1Department of Biobehavioral Health, 2Department of Kinesiology, and 3The Gerontology Center, The Pennsylvania State University, University Park, Pennsylvania 16802
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ABSTRACT |
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Slifkin, Andrew B., David E. Vaillancourt, and Karl M. Newell. Intermittency in the Control of Continuous Force Production. J. Neurophysiol. 84: 1708-1718, 2000. The purpose of the current investigation was to examine the influence of intermittency in visual information processes on intermittency in the control continuous force production. Adult human participants were required to maintain force at, and minimize variability around, a force target over an extended duration (15 s), while the intermittency of on-line visual feedback presentation was varied across conditions. This was accomplished by varying the frequency of successive force-feedback deliveries presented on a video display. As a function of a 128-fold increase in feedback frequency (0.2 to 25.6 Hz), performance quality improved according to hyperbolic functions (e.g., force variability decayed), reaching asymptotic values near the 6.4-Hz feedback frequency level. Thus, the briefest interval over which visual information could be integrated and used to correct errors in motor output was approximately 150 ms. The observed reductions in force variability were correlated with parallel declines in spectral power at about 1 Hz in the frequency profile of force output. In contrast, power at higher frequencies in the force output spectrum were uncorrelated with increases in feedback frequency. Thus, there was a considerable lag between the generation of motor output corrections (1 Hz) and the processing of visual feedback information (6.4 Hz). To reconcile these differences in visual and motor processing times, we proposed a model where error information is accumulated by visual information processes at a maximum frequency of 6.4 per second, and the motor system generates a correction on the basis of the accumulated information at the end of each 1-s interval.
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INTRODUCTION |
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A large body of evidence has
been amassed demonstrating that vision supports achievement of a
variety of goals of action, including transportation of the whole
organism to a new destination, as in locomotion, and movement of an
effector to a new position, as in reaching and aiming. In the latter
category of action, at least, vision has been shown to serve the goals
of movement according to the principles of closed-loop feedback control
(e.g., Carlton 1992; Jeannerod 1991
). A
dominant characterization of this process is that, because of
refractory periods and other delays in the system, visual feedback can
only be used to modify motor output periodically or intermittently
(e.g., Crossman and Goodeve 1983
; Meyer et al.
1988
; Vince 1948
). The purpose of the current
investigation is to characterize intermittency in the visual control of
continuous force production.
The influence of visual information processes on movement control may
express itself in motor output as changes in the form of movement
trajectories (e.g., Doeringer and Hogan 1998;
Miall et al. 1993a
). In general, intermittency in
movement control related to the processing of visual feedback has been
evidenced by the appearance of "submovements" or discontinuities in
movement trajectories, and their duration is thought to reflect the
time necessary for the visuomotor system to sample current effector
position against a target position and initiate a correction to the
ongoing movement (Crossman and Goodeve 1983
;
Meyer et al. 1988
). When vision is available during
point-to-point movements of the hand (e.g., Carlton 1992
; Elliott et al. 1997
) and in the manual
tracking of continuously varying waveforms (e.g., Miall et al.
1993a
), submovements are reliably observed. However, when such
movements are generated in the absence of vision, the number of
submovements decline and there is a reduction in the accuracy of target
approximation (e.g., Crossman and Goodeve 1983
;
Elliott et al. 1997
; Miall et al.
1993a
). These findings provide a basis for the inference that
intermittencies in motor output (e.g., submovements, discontinuities)
reflect the operation of intermittent, corrective visual feedback processes.
However, inferences about the visuomotor information and neural
processes underlying the appearance of intermittencies in the control
of limb position may be obscured by at least two mediating sources.
These factors are minimized in continuous isometric control tasks where
participants are required to maintain their force at target levels over
extended durations: first, in isometric control, there is, by
definition, no movement during force production; therefore, intervening
biomechanical factors that may influence position control are
minimized. On the other hand, during movement, there are complex shifts
in the internal and external forces acting on the joint; stretch
reflexes are elicited by changes in muscle length (Ghez and
Gordon 1987; Taira et al. 1996
; Ulrich
and Wing 1993
), and large portions of movement trajectory may
unfold without correlated neural innervation of the musculature (e.g.,
McMahon 1984
). Second, generating the appropriate output
to meet the task demands of continuous force production seems at least
logically less complicated than in the production of brief
point-to-point (discrete) actions (Taira et al. 1996
) or
in the tracking of continuously varying waveforms. For instance, even
in simple discrete actions (isotonic or isometric), the response needs
to be initiated; it needs to meet the target requirement and then
terminate (e.g., Gordon and Ghez 1987
; Gottlieb
et al. 1989
). This sequence of events usually unfolds over a
brief duration. While the tracking of continuously varying waveforms
may minimize sudden movement initiation and termination, frequent
reversals in position of the target and effector are common. Thus, in
these tasks, evidence of closed-loop sensorimotor processes may be
obscured or distorted by biomechanical factors and the presence of
additional, ongoing information processes.
In the current study, we examine the control of continuous isometric force production when participants were instructed to maintain force at a target level [40% of the maximum voluntary contraction (MVC)] over an extended period (15 s) and to minimize force fluctuations around the target. To examine the relation between changes in the intermittency of visual information and intermittency in motor control, visual feedback about current force level was varied across conditions such that a feedback sample of the current force value in relation to the target was presented on a video monitor as infrequently as every 5 s to as frequently as approximately every 0.04 s (0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6 Hz). This manipulation should be informative about the capacity of the sensorimotor system to make use of the visual feedback information with which it is presented.
For this purpose, we assessed changes in force variability
(within-subject standard deviation) and a measure of information transmission analogous to that used in the study of information transmission in physical (Shannon 1948) and biological
systems (Fitts 1954
; MacKenzie 1989
;
Slifkin and Newell 1999
). Our measure of information
transmission was the ratio of mean force output divided by the
within-participant standard deviation (Doeringer and Hogan
1998
; Slifkin and Newell 1999
). An expectation
is that increases in the amount of visual information would result in decreases in the within-participant standard deviation and increases in
information transmission, although the exact form of these relations
has yet to be established.
A linear regression equation with a y-intercept of zero and
a slope specifying a 1:1 ratio between incoming visual information and
information transmitted to motor output would characterize a perfect
information transmission system. However, it is well documented that
although the visual system by itself can pick up information at
relatively high rates (~60 Hz: e.g., Gregory 1997),
there are limits on the speed with which feedback information can be
utilized in the service of correcting errors in motor control (e.g.,
Carlton 1992
). Therefore, it was anticipated that
performance would improve up to a point with increases in visual
information, and slow or cease improving with further increases in the
frequency of visual feedback information. In this case, the relation
between increases in the frequency of visual information and
information transmitted to motor output should be specified by a
hyperbolic increase or negatively accelerating function. Alternatively,
a hyperbolic decay or negatively decelerating function would be the
predicted relation between feedback frequency and the within-subject standard deviation. In the case of either a hyperbolic increase or
decay, a slowing or a stop on improvement in performance quality should
point to limitations of the speed with which visual information can be
used to implement corrections in motor output.
We also examined the frequency content of force output, using the power
spectrum, to identify the frequencies of force output intermittencies
related to closed-loop visuomotor control. According to previous
research, the frequencies in the power spectrum of motor output
associated with closed-loop sensorimotor control are located in the
1-2 Hz frequency band (e.g., Freund and Hefter 1993;
Kunesch et al. 1989
; Miall 1996
;
Miall et al. 1993a
). In this case, one hypothesis is
that the feedback frequency manipulation should exclusively influence
changes in power in this range, while the power at other frequencies
does not change. In particular, if increases in feedback frequency
result in reductions in force variability, then it is anticipated that
those reductions would exclusively be mediated by reductions in the
amount of spectral power in the 1-2 Hz frequency range. An alternative
hypothesis would be that participants generate a corrective motor
response to each feedback delivery. In this case, increases in feedback frequency might appear to couple or entrain increases in the frequency of oscillations in force output. This should be reflected by a positive
correlation between feedback frequency and shifts of power to higher frequencies.
In summary, the current experiment was designed to precisely manipulate
a range of visual feedback intermittencies (feedback frequencies) and
examine their influence on intermittency in continuous isometric force
control. Two issues were addressed in the current experiment. First, we
wanted to identify the capacity of the motor system to make use of the
available visual information through examining the effect of the
scaling of the frequency of visual feedback information on changes in
the quality of performance outcome. Second, we sought to identify the
spectral frequencies of force output related to the processing of
visual feedback information (Freund and Hefter 1993;
Miall 1996
). The hypothesis examined was that changes in
visual feedback should exclusively influence motor output
intermittencies with frequencies in the 1-2 Hz band of the power spectrum.
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METHODS |
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Participants
Ten individuals, with a mean age of 25.4 yr (SD = 4.43), from The Pennsylvania State University community participated as volunteers in the experiment. Four of the participants were female, and none of the 10 participants had a prior history of a neurological disorder. Participants performed the task with the index finger of their dominant hand: six were right- and four were left-hand dominant. Eight of the participants were unfamiliar with the task and the purpose of the experiment, and the remaining participants were the first (A.S.) and second (D.V.) authors of the current paper. The eight naive participants provided informed consent, which was approved by the local institutional review board.
Apparatus
Much of the apparatus, procedures, and data analyses used in the
current protocol have previously been described (Slifkin and
Newell 1999). Seated participants produced force by pressing on
a load cell with the pad of their distal interphalangeal segment of the
index finger. During an experimental trial, force output from the load
cell was amplified and then sampled at 100 Hz by a 16-bit A/D board
that measured force in units of .0015 N (0.147 g).
The load cell was located 40 cm in front of the participant's body midline and fixed to a desktop. Although no physical restraint was used, participants were instructed to keep their elbow, forearm, and all fingers flat against the surface of the desktop and to limit force production to index finger flexion. Participants were reminded of these instructions during the experiment. A 14-in. computer monitor was placed on a separate tabletop so that it was located at a distance of 75 cm from the center of participants' eyes. Participants viewed their force output on the computer monitor. It had a viewing area composed of 459 vertical pixels by 638 horizontal pixels. The dot pitch (the width of the dots that make up each pixel) was 0.028 cm. We set the display-to-control gain at 50 pixels/N, and this resulted in an excursion of the force-time trajectory on the video monitor over a distance of 50 pixels for a change in force of 1 N.
During each trial, participants adjusted their force output to a force
target that appeared as a horizontal line (1 pixel in width) spanning
the length of the video monitor. The force target represented 40% of
the MVC and was always vertically centered on the video monitor. Thus,
the target line divided the video display such that half of the 459 pixels comprising the vertical dimension of the display appeared above
the target line (+229 pixels), and half below the target line (229
pixels). Given that the display-to-control gain was set at 50 pixels/N, the force-time trajectory could deviate by as much as
4.59 N above and 4.59 N below the target and still remain in view on
the video monitor. For example, if the 40% MVC level for a participant
was 15 N, then the force-time trajectory remained visible when it
remained between 10.41 and 19.59 N. On the basis of prior data (e.g.,
Slifkin and Newell 1999
), this range of permissible
variability around the target was in far excess of the levels of
variability participants exhibit at a 40% MVC force requirement. It
was only during the very start of the trial when participants adjusted
their force to the target level that the force-time trajectory was not
in view. Although we recorded the full 15-s force-times series, we were
only interested in, and only examined force output after, this initial
period of adjustment. All participants during all trials quickly
increased their force to levels near the requirement and maintained
their force within the visible range.
Procedures
During the initial portion of the experiment, the participant's
MVC was assessed (see Methods of Slifkin and Newell
1999). During both the familiarization and the
experimental trials, the force requirement for each participant was
based on 40% of their MVC. There were eight feedback frequency levels
imposed, and feedback frequency was defined as the number of pixels lit
per second. The feedback frequency levels used here were 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, and 25.6 Hz.
The left column of Fig. 1 is a representation of some aspects of the image viewed by the participant on the computer monitor at the end of the trial. As seen from top to bottom on the left side of Fig. 1, as the feedback frequency increased, both the time interval and distance between the appearance of consecutive pairs of illuminated pixels decreased. For example, at 0.2 Hz, there was a horizontal spatial interval of 5.95 cm between consecutive feedback samples and a temporal interval of 5000 ms. At 0.8 Hz, the spatial and temporal intervals were quartered to 1.49 cm and 1,250 ms, respectively.
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From trial onset, the first feedback sample was displayed when the time interval associated with the active feedback frequency interval elapsed. Then, as each subsequent fixed time interval elapsed, feedback samples (illuminated pixels) were displaced, at the specified distance and time, from the left of the previous feedback presentation. This process iterated until the end of the 15-s trial and resulted in the compilation of a sequence of illuminated pixels on the display as time elapsed into the trial. Once displayed, each feedback sample remained illuminated until the end of each 15-s trial when the display was cleared in preparation for the next trial. For example, in the 0.2-Hz condition, the first feedback sample was presented at 5 s into the trial; the second feedback sample was presented at 10 s into the trial, and the third feedback sample was presented at 15 s into the trial. With a spatial interval of 5.95 cm between feedback samples in the 0.2-Hz condition, the first feedback sample appeared at a horizontal distance of 5.95 cm, the second at 11.90 cm, and the third at 17.85 cm from the left edge of the feedback display.
To familiarize participants with the force matching procedure, and to
ensure that they understood the instructions, participants practiced
one trial at each of the eight feedback frequency levels. During the
experiment itself, participants completed four consecutive trials at
each feedback frequency level (a block). The order of each feedback
frequency trial during the initial familiarization phase of the
session, and the order in which each feedback frequency block was
administered during the experiment itself, was completely randomized
for each participant. During the familiarization phase, the
instructions were given to match force to, and minimize deviations around, the force target. During the experiment, to provide
participants with feedback regarding their ability to comply with these
instructions, and to maintain a high level of motivation throughout the
experiment, we employed a previously described feedback regimen (see
Methods of Slifkin and Newell 1999).
Data analysis
GENERAL DATA PROCESSING. The first 4 s and last 1 s of each force-time series were omitted from all analyses. The initial 4 s was omitted in order to ensure that the time series did not include the period over which force was being adjusted and stabilized, and the final 1 s was omitted, as on some occasions, some participants released their finger from the load cell during the final moments of the trial. Aside from the calculation of the mean force output, a linear regression equation was fit to each time series and the residuals from the line of best fit were used for additional data analysis. This procedure removed any trend (nonzero slope) from the time series. Although the presence of such trends was negligible, we used this detrending procedure as it is known that time series analyses can be biased by nonstationarities in a signal. Following detrending, each time series was conditioned with a ninth-order Butterworth filter having a 30-Hz low-pass cutoff.
MEASURES OF PERFORMANCE OUTCOME QUALITY.
The descriptive statistics submitted to analyses were the mean force,
the standard deviation, and a measure of information transfer (mean
force/standard deviation of force). Analyses of mean force output and
the within-subject standard deviation provided an opportunity to assess
how changes in feedback frequency influenced participant's ability to,
respectively, adjust their force to the force requirement and minimize
force variability as feedback frequency increased. The measure of
information transmission used here can be seen as analogous to
informational measures adopted for use in the study of motor control.
Such indices have been based on logarithms of ratios of movement
amplitude requirements divided by the region of permissible endpoint
variability [viz., Fitts 1954:
log2 (2A/W)], or the
actual (effective) average response amplitude divided by the actual
variability of response endpoints (e.g., Welford 1968
).
THE STRUCTURE OF FORCE OUTPUT.
In addition to analyses aimed at addressing the main issues, we also
provide an assessment of the influence of intermittencies in visual
feedback on intermittencies in the global dynamics of continuous force
output. This was accomplished in two ways: approximate entropy was used
as an index of force output dynamics in the time domain (see
Pincus 1991; Pincus and Goldberger 1994
),
and spectral analysis was used to evaluate the profile of the frequency
domain (e.g., Lipsitz 1995
).
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(1) |
TREND AND BREAKPOINT ANALYSES. The ANOVAs enable a test of the null hypothesis that visual feedback should not influence continuous isometric force production. Given an effect, it was then of interest to specify the form of the relation between changes in visual information and the dependent variables considered here. This would provide information about the capacity of the system to use visual information in the modulation of force output. Accordingly, the trend and breakpoint analyses provided, respectively, an opportunity to identify possible constraints on the use of visual information and the level of feedback frequency where the limitation occurs.
Changes in the dependent variables as a function of feedback frequency were characterized by three parameter hyperbolic regression equations specifying increases (Eq. 2), or decreases (Eq. 3), depending on the direction of change in the dependent variable
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(2) |
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(3) |
FREQUENCY ANALYSES. In an attempt to provide a more detailed examination of the feedback frequency manipulation than could be provided by the more global indices of the structure of force output (approximate entropy, the power spectrum exponents), we examined changes across the feedback frequency level at successive bin widths of 1.95 Hz over a range from 0 to 15.63 Hz. This provided eight consecutive frequency bins. For each trial within a feedback frequency level and for each participant, the power across the five smaller 0.39-Hz bins within the 1.95-Hz range was averaged. The average power in each 1.95-Hz bin was again averaged across the four trials at the respective feedback frequency level. The eight resultant values for each participant were then entered into a two-way feedback frequency (8) by spectral bin (8) ANOVA. One-way ANOVAs were subsequently used to examine changes in average power as a function of feedback frequency level, at each spectral frequency bin. This analysis was aimed at determining which frequencies in the spectrum were influenced by the visual feedback manipulation.
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RESULTS |
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Performance outcome quality
The across participant average MVC was 31.44 N (SD = 11.11 N) so that the 40% MVC force requirement was on average 12.58 N. Figure 1, right column, provides illustrations of the force-time trajectories sampled and stored at 100 Hz. These images, from a randomly selected participant, were taken from the first trial at each of the displayed feedback frequency levels. It can be observed that with increases in feedback frequency (from top to bottom, right column) came improved approximation of the target level (40% MVC) and declines in the magnitude of variations around the target force values. The decline in variability also appeared to be related to reductions in the contribution of lower frequency oscillations to the signal. What is clear from this illustration is that increasing the temporal resolution of force-feedback results in performance enhancement.
As seen in the top left of Fig. 2, group averages for mean force output increased sharply, although only slightly, in an absolute sense or in terms of %MVC: mean force increased from about 12 N at 0.2 Hz to 12.4 N at 1.6 Hz, across the first five feedback frequency levels, and this translated into just less than a 1.5% MVC increase in force. Then, with increases in feedback frequency, mean force output appears to remain stable from the 1.6 to 25.6 Hz feedback frequency levels, where mean force output remained at levels just below (about 0.18 N or 0.5% MVC) the force target. The increases in mean level of force output were significant over the feedback frequency range, F(7, 63) = 6.01, P < 0.001, but the Tukey HSD test revealed that this effect was carried by the mean force under the lowest feedback frequency level (0.2 Hz) falling below the means of all other feedback frequency levels. Thus, even though participants did not deviate very far below the force requirement over the 128-fold change in feedback frequency (from 0.2 to 25.6 Hz), and the significance of the ANOVA was carried by differences only at the 0.2-Hz feedback frequency level, it may be concluded that increases in feedback frequency did enhance participant's ability to approximate the target.
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As seen in the top right of Fig. 2, the standard deviation declines in a negatively decelerating fashion from about 0.9 N at 0.2 Hz to about 0.3 N at 6.4 Hz and then essentially stabilizes thereafter. This large (~66%) decline in the standard deviation as a function of feedback frequency was highly reliable, F(7, 63) = 24.23, P < 0.001. Figure 3 provides an illustration of changes in the standard deviation as a function of feedback frequency for each of the 10 individual participants. In very good agreement with the group mean trends, it can be seen that all individuals show a sharp decrease in the standard deviation over the initial levels of feedback frequency and then little, if any, change thereafter. The point at which the standard deviation appears to stop changing, or substantially slows its change, appears to occur near the 3.2- or 6.4-Hz feedback frequency level in all individuals.
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As seen in the middle of Fig. 2, expressing the disproportionate reductions in the standard deviation relative to the mean force output, information transfer (M/SD) sharply increased from the initial intermittency level until the 6.4-Hz level and then continued to increase, but at a slower rate over the remaining levels of the variable. There was a threefold, highly significant, F(7, 63) = 37.74, P < 0.001, increase in information transfer over the feedback frequency range. Thus, there was neither a 1:1 relation between the frequency of visual information and information transferred to motor output, nor was the relation linear: there was nearly a fourfold increase in information transfer across the first six increments (0.2 to 6.4 Hz), but only about a 0.3:1 increase across the final three increments (6.4 to 25.8 Hz).
The structure of force output
In parallel with the measure of information, and varying inversely with the standard deviation, Fig. 2, bottom left, shows that approximate entropy increases according to a hyperbolic or negatively accelerating trend. Thus, noisiness in the intermittencies of force output increased over the initial levels, but substantially ceased increasing following the 6.4-Hz feedback frequency level. These changes over the range of feedback frequency values were highly significant, F(7, 63) = 44.87, P < 0.001.
As illustrated in Fig. 3, it can be seen that in agreement with the group mean trend (Fig. 2), all individuals show sharp increases in approximate entropy over the initial levels of feedback frequency and then little, if any, change thereafter. A comparison between the group mean trends for the standard deviation (Fig. 2, top right) and approximate entropy (Fig. 2, bottom left), as well as their individual trends (Fig. 3), reveal that reductions in force variability were related to increased complexity or noisiness in the intermittencies of force output.
Figure 2, bottom right, shows that the power function exponents taken from the power spectrum changed in a parallel fashion with information and approximate entropy and were inversely related to changes in the standard deviation: the power function exponents became increasingly less negative from the first to fourth increment in feedback frequency. There was a more gradual increase toward zero across the next three increments. Overall, these changes gave rise to a significant effect for feedback frequency, F(7, 63) = 10.11, P < 0.001. Thus, the processing of increasing amounts of visual information was related to a broadened distribution of spectral power that can be said to reflect increased noisiness in the frequency domain of continuous force output.
Trend and breakpoint analyses
As can be seen by viewing the group mean data in the panels of Fig. 2, the hyperbolic regression equations provided very good descriptions of changes in each dependent variable as a function of feedback frequency. The proportion of variance accounted for (r2) by the hyperbolic regression equations fit to the group mean trends and averages based on r2 values from each of the 10 individual trends were, respectively, 0.88 and 0.61 (SD = 0.39) for mean force output, 0.98 and 0.88 (SD = 0.09) for the within-participant standard deviation, 0.99 and 0.90 (SD = 0.05) for information transfer, 0.98 and 0.89 (SD = 0.08) for approximate entropy, and 0.93 and 0.52 (SD = 0.36) for the power spectrum exponents. Thus, for the standard deviation, information, and approximate entropy there was only about a 10% decrease in the averaged-individual r2 values from that of the corresponding group mean values. Indeed, a comparison of the individual participant trends for the standard deviation and approximate entropy (Fig. 3) to their group mean trends indicates that the form of the individual trends have a very good correspondence with their respective group mean trends. On the other hand, for mean force and the power spectrum exponents, there were about 30 and 40% decreases, respectively, in the averaged-individual r2 values from that of their group mean trends.
The feedback frequency associated with the point in the hyperbolic function where it stopped changing (the breakpoint) was taken as the estimate of the minimum visual processing time, or, in other words, the shortest time interval over which visual information could be integrated and used to improve the quality of performance outcome or affect a change in the dynamics of force output. The breakpoints are reported here in terms of their associated feedback frequency (Hz) level, and, parenthetically, are translated into their corresponding time intervals (ms). The breakpoints for the group mean and averages based on the 10 individual functions were, respectively, 5.06 Hz (198 ms) and 5.91 Hz [169 ms (SD = 55 ms)] for mean force output, 6.55 Hz (153 ms) and 6.26 Hz [160 ms (SD = 35 ms)] for the standard deviation, 8.04 Hz (124 ms) and 7.94 Hz [126 ms (SD = 15 ms)] for information transfer, 6.95 Hz (144 ms) and 7.13 Hz [140 ms (SD = 22 ms)] for approximate entropy, and 10.62 Hz (94 ms) and 6.43 [156 ms (SD = 36 ms)] for the power spectrum exponents.
Of the variables considered, the mismatch between the minimum visual
processing times based on the hyperbolic trends fit to the group mean
data and averages of the individual minimum visual processing times was
greatest for the power spectrum exponents and then the mean force.
Visual inspection of the individual-participant trends for these
dependent variables revealed that this lack of correspondence was
related to a lack of between-participant consistency in the form of the
individual hyperbolic trends and, as just reviewed, the quality of the
hyperbolic function fit. Alternatively, there were very small
differences between the group mean and averaged-individual breakpoints
for the standard deviation, information, and approximate entropy, and
this points to high levels of consistency in the form of the
individual-participant functions and the quality of their fit.
Nevertheless, in general, taken together, the identified processing
times fell within a narrow range that is similar to the range of
estimates identified in studies on discrete (e.g., Carlton
1992: ~135-300 ms) and tracking (Miall et al. 1985
,
1993b
: ~150 ms) actions.
Frequency analyses
The exponents from power functions fit to the power spectrum provided a global index of changes in the distribution of spectral power as a function of changes in the amount of visual information. To gain a more fine-grained view of how changes in the amount of visual information influenced the frequency content in specific regions of the power spectrum, the spectrum was subdivided into eight bins with widths of 1.95 Hz. The independent and dependent variable values in both panels of Fig. 4 were submitted to a logarithmic (base 10) transformation. This was done to provide an enhanced view of aspects of the data presentation that would otherwise be masked when viewed in untransformed coordinates. Namely, this procedure provided a clearer image of the form of the functions describing changes in spectral power with feedback frequency, at the spectral frequency bins greater than 1.95 Hz (Fig. 4, top). All statistical analyses of power spectra reported here were based on the untransformed data. However, the same main effects and interactions were found when the ANOVA was applied to either the transformed or untransformed data.
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Figure 4, top, shows that the average power in the 0-1.95 Hz bin was elevated above that seen at the higher spectral frequencies, but was systematically reduced with increases in feedback frequency level. However, unlike the declines in power seen in the 0-1.95 Hz spectral bin, it appears (Fig. 4, top) that changes in average power over feedback frequency are absent in the higher frequency bands of the power spectrum. Therefore, the decrease in power in the 0-1.95 Hz band would seem to be responsible for both a significant feedback frequency effect, F(7, 63) = 4.48, P < 0.001, as well as a feedback frequency by spectral bins interaction, F(49, 441) = 4.60, P < 0.001, in the two-way feedback frequency by spectral bins ANOVA. This observation was confirmed by one-way ANOVAs used to examine changes in power over feedback frequency levels, at each spectral frequency bin: significant declines in power were observed only in the 0-1.95 Hz, F(7, 63) = 2.52, P < 0.05, but not at higher spectral bins.
When viewed in linear coordinates, decreases in power in the 0-1.95 Hz spectral frequency bin appear to follow a hyperbolic decay similar to that seen for the standard deviation (Fig. 2, top right), with power ceasing to change beyond the 6.4-Hz (~150 ms) feedback frequency level. In support of this observation, there was a high correlation, r(6) = 0.94, P < 0.01, between the group means for the standard deviation and average power in the 0-1.95 Hz spectral bin. Taken together, the results indicate that reductions in the standard deviation, an index of the amplitude of force variability, were mediated by reductions of power only in the 0-1.95 Hz bin.
As seen in Fig. 4, top, the average power at each feedback frequency level in the 0-1.95 Hz spectral bin was elevated above the corresponding group means in all other spectral bins. Then, as the spectral frequency bin increased, there were systematic declines in average power. Indeed, the two-way ANOVA revealed that there was a significant main effect for spectral bin, F(7, 63) = 10.12, P < 0.001. However, the Tukey HSD post hoc test showed that this resulted from the average power in the 0-1.95 Hz bin being significantly elevated over the power in every other spectral frequency bin: no differences in power were found among the seven higher spectral frequency bins.
Figure 4, bottom, shows changes in power as a function of spectral frequency bins, in five 0.39-Hz increments, at each of the eight feedback frequency levels. This analysis provided a more detailed image of the power spectrum in the region where changes in spectral power were found (0-1.95 Hz). It can be seen that as a function of spectral frequency bin, power increases from the initial bin with an upper limit of 0.39 Hz and reaches maximum levels at bins with upper limits of 0.78 and 1.17 Hz, and declines thereafter. This inverted U shape was preserved for the spectra at each feedback frequency level and resulted in a significant spectral bins effect, F(4, 36) = 6.67, P < 0.001, in the two-way feedback frequency (8) by spectral bins (5) ANOVA. A reliable feedback frequency effect, F(7, 63) = 4.59, P < 0.001, reflects the trend for power to decrease as feedback frequency increased. A feedback frequency by spectral bins interaction was present, F(28, 252) = 3.45, P < 0.001, and resulted from differences in the degree of change in spectral power as a function of feedback frequency, at the different spectral frequency bins. For example, in the spectral bins with upper limits of 0.78 and 1.17 Hz, there were large declines in power as feedback frequency increased, but relatively small changes at the 0.39-Hz and especially 1.95-Hz bins.
One-way ANOVAs were used to determine if the declines in power as a function of feedback frequency, within each spectral bin, were significant. The results showed that the declines were reliable at all [0.39 Hz: F(7, 63) = 6.06, P < 0.001; 0.78 Hz: F(7, 63) = 5.20, P < 0.001; 1.17 Hz: F(7, 63) = 3.35, P < 0.01; 1.56 Hz: F(7, 63) = 2.41, P < 0.05)], but the highest spectral frequency bin [1.95 Hz bin: F(7, 63) = 1.87, P > 0.05]. Thus the feedback frequency manipulation only influenced changes in the spectral power at spectral frequencies between 0 and 1.56 Hz.
One-way ANOVAs were also used to assess the reliability of changes in
spectral power as a function of spectral frequency bin, at each
feedback frequency level. ANOVA significance would point to the
reliability of the elevation of peaks in the spectra. Indeed, analyses
revealed that as a function of spectral bin, power changed significantly within the spectra at each feedback frequency level [0.2
Hz: F(4, 36) = 10.22, P < 0.001; 0.4 Hz: F(4, 36) = 3.93, P < 0.01; 0.8 Hz:
F(4, 36) = 3.75, P < 0.05; 1.6 Hz:
F(4, 36) = 6.04, P < 0.001; 3.2 Hz:
F(4, 36) = 3.55, P < 0.05; 6.4 Hz: F(4, 36) = 5.16, P < 0.01; 12.8 Hz:
F(4, 36) = 6.65, P < 0.001; 25.6 Hz:
F(4, 36) = 3.15, P < 0.05]. Thus, the
dominant oscillation in continuous force production occurs at low
frequencies, between 0.78 and 1.17 Hz (Fig. 4, bottom) and
remains dominant across increases in feedback frequency. This finding
is consonant with the hypothesis that expressions of closed-loop
sensorimotor information processes are restricted to a distinct,
low-frequency bandwidth of motor output (Freund and Hefter
1993).
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DISCUSSION |
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The experiment presented a novel means for examining the influence of intermittency in visual information on the control of continuous force output. Using this paradigm in which the intermittency of visual feedback was parametrically varied, it was possible to address several theoretical issues regarding the influence of variations of the intermittency of visual information on intermittency in force output.
Visual feedback intermittency and performance outcome
Increases in the frequency of visual feedback had a strong impact on the quality of performance outcome and the dynamics of continuous force production. Given this result, it was of interest to determine the nature of these relations. Were there linear and proportional changes in the characteristics of motor output accompanying increases in visual information? Such a result would indicate that the motor system could continuously access and utilize all incoming visual information to meet the goals of matching force to, and minimizing fluctuations around, the force requirement. However, changes in dependent variables as a function of feedback frequency departed greatly from a linear regression equation with a slope specifying 1:1 relations between the independent and dependent variables. In fact, in confirmation of the prediction (see INTRODUCTION), changes in dependent variables were best described by hyperbolic increases or decreases, changing sharply over the initial force requirements and remaining at asymptotic levels over the final few feedback frequency levels. The slowing and then asymptote of these functions suggest that the feedback frequency levels used here were sufficient to assess performance over the range which participants have sensitivity to the manipulation, and, moreover, we were able to capture the upper limit at which the visuomotor system can effectively use the intermittency of visual feedback information delivered.
Visuomotor processing times
VISUAL FEEDBACK PROCESSING TIMES. According to the breakpoint analysis, participants were unable to further improve their compliance with the instruction to minimize force variability (the standard deviation) when the interval between successive feedback deliveries was shorter than about 150 ms (6.4 Hz feedback frequency). Changes in the dynamics of force output, as indexed by approximate entropy, continued until slightly faster frequencies, while changes in information transmission persisted over even shorter intervals. The ordering of the breakpoint values for the different variables suggests that different dimensions of motor output have different capacities of influence by visual information. Nevertheless, these between-variable differences in breakpoint estimates were quite small.
While it is clear that changes in the dependent variables as a function of feedback frequency were well described by hyperbolic equations, there was a tendency for the group mean functions to change slightly over the final feedback frequency levels. However, this would seem to come as a result of averaging across the individual data. An examination of the individual participant trends for the standard deviation and approximate entropy (Fig. 3) revealed that, in comparison with the group mean trends, the functions stop changing more abruptly and remained stable over the final feedback frequency levels.MOTOR OUTPUT PROCESSING TIME. Improvements in performance outcome accompanying increases in feedback frequency were related to reductions in the amplitude of power at low frequencies (0-1.95 Hz), with no changes in power across the higher frequency bands. Decreases in power in the 0-1.95 Hz frequency bandwidth over the range of feedback frequencies could best be described, when viewed in linear coordinates, according to a hyperbolic decline that paralleled decreases in the variability of force output. Thus, visual information facilitated compliance with the instruction to minimize variability through a mechanism that operates exclusively on reductions in low-frequency fluctuations of force output. When we examined the power spectrum in the 0-1.95 Hz region more closely, it was found that power was peaked at either the spectral bins with upper limits of 0.78- or 1.17-Hz and did not shift to higher spectral frequencies with increases in feedback frequency. Thus, the hypothesis that the frequencies of force output oscillations should entrain with, or be coupled to, increases in the frequency of visual feedback presentations, can be rejected. Higher frequency oscillations in force output were not amenable to control through visual feedback.
The finding that variations of visual information influences force output within the 0-1.95 Hz frequency range is consonant with the findings of other studies on manual (isotonic) tracking of continuously varying waveforms (e.g., Miall 1996INFERRING PROCESSING TIMES.
Two techniques have been used to draw inferences about the speed of the
visuomotor feedback loop. One method is based on the use of data
analytic techniques that examine the dynamics of movement trajectories
to assess markers of the cycle time of feedback-based corrections. This
includes assessing submovement durations (e.g., Carlton
1992; Crossman and Goodeve 1983
; Meyer et
al. 1988
) or looking for shifts in the peak frequency of the
power spectrum as a function of a visual feedback manipulation (e.g.,
Miall 1996
). Indirect methods are experimental
techniques that involve changing the duration of exposure to visual
feedback during movement and then examining resultant changes in
movement accuracy (e.g., Keele and Posner 1968
). For
example, the minimum interval needed to process visual information has
been inferred through identification of the shortest duration exposure
to on-line visual feedback information where performance quality (e.g.,
deviations from the movement target) is improved over a condition where
no vision was available (e.g., Keele and Posner 1968
;
Vince 1948
; Woodworth 1899
).
Visual feedback information and force output noisiness
As a result of the reductions in power as a function of feedback frequency in the 0-1.95 Hz frequency band (Fig. 4, top), power became more equally distributed (broadband) across the range of force output frequencies considered. Thus, intermittencies in force output become closer in structure to white Gaussian noise. However, this occurs not because of a spread of power to higher frequencies, but rather because of a reduction of power in the 0-1.95 Hz frequency band, with power at higher frequencies remaining constant. Revealing changes in the time domain structure of continuous force output, the group means for approximate entropy increased hyperbolically, indicating that intermittency in force output tends toward increased complexity or noisiness with increases in visual feedback information.
Very high correlations were found between measures of performance
outcome quality and measures of force output noisiness, both when the
group means and the individual data were considered. For example, as
force variability declined (the standard deviation) as a function of
increases in feedback frequency, there were parallel increases in
approximate entropy. The correlation of the group mean data for the
standard deviation (Fig. 2, top right) and approximate entropy (Fig. 2, bottom left) was r = 0.99, and an average of the 10 individual participant correlation
coefficients for this relation was r =
0.94 (Fig. 3).
The same relationship, in terms of increases in the noisiness in the
intermittencies of force output and increases in the quality of
performance outcome, was also found when performance was modulated, not
by varying the amount of available visual information, but rather by
challenging the force production capacity of the motor system
(Slifkin and Newell 1999
). Thus, the findings of the
current study provide additional support for the notion that, in
contrast to prevailing information processing accounts of human
performance (e.g., Meyer et al. 1988
; Schmidt et
al. 1979
), increases in the noisiness of force output were
related to enhancement, and not decrement, in the quality of
performance outcome.
Conclusion
The current study has provided an examination of the influence of
variations of the intermittency of visual feedback on intermittencies in continuous force production. We found, first, that increases in the
amount of visual information resulted in highly reliable improvements
in performance that continued until about the 6.4-Hz feedback frequency
level, yielding a minimum visual processing time of 150 ms. Second,
these improvements in performance across feedback frequency were
mediated exclusively by correlated reductions of power at about 1 Hz in
the power spectrum, without changes at higher spectral frequencies.
Support was not found for a hypothesis that increases in feedback
frequency should entrain correlated shifts in power to higher
frequencies in force output: the stability of the modal spectral
frequency over the 128-fold increase in feedback frequency is
consistent with findings in other domains showing that sensorimotor
control operates only at low frequencies in motor output power spectra
(e.g., Freund and Hefter 1993; Miall 1996
). To reconcile the differences between visual (6.4 Hz) and motor (1 Hz) processing times, we proposed a model where error information is accumulated by the visual system at a maximum frequency of about 6.4 per second, and the motor system generates a correction on
the basis of that information at the end of each 1-s interval. An
additional observation, through global analyses of the dynamics of
force output (power spectrum exponents, approximate entropy), revealed
that as feedback frequency increased there was an increase in the
noisiness of the intermittencies in force output structure. In turn,
these increases in signal noisiness were related to improvement in the
quality of performance outcome. This finding extends previous work
where the same relation between information transmission and signal
noisiness was found (Slifkin and Newell 1999
), but the
relation was mediated by maintenance of continuous isometric force
output at different force levels and not variations of visual feedback information.
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ACKNOWLEDGMENTS |
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This research was supported in part by National Institutes of Health Grants F32-HD-07885, T32-AG-00048, and RO1-HD-21212.
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FOOTNOTES |
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Present address and address for reprint requests: A. B. Slifkin, Dept. of Psychology, Cleveland State University, Cleveland, OH 44115.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 13 July 1999; accepted in final form 16 May 2000.
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REFERENCES |
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