Coordination and Efficiency of Rhythmic Arm Movements

1
Contributions of Visual Perception to the
Selection and Performance of Multifrequency Ratios
Eric E. Hessler, Laura M. Gonzales, Polemnia G.
AmazeenDepartment of PsychologyArizona State
University
Motor-Respiratory Coordination
Conclusions
Perception
Performance

• The synchronization of movement and breathing
• Operationalized as the ratio of movement
  frequency to breathing frequency

• Ratios from different Farey tree levels are more
  likely to be judged as different
• First support for the Farey Tree in visual
  perception of multifrequency ratios

2 different ratios were depicted at a
time(randomized presentation random starting
phasesame ratio comparisons presented twice)
Participants performed the same ratios while
following a display (randomized ratio
presentation 2 repetitions per ratio)
Visual-perceptual goal is different from ratio to
ratio
11, 21, 32, 43, 53, 54, 74, 75, 85
Many Ratios Are Possible
Few are observed across exercises

• Accuracy and variability of ratio performance
  are differentiated by Farey tree level until
  visual-perceptual differences between ratios
  are removed
• Differences in multifrequency performance are at
  least partly a product of perceptual abilities

Optotrak
11
75
83
73
21
21
52
32
54
S
D
72
74
31
41
31
61
43
41
Visual-perceptual goal is the same from ratio to
ratio
Participants judged whether the ratios were the
same or different
Running (Bramble Carrier, 1983) Bicycling
(Garlando, Kohl, Koller, Pietsch, 1985) Rowing
(Mahler, Hunter, Lenting, Ward, 1991) Manual
Wheelchair (Amazeen, Amazeen, Beek, 2001)
51
Pneumotachometer
52
11
85
32

• Higher-level ratios are perceptually similar to
  other higher-level ratios, whereas lower-level
  ratios are more perceptually salient
• New Hypothesis During performance, perceptual
  confusion between higher-level ratios results in
  transitions toward the more perceptually salient
  lower-level ratios

System Control Unit
53
The Farey Tree
Perception Results
Performance Results
A numerical ordering of the stability of all mn
ratios, where m and n are integers
Supporting Statistics
Accuracy of performance was higher with the
ball-ball display
Multidimensional Scaling
-Main Effect (df 1,24)-Display, F 0.77, p
.468
Perceptually-Manipulated
Level
Stability
Ball-Ball
Higher-level ratios cluster, indicating that they
are likely to be judged as similar
When participants intended to perform
higher-level ratios transitions toward
lower-level ratios occurred, but often in a
chunked pattern
0
10
With the perceptually-manipulated display,
accuracy of performance was similar across ratios
from different Farey levels
11
-No Simple Effect (df 2,48)-Farey Level at
Perceptually-Manipulated, F 0.77, p .468
HIGH
1
21
2
Farey Tree Level
32
31
-Simple Effect (df 2,48)-Farey Level at
Ball-Ball, F 4.24, p lt .05 -Simple
Comparisons (df 1,24)-Level 0-2 v. Level 3 at
Ball-Ball, F 9.56, p lt .01-Level 3 v. Level
4 at Ball-Ball, F 5.22, p lt .05-Level 0-2 v.
Level 4 at Ball-Ball, F 8.96, p lt .01
Frequency Ratio Accuracy
Future Direction
Lower-level ratios are further apart, indicating
that they are more perceptually salient
3
With the ball-ball display, accuracy of
performance was higher for lower-level than
higher-level ratios
52
53
43
41

• Can additional performance results partly be a
  result of visual-perceptual abilities?
• When the speed of ratio performance is increased,
  transitions toward simpler ratios are observed
  (Peper, Beek, van Wieringen, 1995b)
• - What effect does increased speed of stimulus
  movement have on judgments of ratio stability?

LOW
4
72
73
85
54
75
74
83
51
Difference in Frequency ?

• Farey tree predictions supported by previous
  experiments
• Performance of lower-level ratios is more stable
  than performance of higher-level ratios
• Motor-respiratory coordination (Hessler
  Amazeen, submitted)
• Bimanual coordination (Treffner Turvey, 1993)
• Drumming (Peper, Beek, van Wieringen, 1995a)
• Performance of less stable ratios is likely to
  transition toward more stable ratios along the
  branches of the Farey tree (m1n2 m2n1 1)
• Bimanual coordination (Treffner Turvey, 1993)
• Drumming (Peper, Beek, van Wieringen, 1995a,
  1995b)

-Interaction (df 2,48), -Display x Farey
Level, F 7.27, p lt .01
Display x Farey Level interaction on variability
R2
0.528,
With the perceptually-manipulated display,
variability of performance was similar across
ratios from different Farey levels
ß .15, t 6.17, p lt .001
-No Simple Effect (df 2,48)-Farey Level at
Perceptually-Manipulated, F 0.08, p .924
Frequency Ratio Variability
Perceptual Distance (from MDS)
-Simple Effect (df 2,48)-Farey Level at
Ball-Ball, F 16.24, p lt .001 -Simple
Comparisons (df 1,24)-Level 0-2 v. Level 3 at
Ball-Ball, F 35.27, p lt .001-Level 3 v. Level
4 at Ball-Ball, F 9.83, p lt .01-Level 0-2 v.
Level 4 at Ball-Ball, F 20.94, p lt .001
References
Ratios from more distant levels are more likely
to be judged as different
With the ball-ball display, variability of
performance was higher for higher-level than
lower-level ratios
Amazeen, P.G., Amazeen, E.L., Beek, P.J.
(2001). Patterns of locomotor respiratory
coupling during manual wheelchair propulsion.
Journal of Experimental Psychology Human
Perception and Performance, 27,
1243-1259. Bingham, G.P., Schmidt, R.C., Zaal,
F.T.J.M. (1999). Visual perception of the
relative phasing of human limb movements.
Perception and Psychophysics, 61,
246-258. Bingham, G.P., Zaal, F.T.J.M., Shull,
J.A., Collins, D.R. (2001). The effect of
frequency on the visual perception of relative
phase and phase variability of two oscillating
objects. Experimental Brain Research, 136,
543-552. Bramble, D.M., Carrier, D.R. (1983).
Running and breathing in mammals. Science, 219,
251-256. Garlando, F., Kohl, J., Koller, E.A.,
Pietsch, P. (1985). Effect of coupling the
breathing and cycling rhythms on oxygen uptake
during bicycle ergometry. Journal of Applied
Physiology, 48, 1060-1064. Haken, H., Kelso,
J.A.S., Bunz, H. (1985). A theoretical model of
phase transitions in human hand movements.
Biological Cybernetics, 51, 347-356. Hessler,
E.E., Amazeen, P.G. (submitted). Displays that
facilitate performance of multifrequency ratios
during motor-respiratory coordination. Mahler,
D.A., Hunter, B., Lentine, T., Ward, J. (1991).
Locomotor-respiratory coupling develops in novice
female rowers with training. Medicine and Science
in Sports and Exercise, 23, 1362-1366. Peper,
C.E., Beek, P.J., van Wieringen, P.C.W.
(1995a). Multifrequency coordination in bimanual
tapping Asymmetrical coupling and signs of
supercriticality. Journal of Experimental
Psychology Human Perception and Performance,
21, 1117-1138. Peper, C.E., Beek, P.J., van
Wieringen, P.C.W. (1995b). Frequency-induced
phase transitions in bimanual tapping. Biological
Cybernetics, 73, 301-309. Treffner, P.J.,
Turvey, M.T. (1993). Resonance constraints on
rhythmic movement. Journal of Experimental
Psychology Human Perception and Performance, 19,
1221-1237. Zaal, F.T.J.M., Bingham, G.P,
Schmidt, R.C. (2000). Visual perception of mean
relative phase and phase variability. Journal of
Experimental Psychology, 26, 1209-1220.
0-2
3
4
Same Level
1 Level Apart
2 Levels Apart
3 LevelsApart
4 Levels Apart
Level
When visual-perceptual differences between ratios
are removed, Farey tree correspondence
deteriorates
Farey Tree Distance
Visual Perception of Monofrequency Ratios
Performance of monofrequency ratios (11) is at
least partly a product of perceptual ability
Performance Transitions
Cross-Recurrence (Single Participant)
Frequency Ratio Histograms Across Participants
Performance Results In- and Anti- phase are the
most stable Inphase is more stable than Antiphase
12
Participants often chunk their performance into
easier ratios, which results in a repetitive
pattern of coordination and release
Intended 32
10
Reconstructed Breathing (s)
Intended 53
Transitions toward 11 and 21 are often observed
when individuals intend to perform higher-level
ratios
Inphase (0º)
Antiphase (180º)
8
(e.g., Haken, Kelso, Bunz, 1985)
Perception Results Inphase and Antiphase are
judged as the least variable Inphase is judged
as less variable than Antiphase Less stable
relative phases perceived as more variable when
frequency is increased
Percentage of Total Cycles
6
4
Reconstructed Movement (s)
32 21 53
2
(Zaal, Bingham, Schmidt, 2000 Bingham,
Schmidt, Zaal, 1999 Bingham, Zaal, Shull,
Collins, 2001)
Breath Amplitude
Movement Amplitude
0
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Is multifrequency performance partly a product of
perceptual abilities?
Frequency Ratio (movementbreathing)
National Science Foundation Grant BCS 0447039
Graduate and Professional Student Association
Grant Eric Amazeen, Peter Killeen and Steve
Goldinger for their assistance in developing this
study
Multifrequency transitions occur toward ratios
that are more visually-perceptually salient
Time (s)
Correspondence should be addressed to
Eric.Hessler_at_asu.edu For additional information
on Erics research go to http//www.public.asu.edu
/ehessler