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Scaling Movement Amplitude: Adaptation of Timing andAmplitude Control in a Bimanual TaskJohn J. Buchanan a & Young U. Ryu ba Human Performance Labs, Department of Health and Kinesiology, Texas A&M University,College Stationb Department of Physical Therapy, Catholic University of Daegu, Gyeongbuk, South Korea

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Journal of Motor Behavior, Vol. 44, No. 3, 2012Copyright C© Taylor & Francis Group, LLC

RESEARCH ARTICLE

Scaling Movement Amplitude: Adaptation of Timing andAmplitude Control in a Bimanual TaskJohn J. Buchanan1, Young U. Ryu2

1Human Performance Labs, Department of Health and Kinesiology, Texas A&M University, College Station. 2Department ofPhysical Therapy, Catholic University of Daegu, Gyeongbuk, South Korea.

ABSTRACT. Participants traced two circles simultaneously and thediameter of one circle was scaled as the diameter of the other circleremained constant. When the scaled circle was larger, amplitudeerror shifted from overshooting to undershooting, while shiftingfrom undershooting to overshooting when this circle was smaller.Asymmetric coordination was unstable when the left arm traceda circle larger than the right arm, yet stable when the left armtraced a smaller circle. When producing symmetric coordinationand the left arm traced the larger circle, relative phase shifted by30◦, but a right arm lead predominated. When the left arm tracedthe smaller circle and symmetric coordination was required, a 30◦

shift in relative phase occurred, but hand lead changed from left toright. The modulation of movement amplitude and relative phaseemerged simultaneously as a result of neural crosstalk effects linkedto initial amplitude conditions and possibly visual feedback of thehands’ motion.

Keywords: amplitude assimilation, coordination dynamics, neuralcrosstalk, relative phase

T he ability to coordinate the temporal relationshipbetween two or more limbs or joints as well as produce

different amplitudes for each limb or joint simultaneouslyallows us to perform common everyday skills (opening a jar)as well as achieve high levels of success in complex skills(playing the drums or a piano). In many tasks, environmentalconditions change and an adaptation of timing patterns andmovement amplitudes must occur for coordination to remainstable. Familiar examples of adaptive changes in coordi-nation are the transitions between behavioral patterns thatoccur when movement frequency is increased (Buchanan,Kelso, deGuzman, & Ding, 1997; Byblow, Summers,Semjen, Wuyts, & Carson, 1999; Carson, Goodman, Kelso,& Elliott, 1995; Kelso, 1984; Kelso & Jeka, 1992). A lessexamined, although just as important aspect of adaptiveprocesses in human motor control, is how limb amplitudesand relative timing patterns are modulated when amplituderequirements change within a trial (Spijkers & Heuer,1995).

Amplitude assimilation effects are very well documentedin discrete and rhythmic bimanual tasks that require eachlimb to move a different distance. The typical assimilationeffect is that the limb moving a shorter distance overshoots(positive error) the required amplitude and the limb moving alonger distance undershoots (negative error) the required am-plitude (Buchanan & Ryu, 2006; Doumas, Wing, & Wood,2008; Heuer & Klein, 2005; Marteniuk, MacKenzie, & Baba,1984; Sherwood, 1994b; Sherwood & Nishimura, 1992; Spi-

jkers & Heuer, 1995; Weigelt & Cardoso de Oliveira, 2003).The larger the amplitude disparity the larger the assimila-tion effect with research indicating an amplitude ratio of2:1 necessary for significant assimilation (Sherwood, 1994b;Sherwood & Nishimura, 1999). A common explanation ofamplitude assimilation is that it arises from neural crosstalkoccurring at the execution level as the action unfolds (Carson,2005; Heuer & Klein; Marteniuk et al.; Sherwood, 1994b;Sherwood & Nishimura, 1999; Spijkers & Heuer; Swinnen,2002). When arm amplitudes are unequal, neural crosstalkis conceptualized as an interaction between the different sizeforce commands sent to the arms (Marteniuk et al.; Sherwood& Nishimura, 1992; Spijkers & Heuer). The arm moving thelonger distance requires stronger commands and those com-mands have a larger impact on the commands sent to theshorter moving limb than vice versa. The crosstalk oftenleads to an asymmetry in amplitude coupling and the shortermoving limb overshoots to a greater extent than the longermoving limb undershoots (Marteniuk et al.; Sherwood &Nishimura, 1992; Spijkers & Heuer).

With regard to relative phase, required amplitude differ-ences in rhythmic bimanual tasks have been shown to pro-duce consistent shifts away from the relative phase valuesof 0◦ for symmetric and 180◦ for asymmetric coordination(Amazeen, Ringenbach, & Amazeen, 2005; Buchanan &Ryu, 2006; de Poel, Peper, & Beek, 2009; Peper, de Boer, dePoel, & Beek, 2008). For example, in a bimanual circle trac-ing task, the shift in relative phase away from 0◦ (symmetrictracing) and 180◦ (asymmetric tracing) ranged from 15◦ to25◦ when the left arm traced a 5-cm circle and the right armtraced a 10-cm circle (1:2 amplitude ratio). The magnitudeof the shift was similar when the left arm traced the 10-cmcircle and the right arm the 5-cm circle. The shift in relativephase away from 0◦ and 180◦ increased to 30–45◦ when theleft arm traced a 3-cm circle and the right arm traced a 15-cmcircle (1:5 amplitude ratio; Buchanan & Ryu, 2006). Ampli-tude assimilation also occurred in the Buchanan and Ryu taskand the assimilation effect was smaller in the 5–10 and 10–5circle pairs compared with the 3–15 and 15–3 circle pairs.These results show that under static amplitude conditions,relative phase and amplitude assimilation effects are linkedto the disparity in limb amplitudes.

Correspondence address: John J. Buchanan, Department ofHealth and Kinesiology, Texas A&M University, College Station,TX 77843–4243, USA. e-mail: jbuchanan@hlkn.tamu.edu

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Unequal amplitudes in bimanual tasks produce assimi-lation and shifts in relative phase, and these effects havetypically been examined by holding amplitude constant in atrial. Even when movement amplitude was changed within atrial, the change in amplitude was designed to isolate ampli-tude assimilation effects or relative phase effects and not aninteraction between these effects. Spijkers and Heuer (1995)manipulated movement amplitude within a trial by requiringparticipants to oscillate one hand with a constant amplitudewhile the other hand alternated between a large and smallamplitude. The alternating amplitude condition revealed thatneural crosstalk effects could be isolated to either a pro-gramming level or to an execution level (Spijkers & Heuer);however, a detailed analysis of relative phase was not pre-sented. A study by Ryu and Buchanan (2004) scaled circlediameter within a trial under two conditions: (a) startingwith a pair of 3-cm-diameter circles and ending with a pairof 15-cm-diameter circles, and (b) starting with a pair of 15-cm-diameter circles and ending with a 3-cm-diameter pair.The circles traced by each arm were always equal goingthrough diameters of 6, 9, and 12 cm. The change in diame-ter induced transitions from asymmetric to symmetric coor-dination in a manner similar to scaling movement frequency,but amplitude assimilation effects did not emerge nor wheresignificant shifts in relative phase away from 0◦ and 180◦

observed (Ryu & Buchanan). Even though the previous twostudies changed amplitude in a trial, the experiments werenot designed to examine how scaling movement amplitudemay lead to an interaction between assimilation processesand processes associated with shifts in relative phase.

The present experiment scaled movement amplitude toidentify how the motor system adapts individual arm ampli-tudes and bimanual relative phase patterns simultaneously. Abimanual circle tracing task was selected and amplitude scal-ing was linked to a change in circle diameter. The initial circlepair was either a 3-cm circle (left arm) paired with a 15-cmcircle (right arm; 3–15 pair) or a 15-cm circle (left arm) pairedwith a 3-cm circle (right arm; 15–3 pair). The diameter of onecircle was either increased or decreased until the circles hadequivalent diameters. Two bimanual patterns of coordinationwere required, symmetric and asymmetric. Two hypothesesare put forth with regard to amplitude assimilation.

Hypothesis 1: The initial circle pairs of 15–3 and 3–15would produce amplitude assimilation with the errorlarger in the arm tracing the smaller circle.

Hypothesis 2: Equalizing circle diameter in a trial wouldremove the initial assimilation effect with the arm trac-ing the larger circle always undershooting and the armtracing the smaller circle always overshooting.

Hypotheses 1 and 2 are based on neural crosstalk as a the-oretical account for amplitude assimilation (Heuer & Klein,2005; Marteniuk et al., 1984; Sherwood & Nishimura, 1992;Spijkers & Heuer, 1995; Swinnen, 2002). Two hypothesesare put forth with regard to shifts in relative phase.

Hypothesis 3: The 15–3 and 3–15 circle pairs would pro-duce a shift in relative phase away from the values of 0◦

and 180◦, with the phase lead linked to the hand tracingthe smaller circle and the shift in relative phase largerfor asymmetric compared with symmetric coordination.

Hypothesis 4: Equalizing circle diameter will remove thephase shift but not alter the phase lead.

Hypotheses 3 and 4 are based on the theory of coordina-tion dynamics (Kelso, 1995; Schoner & Kelso, 1988) as anexplanation for pattern transitions and shifts in relative phasethat have emerged in rhythmic bimanual tasks with ampli-tude asymmetries (Amazeen et al., 2005; Buchanan & Ryu,2006; de Poel et al., 2009).

Method

Participants

The experimental protocol and consent form were ap-proved by the Institutional Research Board for the ethicaltreatment of human participants at Texas A&M Universityin accordance with the Helsinki Declaration. All participantswere self-reported right-handed and classified as being right-handed based on answering “yes” to the four questions on theCoren Handedness Inventory (Coren, 1993). All participantswere naive to the purpose of the study and received classcredit for participation. Twenty-four individuals participatedin the experiment (M age = 21.6 years, SD = 10.5 months).

Task and Procedures

Participants were presented with one of two initial circlepairs displayed on a computer monitor. The circles were gen-erated with a QuickBASIC program (version 4.5, Microsoft,Redmond, WA, USA) and the monitor was covered with apiece of Plexiglas. One circle pair required the left arm totrace a 3-cm circle and the right arm to trace a 15-cm circle.The other circle pair required the left arm to trace a 15-cmcircle and the right arm to trace a 3-cm circle (Figures 1Aand 1B). For each initial condition, the diameter of one cir-cle was scaled as the diameter of the other circle remainedconstant. The most inside point of the scaled circle near thebody midline was fixed with circle diameter scaled in refer-ence to this point. In the decreasing condition, circle diameterdecreased toward this point (Figure 1A, dashed circles). Inthe increasing condition, circle diameter expanded from thispoint (Figure 1B, dashed circles). There were two decreasing-diameter conditions—3–15d and 15d–3—with the initial15-cm-diameter circle scaled to a 3-cm-diameter circle.There were two increasing-diameter conditions—3i–15 and15–3i—with the initial 3-cm-diameter circle scaled to a 15-cm-diameter circle. The change in circle diameter was 3 cmand the arm tracing the scaled circle traced five circles of3, 6, 9, 12, and 15 cm diameter, resulting in five circle-pair plateaus with diameter differences of ±12, ±9, ±6,±3, and ±0 cm. Negative diameter differences represent the

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body midline(z-axis)

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Initial staringposition

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LA RA

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FIGURE 1. (A) The 3–15 circle pair with a decrease in the circle diameter of the 15-cm circle (right arm, 3–15d condition).(B) The 15–3 circle pair with an increase in circle diameter of the 3-cm circle (right arm, 15–3i condition). The dashed circlesrepresent the four changes in circle diameter in the decreasing (A) and increasing (B) scaling conditions. (C) The experimental setupshowing the positioning of the participants with respect to the computer monitor displaying the circle templates. (D) The symmetricand asymmetric patterns are defined with respect to the body midline.

3–15 condition and positive diameter differences representthe 15–3 condition.

The monitor was positioned horizontally in a cabinet andparticipants traced the circles in the horizontal plane usingplastic styli held in the hands (Figure 1C). The styli werethe size of a standard ballpoint pen. When tracing the circleswith the styli, motion along the x-axis of the circle corre-sponded to mediolateral motion and motion along the z-axiscorresponded to anteroposterior motion. With the use of plat-forms (2′ wide × 2 ′ long × 1

′, 2′′, 3′′, or 4′′ high), participants

were positioned so that the monitor was approximately waisthigh with the participants standing 2 inches from the cabi-net. This placed the center of the circles approximately 25cm from a participant’s waist. Participants stood in front ofthe cabinet and traced the circles with motion about theirelbows and shoulders, keeping the wrists fixed. The initialstarting position of each hand was always the top of eachcircle. There were a total of 57 metronome beats per trial.Two initial metronome beeps of a higher pitch served asa prestart signal prior to the main metronome signal. Theprestart beeps occurred 1 s before the first beep of the pacing

metronome signal. The diameter of the scaled circle changedon the 11th metronome beat, with the present circle disap-pearing abruptly and the new circle appearing abruptly. Theparticipants were informed to keep the pens on the tracingsurface and to move on to the new circle as rapidly as possiblewithout stopping. The pacing frequency was set at 1 Hz andparticipants were instructed to trace the circles as accuratelyas possible at this pace.

The 24 participants were assigned to either the 3–15 trac-ing group or to the 15–3 group (12 participants per initial cir-cle pair). The participants were required to trace the circlesin either a symmetric or asymmetric pattern of coordination.The symmetric pattern required the left arm to trace in aclockwise direction and the right arm to trace in a counter-clockwise direction, whereas the asymmetric pattern requiredboth circles to be traced in a clockwise direction (Figure 1D).An individual in the 3–15 group would trace the circles un-der the scaling conditions of 3i–15 and 3–15d. An individualin the 15–3 group would trace the circles under the scalingconditions of 15d–3 and 15–3i. Each participant performed24 trials with five circle-pair plateaus traced within a trial

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and 12 trials per scaling direction (increasing or decreas-ing) and six trials per pattern (asymmetric, symmetric). Afamiliarization trial for each condition was performed with-out a metronome. The familiarization trial was followed bya trial with the metronome. After these two trials, the experi-mental trials were collected. Trial length was 1 min and par-ticipants rested for 30 s after a trial and 5 min after every sixtrials. The experimental session lasted 50 min. Participantswere instructed not to resist a pattern change if it occurred.

Data Collection and Analysis

An OPTOTRAK 3020 camera system (Northern Digital,Waterloo, Ontario, Canada) was used to record the motion of6 infrared diodes (IREDs). An IRED was attached 5 mm fromthe bottom of each stylus (IREDs 1 and 2), an IRED was at-tached to each elbow joint (IREDs 3 and 4), and an IRED wasattached to each shoulder (IREDs 5 and 6). The OPTOTRAK3020 camera system consists of three lenses with each lenshaving a 34◦ × 34◦ field of view with the sensor array havinga precalibrated resolution of 0.1 mm in the x and y directionsand 0.15 mm in the z direction at a distance of 2.5 m. Thecenter of the cabinet holding the computer monitor display-ing the circles was positioned at 2.5 m from the OPTOTRAKcamera. The IREDs were sampled at 100 Hz and stored ondisk during the experiment for later offline analysis utilizingMatlab 7.0 (The Mathworks, Natick, Massachusetts). To re-move transient effects, the first cycle of a trial and the firstcycle following every change in circle diameter were notanalyzed. The remaining cycles were used to compute thedependent measure means that were statistically analyzed.

Temporal Measures

The x-axis (medialateral) and z-axis (anteroposterior) timeseries from IREDs 1 and 2 were used to compute a contin-uous tangential angle (θ i) representing motion around thetraced circle for each arm (Carson, Thomas, Summers, Wal-ters, & Semjen, 1997). The x and z position time series werelow-pass filtered using a second-order dual-pass Butterworthfilter with a cutoff frequency of 10 Hz. Velocity time serieswere computed and then also filtered at 10 Hz. The velocitytime series were normalized on a cycle-to-cycle basis to therange from –1 to 1 before computing the continuous tan-gential angles, θ i. The spatiotemporal coordination betweenthe two hands was quantified with a continuous relative tan-gential angle (φRTA) calculated as the signed difference indegrees between the tangential angle of the left arm (θ l) andright arm (θ r) end-effector traces, φRTA = θ l – θ r. Circu-lar statistics were applied to the continuous φRTA values foreach trial individually. The circular transformation provideda mean value of the relative tangential angle for a given trialand a mean vector length R for that trial. The two requiredrelative phases were φRTA = 0◦ for symmetric and φRTA =180◦ for asymmetric coordination. A constant error in relativephase was computed (φCE) such that φCE > 0◦ representeda left-arm lead for both coordination patterns and φCE < 0◦

represented a right-arm lead for both patterns. The vectorlength R is a measure of dispersion of the continuous rela-tive tangential angle (Burgess-Limerick, Abernethy, & Neal,1991; Mardia, 1972). A value of R = 1 represents perfectuniformity or no dispersion, whereas decreasing values ofR represent a decrease in uniformity or an increase in dis-persion. The R values ranged from 0 to 1 and these valueswere transformed (TR) to the range 0 to ∞ to submit themto inferential statistics. The TR values represent dispersionwith larger TR values representing less variability or lessdispersion (more stable coordination) in the φRTA measure.

Tracing frequency was calculated from the z-axis time se-ries of IREDs 1 and 2 on the styli. Each z-axis time seriesrepresenting anteroposterior motion around the circle wasmean centered. The time of the peak (P) events in the z-axistime series corresponding to maximum anterior displacementof the styli when tracing the circles were located with a peak-picking algorithm. Tracing frequency (TF) was computed ona cycle-to-cycle basis for each arm (l, r) in the following way:TFl, r = 1/(Pi+1 – Pi). The individual cycle TF values wereaveraged within a circle-pair plateau for each arm individu-ally. A frequency ratio (FR) was calculated between the arms(FR = TFr/TFl) for each circle pair in a trial. This measureis analyzed to characterize frequency entrainment across thedifferent conditions. Demonstrating 1:1 frequency entrain-ment is important and indicates that any observed shift inφRTA away from the values of 0◦ and 180◦ represents stablecoordination and not a shift that occurs because of unstablecoordination or the production of a higher order frequencyratio (1:2 or 2:3). A value of FR > 1 indicates the right armis tracing at a frequency faster than the left arm.

End-effector Amplitude

The x and z time series from IREDs 1 and 2 were meancentered and for each xi and zi point in a cycle a radius(Ri = √

xi + zi) was computed. The Ri values were usedto compute a mean radius for each cycle of motion. Theindividual cycle radius means were averaged for each armfor each circle pair in a trial. The average was multiplied by2 to provide an estimate of produced circle diameter. Theestimated circle diameters (CD) were subtracted from thegoal diameter values (3, 6, 9, 12, and 15 cm) to create aconstant error (CDCE) to examine directional bias and anabsolute error (CEAE) to examine the magnitude of error.

Statistics

All dependent variables were analyzed with analyses ofvariance (ANOVAs). Significant interactions were analyzedwith simple effects tests, and post hoc tests using Tukey’sHSD procedure (α = .05) were performed when appropriate.

Results

Amplitude Assimilation

A decreasing circle diameter trial and an increasing circlediameter trial are plotted in Figure 2. Note that for the arm

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FIGURE 2. Example end-effector trajectories are shown for the 3–15d condition (A) and the 3i-15 condition (B). In A, the diameterof the circle traced by the right arm (RA) decreases, and in B, the diameter of the circle traced by the left arm (LA) increases. Therequired pattern was asymmetric for the trial in A and symmetric for the trial in B. Motion in the x direction is mediolateral (med)and motion in the z direction is anteroposterior (pos).

undergoing the amplitude scaling there is a noticeable changein the diameter of the circle produced by the end effector.Overall, the observed amplitudes were very consistent as afunction of initial circle pair, scaling direction, and coordi-nation pattern, and demonstrate that participants satisfied thetask goal of producing circles with different diameters whenrequired and changing diameter when required (Figures 3Aand 3B).

Hypothesis 1 stated that the initial 3–15 or 15–3 circlepairs would produce amplitude assimilation with overallerror larger for the arm tracing the smaller circle. To testthis hypothesis, the CDCE and CDAE scores for the 3–15 and15–3 circle pair groups were analyzed in an ANOVA withinitial circle pair as a between-subjects factor (3–15, 15–3)and pattern (symmetric, asymmetric) and circle (3 cm, 15cm) as within-subjects factors. The analysis of the CDCE

FIGURE 3. Observed circle diameter (CD) is plotted as a function of arm (LA = left arm, RA = right arm), pattern (Asym =asymmetric, Sym = symmetric), and diameter difference (e.g., ± 12 cm) for the 15d–3 and 3–15d conditions (A) and the 15–3iand 3i–15 conditions (B). The dashed lines in A and B represent the five target diameters for the scaled circle. The means for the3–15 groups should be read left to right, and the means for the 15–3 groups should be read from right to left. Constant error (C) andabsolute error (D) of circle diameter are plotted as a function of diameter difference (read right to left) and whether the circle had aconstant diameter (3 con, 15 con) or scaled diameter (3 inc, 15 dec).

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data revealed a main effect of circle, F(1, 10) = 9.73, p <

.01, and a significant circle pair by circle interaction, F(1,10) = 668.63, p < .0001. Post hoc tests (p < .05) revealedsignificant differences in bias with negative error for the 15-cm circle and positive error for the 3-cm circle in both the15–3 (M = –1.91 cm, SD = 0.66 cm and M = 1.48 cm,SD = 0.43 cm, respectively) and 3–15 (M = 2.12 cm, SD= 0.51 cm and M = –2.2 cm, SD = 0.64 cm, respectively)initial circle pairs. The CDAE analysis found a main effect ofcircle pair, F(1, 10) = 9.33, p < .05. The circle pair by circleinteraction effect was not significant (p > .1). Overall, CDAE

for the 3-cm and 15-cm circles for the 3–15 group were (3cm, M = 2.12 cm, SD = 0.51 cm; 15 cm, M = 2.2 cm,SD = 0.64 cm), with CDAE for the 15–3 circle-pair group(3 cm, M = 1.48, SD = 0.43 cm; 15 cm, M = 1.94, SD =0.61 cm) circle. Amplitude assimilation was present and inthe appropriate direction for both initial circle pairs, but thesmaller circle was not characterized by significantly largererror as predicted.

Hypothesis 2 stated that equalizing circle diameter wouldremove the amplitude assimilation effect without influencingthe overshoot and undershoot characteristics. This hypothe-sis was tested by taking the CDCE and CDAE values andanalyzing them in the ANOVA with initial circle pair as abetween factor and diameter difference (12, 9, 6, 3, 0 cm),pattern (symmetric, asymmetric), and scaling (increasing,decreasing) as within-group factors.

The analysis of the CDCE values provided a direct testof the directional bias for the small (overshoot) and large(undershoot) circles. The analysis revealed a main effect ofscaling, F(3, 30) = 177.05, p < .0001, and significant inter-actions of circle pair by scaling, F(3, 30) = 14.46, p < .0001,and scaling by diameter difference, F(12, 120) = 268.30, p< .0001, were also found. The post hoc tests (p < .05) of thescaling by diameter difference interaction revealed two find-ings regarding directional bias (p < .05). First, for the 3–15and 15–3 groups, the 3-cm constant circle was traced withpositive error and the 15-cm constant circle was traced withnegative error as predicted, with CDCE decreasing signifi-cantly across diameter differences of 3 cm and 0 cm (Figure3C). Second, for the 3–15 and 15–3 groups, a shift from pos-itive error for diameter differences of 9 and 12 cm to negativeerror for diameter differences of 3 and 0 cm occurred whentracing the 3-cm increasing circle, with just the oppositetrend when tracing the 15-cm decreasing circle. This changein directional bias is not consistent with Hypothesis 2.

The analysis of the CDAE values provides a direct test ofwhether the absolute error was always larger when tracinga smaller circle. The analysis found main effects of circlepair, F(3, 10) = 12.62, p < .01, and diameter difference,F(3, 40) = 123.10, p < .0001. The scaling by diameter dif-ference interaction was also significant, F(12, 120) = 12.50,p < .0001. Post hoc tests (p < .05) of the scaling by diam-eter difference interaction found two revealing results withregard to Hypothesis 2. First, for the 3–15 and 15–3 groups,the 3-cm increasing circle had a smaller absolute error for

diameter differences of 9, 6, and 3 cm compared with the15-cm constant circle, with no difference in error for diam-eter differences of 12 and 0 cm (Figure 3D). Second, forthe 3–15 and 15–3 groups, the 15-cm decreasing circle didnot have significantly smaller absolute error for any diameterdifference, with a larger error when diameter difference was0 cm at the end of the trial. These results do not supportthat component of Hypothesis 2 stating that the arm tracingthe smaller diameter circle would be characterized by largererror on average.

Shifts in Relative Phase

Any shift in relative phase to support Hypotheses 3 and 4must be based on 1:1 frequency locking between the arms.The required tracing frequency was 1 Hz and the averagetracing frequency across all trials and conditions was 1.04 Hz.The FR values were analyzed in an ANOVA with initial circlepair as a between-groups factor, and diameter difference (12,9, 6, 3, 0 cm difference), pattern (asymmetric, symmetric),and scaling (increasing, decreasing) as within-group factors.The analysis found significant main effects of circle pair, F(1,10) = 5.70, p < .05; diameter difference, F(4, 40) = 9.91, p< .0001; and scaling, F(1, 10) = 5.50, p < .05. The analysisrevealed significant interactions of circle pair by diameterdifference, F(4, 40) = 10.34, p < .0001; circle pair by scaling,F(1, 10) = 6.24, p < .05; pattern by diameter difference,F(4, 40) = 6.03, p < .001; and pattern by scaling, F(1,10) = 5.49, p < .05. The three-way interaction of circle pair,pattern, and scaling, F(1, 10) = 7.05, p < .05, was significant.Simple effect tests followed by post hoc tests of the three-wayinteraction (p < .05) revealed that the FRs in the asymmetric15d–3 and 15–3i conditions were significantly different fromthe FRs for the other combinations of circle pair, Pattern, andScaling (Table 1).

The FR means for the asymmetric 15d–3 and 15–3i condi-tions reported in Table 1 are larger than the upper boundarydefining 1:1 frequency locking (> 1.0714) according to Tr-effner and Turvey (1993). The percentage of FR valuesclassified as 1:1 frequency locking based on the previousboundary are presented in Table 2. The non-1:1 FR per-formance in the asymmetric 15d–3 and 15–3i conditionswas characterized as either a higher order ratio (Figures4A and 4B) or wrapping–drift (Figure 4C). An extensiveanalysis of the FR data could be performed based on theFarey Tree (Buchanan & Ryu, 2006; deGuzman & Kelso,1991; Peper, Beek, & van Wieringen, 1995; Peper, Beek, vanWieringen, Requin, & Stelmach, 1991; Treffner & Turvey);however, with only 36% of the non-1:1 circle-pair plateausactually exhibiting stable multifrequency locking that anal-ysis would go beyond the scope of the present paper. Asa result of the extensive non-1:1 frequency behavior in the15–3 asymmetric trials, the φCE and TR data for these trialswere not statistically analyzed with respect to Hypotheses3 and 4.

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TABLE 1. Tracing Frequency Ratios as a Function of Group (3–15, 15–3), Scaling Direction, and CoordinationPattern

15d–3∗ 15–3i∗ 3i–15 3–15dM SD M SD M SD M SD

Asymmetric 1.22 0.22 1.12 0.17 1.00 0.004 0.99 0.004Symmetric 1.00 0.02 1.00 0.03 0.99 0.011 1.00 0.005

Note. d = decrease; i = increase.∗p < .05.

Hypothesis 3 proposed that the initial circle pairs of 3–15and 15–3 would produce a shift away from the required rel-ative phase values of 0◦ (symmetric) and 180◦ (asymmetric)with the hand tracing the smaller circle leading and the shiftlarger for asymmetric coordination. To test this hypothesis,the φCE data for the first circle-pair plateau for the 3–15symmetric, 3–15 asymmetric, and 15–3 symmetric condi-tions were tested to determine if the means were significantlydifferent from zero. Based on Student’s t test (p < .0001), theinitial φCE values for each condition were found to be signif-icantly different from zero with the observed mean havingthe expected directional bias: 3–15 symmetric, t = 4.41, M= 7.5◦, SD = 12◦; 3–15 asymmetric, t = 14.59, M = 25.1◦,SD = 11◦; 15–3 symmetric, t = –19.3, M = –36.9◦, SD =14◦. The shift observed in the 3–15 asymmetric pattern wasalso larger than the 3–15 symmetric pattern, t(10) = 2.89, p< .05.

Hypothesis 4 stated that equalizing circle diameter withina trial would eliminate the initial phase shift induced bythe 3–15 and 15–3 circle pairs but not alter the phase leadfeature of the shift. A complete trial from the 3–15 symmetriccondition showing a shift in relative phase with each changein circle diameter is plotted in Figure 5. The phase leadshifts from a left arm lead to right arm lead, an unexpectedfinding. Because of the loss of the 15–3 group asymmetricpattern data, the test of Hypothesis 4 is carried out withtwo ANOVAs. The data of the 3–15 group were analyzedwith a repeated measures ANVOA with scaling (increasing,decreasing), pattern (symmetric, asymmetric), and diameterdifference (12, 9, 6, 3, 0 cm) as factors. The symmetric data

TABLE 2. Percentage of 1:1 FrequencyPerformance Based on Initial Circle Pair, ScalingDirection, and Coordination Pattern

15d–3 15–3i 3i–15 3–15d

Asymmetric 42.22 55.55 100.0 100.0Symmetric 96.11 96.36 99.43 99.41

Note. d = decrease; i = increase.

of the 15–3 group were analyzed with a repeated measureANOVA with scaling and diameter difference as factors.

The analysis of the φCE data from the 3–15 group revealeda significant main effect of Scaling, F(1, 95) = 9.60, p < .01,with the value of φCE larger in the decreasing (M = –7.2◦, SD= 17◦) compared with the increasing (M = –2.4◦, SD = 18◦)scaling condition. The value of φCE for the asymmetric pat-tern (M = 1.2◦, SD = 17◦) was different from the symmetric(M = –10.8◦, SD = 15◦) pattern, F(1, 95) = 59.90, p <

.0001. Last, the main effect of diameter difference, F(4, 95)= 80.50, p < .0001, was significant (Figure 5A, left side).Post hoc tests of the diameter difference effect revealed thatthe value of φCE changed significantly across the diameterdifferences of 9 to 6 cm, 6 to 3 cm, and 3 to 0 cm, with thevalue of φCE observed for the diameter difference of 12 cmsignificantly different from diameter differences of 6, 3, and0 cm. The stability of coordination was assessed through ananalysis of the TR values with larger values reflecting morestable coordination (less dispersion in φRTA). The analysisfound the asymmetric pattern (TR = 2.76) to be morevariable than the symmetric pattern (TR = 2.81), F(1, 95) =5.10, p < .05. The main of effect of scaling, F(4, 95) = 29.10,p < .0001, and the scaling by diameter difference interaction,F(4, 95) = 9.50, p < .0001, were significant. Post hoc tests(p < .05) of the interaction found that variability decreased(TR increases) in the increasing condition with TR valuesdifferent between scaling conditions for diameter differencesof 3 and 0 cm (Figure 5B, left side; see also Figure 6).

The analysis of the 15–3 group’s symmetric conditionfound that the values of φCE were larger in the decreasing(M = –26.3, SD = 18) compared with the increasing (M =–21.9, SD = 16) scaling direction, F(1, 45) = 8.79, p < .01.The analysis also found a main effect of diameter difference,F(4, 45) = 45.70, p < .0001. Post hoc tests revealed that thevalue of φCE changed across the diameter differences of 9 to6 cm, 6 to 3 cm, and 3 to 0 cm, with the value of φCE for the12-cm-diameter difference larger in comparison to diameterdifferences of 6, 3, and 0 cm (Figure 5A, right side). Theanalysis of the TR data revealed significant main effects ofscaling, F(1, 45) = 38.80, p < .0001, and diameter differ-ence, F(4, 45) = 8.40, p < .0001. The scaling by diameterdifference interaction was significant, F(4, 45) = 7.10, p <

.001. Post hoc tests of the interaction found that variability

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LA x-axis RA x-axis

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FIGURE 4. Time series of left- and right-arm x-axis motion for three separate trials from the 15–3 asymmetric condition are shownin the top plots of A, B, and C. In the bottom plots, the φRTA trace representing spatiotemporal coordination between the arms isplotted. The trial in A portrays several intervals of a 2:3 frequency ratio for a 9–3 circle pair from the condition 15d–3. The examplein B shows a 4:5 frequency ratio for a 12–3 circle pair from the condition 15d–3. The trial in C portrays drift (no frequency locking)for a 15–9 circle pair from the 15–3i condition.

decreased (TR increases) in the increasing condition, withdifferences between conditions for the diameter differencesof 3 and 0 cm (Figure 5B, right side).

Discussion

The present experiment produced two distinct findings notin agreement with previous research on amplitude assimi-lation and a novel finding regarding the impact of scalingmovement amplitude on amplitude assimilation. The firstdistinct finding was that the observed amplitude error wasnot larger for the limb tracing the smaller circle in com-parison with the limb tracing the larger circle. Previous re-search has consistently demonstrated that amplitude error

for the limb moving the smaller distance is larger comparedwith the limb moving the larger distance (Marteniuk et al.,1984; Sherwood, 1994b; Sherwood & Nishimura, 1992; Spi-jkers & Heuer, 1995; Weigelt & Cardoso de Oliveira, 2003).Thus, Hypothesis 1 was only partially supported. The seconddistinct finding was that amplitude error was not linked toarm dominance. Several studies have reported an asymmetryin amplitude assimilation, with the left limb often charac-terized by larger directional error (Marteniuk et al.; Sher-wood, 1994b; Spijkers & Heuer). The most novel findingin the present experiment was that the specific on-line am-plitude adjustments that emerged for the scaled circle weredifferent from the fixed-diameter circle, regardless of the ini-tial amplitude condition. The amplitude error for the circlewith the constant diameter was always in the right direction

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7.5

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FIGURE 5. An entire trial from the 3i–15 symmetric condition is plotted. The x-axis time series for the left (LA; dashed line) andright arm (RA) are plotted in the top plot of each circle pair and the φRTA time series is plotted in the bottom plot. The numbersreported in the upper right-hand corner of the bottom plot represent the mean φRTA value for each circle pair. Across this trial, therewas a shift from a left arm to right arm lead.

(15 cm undershoot, 3 cm overshoot), a finding consistentwith Hypothesis 2. The arm tracing the scaled circle wascharacterized by a change in error bias, going from over (asexpected) to under for the increasing 3-cm circle and going

from under (as expected) to over for the decreasing 15-cmcircles. This finding is inconsistent with Hypothesis 2.

Neural crosstalk models propose that bimanual ampli-tude assimilation effects result from an interaction between

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FIGURE 6. (A) The φCE means are plotted as a function ofinitial circle pair (3–15, 15–3), coordination pattern (asym-metric, symmetric), and diameter difference. (B) The trans-formed (TR) means are plotted as a function of initial circlepair (3–15, 15–3) and scaling direction (I = increasing, d =decreasing). On the abscissas (A and B), the positive valuesrepresent the diameter differences for the 15–3 condition(read right to left) and the negative values represent diam-eter differences for the 3–15 condition (read left to right).On the ordinate (A only), positive values of φCE represent aleft arm lead and negative values represent a right arm lead.The error bars represent ±1 standard deviation around themeans.

muscle commands of different sizes that are required to pro-duce different limb amplitudes (Swinnen, 2002). The assim-ilation effect is typically identified as being asymmetric withthe limb producing the larger amplitude linked to larger mus-cle commands that more strongly influence the limb mov-ing the smaller distance (Marteniuk et al., 1984; Sherwood,1994b; Sherwood & Nishimura, 1992; Spijkers & Heuer,1995; Weigelt & Cardoso de Oliveira, 2003). This is why

neural crosstalk models predict amplitude error to be largerin the limb moving the smaller distance. The scaling of circlediameter did not support this prediction in the present task.Previous research has examined the influence of visual andproprioceptive information on directional bimanual interfer-ence (neural crosstalk) and concluded that the directionalinfluence emerges solely from the execution level (Swinnenet al., 2002). This idea also found support in another studyexamining neural crosstalk through amplitude manipulation(Spijkers & Heuer). Although speculative, we subsequentlyoutline a way to account for the present findings with regardto an interaction between visual feedback and changes in neu-ral crosstalk effects linked to changes in muscle commands.

To control the disparity in movement amplitude, moststudies have used visual targets as endpoints (a pair of lines,dots, or squares) to define the required limb amplitudes(Kovacs & Shea, 2010; Marteniuk et al., 1984; Peper etal., 2008; Sherwood, 1994b; Spijkers & Heuer, 1995). Inmany assimilation tasks, vision of both limbs is blocked andamplitude is controlled by feedback presented on a computermonitor (Sherwood, 1994a, 1994b; Sherwood & Nishimura,1999; Spijkers & Heuer, 1995) or vision of one limbmay be allowed (Swinnen et al., 2002). The circles in thepresent task provided a visual target that defined the entiretrajectory of the hand’s motion and participants watchedtheir hands trace the entire circle. The presence of a templatethat constantly defined movement amplitude and the factthat participants received continuous visual feedback ofamplitude performance may have helped them to modulatethe outgoing muscle commands. The assimilation effect wasnot eliminated, but was instead modulated to produce equalamplitude adjustment across limbs making performance asefficient or stable as possible.

The presence of continuous visual feedback may explainthe finding that the scaled circles overall had smaller AEfor three (6, 9, 12, cm) of the five circles in a trial. Withcontinual visual monitoring of hand motion under changingconditions more attention may have been devoted to the limbtracing the scaled circle and this may have reduced error. Interms of neural crosstalk, there may also have been an aftereffect linked to the scaling direction. For the increasing 3-cmcircle, the limb tracing it would be associated with smallermuscle commands until the last circle pair. The undershootwith equal amplitudes ending on the 15-cm circles may bethe result of the limb that was constantly moving the largerdistance still influencing the limb that moved the smallerdistance most of the trial. A similar explanation may applyto the limb tracing the 15-cm decreasing circle. This limbalways required larger commands and the final error mayrepresent an after effect of the larger commands. The presentfindings suggest that amplitude assimilation is not a processsolely influenced by initial task conditions and outgoingefferent signals, as previous studies have demonstrated(Marteniuk & MacKenzie, 1980; Marteniuk et al., 1984;Sherwood, 1994b; Spijkers & Heuer, 1995; Swinnen et al.,2002). Future research needs to explore in more detail the

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role of visual feedback (possibly attention) in amplitudeassimilation processes, especially under scaled amplitudeconditions in comparison with fixed amplitude conditions.

The initial amplitude asymmetries produced significantshifts in relative phase away from 0◦ and 180◦, a finding con-sistent with previous work (Amazeen et al., 2005; Buchanan& Ryu, 2006; de Poel et al., 2009; Peper et al., 2008) andsupporting Hypothesis 3. The initial shift in relative phasebrought on by the amplitude difference may be the result of aninduced frequency disparity between the limbs when mov-ing different amplitudes, an interpretation consistent withprevious research (Amazeen et al.; Buchanan & Ryu; dePoel et al.; Ryu & Buchanan, 2004). The novel finding in therelative phase data was that equalizing circle diameter inter-acted with the required coordination pattern and initial circlepairing to influence the observed shifts in relative phase. Theshift in relative phase back towards the required values of 0◦

and 180◦ found in the symmetric 15–3 conditions providedsupport for Hypothesis 4 (Figure 5, right side). In the 3–15symmetric and asymmetric conditions, the observed shiftwas from an initial left arm lead to large right arm lead, afinding not in support of Hypothesis 4. The 15–3 asymmetriccondition produced extensive non-1:1 frequency behavior, afinding also not consistent with Hypothesis 4.

Studies requiring amplitude asymmetries have shown thatthe limb producing the larger amplitude is more stronglycoupled to the limb producing the smaller amplitude (Peperet al., 2008; Ridderikhoff, Peper, & Beek, 2005). This idea isconsistent with the conceptualization of different-size musclecommands in neural crosstalk accounts of amplitude assim-ilation. The strength of the coupling asymmetry effect waslarger for the right arm than the left arm in the Peper etal. study, and their participants, similar to the participantsin this study, were right-arm dominant. Research has shownthat the dominant arm tends to be more strongly coupledto the nondominant arm than vice versa and this can resultin a phase lead by the dominant arm in rhythmic tasks (dePoel, Peper, & Beek, 2007). For the 15–3 symmetric condi-tion, the coupling based on amplitude suggests the left armis more strongly coupled to the right arm in this condition.The coupling linked to hand dominance suggests the rightarm will be more strongly coupled to the left arm. The fre-quency detuning effect produces a right arm lead and rightarm dominance coupling may increase this lead. Reducingthe diameter of the 15-cm circle (left arm) or increasing theamplitude of the 3-cm circle (right arm) should reduce the leftarm amplitude coupling factor. As a result, a right arm leademerged and was maintained in the 15–3 symmetric condi-tion. For the 3–15 symmetric condition, frequency detuningpredicts a left arm lead as observed. The right arm producesthe larger amplitude and may be more strongly coupled tothe left arm (Peper et al., 2008). Based on hand dominancethe right arm should also be more strongly coupled to theleft arm (de Poel et al., 2007). The change in diameter in the3–15 condition should reduce the frequency detuning effect.The right arm will have the larger amplitude until the final

circle pair and should be more strongly coupled to the leftarm throughout the trial. This combination of amplitude cou-pling and arm dominance may account for the change from aleft arm lead to a large right arm lead as circle diameter wasequalized.

Why were higher order frequency ratios and wrapping ob-served in the asymmetric 15–3 condition? Research indicatesthat asymmetric circle tracing is less stable than symmetriccircle tracing (Buchanan & Ryu, 2005; Byblow et al., 1999;Carson et al., 1997; Summers et al., 1995; Wuyts et al., 1998;Wuyts, Summers, Carson, Byblow, & Semjen, 1996). Phasewrapping typically results from scaling a control parametersuch as movement frequency (Carson et al., 1997; Summerset al., 1995) and multi-frequency patterns typically must bedefined by external environmental information (deGuzman& Kelso, 1991; Kovacs, Buchanan, & Shea, 2010; Peper etal., 1995; Summers & Kennedy, 1992). A frequency of 1 Hztypically does not induce phase transitions or loss of stabil-ity in asymmetric coordination when tracing equal diametercircles (Carson et al., 1997; Summers et al.). This indicatesthat the initial stability difference between asymmetric andsymmetric coordination for the movement frequency of 1Hz cannot account for performance in the 15–3 asymmetriccondition. A model developed by Cattaert, Semjen, and Sum-mers (1999) captured the greater instability of asymmetriccircle tracing by decreasing the coupling strength linked toneural crosstalk between the arms. With very weak crosstalkbetween the arms, the model captured a frequency detuningeffect with the left arm tracing significantly slower than theright arm for the same-size (10-cm) circles (Carson et al.,1997; Cattaert et al.). This is the exact finding reported herefor the 15–3 asymmetric condition and also reported in previ-ous work using the same condition (Buchanan & Ryu, 2006).A recent model developed by Banerjee and Jirsa (2006) alsolinked a decrease in neural crosstalk to a destabilization ofantiphase bimanual coordination and offered this as an ex-planation for the inability of split-brain patients to produceantiphase coordination.

Even though models indicate that a decrease in couplingstrength can destabilize asymmetric coordination, the mod-els cannot account for the distinct difference in performancebetween the 3–15 and 15–3 asymmetric conditions. Recentresearch has shown that the intersegmental dynamics of theleft arm may contribute significantly to decreased stabilityof an asymmetric coordination pattern when two ellipses ofequal size are traced with the left and right arms (Rodriguez,Buchanan, & Ketcham, 2010). This link between intralimband interlimb control has lead some authors to suggest thatbimanual coordination of multijoint actions may be viewedas hierarchical in nature, with interlimb synergies assem-bled independently of intralimb synergies (Tseng, Scholz, &Galloway, 2009). Future researchers need to explore furtherthe breakdown of asymmetric coordination under the 15–3condition because it may reveal insights into the interactionbetween intralimb and interlimb synergies in bimanual coor-dination patterns.

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The findings reported support the conclusion that am-plitude assimilation effects observed in bimanual tasks aresensitive to initial task conditions (neural crosstalk), chang-ing task conditions, and the possible availability of visualfeedback. Amplitude modulations occurred independentlyof the required coordination pattern, required circle pair,and required scaling direction. The results showed that acombination of factors (frequency detuning, handedness)can influence interlimb coupling strength and when com-bined with different initial circle-pair combinations producedistinct shifts in relative phase. The present results showthat amplitude manipulations, possibly in combination withvisual feedback, can extensively influence the coordinationdynamics of basic symmetric and asymmetric coordination ina manner distinct from frequency scaling. Future researchersneed to more fully explore movement amplitude as a specificcontrol parameter that can influence bimanual coordinationdynamics.

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Received September 9, 2010Revised December 5, 2011Accepted January 6, 2012

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