a theoretical model of phase transitions in human hand movements

8/10/2019 A Theoretical Model of Phase Transitions in Human Hand Movements

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Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 4, No. 4, 2000

A Dynamic Systems Approach to UnderstandingReaching Movements with a Prosthetic Arm

Stephen A. Wallace,1,3 D. L. Weeks,1 and P. Foo2

A case study was conducted on an experienced upper extremity prostheticuser that required him to perform a reaching and grasping task with both his

prosthetic and normal anatomical hand. We used a scanning task (Wallace,Stevenson, Spear, & Weeks, 1994; Button, Bennett, & Davids, 1998) thatrequired the participant to perform a wide range of coordination patternsdefined by the relative phasing between the aperture of the fingers (or artificial

prehensor) and the arm. Visual templates of the required finger trajectoriesin thevarious required phase conditions servedasenvironmental information

for the subject to follow. Based on previous work, we hypothesized that theparticipant would exhibit at least one stable reaching and grasping patternin both his anatomical and prosthetic arm. In support of this hypothesis, theresults showed a negative sloping relationship between the required relative

phase and the mean delta relative phase (required relative phase minus theactual relative phase). The smallest delta relative phase occurred at approxi-

mately 80 and 115 relative phase for the anatomical and prosthetic arm,respectively during the scanning task. These results confirm our previouswork of the presence of only one attractor in reaching and grasping move-ments using either the anatomical or prosthetic arm.

KEY WORDS: dynamical systems; artificial limbs; motor coordination.

There are nearly 100,000 people with upper extremity amputations inthe United States alone (Frey, Carlson, & Ramaswamy, 1995) and manyof these individuals choose to wear an artificial limb that allows for the

1Department of Kinesiology, San Francisco State University, Department of Physical Therapy,Regis University.

2Center for Complex Systems and Brain Sciences, Florida Atlantic University.3Address for correspondence: Stephen A. Wallace, Ph.D., Professor, Department of Kinesiol-ogy, 1600 Holloway Ave., San Francisco State University, San Francisco, California 94132.

e-mail: [email protected].

311

1090-0578/00/1000-0311$18.00/0 2000 Human Sciences Press, Inc.


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312 Wallace, Weeks, and Foo

reaching, grasping and manipulation of objects. While much is known abouthow reaching and grasping behavior is accomplished using the normal,anatomical limb, there is much less research on the control of upper extrem-ity artificial limbs. Reacting to this paucity of research, several leaders in

the prothetic field attending the Research Planning Conference on Pros-thetic and Orthotic Research for the Twenty First Century in 1992, recom-mended that more emphasis be placed on fundamental studies that providea better understanding of biological controls of different types of upperextremity prostheses. Childress (1992) stated, The fields of orthotics andprosthetics today are similar to many other areas of rehabilitation. They lacka scientific basis for much of what is practiced(p. 10). Unlike established

disciplines such as geology and astronomy, Childress argued that prosthet-ics, while strongly influenced by advances in technical developments, lackedtheoretical structure. Similarly, LeBlanc (1992) stated that aside from someearly scientific work on prosthetics, . . .for the most part the field hasrelied heavily on the older studies, and has been coasting in the sense ofnot building on those original blocks to help put prosthetics and orthoticson as much of a scientific basis as possible. (p. 50). It is our view that abetter understanding of the control of upper extremity prostheses can be

achieved by becoming more acquainted with a field of human motor controlthat deals with prehension movements, an area that has garnered consider-able research in the last decade or so.

Prehension movements involve the use of the upper extremities inreaching, grasping and manipulating objects in our environment. Alongwith speech, prehension is a highly specialized motor skill in humans andhas been the subject of considerable investigation by motor control scientists

in psychology, kinesiology, neuroscience, and engineering (particularly inthe robotics area). Since the seminal work of Jeannerod (1981), there hasbeen much interest in how reaching and grasping movements are controlled(Fraser & Wing, 1981; Haggard, 1991; Marteniuk, MacKenzie, Jeannerod,Athenes, & Dugas, 1987; Marteniuk, Leavitt, MacKenzie & Athenes, 1990;Weir, MacKenzie, Marteniuk & Cargoe, 1991; Wing & Fraser, 1983; Wing,Turton & Fraser, 1986) and developed (Corbetta & Thelen, 1994; Thelen,et al., 1993; Von Hofsten & Ronnqvist, 1988). Jeannerod characterized the

anticipatory aspects of grasping (i.e., the movement control required toposition the hand in the correct orientation prior to the grasp) as the controlof two separate components, termed transport and manipulation. The trans-port component, composed primarily of proximal joint and muscle groupsrelative to the hand, is responsible for correctly positioning the hand nearthe object to be grasped. Measurement of the transport component typicallyinvolves the changes in kinematics of the arm (e.g., displacement and veloc-

ity) from the start of the movement to the grasp. The manipulation compo-


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Prosthetic Reaching 313

nent involves the distal joints and muscles of the hand and is responsiblefor grasping the object. To simplify the task, researchers often analyze onlythe participants index finger and thumb and measure the resultant distantbetween them (i.e., aperture) as a representative measure of the manipula-

tion component. Thus, using similar kinematic measures, it is possible toinvestigate the control of an artificial limb by paying special attention tothe movements produced by the prosthetic user while engaged in the reach-ing and grasping of an object.

In the present study, we investigated the prehension movements per-formed by a person with a below elbow amputation who wore an upperextremity prosthetic (artificial) limb. While the basic mechanics of the upper

extremity prosthesis are known, how this device is actually controlled bypeople with amputations is still an open question. Unlike the normal ana-tomical hand, joint movement much more proximal to the hand executesthe control of the fingers of the prosthesis. Specifically, opening and closingof the artificial hand (prehensor) is accomplished by changes in the tensionof a cable that connects the prehensor to a harness around the contralateralshoulder. Relative body motions of the torso, shoulders and the arm areused to change cable tension to achieve opening and closing of the artificial

hand during prehension (Atkins, 1989). It is the nature of these relativebody motions that is the focus of the current study.

While the body-powered prosthesis is an interesting model to studymovement coordination because of its mechanical configuration, there is lit-tle published work on the coordination strategies used by experienced usersof upper extremity body powered prostheses. For example, Wing and Fraser(1983) presented a case study detailing the control of a reaching and grasping

movement in a 13-year-old girl with congenital absence of her left arm belowthe elbow. Their research focused on describing the changes of the transporttransport and grasp components in reaching movements with both the ana-tomicalhandandtheartificialhand.However,therelativebodymotionsusedin controlling the prosthesis were not investigated. The difficulty in control-ling an upper extremity prosthesis by inexperienced users was recently docu-mented by Wallaceet al. (1999). They showed that inexperienced users werenearly three times slower and more variable in performing a simple reaching

and grasping task with a prosthetic limb compared to the normal, anatomicallimb. However, no measures of coordination among relative body motionsused to control the prehensor were taken. Thus, there is a need to examinethe coordination among the important joint movements in prosthetic reach-ing and grasping. It is likely that because there are a number of proximal jointmotions used to control the prehensor (Atkins, 1989),patternsof coordina-tion among these joints are likely to emerge as the user attempts to reach and

grasp an object (Wallace, 1996). How might these patterns of coordination


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be discovered? What theoretical framework is best suited to understand thenature of this coordination?

Most theoretical models of reaching and grasping assume that each com-ponent has a controller that prescribes behavior and that the coordination

between the components necessitates a further mechanism (e.g., Arbib, 1981,1985; Hoff & Arbib, 1993; Jeannerod, 1981, 1984; but see Bootsma & VanWieringen, 1992, for an exception). In contrast to these prescription models,dynamical pattern theory (e.g., Kelso, 1995; Kelso & Schoner, 1988;Schoner & Kelso, 1988; Wallace, 1996), modeled after synergetic theory (Ha-ken,1983),describesthecoordinationamongthevariousjointsusedinmove-ment as aself-organizing processthat results in explicit patterns of behavior.

Many of these patterns represent stable collective states, called attractors,that may be described by a system variable termed an order parameter.Inmovements requiring the use of at least two articulators (joints), modeled ascoupled oscillators, the relative phasing between the articulators has beenshown to be a excellent order parameter because it best captures the temporalcoordination involved in the movements and behaves in accordance with thetheoretical modeling (Haken, Kelso, & Bunz, 1985).

One way to observe these attractors, at least with humans performing

a motor task, is through the use of what has been termed a scanningprocedure (Kelso, 1995; Wallace, 1996; Zanone & Kelso, 1992). In thescanning procedure, the human participant attempts to perform a varietyof patterns of coordination, each requiring a different required relativephase. The mean and standard deviations of the various relative phasepatterns describe the entire attractor layout for each participant. In biman-ual experiments, it has been shown that the 0 and 180 deg relative phase

patterns are attractors, exhibiting the most accurate and consistent perfor-mance (Tuller & Kelso, 1989; Yaminishi, Kawato & Suzuki, 1980; Zanone &Kelso, 1992). But are there attractors in the case of reaching and graspingmovements? One extension of dynamic pattern theory to reaching move-ments involving coordination of the hand and arm was done by Wallace,Stevenson, Spear and Weeks (1994). In this experiment, the scanning proce-dure was used to help identify stable reaching coordination patterns. Inthis experiment, participants produced rhythmical reaching movements by

following an auditory metronome at a comfortable pace such that the graspof an object was synchronized with each beat of the metronome. Participantsattempted to produce different finger and thumb trajectories by followingvisual templates placed beneath the arm on a table surface that effectivelyaltered the relative phase of maximum aperture (or final hand closing),considered to be the order parameter in this task. Participants were capableof accurately and consistently producing only one temporal pattern of

coordination, unique for each participant. In contrast to the bimanual coor-


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dination literature, evidence was provided for a uni-stable attractor land-scape, with only one stable pattern.

Further evidence for only one attractor in reaching movements involv-ing the coordination of the hand and arm has been recently provided by

Button, Bennet, & Davids (1998). Both discrete and rhythmical movements:were studied. While the results for discrete movement were more variable,the general trends of their data supported a uni-stable attractor landscapethat may change depending on task conditions. Button et al., scrutinizedthe use of the scanning procedure, which we will address in the discussion.

In the scanning procedure two important factors or forcesare thoughtto affect performance in the task (Kelso, 1995; Wallace, 1996). According to

dynamic pattern theory, the participantsintrinsic dynamicsor coordinationtendencies are the capacities that exist at the time a new task is to be learnedor performed. In bimanual movements, it is common for participants tobe able to perform only the 0 and 180 coordination patterns accuratelyand consistently. It can be said that in these cases, the participants intrinsicdynamics are strong for the 0 and 180 patterns and weaker for the otherpatterns. Theoretically, the intrinsic dynamics reflect the participants abilityto perform coordination patterns in the absence of the second important

factor, called environmental information. Environmental information pro-vides the participant or learner with details about how the coordinationtask should be performed. Environmental information is expressed in thesame terms as the intrinsic dynamics, namely, in terms of the order parame-ter. In the present experiment, the environmental information was providedby visual templates that expressed the required relative phasing for theparticipants to attempt (i.e., occurrence of final closing of the hand or

prehensor). According to dynamic pattern theory, if the participants intrin-sic dynamics match the environmental information, cooperation betweenthese forces occurs, and stable performance results. A contrast betweenthe two, will result in less stable performance. This theoretical accountnicely explains the performance on previous experiments using the scanningprocedure (Tuller & Kelso, 1989; Wallace, Stevenson,et al., 1994; Yaminishiet al., 1980; Zanone & Kelso, 1992). That is, the discrepancy between therequired relative phase (environmental information) and the actual relative

phase produced, called the delta relative phase, is smallest for the moststable coordination patterns.

Our participant, a below-elbow amputee and experienced prosthesisuser, performed the scanning procedure with his unaffected, anatomicalhand and with his artificial hand. Based on the earlier Wallace et al. study,we hypothesized that only one attractor would be identified for both ana-tomical and prosthetic reaching. In addition, we asked the participant to

perform the reaching and grasping task both before and after the scanning


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procedure in the absence of environmental information. We called thesetrials the participants pre- and post-preferred trials. We wished to seewhether the coordination pattern performed during these preferred trialswould be similar to the patterned identified as the attractor in the scan-

ning procedure.

METHOD

Participant

The participant was a 48 year old male with a short below elbowamputation of his left arm with 25 years of experience using a body poweredprosthesis. He wore a voluntary closing body-powered prosthesis with aTRS Grip terminal device (see Fig. 1A and 1B). At the time of the testing,the participant had been using a voluntary closing body powered prosthesisfor nine years. The participant used his right (anatomical) hand for con-trol trials.

Apparatus and Task

A WATSMART 3-D motion analysis system was used for data collec-tion and analysis. To record joint motions of the participant, infrared lightemitting diodes (IREDs) were placed on the following locations: (a) distalthumb (or radial-most portion of the prosthetic prehensor), (b) distal index

finger (or ulnar-most portion of the prosthetic prehensor), (c) dorsal radialwrist (approximate location on the prosthetic prehensor of where the scaph-oid-radial joint would lie), (d) ipsilateral (tested upper extremity) anteriorglenohumeral joint (just caudal to acromio-clavicular joint), (e) sternum(two IREDs positioned on either side), (f) contralateral (non-tested upperextremity) anterior glenohumeral joint (just caudal to acromio-clavicularjoint).

The participant was comfortably seated at the table facing the two

calibrated WATSMART cameras. To help stabilize and standardize theparticipants body position during testing, he grasped a handle mountedon the table with his non-tested arm. The participant gripped the handlewith the shoulder flexed slightly forward, and elbow on the table. Calibra-tion error was less than 2 mm and the sampling rate was set at 200 Hz.IRED data collected on-line as the participant performed the scanning task,were subsequently digitized and smoothed with a second order Butterworth

filter (10 Hz cutoff) and were converted to three dimensions using


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A

B

Fig. 1.In A and B, a front and back view, respectively, of the participant wearing a voluntaryclosing prosthesis on his left arm. Notice how the cable from the prehensor is anchored bya harness on the contralateral shoulder. Also, notice that at the start of movement, theparticipant achieves minimum aperture by an outward lateral movement of elbow that in-

creases cable tension causing the prehensor to close.


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WATSMART software to yield displacement records of the joint motions.In addition, the resultant distance between the finger and thumb of bothanatomical and prosthetic hands was calculated as a measure of the finger-thumb aperture.

The target object was a vertical wooden dowel 18 mm in diameter and100 mm in height, which was positioned 41 cm from the table edge. Theparticipant began each trial by resting the tested hand on a small foam padnear the table edge with his finger and thumb pinched together (minimumaperture) directly over the start position. The start position, the targetdowel and the template representing the required trajectories of the fingerand thumb were defined by a metal trammel that could be adjusted for

each required relative phase condition. Figure 2 illustrates a schematicrepresentation of an exemplary template. A thick rubber band was wrappedaround the start position peg, the target dowel and each end of the metaltrammel arm to define template for the required finger and thumb trajector-ies. Thus, the template, was flush with the surface of the table and in fullview throughout a trial (during the scanning trials). To define each relativephase of final closing, the trammel arm was moved to a given position alongthe movement path and fixed with an adjustable screw. Ten required relative

phase conditions were examined by fixing the trammel arm at the followingdistances from the start peg: 3.1, 6.2, 9.3, 12.4, 15.5, 18.6, 21.7, 24.8, 27.9,and 31 cm yielding the following required relative phases, respectively:

Fig. 2. A schematic picture of the apparatus (top view). The

participant rested his hand on a foam pad at the beginning ofthe trial with the fingers in a pinched position (minimal aperture)directly over the start position (0 deg). The required trajectoriesof the index finger and thumb (in the anatomical hand, forexample) were produced by wrapping a large red rubber bandaround the start peg, the two ends of the adjustable trammel,and the base of the target dowel. The template shown is for the147.5 deg required relative phase condition. The trammel couldbe moved forward and back to create the various required rela-tive phase conditions and the maximum aperture could be ad-

justed to fit the participants hand (or prehensor).


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16.5, 33, 49, 65, 82.5, 98.5, 115, 131.25, 147.5 and 164.5 deg. The requiredrelative phase for each position was calculated by measuring the distanceof the trammel arm from the start position relative to the total distance(approximately 67.63 cm) during one complete arm transport cycle (from

the start to the grasp and back to start) and multiplying this ratio by 360deg. An auditory metronome was used to establish the cycling frequencyof the grasping motion. The metronome was set such that an auditory beepsignaled at .67 Hz, a comfortable pace for the participant.

Procedure and Design

The participant was told that the purpose of the experiment was tostudy various grasping patterns using both his anatomical and prostheticlimb. The trammel was initially moved to the first position, 3.1 cm fromthe start position, creating the 16.5 deg required relative phase trajectorytemplate. The required grasping movement was demonstrated in slow mo-tion by the experimenter: the thumb and index finger opened from theinitial pinched position and the maximal finger-thumb aperture prior to

final closing was attained at position 1. Final closing began as the finger-thumb aperture decreased monotonically while the hand approached theobject. The object was grasped between the tips of the thumb and indexfinger. The movement continued smoothly as the thumb and index fingerreleased the object and returned to the initial marked location, so that thethumb and index finger were in the original, pinched position. No specificinstructions were given concerning the finger-thumb aperture on the return

trip. Thus, one cycle of the continuous motion consisted of a reach forwardto momentarily grasp the target object, followed by a return to the startposition. After two to three slow motion demonstrations of this movementby the experimenter, the participant was asked to practice. Verbal feedbackwas given, and the participant was encouraged to concentrate on reachingmaximal finger-thumb aperture and beginning the final closing at the posi-tion indicated by the marker. When the participant appeared to be capableof performing the task in slow motion, the metronome was turned on and

set to the .67 Hz cycling frequency (determined through pilot testing to bea comfortable pace for both the anatomical and prosthetic limb). Theparticipant was asked to attempt to perform the task at this frequency,synchronizing the grasp of the object with the beat of the metronome. Withthe metronome operating, the experimenter again observed the participantperform the task, emphasizing that the requirements of the task were tofollow the beat set by the metronome and to begin final closing after

attaining maximal finger-thumb aperture at the position indicated by the


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marker. When the participant appeared to be comfortable with the task,he was told that the movements would be recorded after 3 additionalpractice cycles. The grasping movements of the participant were recordedby the WATSMART system continuously for 16 seconds, which included

between 11-12 cycles. The middle 9 or 10 of these cycles was used asexperimental data. This initial training segment with the marker at position1 lasted approximately 5 minutes.

This procedure of practice followed by data recording was repeatedas the trammel arm was moved systematically to each of the remainingpositions. This procedure is similar to the one used by Wallace, et al.(1994) and Zanone and Kelso (1992). Previous pilot work using a random

presentation of required relative phases showed no differences comparedto this more systematic procedure. The experimenter made certain thatthe participant kept up with the beat of the metronome, but did not attemptto judge or provide feedback on the accuracy of the position of the finalclosing prior to the grasp. The intertrial time between consecutive requiredrelative phase conditions was approximately 2 minutes. Recording at agiven required relative phase condition did not begin until the participantindicated readiness to perform the task.

Prior to and after the anatomical and prosthetic required phase trialsthe trammel apparatus was removed and the participant was asked topractice grasping the object naturally, with no regard to the position offinal closure prior to the grasp. The participant was instructed to performthe cyclical grasping task using their preferred pattern of coordinationfollowing the auditory metronome. After approximately 1 minute of prac-tice at the same cycle time, 10 cycles were recorded. The IREDs were then

removed and the session was concluded.

Relative Phase Calculation

Figure 3 illustrates how the point estimate of relative phase of finalclosing was calculated. From Wallace, Stevenson, et al. (1994), the relative

phase of final closing (Trfc) for each cycle was computed according to thefollowing formula:

Trfc ((tclose t0)/tcycle)) X 360 deg (1)

where tclose denotes the time of final closing prior to the grasp, t0 denotesthe starting time of the cycle and tcycledenotes the elapsed time during thecycle (Fig. 3). In most cases, the time of final closing prior to the grasp

occurred at maximum aperture. In cases of long aperture plateaus or


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Fig. 3.Calculation of the point estimate of the relative phase of final aperture closing. t cycleisthe time between peak wrist cycle, where the peaks represent the start of the movement(closest to the participant). tois the start of the wrist cycle and t closeis the time of maximumaperture prior to closing down on the target object (see formula 1 in text).

double peaks in the aperture separated by 50 ms or more, the point of finalclosing immediately prior to the grasp was selected as tclose.

RESULTS

Analyses of cycle time and relative phase were conducted with 2

12

10 limb (anatomical or prosthetic) by required phase (pretest, required


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phases 1 to 10, or posttest) by trial (110) repeated measures analyses ofvariance (ANOVAs). A similar ANOVA was conducted on the delta rela-tive phase data. Any significant main effects were further analyzed withTukey post hoc tests. All analyses used a Type I error rate ofp .05.

Example Wrist and Aperture Displacements

Figures 4A and 4B illustrate example tracings of the wrist and aperturedisplacements in the pre-preferred anatomical and prosthetic trials. Noticethat in both cases the wrist displacements are rhythmical and there is a

slight delay of wrist movement as the participant grasps the target dowel.While the aperture displacements are not quite as smooth, the openingand closing of the hand or prehensor for the outward and return trips ofthe wrist are clearly identifiable.

Cycle Time Analyses

The mean cycle times for the prosthetic and anatomical hands acrossrequired phase conditions are shown in Table 1. The ANOVA on cycletimes revealed no main effect for limb or required phase (both ps .68).In addition, none of the interactions approached significance (allps .18).There was, however, a trial main effect, F(9,207) 2.48, p .05. Tukeyanalyses indicated that trial 7 was significantly slower than trials 1, 2, 5, 6,9, and 10, while trial 8 was significantly slower than trial 4, 5, and 6. The

largest mean difference in any of these significant contrasts was found tobe 47 milliseconds; thus the consequence of the trial main effect was judgedas statistically significant, but not practically significant. Instead, participantswere judged to generally be able to adhere to the protocol by successfullypacing their motion with the metronome regardless of limb or requiredphase.

Relative Phase

Figure 5 illustrates mean relative phases produced by the anatomicaland prosthetic hands across the required relative phase conditions. Forboth hands, the pre and post-preferred conditions are similar, suggestingsome stability of the preferred pattern across the experimental session.For the anatomical hand and prosthetic hands, the preferred patterns are

approximately 80 and 95 deg, respectively. The ANOVA on relative phase


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Table 1.Means and Standard Deviations (in parentheses)of Cycle Times (sec) for Anatomical and Prosthetic Hands

Across Required Relative Phase Conditions

Hand

Required Phase Anatomical Prosthetic

Pre-Preferred 1.56(0.12) 1.60(0.06)16.5 1.58(0.04) 1.59(0.07)33 1.62(0.06) 1.60(0.03)49 1.61(0.04) 1.61(0.05)65 1.62(0.06) 1.60(0.05)82.5 1.60(0.04) 1.60(0.07)98.5 1.61(0.07) 1.57(0.04)115 1.59(0.03) 1.61(0.06)

131.25 1.60(0.05) 1.61(0.05)147.5 1.62(0.04) 1.61(0.07)164.5 1.60(0.06) 1.61(0.05)Post Preferred 1.61(0.05) 1.63(0.05)

Fig. 5.The means and standard deviations of the actual relative phases produced as a function

of the required relative phase condition in both anatomical and prosthetic reaching.


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values revealed a main effect for limb,F(1,9) 72.37,p .0001. This maineffect was due to the significantly higher relative phase values for theprosthetic limb than the anatomical limb. The mean relative phase for theanatomical limb was 85.31 (std. error 2.60), while the mean relative

phase for the prosthetic limb was 113.39 (std. error 1.40). The requiredphase main effect was also significant, F(11,99) 18.76, p .001. Resultsof the Tukey analysis indicated that the initial required phase differedsignificantly from all other required phases including the pretest and theposttest. Required phases 2 (33) through 5 (82.5) tended not to differ fromone another, including the posttest and pretest relative phases. However,beginning with required phases 6 (98.5) and 7 (115), differences began

to occur with the lower required phases. This trend was exaggerated in theupper required phases 8 (131.25), 9 (147.5), and 10 (164.5) which differedsignificantly from required phases lower than 6 (98.5) and 7 (115). Thelimb by required phase interaction was not significant (p .26) indicatingthat these differences between required phases were similar across limbs.The trial main effect and associated interactions also were not significant(all p .21). In general, these results suggest that higher relative phaseswere produced by the prosthetic hand, including the pre- and post-pre-

ferred patterns.

Delta Relative Phase

If the participant perfectly produced each required relative phase pat-tern, the mean delta relative phases would fall on to the gray horizontal

line in Fig. 6, representing no difference between actual and requiredrelative phase. However, the mean delta relative phases were a negativefunction of the required relative phase condition with slopes of.64 and.73 (delta relative phase deg/required relative phase deg) for the anatomi-cal and prosthetic hands, respectively. There was no significant differencebetween these two slopes, t(16) 1. The correlations between the meandelta relative phase and the required relative phase were .97 and .98for the anatomical and prosthetic hands, respectively. In addition, the points

of crossing the 0 deg delta relative phase line were different for the twohands. For the anatomical hand, 0 deg delta relative phase occurred approxi-mately at the 82.5 deg required relative phase condition. For the prosthetichand, 0 deg delta relative phase occurred near the 115 deg required relativephase condition. These two points were similar to the participants preferredpatterns produced in the pre and post test conditions. The ANOVA ondelta relative phase resulted in a main effect for limb, F(1,8) 45.99,

p

.001, (anatomical limb mean

3.64 [std. error

3.51], prosthetic limb


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Fig. 6. The means and standard deviations of delta relative phase as a function of requiredrelative phase in both anatomical and prosthetic reaching.

mean 26.52 [ std. error 1.84]). The required phase main effect wasalso significant,F(9,72) 62.96,p .001. Tukey post hoc analysis indicated

that the later required phases 7 (115 deg), 8 (131.25 deg), 9 (147.5 deg),and 10 (164.5 deg) resulted in positive delta relative phases that differedsignificantly from the middle required phases 5 (82.5 deg) and 6 (98.5 deg)and the early required phases 1 (16.5 deg), 2 (33 deg), and 3 (49 deg).The middle required phases 5 (82.5 deg) and 6 (98.5 deg) also differedsignificantly from the early required phases 1 (16.5 deg) 2 (33 deg), and 3(49 deg). The limb by required phases interaction was not significant (p .80) indicating that these differences between required phases were similar

across limbs. The trial main effect and associated interactions also werenot significant (all ps .19).

Proximal Joint Contributions

In an attempt to further understand the patterns of coordination used

in this rhythmic reaching and grasping task, particularly in the prosthetic


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limb condition, we examined the movements of the IREDs placed on themore proximal joints in relation to the prehensor. Our strategy was toexamine each marker and determine whether any significant, or systematicmovement occurred that could be related to the coordination of the hand

and ipsilateral prosthetic arm. It should be recalled that with the voluntaryclosing prosthesis, increases and decreases in cable tension cause the pre-hensor to close and open, respectively. Thus, it was clear that a movementof the ipsilateral arm (of the grasping prehensor) toward the target dowel,would help to close the prehensor. However, after the experiment, weasked the participant what strategy he used in approaching and graspingthe object. He said that in addition to extending his ipsilateral arm toward

the target dowel, he also used contralateral shoulder movement near theend of arm transport. In principle, shrugging the contralateral shoulderis another body motion that can increase cable tension in a voluntary closingprostheses. Therefore, we examined this motion in relation to changes inaperture. We were particularly interested in timing of onset of contralateralshoulder adduction in relation to aperture changes.

Contralateral Shoulder Motion Contribution

We first determined the extent of contralateral shoulder movementduring both anatomical and prosthetic reaching. To represent this motion,we chose movement of the IRED placed on the participants contralateralshoulder (see Methods section for details), in the plane of motion parallelto ipsilateral arms reach forward and back (in the Y-direction). During

prosthetic reaching this motion was cyclical, with minimal contralateralshoulder movement occurring at start of forward movement of the ipsilat-eral reaching arm on each cycle. Peak contralateral shoulder movementappeared sometime before the grasp. We measured the amplitude of contra-lateral shoulder motion from minimum to maximal excursion during eachcycle across all required phasing conditions. Figure 7 illustrates the meanamplitudes of contralateral shoulder motion during anatomical and pros-thetic reaching. The amplitudes of contralateral shoulder motion during

prosthetic reaching was roughly twice that during anatomical reaching.The motion during anatomical reaching of the contralateral shoulder

appeared to be synchronized with motion of the ipsilateral, reaching arm,suggesting that the participant was moving his torso forward and backwardas a unit, even though this torso movement during anatomical reachingwas rather small. This was confirmed by inspecting the Y-direction motionof the sternum that was also synchronized with both shoulders. Whereas,

motion of the contralateral shoulder during prosthetic reaching was delayed


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Fig. 7.Contralateral shoulder amplitudes in the Y-direction for both anatomical

and prosthetic arms.

with respect to the ipsilateral arm and torso in the Y-direction and itchanged depending on the required relative phase condition.

To examine the coordination of the contralateral shoulder during pros-thetic reaching, we calculated the relative phase of peak contralateral mo-

tion with respect to the ipsilateral arm cycle and compared this phasingwith the relative phase of final closing of the aperture. Figure 8 shows thatthe relative phases of peak contralateral shoulder motion and of finalaperture closing were very similar in the pre and post preferred conditions.The contralateral shoulder relative phase was greater than the aperturerelative phase between the 16.5 and 82.5 deg relative phase conditions, andless than the aperture relative phase between the 98.5 and 164.5 relativephase conditions. A 2 12 10 (Type of Phasing Required Relative

Phasing Cycle) ANOVA revealed no main effect for type of phasing,p .754. The cycle main effect and associated interactions also were notsignificant (allp .725). However, the required relative phase main effectwas significant,F(11,99) 10.48,p .001. This main effect was supersededby a significant required relative phasing by type of phasing interaction,F(11,99) 30.03, p .001. As seen in Fig. 8, the nature of this interactionwas such that shoulder initiation was not significantly different than aperture

final closing in the pre- and post-preferred relative phase trials. However,


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Fig. 8.Mean and standard deviations of the aperture and contralateral shoulder relative phase

as a function of the required relative phase in prosthetic reaching.

in the early required relative phases (cycles 1 to 5), onset of adduction inthe shoulder was significantly delayed with respect to onset of aperturefinal closing. By contrast, in the later required relative phases (requiredrelative phases 115 to 164 deg), shoulder adduction significantly preceded

final aperture closing.

Ipsilateral Arm Coordination

Another type of coordination was prevalent within the prosthetic armitself, namely the coordination between forward and lateral transport asthe participant reached for the target and returned to the start position

across the several cycles within a given trial. It should be recalled that werequired the participant to start the arm cycle with the prosthetic fingersin a pinched position (as was the case with the anatomical hand). Becausethe prehensor of the voluntary closing prosthesis is normally open at rest(with no cable tension), the participant had to compensate in some way toeffectively close the prehensor at the beginning of the movement. He didso by moving the ipsilateral elbow laterally outward at the beginning of

transport. From this position, he moved his elbow laterally inward as he


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reached forward. The coordination between lateral and forward prostheticelbow movement is illustrated in Figures 9A-E (i.e., pre-preferred, 33 deg,115 deg, 147.5 deg and post-preferred conditions) as Lissajou portraitsbetween the displacement of the prosthetic reaching arm in the Y-direction

(in the direction of the target dowel) and in the X-direction (perpendicularto forward and backward arm transport). Displacement from right to leftin the Y-direction represents forward arm transport and displacement upto down in the X-direction represents lateral elbow movement from abduc-tion to adduction (i.e., toward the body midline). In the pre- and post-preferred conditions, there was a near in-phase relationship between theX and Y directions, that is, forward elbow movement was synchronized

with elbow adduction, and backward elbow movement was synchronizedwith elbow abduction. Interestingly, a similar pattern was shown in the 115deg relative phase condition, which exhibited the smallest delta relativephase values during the scanning procedure. In the 33 deg condition, theforward and lateral elbow movement was less synchronized particularlyduring forward transport. Finally, the phasing relationship changed againin the 147.5 deg condition to approximately a 45 deg relative phase (i.e.,representative of an elliptical shaped Lissajou portrait). These results can

be interpreted as demonstrating that the required relative phase conditionaffected prosthetic elbow coordination.

DISCUSSION

The purpose of the present case study was to identify stable patterns

of coordination in reaching and grasping movements performed a personwith a below-elbow amputation using his anatomical and prosthetic arms.We tested the hypothesis that only one stable pattern would be performedby the participant during the scanning procedure (Wallace, Stevenson, etal., 1994). Mean delta relative phase and mean relative phase results sup-ported the hypothesis and suggested that the most stable pattern of coordi-nation between final aperture closing and arm transport occurred muchearlier during arm transport in the anatomical arm than in the prosthetic

arm. In addition, the fact that there was a negative sloping relationshipbetween mean delta relative phase and required relative phase suggestedthat performance of nearby phases was attracted toward the participantspreferred pattern in both arms. These results provide evidence that theparticipants preferred pattern in each arm can be considered an attractor,in the language of dynamic pattern theory (e.g., Kelso, 1995; Wallace, 1996).

While the mean delta relative phase results confirmed that the partici-

pants preferred pattern was performed most accurately, the standard devia-


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Fig. 9. Lissajou portraits of ipsilateral elbow displacement in the X and Y-directions inprosthetic reaching during the pre-preferred (A), 33 deg (B), 115 deg (C), 147.5 deg (D), andpost-preferred conditions (E).

tion of the mean delta relative phase showed no difference in performancevariability across the various required relative phase conditions. Similarresults have been found using adult, non-amputee participants (Button etal., 1998; Wallace, Stevensonet al., 1994). It is unclear why the participantspreferred pattern was not produced more consistently than the other pat-terns. One possible explanation is that the participant may have had diffi-

culty performing any pattern except his preferred pattern. This explanation


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Fig. 9.Continued.

suggests that he performed the preferred pattern in all required relativephase conditions. However, the results of the mean relative phase analysisdo not completely support this explanation (see Figure 5), because therewere significant differences in mean relative phase across the various re-

quired relative phase conditions. Thus, the conclusion we must reach isthat patterns other than the participants preferred pattern were performedwith similar variability but less accurately.

The fact that there were significant differences in mean relative phaseacross the various required relative phase conditions provides some supportthat environmental information influenced the participants intrinsic dy-namics (coordination tendencies). For example, in both arms, the actualmean relative phase tended to be less than the preferred pattern in required

relative phases below the participants preferred pattern, and tended to belarger in required relative phases above the preferred pattern (see Figure5). Thus, even though the participants preferred pattern exhibited signsof strong stability, the environmental information in the form of the visualtemplates may have altered the participants intrinsic dynamics to somedegree. This effect appeared to be strongest in the required relative phaseconditions most disparate from the preferred pattern in both arms (i.e.,

the 16.5 and 164.5 deg required relative phase conditions). However, any


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shift in the intrinsic dynamics appeared to be temporary, affecting perfor-mance primarily on the scanning trials. The pre- and post-preferred trialswere similar in both arms, suggesting the preferred pattern within eacharm remained rather stable.

Another important feature of the present study was the analysis ofproximal joint coordination of the shoulder and elbow. It was found thatthe coordination of the contralateral shoulder during prosthetic reachingappeared to be affected by the required relative phase condition. Duringthe pre- and post-preferred trials, the initiation of forward contralateralshoulder motion occurred approximately at the same time as initiation offinal aperture closing (see Figure 8). In required relative phase conditions

between 16.5 and 82.5 deg, the initiation of forward contralateral shouldermotion followed that of final aperture closing, and between the 98.5 and164.5 required relative phase conditions it preceded that of final apertureclosing. A possible explanation for the unintuitive finding is that the contra-lateral shoulder was used to facilitate final closing of the prehensor ontothe object only during the preferred pattern. Indeed, in post-exit interviews,the participant indicated that the contralateral shoulder was being used tohelp close the prehensor. However, he was unaware of the relative timing

differences in the use of the contralateral shoulder during the differentrelative phase conditions. In the future, it would be important to determinewhether coordination of the contralateral shoulder is affected by character-istics of the grasped object, such as its relative location, size or weight.Previous work in non-amputee prehension has shown some of these charac-teristics to affect arm transport and aperture configuration prior to thegrasp; see Paulignan and Jeannerod (1996) for a review. In addition, the

type of prosthesis (i.e., voluntary opening or voluntary closing) would bepredicted to affect the coordination of the contralateral shoulder.Another interesting feature of the results was the coordination of the

ipsilateral elbow in prosthetic reaching. A nearly in-phase relationshipwas found between the X-direction (abduction/adduction) and Y-direction(forward/backward) of the elbow motion during pre and post preferredtrials (see Figures 9A and 9E) and during the 115 deg required relativephase pattern (see Figure 9B). A change in the coordination was shown

as the participant attempted to perform the other required phase patterns.These results, when coupled with the contralateral shoulder results, sug-gested the required relative phase pattern between arm transport and aper-ture affects coordination patterns among other joints during prostheticreaching. We speculate that the coordination of the ipsilateral elbow andthe contralateral shoulder helps support the pattern of coordination be-tween the arm and the aperture. This view is reminiscent of the concept

of motor equivalence which can be defined as the motor systems ability


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to achieve the same goal in many different ways (Bernstein, 1967). Forexample, an examination of the Figure 8 reveals that the mean relativephase of final aperture closing deviated little, particularly between 33 and131.25 deg required relative phases. However, both the contralateral shoul-

der and ipsilateral elbow coordination changed considerably. This type ofbehavior might thus represent a form of motor equivalence during pros-thetic reaching.

The performers intrinsic dynamics (coordination tendencies) play astrong role in the coordination patterns that emerge in a given task (seeKelso, 1995). Until now, these coordination tendencies have been associatedwith the constraintswithinthe performer and represent the stability of the

various coordination patterns involved in the task. However, we wouldlike to extend this concept to the mechanical constraints (or coordinationtendencies) of the prosthesis. For example, in the voluntary closing prosthe-sis used by our participant, the prehensor is closed and opened by increasingand decreasing cable tension, respectively. Presumably, the effective opera-tion of the prosthesis requires an interaction between the wearers intrinsicdynamics (within the wearers body) and the mechanical constraints of theprosthesis. We speculate that a change in the mechanical constraints of the

prosthesis may interact with the intrinsic dynamics of the wearer, thusaltering theobservedcoordination patterns. For example, in a second typeof prosthesis referred to as a voluntary openingprosthesis, the mechanicalconstraints are reversed such that increasing and decreasing cable tensioncauses the prehensor to open and close, respectively. Hence, in prostheticreaching and grasping, both the preferred patterns among the relevantjoints of the wearer and the mechanical constraints of the prosthesis are

proposed to contribute to the wearers total intrinsic dynamics.While not manipulated in the present study, we contend that controlparameters (Haken, 1983) could also influence the observed coordinationpatterns in prosthetic prehension. In dynamic pattern theory, control pa-rameters are outside (external to the participant) variables that are imposedon the performer that theoretically alter the attractor landscape associatedwith the order parameter (Kelso, 1995; Schoner & Kelso, 1988; Wallace,1996). Systematic changes in the control parameter serve to de-stabilize

certain patterns and induce switching from less to more stable patterns ofcoordination. Both movement speed as dictated by an external metronome,for example, and a required postural orientation of the limb has been shownto be potent control parameters in bi-manual coordination studies; seeKelso (1995) and Wallace (1996) for a review. Phase shifts towards preferredpatterns of coordination in prehension movements have been documented(Foo, 1995; Wallace, Green, Graese, & Foo, 1994) but more work needs to

be done to verify this prediction in both anatomical and prosthetic reaching.


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There have been some criticisms of the scanning technique as a methodfor identifying attractors in reaching and grasping. Using similar proceduresas ours, Button et al., found that the attractors in cyclical movements (asused in the present study) and discrete movement were different in some

individuals. Their explanation was that different intrinsic dynamics acrossindividuals could account for these discrepancies. While this may be true,another possibility is that the demands of reaching and grasping for cyclicaland discrete movements are different. Thus, it may not necessarily be thecase that the attractor for discrete reaching and grasping is the same forthe cyclical case. It should be emphasized that the observed behavior duringthe scanning task is the result of an interaction between the intrinsic dynam-

ics of the performer and the environmental information of the task. Whilecyclical and discrete reaching movements have some commonality, such asthe use of similar joints and muscles and an actual object to be grasped,functional control of the two movement types, such as acceleration anddeceleration requirements or even deviations in grip behavior, may affectthe observed behavior, a point acknowledged by Button et al. themselves(p. 818). In contrast, we believe that the scanning procedure is one ofseveral viable and complimentary procedures that can be used to explore

the intrinsic dynamics of the performer.In summary, the present case study of a uni-lateral upper extremity

amputee provided evidence for only one stable coordination pattern amongthe transport and manipulation components of both normal anatomicaland prosthetic reaching and grasping. In addition, coordination of otherjoint motions appear to support the stable reaching and grasping patternused in the prosthetic arm. As such, these results support and extend theprevious findings of Wallace, et al. (1994) and Button, et al. (1998).

ACKNOWLEDGMENTS

We wish to thank Robert Radocy, Shirley Taylor, Nancy Hosterman,Eric Anderson and Lawrence Carlson and Larry Greene for their contribu-tions to the study.

This investigation was supported by a Research Infrastructure in Mi-

nority Institutions award from the National Center for Research Resourceswith funding from the Office of Research on Minority Health, NationalInstitutes of Health #5 P20 RR11805.

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a theoretical model of phase transitions in human hand movements

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