because they suggest that dynamical properties such as pattern stability, not just the component elements of which the pattern is comprised, govern how the brain organizes behavior. A further benefit of coordination dynamics is that it provides a quantitative means to assess the neural basis of pattern stability, complementing—if not replacing—more colloquial notions such as task difficulty and complexity (Temprado, Monno, Zanone, & Kelso, 2002).

Here we use a sensorimotor coordination paradigm in which patterns of differing stability can be readily quantified (Kelso et al., 1990) to uncover the circuitry underlying behavioral pattern formation and change in the human brain. Both empirical and modeling studies have established that at low values of the rate control parameter, coordination may be performed stably at a relative phase of both 0° (synchronization; Figure 1A) and 180° (syncopation; Figure 1B). However, as rate or frequency (f) is systematically increased, the syncopated pattern progressively loses stability until at a critical value (fc) of approximately 2 Hz the system undergoes a spontaneous transition to the synchronized pattern. Notably, no such loss of stability occurs over the same parameter range when subjects begin in the synchronized pattern. Thus, this sensorimotor coordination paradigm provides the necessary means to dissociate neural systems underlying pattern formation and stability from those involved in parametrically changing control parameters such as movement rate.

Figure 1. 

(A) Stylized depiction of a synchronized coordination pattern requiring temporal coincidence between peak finger flexion (solid line) and an auditory metronome (dotted line). (B) Syncopation requires the temporal placement of peak flexion directly between consecutive metronome pulses. The relative phase (Φ) between metronome and movement is the temporal difference (Δ) between the signals divided by the interbeep interval (T). When expressed in degrees, ideal synchronization and syncopation have a relative phase of 0° and 180°, respectively. (C) Average performed frequency plotted as a function of required frequency for synchronization (open circle) and syncopation patterns (closed squares). The dotted line represents perfect performance. (D) Group mean relative phase (±SEM) between metronome and finger flexion plotted as a function of frequency for both coordination patterns. (E) Group mean of the standard deviation of relative phase plotted as a function of frequency for both coordination patterns. Rate-dependent increases in variability are significantly more prominent when syncopating compared to synchronizing as indicated by the slope of the linear fit to the data (dotted lines).

Figure 1. 

(A) Stylized depiction of a synchronized coordination pattern requiring temporal coincidence between peak finger flexion (solid line) and an auditory metronome (dotted line). (B) Syncopation requires the temporal placement of peak flexion directly between consecutive metronome pulses. The relative phase (Φ) between metronome and movement is the temporal difference (Δ) between the signals divided by the interbeep interval (T). When expressed in degrees, ideal synchronization and syncopation have a relative phase of 0° and 180°, respectively. (C) Average performed frequency plotted as a function of required frequency for synchronization (open circle) and syncopation patterns (closed squares). The dotted line represents perfect performance. (D) Group mean relative phase (±SEM) between metronome and finger flexion plotted as a function of frequency for both coordination patterns. (E) Group mean of the standard deviation of relative phase plotted as a function of frequency for both coordination patterns. Rate-dependent increases in variability are significantly more prominent when syncopating compared to synchronizing as indicated by the slope of the linear fit to the data (dotted lines).

Recent fMRI (Debaere, Wenderoth, Sunaert, Van Hecke, & Swinnen, 2004) and PET (Meyer-Lindenberg et al., 2002) studies of bimanual coordination, where phase relations are defined between the hands, have demonstrated stability related activity across distributed cortical and subcortical structures. Whereas increases in movement rate during in-phase coordination had little effect on pattern stability, similar increases during alternative phasing patterns such as antiphase (180°) or 90° resulted in progressive decreases in stability and pattern switching (Zanone & Kelso, 1992; Kelso, 1984). Decreases in pattern stability were associated with increases in activity in bilateral dorsal premotor cortex (PMC), supplementary motor area (SMA), cingulate, and the right cerebellum (Cbl) (Debaere et al., 2004; Meyer-Lindenberg et al., 2002). The combined PET and TMS data of Meyer-Lindenberg et al. (2002; see also Steyvers et al., 2003; Serrien, Strens, Oliviero, & Brown, 2002) further showed that transitions from the 180° to 0° pattern can be induced by disruption of activity in premotor regions but not motor cortex, supporting the present hypothesis that brain networks related to dynamic features of the global coordination pattern may be distinguished from more elementary modality-dependent sensory and motor features.

Overall, the foregoing results support the hypothesis that pattern stability during bimanual coordination is mediated by a number of cortical and subcortical regions that include the SMA, lateral PMC, and the Cbl. Here we seek to determine whether similar neural circuitry underlies pattern stability during sensorimotor coordination. This question is important because the same dynamical features such as multistability, loss of stability, and phase transitions have been observed across different task contexts such as coordination between homologous limbs (Kelso, 1984) and nonhomologous limbs (Swinnen, Jardin, Meulenbroek, Dounskaia, & Hofkens-Van Den Brandt, 1997; Jeka & Kelso, 1995; Kelso & Jeka, 1992), between persons and their environment (Jirsa, Fink, Foo, & Kelso, 2000; Wimmers, Beek, & Vanwieringen, 1992; Kelso et al., 1990), and even in social coordination between people (Oullier, de Guzman, Jantzen, Lagarde, & Kelso, 2008; Tognoli, Lagarde, De Guzman, & Kelso, 2007; Richardson, Marsh, & Schmidt, 2005; Schmidt, O'Brien, & Sysko, 1999; Schmidt, Bienvenu, Fitzpatrick, & Amazeen, 1998). That the same coordination dynamics handles basic coordination phenomena in quite different systems hints at the existence of a large-scale neural network tied to the stability of behavioral patterns. The present experiment tests the specific hypothesis that activity of the SMA and lateral PMC is related to the stability of coordination patterns regardless of which effectors or perceptual modalities are coordinated. We further seek to uncover the nature of the functional interaction, if any, between brain areas sensitive to pattern stability and brain regions that are modality and effector dependent. Participants coordinated finger flexion–extension movements with an auditory metronome in either a synchronized or syncopated pattern at five different movement rates (0.75, 1.0, 1.25, 1.50, 1.75 Hz) all below the critical frequency (≈2 Hz) at which spontaneous transitions from syncopation are known to occur without special training (Kelso et al., 1990). The 10 conditions constituted a parametric design for modeling the blood oxygen level dependent (BOLD) fMRI, thereby allowing for a mapping between pattern stability, coordination rate, and large-scale neural interactions. Structural equation modeling was used to investigate how the functional coupling between key brain areas is modified as a function of coordination rate and pattern stability.

METHODS

Participants

Fourteen right-handed neurologically normal volunteers (10 men, 4 women; mean age = 26.8 years) gave informed, written consent to participate in the study. Procedures were carried out in accordance with the guidelines set out by the Internal Review Board at Florida Atlantic University and the human subject guidelines of NIH. None of the participants were professional musicians or enrolled in music programs.

Experimental Protocol

A single recording session comprised six alternating blocks of coordination and rest (lying quietly with eyes closed). During coordination, participants were required to coordinate finger flexion of their right hand with auditory pacing tones (440 Hz carrier, 60-msec duration). A total of 10 sessions was completed at five different stimulus rates (0.75, 1.0, 1.25, 1.50, and 1.75 Hz) and two different coordination patterns. On half of the sessions, participants were instructed to synchronize such that peak flexion was coincident with the onset of the pacing tone. On the other half, participants were instructed to syncopate such that peak flexion occurs directly between two pacing tones. The order of sessions was randomized across both frequency and pattern. Behavioral responses were recorded as changes in pressure in a small air-filled pillow placed between the index finger and thumb of the right hand. The custom-made device, more fully described in Jantzen, Oullier, and Kelso (2008), consisted of an infant blood pressure bladder connected to plastic tubing leading to a pressure transducer located outside the MR suite. The transducer converted changes in air pressure inside the pillow into an analogue signal ranging between approximately ±1 V. Behavioral data from the pillow, as well as a marker channel indicating the onset of each pacing stimulus, were recorded digitally using an A/D converter sampling at 500 Hz.

Magnetic Resonance Imaging

Changes in neural activity were determined by measurement of changes in local BOLD) contrast using echo-planar imaging on a 1.5-Tesla GE Signa Scanner equipped with real-time capabilities (General Electric Medical Systems, Milwaukee, WI). Echo-planar images were acquired using a single-shot, gradient-echo, echo-planar pulse sequence (TE/FA/FOV: 40 msec/90°/240 mm, matrix = 64 × 64). Twenty-five axial 5-mm-thick slices spaced 1 mm apart were acquired every 3 sec (TR = 3 sec; voxel size = 3.75 × 3.75 × 6 mm). Each session comprised 96 scans with a total of 960 scans per subject.

High-resolution spoiled gradient-recalled at steady state (SPGR) images (TE/TR/FA/FOV: in phase/325 msec /90°/240 mm) were collected using the same slice parameters as the functional images. These images were used to coregister the functional scans onto anatomical 3-D SPGR axial images (TE/TR/FA/FOV = 5 msec/34 msec/45°/260 mm; resolution = 256 × 256; thickness = 2 mm) collected at the end of each experimental session.

Behavioral Analysis

The time of each behavioral response was defined as the point of maximum compression of the air pillow (i.e., peak flexion of the index finger and thumb). Two relative measures of performance were calculated for each condition. The mean movement rate was determined for each subject by averaging the inverse of the interresponse interval (i.e., the time between consecutive peak flexion events). Relative phase was defined as the time between each behavioral response and the preceding stimulus onset, divided by the stimulus period (Zanone & Kelso, 1992). The standard deviation of the relative phase between the metronome and the response provides an effective probe of the stability of coordination with an increase in standard deviation indicating a decrease in stability. Due to technical failures during recording, behavioral data from one subject were not available for off-line analysis. As a result, the behavioral results are based on the analysis of the remaining 13 subjects.

Neuroimaging Analysis

BOLD signals were analyzed within the accepted general linear framework (Friston et al., 1995) using AFNI (Cox & Hyde, 1997; Cox, 1996) installed on a PC running Linux. Preprocessing included correcting for motion by realigning all images to the first image of the first series. Spatial smoothing was performed using a Gaussian filter with a full width half maximum of 7.5 mm. The time series at each voxel was subsequently band-pass filtered between 0.1 and 0.007 Hz to remove low- and high-frequency noise.

Several levels of analysis were performed on the concatenated sessions. To determine the activation level for each experimental condition compared to rest, the BOLD signal at each voxel was modeled by 10 covariates of interest created by convolving a hemodynamic response function with a binary vector representing the relative timing of each condition. Additional covariates included a baseline offset and a linear drift term. SPM99 was employed to coregister the statistical images to the anatomical images prior to transformation into Talairach and Tournoux (1988) coordinates, and to further statistical evaluation.

Detection of the predicted relationship between BOLD intensity and behavioral stability was accomplished using an approach designed specifically for parametric imaging experiments (Buchel, Holmes, Rees, & Friston, 1998). Such an approach allows for the detection of areas that (1) show a linear relationship between stimulus rate and BOLD intensity for both coordination modes and (2) show an interaction such that BOLD intensity increases with increasing movement rate only during syncopation and not during synchronization. The main effects of coordination pattern were accounted for by including one covariate each for the two patterns as part of the baseline model. A Rate by Pattern interaction was quantified by higher-order covariates that modeled BOLD signal activity as a linear function of coordination frequency by multiplying the covariate for each pattern by the stimulus frequency.

As a final step, group level analysis was performed using a between-subject one-sample t test applied to the beta weights derived from each regression. Correction for multiple comparisons involved a combined thresholding and clustering approach. Voxels were considered significant if they exceeded a per-voxel threshold of p < .001 and were members of a cluster (the set of adjacent active voxels) of at least 465 mm3. The resulting group activation map was volume corrected at an error rate of p < .05.

Structural Equation Modeling

Stability-dependent changes in effective connectivity between key cortical regions was assessed by structural equation modeling as outlined by Bullmore et al. (2000) and McIntosh and Gonzalez-Lima (1994) and implemented in LISREL. A selected set of key sensory and motor related brain regions was identified based on the functional data and used to construct an anatomically motivated model. The model comprised a cortical–cerebellar loop with the following projections: PMC to SMA; SMA to M1; M1 to ipsilateral Cbl and Cbl back to PMC. Auditory influence was modeled as a projection from primary auditory cortex (A1) to PMC. PMC receives both sensory and motor (cerebellar) projections in accordance with known anatomical connectivity and demonstrated functional importance in sensory-guided action (e.g., Wise, Boussaoud, Johnson, & Caminiti, 1997) and based on previously published connectivity models (Pollok, Gross, Muller, Aschersleben, & Schnitzler, 2005; Pollok, Sudmeyer, Gross, & Schnitzler, 2005; Solodkin, Hlustik, Chen, & Small, 2004). Additional sources of variance not included in the model were accounted for using a residual variance term for each region set to a constant value of 0.5 (McIntosh & Gonzalez-Lima, 1994).

A single time series was derived for each anatomical region in the model by averaging the voxel with the highest activation amplitude with its six nearest neighbors. To reduce covariance arising from the transition between rest and activation periods, only time points associated with coordination conditions (and not rest) were selected from each time series. In a first analysis, we evaluated path strengths associated with the two coordination modes independent of changes in rate and stability. Time series were averaged across subject and rate, thereby producing a single time series for each coordination condition and region. A cross-correlation matrix was computed for each condition and served as input to the SEM software. The model was fit to the data from each condition separately, yielding two sets of path coefficients. Differences in path strength between synchronize and syncopate conditions were evaluated for each weight using a stacked model approach (McIntosh & Gonzalez-Lima, 1994), where null and alternative models are computed and compared. For the null model, path coefficients for the syncopation condition were constrained to be the same as the synchronization condition and the χ2 was computed. For the alternative model, one path is allowed to vary and a second χ2 is computed. A significant difference between path strengths (p < .01 Bonferroni corrected for the 5 comparisons) occurs at a critical value of χ2diff(df = 1) > 6.63.

In a second path analysis, we evaluated how path strengths changed as a function of coordination stability. Time series from each condition and region were averaged across subjects. Path strengths were computed from the cross-correlation matrix of each condition and rate separately resulting in 10 sets of path weights. A stacked model approach was used to uncover rates at which path strengths for syncopation and synchronization differed significantly. A significant difference (p < .002, Bonferroni corrected for the 25 comparisons) between path strengths of the two conditions occurred at a critical value of χ2diff (df = 1) > 9.95.

RESULTS

Behavior

Correspondence between the metronome and movement frequency (1/IRI; Figure 1C) was strong for all prescribed rates for both synchronization (r2 = .96) and syncopation (r2 = .88). Likewise, the relative phase between metronome onset and peak finger flexion met the task requirements with a mean relative phase across all frequencies of 5.6° for synchronization and 207.2° for syncopation (Figure 1D). A two-way ANOVA with factors of pattern (synchronize, syncopate) and rate revealed an expected main effect of pattern [F(1, 110) = 583.04, p < .001]. There was no significant effect of rate on relative phase and no interaction. Taken together, these data indicate effective performance of both patterns across all rates.

The standard deviation of the coordination variable, relative phase, has been established both theoretically and experimentally as an effective measure of pattern stability (see Schoner & Kelso, 1988, for review) and captures two important features of the coordination dynamics (Figure 1D). First, syncopation was generally less stable (more variable) than synchronization, across all coordination frequencies. This finding is predicted by theory and in line with previous results demonstrating that syncopation is a less stable form of coordination than synchronization (Kelso et al., 1990). Second, relative to the synchronization task, syncopation decreases in stability as rate increases. For every 1.0-Hz increment in movement rate, variability during syncopation increased at a rate of 20.2° compared to only 6.6° for synchronization. A two-way ANOVA revealed a main effect of pattern [F(1, 110) = 192.6, p < .001], a main effect of rate [F(4, 110) = 7.11, p < .001], and a significant Pattern × Rate interaction [F(4, 110) = 2.48, p = .048]. The interaction term reflects the well-established finding that an increase in the rate of coordination induces a progressive loss of coordinative stability for syncopation but not synchronization (Kelso et al., 1990).

Functional Neuroimaging

BOLD signal intensity demonstrated a positive linear relationship with the rate of coordination (Figure 2) in the right precentral gyrus (BA 4) and the bilateral superior temporal gyri (STG, BA 42). This activity profile was observed for both synchronization and syncopation, and is consistent with previous findings showing that increases in the rate of movement or auditory presentation result in linear increases in brain activity within contralateral sensorimotor (Rao et al., 1996) and primary auditory cortices (Binder et al., 1994), respectively. On the other hand, a significant interaction between coordination pattern and movement rate (Figure 3) was observed within dorsal and ventral PMC (BA 6), SMA and pre-SMA, right anterior insula (BA 13), and in two small regions of the contralateral Cbl: the left dentate nucleus and the left inferior semilunar lobe. Across this network, BOLD amplitude increased linearly with increasing movement rate during syncopation but not synchronization.

Figure 2. 

Cortical regions demonstrating a linear relationship between BOLD amplitude and coordination rate are overlaid on a three-dimensional representation of a canonical brain transformed to the coordinate space of Talairach and Tournoux. The panels on the right plot the grand mean BOLD amplitude (±SEM) for the peak voxel in each identified region as a function of coordination frequency for both synchronization (open circles) and syncopation (filled squared). Anatomical designation and Talairach coordinates are provided. SMC = sensorimotor cortex; STG = superior temporal gyrus.

Figure 2. 

Cortical regions demonstrating a linear relationship between BOLD amplitude and coordination rate are overlaid on a three-dimensional representation of a canonical brain transformed to the coordinate space of Talairach and Tournoux. The panels on the right plot the grand mean BOLD amplitude (±SEM) for the peak voxel in each identified region as a function of coordination frequency for both synchronization (open circles) and syncopation (filled squared). Anatomical designation and Talairach coordinates are provided. SMC = sensorimotor cortex; STG = superior temporal gyrus.

Figure 3. 

Neural regions demonstrating a significant Rate by Pattern interaction are overlaid in color on a canonical brain transformed to the coordinate space of Talairach and Tournoux. Individual plots graph the grand mean BOLD amplitude (±SEM) for the peak voxel in each identified region as a function of coordination frequency for both synchronization (open circles) and syncopation (filled squared). Anatomical designation and Talairach coordinates are provided. vPMC = ventral premotor cortex; SMA = supplementary motor area; ISLL = inferior semilunar lobule.

Figure 3. 

Neural regions demonstrating a significant Rate by Pattern interaction are overlaid in color on a canonical brain transformed to the coordinate space of Talairach and Tournoux. Individual plots graph the grand mean BOLD amplitude (±SEM) for the peak voxel in each identified region as a function of coordination frequency for both synchronization (open circles) and syncopation (filled squared). Anatomical designation and Talairach coordinates are provided. vPMC = ventral premotor cortex; SMA = supplementary motor area; ISLL = inferior semilunar lobule.

Effective connectivity between regions, estimated using structural equation modeling, revealed significant differences in premotor coupling for the two patterns of coordination. When collapsed across rate, syncopation exhibited greater neural coupling from PMC to SMA and from SMA to M1, with the latter being statistically significant (χ12 = 8.09, p = .0045; Figure 4B).

Figure 4. 

(A) Anatomical connections (yellow arrows) included in the structural equation model form a basic right-hand motor network. (B) Path weights for the grand mean of the synchronize (blue) and syncopate (red) conditions collapsed across rate. Synchronization was accompanied by significantly lower path strength in the projection from supplementary motor area (SMA) to primary motor cortex (M1). (C) Path strength plotted as a function of coordination frequency for synchronization and syncopation. Each model path is plotted in a separate graph. Asterisks indicate significant differences in path strength between synchronization and syncopation (Bonferroni corrected to p < .002). PMC = premotor cortex; A1 = primary auditory cortex; Cbl = cerebellum.

Figure 4. 

(A) Anatomical connections (yellow arrows) included in the structural equation model form a basic right-hand motor network. (B) Path weights for the grand mean of the synchronize (blue) and syncopate (red) conditions collapsed across rate. Synchronization was accompanied by significantly lower path strength in the projection from supplementary motor area (SMA) to primary motor cortex (M1). (C) Path strength plotted as a function of coordination frequency for synchronization and syncopation. Each model path is plotted in a separate graph. Asterisks indicate significant differences in path strength between synchronization and syncopation (Bonferroni corrected to p < .002). PMC = premotor cortex; A1 = primary auditory cortex; Cbl = cerebellum.

The goodness-of-fit index and the normalized fit index (Table 1) indicate that the connectivity model provided a good fit to the data from all of the individual conditions. Measures of path strength as a function of coordination rate also indicate that strength of neural coupling is dependent on pattern stability (Figure 4C). Significant differences in coupling strength from PMC to SMA and SMA to M1 were found (Syncopate > Synchronize, χ12 > 9.54, p < .002) only for coordination rates above 1.0 Hz. Such findings underscore the existence of a near linear relationship between neural coupling, rate, and stability. At slowest rates, SMA to M1 coupling was similar for the two coordination patterns; however, a rate increase was associated with a linear decrease in coupling strength for synchronization (r2 = .50), but not syncopation (r2 = .001). In contrast, syncopation (r2 = .72), but not synchronization (r2 = .02), was accompanied by a linear increase in the strength of coupling from PMC to SMA. Overall, increasing the rate of coordination without altering pattern stability resulted in a progressive decrease in the influence of SMA on M1; however, when the same rate increase induced a progressive decrease in stability (during syncopation), the coupling between SMA and M1 was maintained and accompanied by compensatory increases in coupling strength from PMC to SMA.

Table 1. 

Goodness-of-fit Index (GFI) and Normed Fit Index (NFI) for the Fit of the Proposed SEM to the BOLD Data from Each Experimental Condition

Pattern
Rate (Hz)
GFI
NFI
Synchronize 0.75 0.93 0.94 
1.00 0.96 0.96 
1.25 0.93 0.90 
1.50 0.97 0.97 
1.75 0.95 0.96 
Syncopate 0.75 0.94 0.91 
1.00 0.91 0.91 
1.25 0.95 0.97 
1.50 0.87 0.91 
1.75 0.43 0.77 
Pattern
Rate (Hz)
GFI
NFI
Synchronize 0.75 0.93 0.94 
1.00 0.96 0.96 
1.25 0.93 0.90 
1.50 0.97 0.97 
1.75 0.95 0.96 
Syncopate 0.75 0.94 0.91 
1.00 0.91 0.91 
1.25 0.95 0.97 
1.50 0.87 0.91 
1.75 0.43 0.77 

DISCUSSION

The present study investigated the neural dynamics of sensorimotor coordination in order to map key behavioral parameters, defined within a coordination dynamics framework, onto underlying neural circuitry. The results provide neurophysiological evidence for the existence of distinct but overlapping brain circuitry organized along the lines of coordination dynamics: one that reflects parametric changes in rate, and one specific to the stability of the coordination pattern. Changes in rate were reflected in primary auditory and motor cortices, whereas stability-dependent changes in cortical activity were reflected across a broader network comprising the SMA, bilateral lateral PMC, and lateral Cbl. Moreover, measures of connectivity revealed how coupling between discrete cortical regions was altered in a stability-dependent manner, showing an increased interaction between medial and lateral premotor regions and primary motor cortex as coordination became increasingly less stable.

Rate-dependent Activity

Activity in primary auditory and motor cortices was linearly related to the rate of coordination independent of pattern stability. Similar linear relationships between rate and level of activity have been observed in primary visual (Fox & Raichle, 1984), auditory (Rees et al., 1997; Binder et al., 1994; Price et al., 1992), and sensorimotor regions (Kawashima et al., 1999; Jancke et al., 1998; Jenkins, Passingham, & Brooks, 1997; Sadato et al., 1997; Rao et al., 1996; Sabatini et al., 1993). When considered together, the foregoing research suggests that activity in primary sensory and motor areas is sensitive to specific stimulus and motor parameters such as number of stimuli/movements (Rao et al., 1996), speed (Jerbi et al., 2007), velocity (Kelso et al., 1998), or force (Wexler et al., 1997). Such findings are compatible with the respective afferent/efferent connections of sensory and motor cortex, and attest to the input and output processing roles these regions play in perception and action. Within a coordination dynamics framework, we may consider primary sensory and motor cortices as related to the activation of the components that comprise the behavioral pattern but not directly to the formation and stabilization of the pattern.

Additional support for this notion comes from the observation that the coupling strength between auditory cortex and PMC was not influenced by either rate or pattern stability. Thus, although the increase in number of auditory stimuli at higher rates resulted in greater activity within A1, the relative influence of this activity remains consistent across conditions. Previous EEG (Carver, Fuchs, Jantzen, & Kelso, 2002) and MEG (Mayville et al., 2001) studies demonstrated qualitative changes in auditory processing at rates coincident with behavioral transitions. Although such findings suggest that rate-dependent modulation in early cortical processing of the auditory metronome may influence auditory–motor coordination, the lack of changes in functional coupling between auditory cortex and lateral PMC found here suggests that coordination constraints arise primarily at the level of sensorimotor integration as opposed to basic changes in auditory processing.

Stability-dependent Cortical Activity

Our results demonstrating that changes in cortical function are related to changes in pattern stability and not merely to increases in movement rate alone support, and extend previous electrophysiological investigations showing that a similar dynamics governs both brain and behavioral levels (Mayville et al., 1999; Wallenstein et al., 1995; Fuchs, Kelso, & Haken, 1992; Kelso et al., 1991, 1992). That is, the stability of the order parameter or coordination variable plays a key role in the neural organization of behavioral patterns. In addition, the results support the hypothesis that previously described neural differences between syncopation and synchronization in lateral and medial premotor areas and the Cbl (Jantzen, Steinberg, & Kelso, 2002, 2004, 2005; Oullier, Jantzen, Steinberg, & Kelso, 2005; Mayville et al., 2002) also depend on pattern stability, as measured by variability of the coordination variable, relative phase.

In a growing number of studies, movement complexity has served as a framework for uncovering neural regions associated with the spatio-temporal organization of coordinated action. For unimanual tasks, increasing complexity has been associated with greater BOLD amplitude and metabolism in dorsal lateral PMC, the SMA, and in some cases, the Cbl (Ehrsson, Kuhtz-Buschbeck, & Forssberg, 2002; Haslinger et al., 2002; Boecker et al., 1998; Catalan, Honda, Weeks, Cohen, & Hallett, 1998), further implicating a distributed premotor–cerebellar circuit in the higher-level organization of movement sequences. However, the specific role of cortical and subcortical regions in guiding action patterns has remained unresolved because the features manipulated in altering complexity vary according to how complexity is conceived. For example, a similar pattern of neural activity is observed in the SMA and dorsal PMC when increasing the number of movements performed (Catalan et al., 1998), altering the relative timing between movements (Lewis, Wing, Pope, Praamstra, & Miall, 2004; Dhamala, Pagnoni, Wiesenfeld, & Berns, 2002) or adjusting the sequential ordering between fingers (Haaland, Harrington, & Knight, 2000; Deiber, Honda, Ibanez, Sadato, & Hallett, 1999).

When taken together with prior imaging studies of bimanual coordination (Debaere et al., 2004; Meyer-Lindenberg et al., 2002), our results suggest that pattern stability may offer a unifying explanation of previous work; that is, variability of the required pattern may serve both as a measure for quantifying behavioral complexity and for describing the organization of neural activity across premotor and cerebellar regions. Support for such a unifying picture comes in the form of growing evidence for stability-dependent networks, regardless of whether patterns of behavior are defined within fingers of a single hand (Nair, Purcott, Fuchs, Steinberg, & Kelso, 2003; Ehrsson et al., 2002), between oneself and the environment (Jantzen et al., 2002, 2004, 2005; Oullier et al., 2005; Mayville et al., 2002), between homologous (Debaere et al., 2004; Ullen, Forssberg, & Ehrsson, 2003; Meyer-Lindenberg et al., 2002; Immisch, Waldvogel, van Gelderen, & Hallett, 2001; Sadato et al., 1997) and nonhomologous limbs (Debaere, Wenderoth, Sunaert, Van Hecke, & Swinnen, 2003), or even when coordination is imagined (Oullier et al., 2005; Nair et al., 2003). Such evidence speaks compellingly for the tenet that, like behavior itself, the patterns of human brain activity can be captured by informationally relevant quantities such as the relative phase among interacting coordinating elements and their coordination dynamics, namely, multistability, meta-stability, phase transitions, fluctuations, and so forth (Deiber, Ibanez, Caldara, Andrey, & Hauert, 2005; Kelso, 1994a, 1994b). The specific neural representation of the coordinating elements or agents recruited is expected to vary in task- and modality-dependent ways. In the examples described here, activity of primary sensory and motor areas is related to the elements being coordinated independent of the pattern of coordination. However, the key insight is that other brain regions form a network that can be differentiated from modality-specific areas by virtue of their relationship to dynamic properties, such as stability.

Functional Coupling

Recent work has begun to identify the large-scale functional coupling underlying sensorimotor and bimanual coordination (Pollok, Gross, et al., 2005; Pollok, Sudmeyer, et al., 2005; Zhuang, LaConte, Peltier, Zhang, & Hu, 2005) as well as how such coupling may be modulated by task-relevant parameters (Solodkin et al., 2004; Rowe, Friston, Frackowiak, & Passingham, 2002; Toma et al., 2002). A growing number of studies have demonstrated modification of functional coupling between premotor and primary motor areas related to task demands (Gerloff et al., 1998), sequence length (Manganotti et al., 1998), learning (Gerloff & Andress, 2002), and level of performance (Hummel, Kirsammer, & Gerloff, 2003). The present results offer a new framework for investigating the neural basis of informational coupling underlying coordination by identifying how theoretically defined parameters guide effective coupling across functionally specialized cortical regions. When coordination is stable, increases in rate result in reduced coupling between SMA and M1 implying a decreased influence of frontal motor planning systems. By comparison, rate-related decreases in stability are characterized by two complementary changes in coupling. First, for syncopation, increases in both dorsal and ventral PMC activity are accompanied by stronger coupling between these regions and the SMA—presumably to stabilize the pattern under conditions that promote instability. Second, the progressive decrease in directed influence from SMA to M1 was not observed when stability decreased during syncopation. It is noteworthy that the strength of coupling was not altered as a function of the behavioral pattern performed or the rate of coordination, rather it was variability of the intended coordinated pattern that was reflected in altered functional connectivity. Our findings suggest that the stability of a relevant order parameter or collective variable, a dynamical property of proven importance in the description and modeling of coordinated action, may also prove to be the critical variable governing coupling between coordinated brain structures.

Although dorsal and ventral PMC subsume slightly different functions (e.g., Hoshi & Tanji, 2006), together they play well-established roles in action planning, selection, and control based on external stimuli (Hoshi & Tanji, 2006; Grafton et al., 1998; Wise et al., 1997; Jackson & Husain, 1996) and are thus critical for the integration of visual (Hoshi & Tanji, 2006; Rizzolatti, Luppino, & Matelli, 1998) and auditory (Chen, Zatorre, & Penhune, 2006; Schubotz & von Cramon, 2003; Schubotz, von Cramon, & Lohmann, 2003) information during action organization. Both the increased activation within lateral PMC and the increased coupling to SMA may indicate a greater demand on integrating auditory and motor information into a behavioral pattern. As the coordination pattern formed between the auditory stimulus and the participant's movements become less stable, the relative influence of the external stimulus in guiding action appears to increase.

Stability-dependent increases in lateral premotor activity are also observed in the bimanual case (Debaere et al., 2004; Ullen, Forssberg, & Ehrsson, 2003; Meyer-Lindenberg et al., 2002), where coordination is between homologous limbs as opposed to with an external stimulus, suggesting that the role of PMC during coordination may not be specific to perceptual–motor integration. In a recent review of human premotor function, Schubotz and von Cramon (2003) contend that lateral PMC is functionally organized along several motor and cognitive features. Dorsal PMC is involved in the temporal prediction of spatial location and more ventral regions are sensitive to object-related properties of temporally evolving stimuli, such as pitch. This proposed subdivision suggests that bimanual coordination may activate more dorsal portions of PMC compared to unimanual coordination, a prediction supported by some (Debaere et al., 2004; Meyer-Lindenberg et al., 2002), but not all (e.g., Ullen et al., 2003), studies. Nonetheless, a general role for lateral PMC in spatio-temporal integration appears to be compatible with their involvement in both unimanual and bimanual coordination.

The SMA and particularly the pre-SMA are heavily implicated in the organization of higher level, spatio-temporal properties of actions (Mayville et al., 2002; Shima & Tanji, 2000; Rao et al., 1996; Tanji & Shima, 1994), particularly for internally versus externally generated movements (Debaere et al., 2003; Jenkins, Jahanshahi, Jueptner, Passingham, & Brooks, 2000; Cunnington, Bradshaw, & Iansek, 1996; Roland & Zilles, 1996; Halsband, Matsuzaka, & Tanji, 1994). Lesions to the SMA disrupt coordination (Stephen, Binkofski, Posse, Seitz, & Freund, 1999), prolong movement initiation (Kazennikov et al., 1999), and degrade the ability to perform sequential movements (Dick, Benecke, Rothwell, & Marsden, 2005; Halsband, Ito, Tanji, & Freund, 1993). The decrease in coupling between the SMA and sensorimotor cortex during synchronization thus suggests that higher-level cognitive control over sequential/temporal aspects of highly stable coordination is reduced at higher movement rates. Importantly, reduced influence from the SMA to motor cortex is not observed during syncopation, where a progressive decrease in stability appears to preserve the need for premotor influence over those regions involved in motor execution and timing. Thus, an increase in the variability of the global sensorimotor pattern may place greater demand on internal planning and organization of temporal aspects of coordination (e.g., Debaere et al., 2004; Mayville et al., 2002).

Taken together, our results suggest that the pattern of neural coupling across widespread cortical motor circuits is influenced by the stability of collective variables that define behavioral patterns. Additional support for this hypothesis comes from EEG studies that reveal that coupling between the SMA and primary motor cortex is greater during performance of complex versus simple motor patterns (Manganotti et al., 1998) and that SMA to motor coupling is reduced as complex movement patterns are stabilized through learning (Gerloff & Andres, 2002; Andres et al., 1999). The definitive role of PMC, and particularly of the SMA, in stabilizing patterns of coordination is reinforced by TMS work, in which transient deactivation of lateral and medial PMC disrupts coordination and eventually culminates in spontaneous switching between patterns (Meyer-Lindenberg et al., 2002). Indeed, recent behavioral work reveals that patients with lesions to the SMA have impairments in the ability to recover from perturbations of coordinated movements (Dick et al., 2005).

Summary and Conclusions

The present results underscore the sensitivity of the premotor–cerebellar network to pattern stability and are in line with recent results showing that an overlapping set of brain regions underlies coordination regardless of whether it is unimanual, bimanual, multilimb, or even imagined (Jantzen & Kelso, 2007). Coordination at the neural level appears to be governed by informational quantities that communicate the relation between components and their dynamics, regardless of the particular components themselves (Kelso, 1994a, 1994b). The dynamic concept of stability-measured here at both behavioral and brain levels may be seen to replace common, yet less well-defined notions such as task difficulty and task complexity. In the future, it will be intriguing to see how global patterns of neural activity and connectivity representing key abstract and task-dependent parameters may be altered by localized interruptions in neural function brought on by stroke, closed head injury, and Parkinson's disease. Such investigations may provide new insights into how large-scale network activity mediates functional recovery, plasticity, and compensation in the human brain.

Acknowledgments

This work was supported by NINDS grant NS48229, NIMH Director's Innovation Grant MH42900, NIMH grant MH80038, a summer research grant from WWU, and the Pierre de Fermat Chair.

Reprint requests should be sent to Kelly J. Jantzen, Western Washington University, 516 High Street, Bellingham, WA 98225, or via e-mail: Kelly.jantzen@wwu.edu.

REFERENCES

Andres
,
F. G.
,
Mima
,
T.
,
Schulman
,
A. E.
,
Dichgans
,
J.
,
Hallett
,
M.
, &
Gerloff
,
C.
(
1999
).
Functional coupling of human cortical sensorimotor areas during bimanual skill acquisition.
Brain
,
122
,
855
870
.
Bardy
,
B. G.
,
Oullier
,
O.
,
Bootsma
,
R. J.
, &
Stoffregen
,
T. A.
(
2002
).
Dynamics of human postural transitions.
Journal of Experimental Psychology: Human Perception and Performance
,
28
,
499
514
.
Beek
,
P. J.
,
Peper
,
C. E.
, &
Stegeman
,
D. F.
(
1995
).
Dynamical models of movement coordination.
Human Movement Science
,
14
,
573
608
.
Binder
,
J. R.
,
Rao
,
S. M.
,
Hammeke
,
T. A.
,
Frost
,
J. A.
,
Bandettini
,
P. A.
, &
Hyde
,
J. S.
(
1994
).
Effects of stimulus rate on signal response during functional magnetic-resonance-imaging of auditory-cortex.
Cognitive Brain Research
,
2
,
31
38
.
Boecker
,
H.
,
Dagher
,
A.
,
Ceballos-Baumann
,
A. O.
,
Passingham
,
R. E.
,
Samuel
,
M.
,
Friston
,
K. J.
,
et al
(
1998
).
Role of the human rostral supplementary motor area and the basal ganglia in motor sequence control: Investigations with H2O-15 PET.
Journal of Neurophysiology
,
79
,
1070
1080
.
Bressler
,
S. L.
, &
Kelso
,
J. A. S.
(
2001
).
Cortical coordination dynamics and cognition.
Trends in Cognitive Sciences
,
5
,
26
36
.
Buchanan
,
J. J.
,
Kelso
,
J. A. S.
, &
De Guzman
,
G. C.
(
1997
).
Self-organization of trajectory formation.
Biological Cybernetics
,
76
,
257
273
.
Buchel
,
C.
,
Holmes
,
A. P.
,
Rees
,
G.
, &
Friston
,
K. J.
(
1998
).
Characterizing stimulus–response functions using nonlinear regressors in parametric fMRI experiments.
Neuroimage
,
8
,
140
148
.
Bullmore
,
E.
,
Horwitz
,
B.
,
Honey
,
G.
,
Brammer
,
M.
,
Williams
,
S.
, &
Sharma
,
T.
(
2000
).
How good is good enough in path analysis of fMRI data?
Neuroimage
,
11
,
289
301
.
Byblow
,
W. D.
,
Chua
,
R.
, &
Goodman
,
D.
(
1995
).
Asymmetries in coupling dynamics of perception and action.
Journal of Motor Behavior
,
27
,
123
137
.
Carson
,
R. C.
, &
Kelso
,
J. A. S.
(
2004
).
Governing coordination: Behavioral principles and neural correlates.
Experimental Brain Research
,
154
,
267
274
.
Carver
,
F. W.
,
Fuchs
,
A.
,
Jantzen
,
K. J.
, &
Kelso
,
J. A. S.
(
2002
).
Spatiotemporal analysis of the neuromagnetic response to rhythmic auditory stimulation: Rate dependence and transient to steady-state transition.
Clinical Neurophysiology
,
113
,
1921
1931
.
Catalan
,
M. J.
,
Honda
,
M.
,
Weeks
,
R. A.
,
Cohen
,
L. G.
, &
Hallett
,
M.
(
1998
).
The functional neuroanatomy of simple and complex sequential finger movements: A PET study.
Brain
,
121
,
253
264
.
Cavallari
,
P.
,
Cerri
,
G.
, &
Baldissera
,
F.
(
2001
).
Coordination of coupled hand and foot movements during childhood.
Experimental Brain Research
,
41
,
398
409
.
Chen
,
J. L.
,
Zatorre
,
R. J.
, &
Penhune
,
V. B.
(
2006
).
Interactions between auditory and dorsal premotor cortex during synchronization to musical rhythms.
Neuroimage
,
32
,
1771
1781
.
Cox
,
R. W.
(
1996
).
AFNI: Software for analysis and visualization of functional magnetic resonance neuroimages.
Computers and Biomedical Research
,
29
,
162
173
.
Cox
,
R. W.
, &
Hyde
,
J. S.
(
1997
).
Software tools for analysis and visualization of fMRI data.
NMR in Biomedicine
,
10
,
171
178
.
Cunnington
,
R.
,
Bradshaw
,
J. L.
, &
Iansek
,
R.
(
1996
).
The role of the supplementary motor area in the control of voluntary movement.
15
,
627
647
.
Debaere
,
F.
,
Wenderoth
,
N.
,
Sunaert
,
S.
,
Van Hecke
,
P.
, &
Swinnen
,
S. P.
(
2003
).
Internal vs external generation of movements: Differential neural pathways involved in bimanual coordination performed in the presence or absence of augmented visual feedback.
Neuroimage
,
19
,
764
776
.
Debaere
,
F.
,
Wenderoth
,
N.
,
Sunaert
,
S.
,
Van Hecke
,
P.
, &
Swinnen
,
S. P.
(
2004
).
Cerebellar and premotor function in bimanual coordination: Parametric neural responses to spatiotemporal complexity and cycling frequency.
Neuroimage
,
21
,
1416
1427
.
Deiber
,
M. P.
,
Honda
,
M.
,
Ibanez
,
V.
,
Sadato
,
N.
, &
Hallett
,
M.
(
1999
).
Mesial motor areas in self-initiated versus externally triggered movements examined with fMRI: Effect of movement type and rate.
Journal of Neurophysiology
,
81
,
3065
3077
.
Deiber
,
M. P.
,
Ibanez
,
V.
,
Caldara
,
R.
,
Andrey
,
C.
, &
Hauert
,
C. A.
(
2005
).
Programming effectors and coordination in bimanual in-phase mirror finger movements.
Cognitive Brain Research
,
23
,
374
386
.
Dhamala
,
M.
,
Pagnoni
,
G.
,
Wiesenfeld
,
K.
, &
Berns
,
G. S.
(
2002
).
Measurements of brain activity complexity for varying mental loads.
Physical Review E: Statistical, Nonlinear and Soft Matter Physics
,
65
,
041917
.
Dick
,
J. P. R.
,
Benecke
,
R.
,
Rothwell
,
J. C.
, &
Marsden
,
C. D.
(
2005
).
Simple and complex movements in a patient with infarction of the right supplementary motor area.
Movement Disorders
,
11
,
255
266
.
Ehrsson
,
H. H.
,
Kuhtz-Buschbeck
,
J. P.
, &
Forssberg
,
H.
(
2002
).
Brain regions controlling nonsynergistic versus synergistic movement of the digits: A functional magnetic resonance imaging study.
Journal of Neuroscience
,
22
,
5074
5080
.
Fox
,
P. T.
, &
Raichle
,
M. E.
(
1984
).
Stimulus rate dependence of regional cerebral blood-flow in human striate cortex, demonstrated by positron emission tomography.
Journal of Neurophysiology
,
51
,
1109
1120
.
Friston
,
K.
,
Holmes
,
A. P.
,
Worsley
,
K.
,
Poline
,
J. B.
,
Frith
,
C. D.
, &
Frackowiak
,
R.
(
1995
).
Statistical parametric mas in functional imaging: A general linear model approach.
Human Brain Mapping
,
2
,
189
210
.
Fuchs
,
A.
,
Kelso
,
J. A. S.
, &
Haken
,
H.
(
1992
).
Phase transitions in human brain: Spatial mode dynamics.
International Journal of Bifurcation and Chaos
,
2
,
917
939
.
Fuchs
,
A.
,
Mayville
,
J. M.
,
Cheyne
,
D.
,
Weinberg
,
H.
,
Deecke
,
L.
, &
Kelso
,
J. A. S.
(
2000
).
Spatiotemporal analysis of neuromagnetic events underlying the emergence of coordinative instabilities.
Neuroimage
,
12
,
71
84
.
Gerloff
,
C.
, &
Andres
,
F. G.
(
2002
).
Bimanual coordination and interhemispheric interaction.
110
,
161
186
.
Gerloff
,
C.
,
Richard
,
J.
,
Hadley
,
J.
,
Schulman
,
A. E.
,
Honda
,
M.
, &
Hallett
,
M.
(
1998
).
Functional coupling and regional activation of human cortical motor areas during simple, internally paced and externally paced finger movements.
Brain
,
121
,
1513
1531
.
Grafton
,
S. T.
,
Hazeltine
,
E.
, &
Ivry
,
R. B.
(
1998
).
Abstract and effector-specific representations of motor sequences identified with pet.
18
,
9420
9428
.
Haaland
,
K. Y.
,
Harrington
,
D. L.
, &
Knight
,
R. T.
(
2000
).
Neural representations of skilled movement.
Brain
,
123
,
2306
2313
.
Haken
,
H.
(
1983
).
Advanced synergetics.
Berlin
:
Springer
.
Haken
,
H.
(
1996
).
Principles of brain function.
Berlin
:
Springer
.
Haken
,
H.
,
Kelso
,
J. A. S.
, &
Bunz
,
H.
(
1985
).
A theoretical-model of phase-transitions in human hand movements.
Biological Cybernetics
,
51
,
347
356
.
Halsband
,
U.
,
Ito
,
N.
,
Tanji
,
J.
, &
Freund
,
H. J.
(
1993
).
The role of premotor cortex and the supplementary motor area in the temporal control of movement in man.
Brain
,
116
,
243
266
.
Halsband
,
U.
,
Matsuzaka
,
Y.
, &
Tanji
,
J.
(
1994
).
Neuronal-activity in the primate supplementary, pre-supplementary and premotor cortex during externally and internally instructed sequential movements.
Neuroscience Research
,
20
,
149
155
.
Haslinger
,
B.
,
Erhard
,
P.
,
Weilke
,
F.
,
Ceballos-Baumann
,
A. O.
,
Bartenstein
,
P.
,
von Einsiedel
,
H. G.
,
et al
(
2002
).
The role of lateral premotor–cerebellar–parietal circuits in motor sequence control: A parametric fMRI study.
Cognitive Brain Research
,
13
,
159
168
.
Hoshi
,
E.
, &
Tanji
,
J.
(
2006
).
Differential involvement of neurons in the dorsal and ventral premotor cortex during processing of visual signals for action planning.
Journal of Neurophysiology
,
95
,
3596
3616
.
Hummel
,
F.
,
Kirsammer
,
R.
, &
Gerloff
,
C.
(
2003
).
Ipsilateral cortical activation during finger sequences of increasing complexity: Representation of movement difficulty or memory load?
Clinical Neurophysiology
,
114
,
605
613
.
Immisch
,
I.
,
Waldvogel
,
D.
,
van Gelderen
,
P.
, &
Hallett
,
M.
(
2001
).
The role of the medial wall and its anatomical variations for bimanual antiphase and in-phase movements.
Neuroimage
,
14
,
674
684
.
Jackson
,
S. R.
, &
Husain
,
M.
(
1996
).
Visuomotor functions of the lateral pre-motor cortex.
Current Opinion in Neurobiology
,
6
,
788
795
.
Jancke
,
J.
,
Peters
,
M.
,
Schlaug
,
G.
,
Posse
,
S.
,
Steinmetz
,
H.
, &
Muller-Gartner
,
H. W.
(
1998
).
Differential magnetic resonance signal change in human sensorimotor cortex to finger movements of different rate of the dominant and subdominant hand.
Cognitive Brain Research
,
6
,
279
284
.
Jantzen
,
K. J.
, &
Kelso
,
J. A. S.
(
2007
).
Neural coordination dynamics of human sensorimotor behavior: A review.
In V. K. Jirsa & A. R. McIntosh (Eds.),
Handbook of brain connectivity
(pp.
421
461
).
Berlin
:
Springer
.
Jantzen
,
K. J.
,
Oullier
,
O.
, &
Kelso
,
J. A. S.
(
2008
).
Neuroimaging coordination dynamics in the sports sciences.
Methods
,
45
,
325
335
.
Jantzen
,
K. J.
,
Steinberg
,
F. L.
, &
Kelso
,
J. A. S.
(
2002
).
Practice-dependent modulation of neural activity during human sensorimotor coordination: A functional magnetic resonance imaging study.
Neuroscience Letters
,
332
,
205
209
.
Jantzen
,
K. J.
,
Steinberg
,
F. L.
, &
Kelso
,
J. A. S.
(
2004
).
Brain networks underlying human timing behavior are influenced by prior context.
Proceedings of the National Academy of Sciences, U.S.A.
,
101
,
6815
6820
.
Jantzen
,
K. J.
,
Steinberg
,
F. L.
, &
Kelso
,
J. A. S.
(
2005
).
Functional MRI reveals the existence of modality and coordination-dependent timing networks.
Neuroimage
,
25
,
1031
1042
.
Jeka
,
J. J.
, &
Kelso
,
J. A. S.
(
1995
).
Manipulating symmetry in the coordination dynamics of human movement.
Journal of Experimental Psychology: Human Perception and Performance
,
21
,
360
374
.
Jenkins
,
I. H.
,
Jahanshahi
,
M.
,
Jueptner
,
M.
,
Passingham
,
R. E.
, &
Brooks
,
D. J.
(
2000
).
Self-initiated versus externally triggered movements: II. The effect of movement predictability on regional cerebral blood flow.
Brain
,
123
,
1216
1228
.
Jenkins
,
I. H.
,
Passingham
,
R. E.
, &
Brooks
,
D. J.
(
1997
).
The effect of movement frequency on cerebral activation: A positron emission tomography study.
Journal of the Neurological Sciences
,
151
,
195
205
.
Jerbi
,
K.
,
Lachaux
,
J. P.
,
N'Diaye
,
K.
,
Pantazis
,
D.
,
Leahy
,
R. M.
,
Garnero
,
L.
,
et al
(
2007
).
Coherent neural representation of hand speed in humans revealed by meg imaging.
Proceedings of the National Academy of Sciences, U.S.A.
,
104
,
7676
7681
.
Jirsa
,
V. K.
,
Fink
,
P.
,
Foo
,
P.
, &
Kelso
,
J. A. S.
(
2000
).
Parametric stabilization of biological coordination: A theoretical model.
Journal of Biological Physics
,
26
,
85
112
.
Jirsa
,
V. K.
,
Fuchs
,
A.
, &
Kelso
,
J. A. S.
(
1998
).
Connecting cortical and behavioral dynamics: Bimanual coordination.
Neural Computation
,
10
,
2019
2045
.
Jirsa
,
V. K.
, &
Kelso
,
J. A. S.
(
2004
).
Coordination dynamics: Issues and trends.
New York
:
Springer
.
Jirsa
,
V. K.
, &
McIntosh
,
A. R.
(Eds.) (
2007
).
Handbook of brain connectivity.
Berlin
:
Springer
.
Kawashima
,
R.
,
Inoue
,
K.
,
Sugiura
,
M.
,
Okada
,
K.
,
Ogawa
,
A.
, &
Fukuda
,
H.
(
1999
).
A positron emission tomography study of self-paced finger movements at different frequencies.
Neuroscience
,
92
,
107
112
.
Kazennikov
,
O.
,
Hyland
,
B.
,
Corboz
,
M.
,
Babalian
,
A.
,
Rouiller
,
E. M.
, &
Wiesendanger
,
M.
(
1999
).
Neural activity of supplementary and primary motor areas in monkeys and its relation to bimanual and unimanual movement sequences.
Neuroscience
,
89
,
661
674
.
Kelso
,
J. A. S.
(
1984
).
Phase-transitions and critical-behavior in human bimanual coordination.
American Journal of Physiology
,
246
,
1000
1004
.
Kelso
,
J. A. S.
(
1994a
).
Elementary coordination dynamics.
In S. Swinnen, H. Hauer, J. Massion, & P. Casaer (Eds.),
Interlimb coordination: Neural, dynamical and cognitive constraints
(pp.
301
317
).
San Diego
:
Academic Press
.
Kelso
,
J. A. S.
(
1994b
).
Informational character of self-organized coordination dynamics.
Human Movement Science
,
13
,
393
413
.
Kelso
,
J. A. S.
(
1995
).
Dynamic patterns: The self-organization of brain and behavior.
Cambridge, MA
:
MIT Press
.
Kelso
,
J. A. S.
,
Bressler
,
S. L.
,
Buchanan
,
J. J.
,
de Guzman
,
G. G.
,
Ding
,
M.
,
Fuchs
,
A.
,
et al
(
1991
).
Cooperative and critical phenomena in the human brain revealed by multiple squids.
In D. Duke & W. Pritchard (Eds.),
Measuring chaos in the human brain
(pp.
97
112
).
New Jersey
:
World Scientific
.
Kelso
,
J. A. S.
,
Bressler
,
S. L.
,
Buchanan
,
S.
,
De Guzman
,
G. C.
,
Ding
,
M.
,
Fuchs
,
A.
,
et al
(
1992
).
A phase-transition in human brain and behavior.
Physics Letters A
,
169
,
134
144
.
Kelso
,
J. A. S.
,
Delcolle
,
J. D.
, &
Schoner
,
G.
(
1990
).
Action-perception as a pattern-formation process.
In M. Jeannerod (Ed.),
Attention and performance XIII
(pp.
139
169
).
New Jersey
:
Erlbaum
.
Kelso
,
J. A. S.
,
Fuchs
,
A.
,
Lancaster
,
R.
,
Holroyd
,
T.
,
Cheyne
,
D.
, &
Weinberg
,
H.
(
1998
).
Dynamic cortical activity in the human brain reveals motor equivalence.
Nature
,
392
,
814
818
.
Kelso
,
J. A. S.
, &
Jeka
,
J. J.
(
1992
).
Symmetry-breaking dynamics of human multilimb coordination.
Journal of Experimental Psychology: Human Perception and Performance
,
18
,
645
668
.
Kelso
,
J. A. S.
,
Schoner
,
G.
,
Scholz
,
J. P.
, &
Haken
,
H.
(
1987
).
Phase-locked modes, phase transitions and component oscillators in biological motion.
Physica Scripta
,
35
,
79
87
.
Kelso
,
J. A. S.
, &
Tognoli
,
E.
(
2007
).
Toward a complementary neuroscience: Metastable coordination dynamics of the brain.
In R. Kozma & L. Perlovsky (Eds.),
Neurodynamics of higher-level cognition and consciousness
(pp.
39
60
).
Heidelberg
:
Springer
.
Lewis
,
P. A.
,
Wing
,
A. M.
,
Pope
,
P. A.
,
Praamstra
,
P.
, &
Miall
,
R. C.
(
2004
).
Brain activity correlates differentially with increasing temporal complexity of rhythms during initialisation, synchronisation, and continuation phases of paced finger tapping.
Neuropsychologia
,
42
,
1301
1312
.
Manganotti
,
P.
,
Gerloff
,
C.
,
Toro
,
C.
,
Katsuta
,
H.
,
Sadato
,
N.
,
Zhuang
,
P.
,
et al
(
1998
).
Task-related coherence and task-related spectral power changes during sequential finger movements.
Electromyography and Motor Control: Electroencephalography and Clinical Neurophysiology
,
109
,
50
62
.
Mayville
,
J. M.
,
Bressler
,
S. L.
,
Fuchs
,
A.
, &
Kelso
,
J. A. S.
(
1999
).
Spatiotemporal reorganization of electrical activity in the human brain associated with a timing transition in rhythmic auditory–motor coordination.
Experimental Brain Research
,
127
,
371
381
.
Mayville
,
J. M.
,
Fuchs
,
A.
,
Ding
,
M. Z.
,
Cheyne
,
D.
,
Deecke
,
L.
, &
Kelso
,
J. A. S.
(
2001
).
Event-related changes in neuromagnetic activity associated with syncopation and synchronization timing tasks.
Human Brain Mapping
,
14
,
65
80
.
Mayville
,
J. M.
,
Jantzen
,
K. J.
,
Fuchs
,
A.
,
Steinberg
,
F. L.
, &
Kelso
,
J. A. S.
(
2002
).
Cortical and subcortical networks underlying syncopated and synchronized coordination revealed using fMRI.
Human Brain Mapping
,
17
,
214
229
.
McIntosh
,
A. R.
, &
Gonzalez-Lima
,
F.
(
1994
).
Structural equation modeling and its application to network analysis in functional brain imaging.
Human Brain Mapping
,
2
,
2
22
.
Meyer-Lindenberg
,
A.
,
Ziemann
,
U.
,
Hajak
,
G.
,
Cohen
,
L.
, &
Berman
,
K. F.
(
2002
).
Transitions between dynamical states of differing stability in the human brain.
Proceedings of the National Academy of Sciences, U.S.A.
,
99
,
10948
10953
.
Nair
,
D. G.
,
Purcott
,
K. L.
,
Fuchs
,
A.
,
Steinberg
,
F.
, &
Kelso
,
J. A. S.
(
2003
).
Cortical and cerebellar activity of the human brain during imagined and executed unimanual and bimanual action sequences: A functional mri study.
Cognitive Brain Research
,
15
,
250
260
.
Oullier
,
O.
,
de Guzman
,
G. G.
,
Jantzen
,
K. J.
,
Lagarde
,
J.
, &
Kelso
,
J. A. S.
(
2008
).
Social coordination dynamics: Measuring human bonding.
Social Neuroscience
,
3
,
178
192
.
Oullier
,
O.
,
Jantzen
,
K. J.
,
Steinberg
,
F. L.
, &
Kelso
,
J. A. S.
(
2005
).
Neural substrates of real and imagined sensorimotor coordination.
Cerebral Cortex
,
15
,
975
985
.
Pollok
,
B.
,
Gross
,
J.
,
Muller
,
K.
,
Aschersleben
,
G.
, &
Schnitzler
,
A.
(
2005
).
The cerebral oscillatory network associated with auditorily paced finger movements.
Neuroimage
,
24
,
646
655
.
Pollok
,
B.
,
Sudmeyer
,
M.
,
Gross
,
J.
, &
Schnitzler
,
A.
(
2005
).
The oscillatory network of simple repetitive bimanual movements.
Cognitive Brain Research
,
25
,
300
311
.
Price
,
C.
,
Wise
,
R.
,
Ramsay
,
S.
,
Friston
,
K.
,
Howard
,
D.
,
Patterson
,
K.
,
et al
(
1992
).
Regional response differences within the human auditory-cortex when listening to words.
Neuroscience Letters
,
146
,
179
182
.
Rao
,
S. M.
,
Bandettini
,
P. A.
,
Binder
,
J. R.
,
Bobholz
,
J. A.
,
Hammeke
,
T. A.
,
Stein
,
E. A.
,
et al
(
1996
).
Relationship between finger movement rate and functional magnetic resonance signal change in human primary motor cortex.
Journal of Cerebral Blood Flow and Metabolism
,
16
,
1250
1254
.
Rees
,
G.
,
Howseman
,
A.
,
Josephs
,
O.
,
Frith
,
C. D.
,
Friston
,
K. J.
,
Frackowiak
,
R. S. J.
,
et al
(
1997
).
Characterizing the relationship between bold contrast and regional cerebral blood flow measurements by varying the stimulus presentation rate.
Neuroimage
,
6
,
270
278
.
Richardson
,
M. J.
,
Marsh
,
K. L.
, &
Schmidt
,
R. C.
(
2005
).
Effects of visual and verbal interaction on unintentional interpersonal coordination.
Journal of Experimental Psychology: Human Perception and Performance
,
31
,
62
79
.
Rizzolatti
,
G.
,
Luppino
,
G.
, &
Matelli
,
M.
(
1998
).
The organization of the cortical motor system: New concepts.
Electroencephalography and Clinical Neurophysiology
,
106
,
283
296
.
Roland
,
P. E.
, &
Zilles
,
K.
(
1996
).
Functions and structures of the motor cortices in humans.
Current Opinion in Neurobiology
,
6
,
773
781
.
Rowe
,
J.
,
Friston
,
K.
,
Frackowiak
,
R.
, &
Passingham
,
R.
(
2002
).
Attention to action: Specific modulation of corticocortical interactions in humans.
Neuroimage
,
17
,
988
998
.
Sabatini
,
U.
,
Chollet
,
F.
,
Rascol
,
O.
,
Celsis
,
P.
,
Rascol
,
A.
,
Lenzi
,
G. L.
,
et al
(
1993
).
Effect of side and rate of stimulation on cerebral blood-flow changes in motor areas during finger movements in humans.
Journal of Cerebral Blood Flow and Metabolism
,
13
,
639
645
.
Sadato
,
N.
,
Ibanez
,
V.
,
Campbell
,
G.
,
Deiber
,
M. P.
,
LeBihan
,
D.
, &
Hallett
,
M.
(
1997
).
Frequency-dependent changes of regional cerebral blood flow during finger movements: Functional MRI compared to pet.
Journal of Cerebral Blood Flow and Metabolism
,
17
,
670
679
.
Schaal
,
S.
,
Sternad
,
D.
,
Osu
,
R.
, &
Kawato
,
M.
(
2004
).
Rhythmic arm movement is not discrete.
Nature Neuroscience
,
7
,
1136
1143
.
Schmidt
,
R. C.
,
Bienvenu
,
M.
,
Fitzpatrick
,
P. A.
, &
Amazeen
,
P. G.
(
1998
).
A comparison of intra- and interpersonal interlimb coordination: Coordination breakdowns and coupling strength.
Journal of Experimental Psychology: Human Perception and Performance
,
24
,
884
900
.
Schmidt
,
R. C.
,
Carello
,
C.
, &
Turvey
,
M. T.
(
1990
).
Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people.
Journal of Experimental Psychology: Human Perception and Performance
,
16
,
227
247
.
Schmidt
,
R. C.
,
O'Brien
,
B.
, &
Sysko
,
R.
(
1999
).
Self-organization of between-persons cooperative tasks and possible applications to sport.
International Journal of Sport Psychology
,
30
,
558
579
.
Schoner
,
G.
, &
Kelso
,
J. A. S.
(
1988
).
Dynamic pattern generation in behavioral and neural systems.
Science
,
239
,
1513
1520
.
Schubotz
,
R. I.
, &
von Cramon
,
D. Y.
(
2003
).
Functional–anatomical concepts of human premotor cortex: Evidence from fMRI and pet studies.
Neuroimage
,
20
,
S120
S131
.
Schubotz
,
R. I.
,
von Cramon
,
D. Y.
, &
Lohmann
,
G.
(
2003
).
Auditory what, where, and when: A sensory somatotopy in lateral premotor cortex.
Neuroimage
,
20
,
173
185
.
Serrien
,
D. J.
,
Strens
,
L. H. A.
,
Oliviero
,
A.
, &
Brown
,
P.
(
2002
).
Repetitive transcranial magnetic stimulation of the supplementary motor area (SMA) degrades bimanual movement control in humans.
Neuroscience Letters
,
328
,
89
92
.
Shima
,
K.
, &
Tanji
,
J.
(
2000
).
Neuronal activity in the supplementary and presupplementary motor areas for temporal organization of multiple movements.
Journal of Neurophysiology
,
84
,
2148
2160
.
Solodkin
,
A.
,
Hlustik
,
P.
,
Chen
,
E. E.
, &
Small
,
S. L.
(
2004
).
Fine modulation in network activation during motor execution and motor imagery.
Cerebral Cortex
,
14
,
1246
1255
.
Stephen
,
K. M.
,
Binkofski
,
F.
,
Posse
,
S.
,
Seitz
,
R. J.
, &
Freund
,
H. J.
(
1999
).
Cerebral midline structures in bimanual coordination.
Experimental Brain Research
,
128
,
243
249
.
Steyvers
,
M.
,
Etoh
,
S.
,
Sauner
,
D.
,
Levin
,
O.
,
Siebner
,
H. R.
,
Swinnen
,
S. P.
,
et al
(
2003
).
High-frequency transcranial magnetic stimulation of the supplementary motor area reduces bimanual coupling during anti-phase but not in-phase movements.
Experimental Brain Research
,
151
,
309
317
.
Swinnen
,
S. P.
(
2002
).
Intermanual coordination: From behavioural principles to neural network interactions.
Nature Reviews Neuroscience
,
3
,
350
361
.
Swinnen
,
S. P.
,
Jardin
,
K.
,
Meulenbroek
,
R.
,
Dounskaia
,
N.
, &
Hofkens-Van Den Brandt
,
M.
(
1997
).
Egocentric and allocentric constraints in the expression of patterns of interlimb coordination.
Journal of Cognitive Neuroscience
,
9
,
348
377
.
Talairach
,
J.
, &
Tournoux
,
P.
(
1988
).
Co-planar stereotaxic atlas of the human brain.
New York
:
Thieme
.
Tanji
,
J.
, &
Shima
,
K.
(
1994
).
Role for supplementary motor area cells in planning several movements ahead.
371
,
413
416
.
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
.
Tognoli
,
E.
,
Lagarde
,
J.
,
De Guzman
,
G. C.
, &
Kelso
,
J. A. S.
(
2007
).
The phi complex as a neuromarker of human social coordination.
Proceedings of the National Academy of Sciences, U.S.A.
,
104
,
8190
8195
.
Toma
,
K.
,
Mima
,
T.
,
Matsuoka
,
T.
,
Gerloff
,
C.
,
Ohnishi
,
T.
,
Koshy
,
B.
,
et al
(
2002
).
Movement rate effect on activation and functional coupling of motor cortical areas.
Journal of Neurophysiology
,
88
,
3377
3385
.
Tschacher
,
W.
, &
Dauwalder
,
J. P.
(
2003
).
The dynamical systems approach to cognition: Concepts and empirical paradigms based on self-organization, embodiment and coordination dynamics.
Singapore
:
World Scientific
.
Ullen
,
F.
,
Forssberg
,
H.
, &
Ehrsson
,
H. H.
(
2003
).
Neural networks for the coordination of the hands in time.
Journal of Neurophysiology
,
89
,
1126
1135
.
Van Mourik
,
A. M.
,
Daffertshofer
,
A.
, &
Beek
,
P. J.
(
2006
).
Deterministic and stochastic features of rhythmic human movement.
Biological Cybernetics
,
94
,
233
244
.
Varela
,
F.
,
Lachaux
,
J. P.
,
Rodriguez
,
E.
, &
Martinerie
,
J.
(
2001
).
The brainweb: Phase synchronization and large-scale integration.
Nature Reviews Neuroscience
,
2
,
229
239
.
Wallenstein
,
G. V.
,
Kelso
,
J. A. S.
, &
Bressler
,
S. L.
(
1995
).
Phase-transitions in spatiotemporal patterns of brain activity and behavior.
Physica D
,
84
,
626
634
.
Wexler
,
B. E.
,
Fulbright
,
R. K.
,
Lacadie
,
C. M.
,
Skudlarski
,
P.
,
Kelz
,
M. B.
,
Constable
,
R. T.
,
et al
(
1997
).
An fMRI study of the human cortical motor system response to increasing functional demands.
Magnetic Resonance Imaging
,
15
,
385
396
.
Wimmers
,
R. H.
,
Beek
,
P. J.
, &
Vanwieringen
,
P. C. W.
(
1992
).
Phase-transitions in rhythmic tracking movements—A case of unilateral coupling.
Human Movement Science
,
11
,
217
226
.
Wise
,
S. P.
,
Boussaoud
,
D.
,
Johnson
,
P. B.
, &
Caminiti
,
R.
(
1997
).
Premotor and parietal cortex: Corticocortical connectivity and combinatorial computations.
Annual Review of Neuroscience
,
20
,
25
42
.
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
.
Zhuang
,
J. C.
,
LaConte
,
S.
,
Peltier
,
S.
,
Zhang
,
K.
, &
Hu
,
X. P.
(
2005
).
Connectivity exploration with structural equation modeling: An fMRI study of bimanual motor coordination.
Neuroimage
,
25
,
462
470
.