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Exp Brain Res. Author manuscript; available in PMC 2010 June 1.

Published in final edited form as:

Published online 2009 May 26. doi: 10.1007/s00221-009-1846-x

PMCID: PMC2745158

NIHMSID: NIHMS138591

Department of Kinesiology, The Pennsylvania State University, University Park, PA 16802

Address for correspondence: Mark Latash, Department of Kinesiology, Rec.Hall-267, The Pennsylvania State University, University Park, PA 16802, USA, tel: (814) 863-5374, fax: (814) 863-4424, Email: ude.usp@11llm

The publisher's final edited version of this article is available at Exp Brain Res

See other articles in PMC that cite the published article.

In a multifinger cyclic force production task, the finger force variance measured across trials can be decomposed into two components, one that affects the combined force output (“bad variance”), and one that does not (“good variance”). Previous studies have found similar time patterns of “bad variance” and force rate leading to an approximately linear relationship between them. Based on this finding and a recently developed model of multifinger force production, we expected the “bad variance” during cyclic force production to increase monotonically with the rate of force change, both within-a-cycle, and across trials at different frequencies. Alternatively, “bad variance” could show a dependence on task frequency, not on actual force derivative values. Healthy subjects were required to produce cyclic force patterns to prescribed targets by pressing on unidimensional force sensors, at a frequency set by a metronome. The task was performed with only the index finger, and with all four fingers. In the task with all four fingers, the “good variance” increased approximately linearly with an increase in the force magnitude. The “bad variance” showed within-a-cycle modulation similar to that of the force rate. However, an increase in the frequency did not lead to an increase in the “bad variance” that could be expected based on the natural relationships between action frequency and the rate of force change modulation. The results have been interpreted in the framework of an earlier model of multifinger force production where “bad variance” is a result of variance of the timing parameter. The unexpected lack of modulation of the “bad variance” with frequency suggests a drop in variance of the timing parameter with increased frequency. This mechanism may serve to maintain a constant acceptable level of variance under different conditions.

When a person performs a task of accurate force production, force variability, estimated as the standard deviation either across trials or over samples of a force time series, typically shows a close to linear increase with the force level (Newell and Carlton 1988). When the force is produced by a set of effectors acting in parallel, for example several fingers pressing on force sensors, each effector's force variability increases with its force level while there is little change in the total force variability with a change in the total force magnitude (Shim et al. 2004; Shapkova et al. 2008). This discrepancy is produced by particular patterns of finger force co-variation that channel the individual finger variability into a sub-space within the space of finger forces that does not affect the total force. This sub-space has been referred to as the uncontrolled manifold (UCM, Scholz and Schöner 1999; Latash et al. 2001), while the hypothetical neural mechanisms that bring about the mentioned patterns of force co-variation have been termed force stabilizing synergies (reviewed in Latash et al. 2002b, 2007).

Studies of force stabilizing synergies commonly used the framework of the UCM hypothesis (Scholz and Schöner 1999; Latash et al. 2002b). According to this hypothesis, the neural controller works in a space of elemental variables and creates in that space a sub-space corresponding to a desired value of a particular performance variable (the UCM). Further, the controller limits variability orthogonal to the UCM (“bad variability”, *V _{ORT}*) while allowing relatively high variability within the UCM (“good variability”,

Earlier studies have shown that the finger mode variance within the UCM, *V _{UCM}*, increases with the force level, while the variance orthogonal to the UCM,

Some of the mentioned studies used cyclic force production tasks (Latash et al. 2001; Scholz et al. 2002) while others used discrete tasks (Latash et al. 2002a; Shim et al. 2004). There has been an ongoing debate on whether discrete and cyclic tasks represent two classes with distinct neural control mechanisms or they are different peripheral consequences of basically the same control process (Schaal et al. 2004; Hogan and Sternad 2007). Note that one of the main characteristics of a cyclic process is its frequency while the rate of change of the variable is modulated within the cycle and depends on both frequency and amplitude. Using cyclic tasks allows distinguishing between effects of the rate of force change and of frequency, because it is possible to require an increase in the force rate with an unchanged frequency by changing only the amplitude. This distinction is potentially important because while frequency can be viewed as set at a high control level, the rate of force emerges at the output of the system as a result of the execution. All the mentioned data and the model by Goodman et al. (2005) suggest that *V _{ORT}* is defined by the time derivative of force. However, a more recent model (Goodman and Latash 2006) suggests that the two components of variability,

We predicted that for a constant amplitude force production task, increasing the frequency will not result in a change in *V _{UCM}*, as this is proportional to the force, but we expect

Eight right-hand dominant subjects, 4 males and 4 females (mean ± standard deviation: age 26 ± 4 years, weight 69.5 ± 8.0 kg, height 1.68 ± 0.010 m) volunteered to participate in this experiment. All subjects were healthy, with no known neurological or peripheral disorders. All of the subjects gave informed consent according to the policies of the Office for Research Protections at The Pennsylvania State University.

Figure 1 shows the experimental setup. It consisted of four unidirectional piezoelectric force sensors (model 208C02; PCB Piezotronic Inc.), each with a diameter of 1.5 cm, to measure the vertical forces applied by the four finger tips of the right hand. The sensors were spaced at 3.0 cm intervals in the medio-lateral plane, and the forward-backward location of the sensors was adjusted to match the anatomy of the individual subjects. The signals from the force sensors were amplified by signal conditioners (M482M66, PCB Piezotronics, Inc., NY), and then sampled at 200 Hz with 12 bit resolution by a LabVIEW program running on a PC.

The experimental setup. The subjects pressed on four unidimensional force sensors with the index, middle, little and ring fingers of the right hand, with feedback on either the index finger (I) or all four fingers (IMRL) shown on the screen. The main **...**

During the measurements, the subject sat comfortably in a chair facing the testing table, with his or her right upper arm at approximately 45° abduction in the frontal plane, 45° flexion in the sagittal plane, and with the elbow at approximately 45° flexion. The forearm rested on a horizontal board on a table, and two pairs of Velcro straps were used to prevent the forearm from moving. The fingers rested on a small wooden wedge to ensure that their posture did not change throughout the measurements. Feedback about the required force production was provided on a 17″ LCD screen placed 65 cm in front of the subjects.

There were three types of tests, maximal voluntary contraction (MVC) tests, single-finger ramp tests, and cyclic force production tests. In all these tests, the subjects were given feedback on the force produced by the instructed finger(s), by a constantly updating plot of the force magnitude (y-axis) against time (x-axis).

In the MVC task, the maximal force produced by the four fingers (I - index, M - middle, R - ring and L - little) and their combination (IMRL) was measured. The subjects were instructed to initially rest their fingers on the sensors. Then, in a self-paced manner after the cursor passed a vertical line (at 10 s after the start of the trial), they were instructed to press “as hard as possible” with the instructed finger(s). After reaching their maximum force (at a self selected time within 10 s), they were told that they could relax. Each trial lasted for 30 s. Two trials were recorded for each finger or combination of fingers, and the largest force produced between the two trials was used in later analysis. In single-finger MVC tests, the subjects were required not to pay attention to possible force production by the other fingers, but were required to ensure that all fingers remained on the sensors throughout the trial.

In the single-finger ramp tests, the subjects were shown a template on the screen, consisting of a horizontal segment at zero force for the first 5 s, then a slanted line from 0% to 40% of MVC over the next 20 s, then another horizontal segment corresponding to 40% MVC for the last 5 s. In each trial, one of the fingers was instructed to produce a force matching this template, and feedback was provided of the force level of that finger. The scale of the feedback was set such that for every trial, the top of the screen corresponded to 50% MVC of the instructed finger. The other three fingers remained on the force sensors, but no feedback on their force was provided. The subjects were instructed not to pay attention to the forces produced by the other fingers. The trials were performed twice for each of the four fingers, with the order balanced across subjects. A rest period of 30 s was provided between trials. The data from these trials were used to compute the enslaving matrix (see further details in the Data Processing section, and in Zatsiorsky et al., 1998).

During the cyclic force production trials, the subjects were required to produce smooth sine-wave like force patterns with either the index finger (I), or with all four fingers (IMRL) pressing together. During the I-finger trials, no feedback was provided on the forces produced by the other fingers; the subjects were instructed not to pay attention to possible force production by the other fingers of the hand. They were instructed to make the peaks and troughs lie within a given target range, indicated by dashed lines on the monitor, and to make the changes in force magnitude between these target ranges smooth. Additionally, a computer-generated metronome indicated when the peak or trough should take place. An example of a typical performance in the cyclic force production task is shown in Figure 1.

Four different frequencies were used, 0.67 Hz, 0.9 Hz, 1.1 Hz and 1.33 Hz. These frequencies were selected based on a pilot experiment, and spanned the range of frequencies over which subjects could successfully complete the task given the error margins. These frequencies are lower than the preferred frequencies of 1.5 – 2 Hz reported in similar tasks (Latash et al. 2001; Scholz et al. 2002); this is probably due to the stricter explicit accuracy constraints in this experiment. In the previous experiments, only a target line was given, whereas here a target range was given. Additionally, subjects in this experiment were required to match the metronome beat both at the peaks and troughs of the force production, whereas in the previous experiments, the subjects were required to match the metronome only at the force peaks.

The two targets were set at 10% of MVC, and 30% of MVC. For the 0.9 Hz frequency, an additional set of targets was used (10% MVC and 40% MVC). Each target consisted of a solid line, with dashed lines at ± 3% MVC. The scale of the feedback was altered such that feedback was always provided in terms of MVC rather than in N.

For each finger combination and frequency, a 30-s practice trial was performed, followed by three recordings of 30 s each. The order of finger combination/frequency was randomized, while the practice trial and three main trials of a particular combination were consecutive.

The data were processed using Matlab (The MathWorks, Natick, MA). The calculations of the variance of the force data was performed on unfiltered data. As the data were smooth to begin with, and the variance is calculated across repetitions of the task, the use of unfiltered force data is not expected to produce different results to using filtered force data as in some of the earlier studies (Latash et al. 2001, 2002a; Scholz et al. 2002). Calculation of the force rate (dF/dt) was performed using a 5-point derivative on filtered data (using a two-way 2^{nd} order low-pass Butterworth filter at 6 Hz).

The data from the cyclic force production task were analyzed within the framework of the uncontrolled manifold (UCM) hypothesis. The UCM hypothesis offers a method to compute the “good” and “bad” components of variance in the space of commands to individual fingers (reviewed in Latash et al. 2002b, 2007). Briefly, the space of elemental variables (commands to individual fingers, finger modes) is divided into two sub-spaces, one corresponding to a fixed value of the total force (the UCM) and the other leading to changes in the total force (orthogonal to the UCM). Further, variance across trials is compared within the two sub-spaces (per dimension); if significantly more variance lies within the UCM, a conclusion is drawn that a multi-element synergy stabilizes the total force.

Due to the mentioned phenomenon of enslaving (Zatsiorsky et al. 1998, 2000), individual finger forces co-vary positively across tasks and force values. To analyze task-specific patterns of co-variation, forces have to be converted into finger modes (Latash et al. 2001), which can hypothetically be changed by the controller one at a time. This was done using the corresponding enslaving matrix, **E**.

Single-finger ramp trials were used to generate **E** for each subject. For each single-finger trial, a linear regression of the forces produced by individual fingers against the total force produced by all four fingers over a 20-s time interval in the middle of the ramp was computed. The ratios between the changes in individual finger forces and the change in the total force were used to construct an enslaving matrix for each subject as follows:

$$\text{E}=\left[\begin{array}{cccc}\frac{\Delta {f}_{I,I}}{\Delta {F}_{I}}& \frac{\Delta {f}_{I,M}}{\Delta {F}_{M}}& \frac{\Delta {f}_{I,R}}{\Delta {F}_{R}}& \frac{\Delta {f}_{I,L}}{\Delta {F}_{L}}\\ \frac{\Delta {f}_{M,I}}{\Delta {F}_{I}}& \frac{\Delta {f}_{M,M}}{\Delta {F}_{M}}& \frac{\Delta {f}_{M,R}}{\Delta {F}_{R}}& \frac{\Delta {f}_{M,L}}{\Delta {F}_{L}}\\ \frac{\Delta {f}_{R,I}}{\Delta {F}_{I}}& \frac{\Delta {f}_{R,M}}{\Delta {F}_{M}}& \frac{\Delta {f}_{R,R}}{\Delta {F}_{R}}& \frac{\Delta {f}_{R,L}}{\Delta {F}_{L}}\\ \frac{\Delta {f}_{L,I}}{\Delta {F}_{I}}& \frac{\Delta {f}_{L,M}}{\Delta {F}_{M}}& \frac{\Delta {f}_{L,R}}{\Delta {F}_{R}}& \frac{\Delta {f}_{L,L}}{\Delta {F}_{L}}\end{array}\right]$$

(1)

where Δ*f _{j,k}* are the changes of individual finger forces

The force data from the cyclic force production trials **f** were converted into mode magnitudes **m** by using the **E** matrix: **m** = [**E**]^{−1}·**f**.

The force data in the cyclic task were segmented into the periods of force increase, and force decrease. The segmentation for periods of force increase was performed by selecting the data between a local minimum and a local maximum of the force rate (*dF/dt*), or vice-versa for the force decrease. Only segments where the force crossed the force mid-line (half way between the targets) were considered. Additionally, segments where the start or the end of movement were more than 15% MVC away from the target, or temporally more than 20% of a cycle away from the metronome tick were discarded. For computation of the variance, the segmented force data were first resampled to 100 data points using cubic spline interpolation.

For later statistical analysis, the mean force (I or IMRL) was calculated across trials for each condition. Nine time samples were selected such that the mean force at these times was 12%, 14%, …, 28% of MVC. The variance was then calculated at these times. In this way, the variances are calculated at evenly spaced force levels. Note that the variance was calculated at these times, rather than averaged across the inter-sample time intervals.

In comparing conditions with different amplitudes, rather than selecting samples with equidistant force levels, the variance was instead calculated at ten different time points, which were at phase 10%, 20%, …, 90%,100% (from 100 samples, using the resampled force data). Using this sampling technique, the variance is calculated at evenly spaced time intervals.

In the IMRL task, changes in the value of the total force *F _{TOT}* can be written as a function of the changes in the modes

$${\text{dF}}_{\text{TOT}}=\left[\begin{array}{llll}\text{1}\hfill & 1\hfill & 1\hfill & 1\hfill \end{array}\right]\text{df}=\left[\begin{array}{llll}\text{1}\hfill & \text{1}\hfill & \text{1}\hfill & \text{1}\hfill \end{array}\right]\text{E}\text{dm}$$

(2)

where **df** = [*df _{i}df_{m}df_{r}df_{l}*]

$$\text{0}=\left[\begin{array}{llll}1\hfill & 1\hfill & 1\hfill & 1\hfill \end{array}\right]\text{E}{\text{e}}_{i}$$

(3)

These directions can be found by taking the null space of the Jacobian of this transformation ([1 1 1 1] **E**). The mean-free modes were projected onto these directions and summed, to give

$${f}_{\Vert}=\sum _{i=1}^{n-p}\left({\text{e}}_{\text{i}}^{T}\cdot \text{dm}\right){\text{e}}_{\text{i}}$$

(4)

where *n* = 4 is the number of degrees of freedom of the **m** vector, and *p*=1 the number of degrees of freedom of the performance variable (*F _{TOT}*). The component orthogonal to the null space is given by:

$${f}_{\perp}=\text{dm}-{f}_{\Vert}$$

(5)

The amount of variance per DOF parallel to (or within) the UCM is then given by:

$${V}_{\text{UCM}}=\frac{\sum {|{f}_{\Vert}|}^{2}}{\left(n-p\right){N}_{\text{trials}}}$$

(6)

This is the variance that is compensated, that is, it does not alter the total force. Similarly, the amount of variance per DOF orthogonal to the UCM is given by:

$${V}_{\text{ORT}}=\frac{\text{\u2211}_{i=1}^{{N}_{\text{trials}}}{|{f}_{\perp}|}^{2}}{{\text{pN}}_{\text{trials}}}$$

(7)

Standard descriptive statistics were used. The accuracy in performing the different conditions was compared using ANOVA on the timing errors (expressed in percent of a half-cycle) and force errors (computed as the distance from the target at force maxima/minima, and expressed in percent of MVC) at the start and end of the force half-cycles, with factors *Combination* (I or IMRL), *Frequency* (0.67 Hz, 0.9 Hz, 1.1 Hz, 1.33 Hz), and *Direction* (force increase, force decrease). These ANOVAs were performed on the data for the amplitude of 20% MVC. To compare the effect of amplitude, additional ANOVAs were performed over the conditions where the frequency was 0.9 Hz with factors *Combination, Amplitude* (20% or 30% MVC), and *Direction.*

To compare the variance between the trials with finger combinations I and IMRL, a two-way repeated measures ANOVA was performed, with factors *Combination* (I or IMRL) and *Representative point* (beginning of force increase/decrease, at time of peak (or trough) of force rate, end of force increase/decrease).

Repeated measures ANOVAs were performed on the two components of the variance described above, *V _{UCM}* and

For *V _{UCM}*, the variances were calculated at 9 samples corresponding to equidistant force levels as described in the Data Processing section above. To test the hypothesis that

For *V _{ORT}*, the variances were calculated at 10 equally spaced times (Phase 10%, 20%, …, 100%). To test the hypothesis that

To test whether the *V _{ORT}* increases with increased force amplitude, a second repeated-measures ANOVA was performed with factors

The data were checked for violations of sphericity, and the Huynh-Feldt (H-F) criterion was used to reduce the number of degrees of freedom where necessary. Post-hoc tests (Tukey's honestly significant difference) were used to further analyze significant effects. The *p* value for significance was set at 0.05.

In Latash et al. (2002a), a linear model was proposed to describe the relationship between the two components of variance (*V _{UCM}* and

$$\begin{array}{l}{V}_{\text{UCM}}={a}_{1}\ast {F}_{\text{TOT}}+{c}_{1}\\ {V}_{\text{ORT}}={a}_{2}\ast {F}_{\text{TOT}}+{b}_{2}\ast \left|\phantom{\rule{0.2em}{0ex}}d{F}_{\text{TOT}}/\text{dt}\phantom{\rule{0.2em}{0ex}}\right|+{c}_{2}\end{array}$$

(8)

This model is slightly modified from the version found in Latash et al. (2002a), in that we consider absolute force rate | *dF _{TOT}/dt* | rather than force rate

After one practice trial, the subjects were all able to perform the cyclic task at the acceptable level of accuracy. An example of a typical trial can be found in Figure 1; this Figure shows the cyclic task performed at 0.9 Hz by the index finger. Across subjects, the mean (±standard deviation) percentage of rejected trials for the force increase was 29.0±7.9%, and for the force decrease was 24.9±9.1%.

For the accepted trials, the error in amplitude (the distance from the target line) was approximately 1-2% of MVC. The timing errors were approximately 20% of the duration of the half-cycle. These errors, averaged across subjects, are shown in Table 1. The errors at the end of the force increase half-cycle are not exactly equal to the errors at the start of the force decrease half-cycle because not all half-cycles were accepted. To determine whether these errors varied across the conditions, an ANOVA was performed on the four quantities shown in Table 1, namely the amplitude error and the timing error, at the start and end of the half-cycle, for all conditions with 20% MVC amplitude. The factors were *Combination* (I or IMRL), *Frequency* (0.67 Hz, 0.9 Hz, 1.1 Hz, 1.33 Hz), and *Direction* (force increase, force decrease), and their interactions. A significant main effect was found only for Frequency, for the timing error at the start (F_{(3,3)} = 4.40, p < 0.01) and end (F_{(3,3)} = 3.57, p < 0.05) of the half-cycle. A Tukey HSD test showed that at the start of the half-cycle, the error was significantly lower at 0.9 Hz and 1.1 Hz than at 0.67 Hz, while at the end of the half-cycle, the error was significantly lower at 0.9 Hz and 1.1 Hz than at 1.33 Hz. An additional ANOVA was performed to test the effect of amplitude. Only the results with 0.9 Hz were used (at the 20% and 30% MVC amplitudes). The factors were *Combination, Amplitude* (20% or 30% MVC), and *Direction.* While no significant main effects were found for Amplitude, for the timing error at the start of the half-cycle, a main effect was found for *Direction* (F_{(1,1)} = 4.21, p < 0.05). A t-test showed that the timing error at the start of the half-cycle was significantly smaller for the force decrease half-cycles compared to the force increase half-cycles. In the remainder of the analysis, the force half-cycles were uniformly resampled to 100 points, and so these timing errors will not affect the variance.

The variance of the total force was calculated over the accepted repetitions, for each sample of the force time series after the time series were resampled to 100 points, for the force increase and decrease, and for each subject separately. The variance showed a bell-shaped profile for all conditions, with the variance at the end of the force increase slightly higher than at the beginning of force increase, with the variance for the condition with a larger amplitude (30% MVC) higher than for all the other conditions. Figure 2 shows these time profiles averaged across all subjects for both I and IMRL tasks. The variances plotted are all normalized by the square of the relevant MVC.

Variance of the total force for the force increase (left) and force decrease (right) half-cycles, for the index finger (I) (top row) and for all four fingers (IMRL) (second row), averaged across subjects. The variance was normalized by the square of the **...**

From Figure 2, it can be observed that the normalized total force variance for the four finger combination (IMRL) was generally lower than the normalized variance when using only the index finger. This was found over most subjects and conditions. The mean and standard deviation (across subjects) of the normalized variance for the index finger and the IMRL combination are compared at three representative points: at the beginning of the force increase/decrease, at the end of the force increase/decrease, and at the time of peak force rate (or the trough of force rate for the force decrease segments). These results are displayed in Table 2.

This finding was confirmed using a two-way repeated measures ANOVA, with the factors *Combination* (I or IMRL) and *Representative point* (beginning of force increase/decrease, at time of peak (or trough) of force rate, end of force increase/decrease). A significant main effect was found for *Combination* (F_{(1,237)} =1.04, p < 0.05) and *Representative point* (F_{(2,237)} = 90.83, p < 0.0001) but not for the interaction *Combination × Representative point*. On average, the variance in trials with the combination IMRL was 8.7% less than in trials with just the index finger. The *Representative point* effect was due to the higher variance at the time of peak force rate. Pair-wise Tukey tests showed that for both combinations, the variance at peak force rate was significantly higher than the variance at the start or end of the force increase/decrease (p < 0.05). An exception to the reduction in variance was for observed for the force half-cycles with 30% MVC amplitude, for this condition, a paired t-test showed no significant difference in variance between the I and IMRL combinations.

The variances within the UCM (*V _{UCM}*), and orthogonal to the UCM (

Components of variance within the UCM (*V*_{UCM} - upper row) and orthogonal to the UCM (*V*_{ORT} - lower row), for force increase (left column) and force decrease (right column) half-cycles, averaged across subjects. The variances are normalized by the square **...**

*V _{UCM}*, which does not affect the variance of the total force, was overall much higher than

Formally, the changes in the components of variance can be considered as functions of the force and force rate. There is an approximately linear relation between the mean force and *V _{UCM}*.

Variance within the UCM (left) and orthogonal to the UCM (right) as a function of mean force (across repetitions and subjects) for the force increase half-cycles. The normalized variance values are the mean across subjects. *V*_{UCM} is similar across conditions **...**

The observations about the variation of *V _{UCM}* and

For *V _{ORT}*, two repeated measures ANOVAs were performed using the

The second repeated measures ANOVA tested whether amplitude had a significant effect on *V _{ORT}*, and so it was performed only on the data from the conditions with frequency of 0.9 Hz, at 20% and 30% MVC amplitudes. The ANOVA was performed with factors

The variance within (*V _{UCM}*) and orthogonal (

The a_{1} parameter quantified the dependence of *V _{UCM}* on the force, and ranged across subjects and conditions from 1.32 × 10

The b_{2} parameter quantified the dependence of *V _{ORT}* on force rate absolute magnitude. It showed a decrease with the increase in frequency. This observation was confirmed using an ANOVA on parameter b

The a_{2} parameter quantifies the dependence of *V _{ORT}* on force magnitude. Its value was different between the force increase and force decrease half-cycles. ANOVA showed a significant main effect for

The intercept c_{2} describes the component of *V _{ORT}* that is not linearly related to either force or force rate. Its value increased with increasing frequency. An ANOVA performed on c

Our experiments resulted in both expected and unexpected findings. On the one hand, when considered for a single frequency and amplitude, the two components of force mode variance, *V _{UCM}* and

We found only minor advantages of the multi-finger combination (IMRL) as compared to performance with the single finger (I) with respect to accuracy of performance. Indeed, force and timing error indices showed no differences between I and IMRL, while normalized force variance was only about 9% lower for the IMRL combination. Note that if individual fingers preserved their variance indices when acting in a group and did not co-vary their force outputs across trials, the IMRL condition would be expected to display a significant drop in the normalized force variance due to the force sharing among the fingers and the well-documented nearly linear scaling of force standard deviation with force magnitude (reviewed in Newell and Carlton 1988). An example presented in Shapkova et al. (2008) demonstrates that a four-finger group is expected to show a nearly 75% drop in the normalized total force variance as compared to individual finger's performance. Our study and a few earlier studies (Latash et al. 2001; Gorniak et al. 2008; Shapkova et al. 2008) have all shown a much lower gain in total force variance, a gain that was sometimes even under the level of statistical significance.

A more detailed analysis in an earlier study (Shapkova et al. 2008) has shown that, when fingers acted in a group, individual finger force variance increased rather dramatically (for comparable finger force values), and this increase was compensated nearly perfectly by co-variation of finger forces – so-called, force stabilizing multifinger synergies. Our study supports this hypothesis indirectly, that is by showing strong multifinger force stabilizing synergies (*V _{UCM}*

As in earlier studies, we performed analysis of variance across cycles at the same task in the space of finger modes, hypothetical variables that are used to generate finger forces (Danion et al. 2003). Using these variables allows avoiding spurious results that might be related to the phenomenon of enslaving, that is, unintended force production by fingers of a hand when one finger produces force intentionally (Li et al. 1998; Zatsiorsky et al. 1998, 2000). The total variance in the finger mode space was quantified separately within two subspaces that kept the total force magnitude constant and that changed the total force, respectively. As in earlier studies (Latash et al. 2001, 2002a; Scholz et al. 2002), the relative amount of variance that did not change total force (*V _{UCM}*) was much larger than the amount of variance that did (

The qualitatively different time profiles of *V _{UCM}* and

To look for an answer to the question formulated at the end of the previous subsection, we accept a model of multi-finger variability suggested by Goodman et al. (2005). Force variability within this model originates from two sources. The first one is the parameters that are set at a control level, while the second one is the peripheral consequences of the control process such as actual force values. Within the model, two parameters are set before each trial, namely an amplitude parameter *β* and a timing parameter, *τ*. Instead of being set perfectly, these values are selected from distributions with some means and standard deviations. A consequence of this model is that the variance of the total force is linearly related to the force rate multiplied by a term containing the variance of *τ*, Var(*τ*). Since variance of the total force is defined by *V _{ORT}*, the model suggests a particular importance of Var(

If Var(*τ*) does not change across tasks, one could expect an increase in *V _{ORT}* with an increase in force rate independently of whether this increase is caused by an increase in the force amplitude or frequency. However, our results suggest that this is not true. Instead, Var(

Estimated value of the coefficient of variation of τ for (a) the index finger I and (b) the four finger combination IMRL, for the force increase and decrease half-cycles, averaged across subjects with standard error bars. For both conditions and **...**

If CV(*τ*) remained constant, then V_{ORT} would increase as the frequency increased. However, the reduction in CV(*τ*) led to a drop in *V _{ORT}* as compared to what could be expected if CV(

There is a natural relationship between action frequency and accuracy of its timing (reviewed in Ivry and Hazeltine 1995; Ivry and Richardson 2002), which is compatible with our conclusion on the drop in Var(τ) with an increase in the action frequency. It may be organized in this way to ensure comparable (predictable) accuracy in force production independently of the frequency of cyclic actions. However, it seems that the same rule does not apply to discrete tasks. In an earlier study of accurate force pulse production (Goodman et al. 2005), *V _{ORT}* scaled within a force pulse magnitude and the scaling increased with a drop in pulse time. This discrepancy may be viewed as an example of a discrete-cyclic control dichotomy in support of the recent hypotheses by Sternad and colleagues (Sternad and Dean 2003; Schaal et al. 2004; Hogan and Sternad 2007). Those authors presented arguments for differentiating between discrete and cyclic tasks based on their kinematic characteristics, such as the mean-squared-jerk (Hogan and Sternad 2007) and based on a fMRI study that has suggested the involvement of different brain circuitries in discrete and cyclic actions (Schaal et al. 2004).

The study was in part supported by NIH grants AG-018751, NS-035032, and AR-048563.

- Danion F, Schöner G, Latash ML, Li S, Scholz JP, Zatsiorsky VM. A mode hypothesis for finger interaction during multi-finger force-production tasks. Biol Cybern. 2003;88:91–98. [PubMed]
- Goodman SR, Latash ML. Feedforward control of a redundant motor system. Biol Cybern. 2006;95:271–280. [PubMed]
- Goodman SR, Shim JK, Zatsiorsky VM, Latash ML. Motor variability within a multi-effector system: Experimental and analytical studies of multi-finger production of quick force pulses. Exp Brain Res. 2005;163:75–85. [PMC free article] [PubMed]
- Hogan N, Sternad D. On rhythmic and discrete movements: reflections, definitions and implications for motor control. Exp Brain Res. 2007;181:13–30. [PubMed]
- Ivry RB, Hazeltine RE. Perception and production of temporal intervals across a range of durations: Evidence for a common timing mechanism. J Exp Psychol: Hum Percept Perform. 1995;21:3–18. [PubMed]
- Ivry RB, Richardson T. Temporal control and coordination: The multiple timer model. Brain Cognition. 2002;48:117–132. [PubMed]
- Latash ML, Scholz JF, Danion F, Schöner G. Structure of motor variability in marginally redundant multi-finger force production tasks. Exp Brain Res. 2001;141:153–165. [PubMed]
- Latash ML, Scholz JF, Danion F, Schöner G. Finger coordination during discrete and oscillatory force production tasks. Exp Brain Res. 2002a;146:412–432. [PubMed]
- Latash ML, Scholz JP, Schöner G. Motor control strategies revealed in the structure of motor variability. Exercise and Sport Science Reviews. 2002b;30:26–31. [PubMed]
- Latash ML, Scholz JP, Schöner G. Toward a new theory of motor synergies. Motor Control. 2007;11:275–307. [PubMed]
- Li ZM, Latash ML, Zatsiorsky VM. Force sharing among fingers as a model of the redundancy problem. Exp Brain Res. 1998;119:276–286. [PubMed]
- Newell KM, Carlton LG. Force variability in isometric responses. J Exp Psychol: Hum Percept Perform. 1988;14:37–44. [PubMed]
- Schaal S, Sternad D, Osu R, Kawato M. Rhythmic arm movement is not discrete. Nat Neurosci. 2004;7:1136–1143. [PubMed]
- Scholz JP, Danion F, Latash ML, Schöner G. Understanding finger coordination through analysis of the structure of force variability. Biol Cybern. 2002;86:29–39. [PubMed]
- Scholz JP, Schöner G. The uncontrolled manifold concept: Identifying control variables for a functional task. Exp Brain Res. 1999;126:289–306. [PubMed]
- Shapkova E Yu, Shapkova AL, Goodman SR, Zatsiorsky VM, Latash ML. Do synergies decrease force variability? A study of single-finger and multi-finger force production. Exp Brain Res. 2008;188:411–425. [PMC free article] [PubMed]
- Shim JK, Lay B, Zatsiorsky VM, Latash ML. Age-related changes in finger coordination in static prehension tasks. J Appl Physiol. 2004;97:213–224. [PMC free article] [PubMed]
- Sternad D, Dean WJ. Rhythmic and discrete elements in multi-joint coordination. Brain Res. 2003;989:152–171. [PubMed]
- Yu H, Russell DM, Sternad D. Task-effector asymmetries in a rhythmic continuation task. J Exp Psychol: Hum Percept Perform. 2003;29:616–630. [PubMed]
- Zatsiorsky VM, Li ZM, Latash ML. Coordinated force production in multi-finger tasks: Finger interaction and neural network modeling. Biol Cybern. 1998;79:139–150. [PubMed]
- Zatsiorsky VM, Li ZM, Latash ML. Enslaving effects in multi-finger force production. Exp Brain Res. 2000;131:187–195. [PubMed]

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