Finger synergies during multi-finger cyclic production of moment of force

Abstract

We investigated multi-finger synergies stabilizing the total moment of force and the total force when the subjects produced a quick cyclic change in the total moment of force. The seated subjects performed the task with the fingers of the dominant arm while paced by the metronome at 1.33 Hz. They were required to produce a rhythmic, sine-like change in the total pronation–supination moment of force computed with respect to the midpoint between the middle and ring fingers. The framework of the uncontrolled manifold hypothesis was used to compute indices of stabilization of the total moment and of the total force across 20 cycles. Variance of the total moment showed a cyclic pattern with peaks close to the peak rate of the moment change. Variance of the total force was maximal close to peak moment into supination. Higher magnitudes of the moment directed against the required moment direction (antagonist moment) were produced by individual fingers during supination efforts as compared to pronation efforts. Indices of multi-finger synergies showed across-trials stabilization of the total moment over the whole cycle but not of the total force. These indices were smaller during supination efforts. We conclude that the central nervous system facilitates multi-finger synergies stabilizing the total rotational action across a variety of tasks. Synergies stabilizing the total force are not seen in tasks that do not explicitly require accurate force control. Pronation efforts are performed more efficiently and with better stabilization of the action.

Introduction

A series of recent studies investigated multi-finger synergies in a variety of isometric tasks that required the production of certain total force patterns (Latash et al. 2001, 2002a, b, c; Scholz et al. 2002). These studies used the framework of the uncontrolled manifold (UCM) hypothesis (Scholz and Schoner 1999). According to the UCM hypothesis, when the central nervous system (CNS) faces a task of producing an action with a mechanically redundant system, it does not select a single, optimal solution but facilitates families of solutions that are equally capable of solving the task (the principle of abundance, Gelfand and Latash 1998, 2002). To do this, the CNS organizes a subspace (a UCM) in the space of elemental variables (those describing outputs of the elements of the redundant system) such that all the points in that subspace correspond to a desired value of an important performance variable. Further, the controller allows relatively large variability within the UCM but not orthogonal to the UCM.

When a person is required to produce a certain time profile of the total force while pressing with several fingers of a hand on force sensors, finger forces and commands to fingers (finger modes, Latash et al. 2001; Danion et al. 2003) show co-variation across repetitive trials. Analysis of the co-variation has shown that the subjects predominantly stabilize not the instructed variable (total force) but the total moment of force produced by the fingers about the longitudinal axis of the forearm/hand (further addressed as simply “moment” for brevity), although they were not instructed to do so and were given no feedback on the moment magnitude (Latash et al. 2001, 2002b, c). This result has led to a hypothesis that moment stabilization is a default conditioned by everyday experience with hand actions that typically impose more strict constraints on errors in the rotational hand action than in its gripping action (consider drinking from a glass).

In a recent study, we investigated multi-finger synergies during the production of an accurate slow time profile of the total moment of force following a template shown on the screen (Zhang et al. 2006). In that study, multi-finger synergies stabilized the total moment, but not the total force. Performance of this task, however, was accompanied by a gradual increase in the total force over the duration of each trial. This apparently non-stationary behavior could by itself influence the results, in particular prevent total force stabilization. Besides, the slowness of the task and the presence of the template might have contributed to the observed synergies stabilizing the total moment of force.

In the current study, we investigated multi-digit synergies when the subjects produced a cyclic, sine-like time profile of the total moment. We expected this process to be stationary and not to lead to a drift in the total force. There was no explicit template, and the rate of moment production was relatively high, comparable to those used in earlier studies with cyclic total force production (Scholz et al. 2002). Note that an increase in the rate of production of a performance variable may by itself lead to apparently weaker synergies stabilizing that variable (Goodman et al. 2005). Nevertheless, our primary hypothesis was that the subjects would be able to show multi-finger synergies stabilizing the total moment of force over the whole cycle. Besides, we expected the stationary nature of the task to contribute to total force stabilization in parallel to total moment stabilization. We also explored the ability of humans to stabilize the moment of force during pro-nation and supination efforts. Several recent studies have provided conflicting evidence regarding possible differences in the ability of healthy young adults to produce such efforts (Shim et al. 2004b).

The pressing task used in the current study may be viewed as reflecting control processes at one of the two hypothetical levels involved in hand action. The two levels are: (1) Distributing the task between the thumb and the “virtual finger” (VF, an imagined finger whose mechanical action is equivalent to the combined action of a set of actual fingers); and (2) distributing the action of the VF among actual fingers (Arbib et al. 1985; MacKenzie and Iberall 1994). A series of earlier studies of prehensile tasks with a rotational components have addressed synergies at the thumb-VF level (Shim et al. 2003, 2005; Zatsiorsky et al. 2003; reviewed in Zatsiorsky and Latash 2004). Our current study addresses synergies involved in rotational action of the VF at the lower level of the hierarchy that does not involve the thumb.

Methods

Subjects

Twelve healthy volunteers (26.4 ± 2.9 years old, six males and six females) participated in the experiments. The weight of the subjects averaged 69.5 ± 16.6 kg, and their height was 1.719 ± 0.095 m. All the subjects were right-handed according to their preferred hand use for writing and eating. The right hand width (measured at the metacarpophalangeal joint level) averaged 0.084 ± 0.009 m, and the right hand length (measured from the midpoint of the transverse wrist crease to the tip of the middle finger) was 0.187 ± 0.015 m. All subjects gave informed consent according to the procedures approved by the Office for Research Protection of the Pennsylvania State University.

Apparatus

The experimental setup is illustrated in Fig. 1, panel b. Four unidirectional piezoelectric force sensors (model 208C02; Piezotronic Inc.) with the diameter of 0.015 m were used to measure forces produced by each of the four fingers of the right hand. Each sensor was mounted on an aluminum post and covered with a cotton pad to increase friction and prevent the influence of finger skin temperature on the measurements. The sensors were placed within an aluminum frame (0.065 m × 0.12 m inner size) placed inside a groove made on a wooden board to assure the stable position of the sensors. The sensors were medio-laterally distributed 0.03 m apart within the frame. The position of the sensors within the frame could be adjusted in the forward–backward direction to fit the individual subject’s anatomy. Analog output signals from the sensors were processed by separate AC/DC conditioners (M482M66, Piezotronic Inc.) with the ±1% error range over the typical epoch of recording of a constant signal. The force measured by each sensor was sampled at 200 Hz, with the 12-bit resolution by a desktop Gateway IBM-compatible computer. The sensors were calibrated 30 min before each testing.

Fig. 1.

a The experimental set-up showing the main tasks: F-MVC, F-Ramp, and M-Cyclic. b The subject and hand positions. The hand position, sensor arrangement and the frame are shown in the right panel. Moment arms with respect to the hand midline were 45 mm for the index and little fingers, and 15 mm for the middle and ring fingers

During testing, the subject sat comfortably in a chair facing the testing table with his/her right upper arm at approximately 45° of abduction in the frontal plane and 45° of flexion in the sagittal plane, the elbow at approximately 45° of flexion (full extension corresponds to 0°). The wooden horizontal board supported the wrist and the forearm; two pairs of Velcro straps were used to prevent forearm or hand motion during the tests. A custom-fitted wooden piece was placed underneath the subject’s right palm to help maintain a constant configuration of the hand and fingers. One more pair of Velcro straps ensured that the wooden piece was stable with respect to the board. A 17″ LCD monitor was placed approximately 0.65 m in front of the subject. It displayed the actual total moment of force in pronation/supination (PR/SU) produced by the normal finger forces with respect to the midpoint between the middle and ring fingers (effort into PR was considered positive, and effort into SU was considered negative).

Procedure

There were two control force production tasks and one main experimental task (Fig. 1, panel a). The first control task required the subjects to produce maximal pressing force by fingers (maximal voluntary contraction, MVC). MVC tests were performed with each individual finger of the right hand separately (I-index, M-middle, R-ring, L-little) and with all four fingers acting together (IMRL). During MVC tests, a sound signal generated by the computer informed the subject to get ready. Then a trace showing the total force produced by the explicitly involved finger(s) (master fingers) started to move across the screen. The subjects were asked to produce peak force within a 2-s time window shown on the screen and then to relax. In one-finger MVC trials, the subjects were instructed to pay no attention to possible force generation by other, explicitly non-involved fingers, as long as the master finger produced maximal force. The subjects were not allowed to lift fingers off the sensors at any time. For each MVC task, two trials were performed with 30-s intervals between the trials, and the data for the trial with the highest force of the instructed finger(s) were used for further analysis.

The second force production task required the subject to follow a thick blue template line shown on the screen with the cursor showing the current value of the force produced by the instructed finger. One trial was performed by each finger after two practice trials. The template line was a combination of straight line segments: a horizontal segment corresponded to zero force for the first 2 s; it was followed by an oblique line going up to 10% of the participant’s individual MVC in the four-finger test over 4 s, then, another horizontal line corresponded to this constant force level for 2 more seconds. These data were used to compute the enslaving matrix for the uncontrolled manifold analysis (described later).

The main task required the subjects to produce a cyclic time profile of the total PR/SU moment of force (M_TOT) computed on-line using force sensor signals as:

$$M_{\text{TOT}}=d_{\text{I}}{F}_{\text{I}}+d_{\text{M}}{F}_{\text{M}}-d_{\text{R}}{F}_{\text{R}}-d_{\text{L}}{F}_{\text{L}},$$ (1)

where d_i and F_i stand for the force and the lever arm for finger i, respectively (i = I, M, R, and L). The lever arms were measured with respect to the mid-point between the M and R fingers such that d_I = d_L = 0.045 m, d_M = d_R = 0.015 m. This approximation assumes no changes in the points of force application on the sensor surfaces in the medio-lateral direction.

In the main task (the cyclic task, Fig. 1a), the subjects started with resting their fingers naturally on the sensors during the first 3 s, and then produced a rhythmic sine-wave of M_TOT switching between PR and SU while being paced by the metronome. The frequency of the metronome was always 1.33 Hz; this frequency was selected as the most comfortable based on pilot trials with several subjects. A thick vertical yellow line shown on the screen indicating the end of the 3-s rest period, and two thick blue horizontal lines indicated the target peak values on M_TOT into PR and SU; thin horizontal lines showed the permissible margin of error. The target amplitude was set for each subject at 10 ± 3% of the product of the maximal force produced by the index finger in the MVC_I task by the lever arm of this finger (d_I = 0.045 m) into PR. Five trials were recorded after five practice trials, and each trial lasted 12 s. The intervals between the trials were 8 s. The intervals between the tasks were at least 1 min. On average, the subjects completed about 10 cycles in each trial. However, the first and the last cycles were typically incomplete and rejected. Therefore, about 8 complete cycles per trial were available for further analysis.

Initial data processing

Data processing was performed off-line using MAT-LAB 7.0, Excel, and Minitab software. In the MVC tests, peak forces were measured at the time when the force produced by the instructed finger(s) reached its peak. For the main task, moments of force produced by each individual finger (M_I, M_M, M_R, and M_L) were computed as the products of the finger’s force and its moment arm (d_i, where i = I, M, R, and L). The sine-wave of M_TOT was viewed as a sequence of cycles with each cycle starting with a SU peak, continuing with a PR peak point in the middle of the cycle, and ending with the next SU peak as the end of the cycle. Hence, in analysis, we defined two half-cycles, from SU peak to PR peak (SU–PR half-cycle) and from PR peak to SU peak (PR–SU half-cycle). All individual half-cycles with overshoots or undershoots beyond the error margin were rejected. We also rejected individual half-cycles with extra peaks of M_TOT between two metronome beats. Based on these criteria, the number of rejected trials was, on average, 26%. Forty individual half-cycles (20 SU–PR and 20 PR–SU, about 54% of the accepted data) were selected for further analysis from those that passed the rejection criteria from each subject’s data set.

Since individual half-cycle could be of different duration, and subjects had different target magnitudes based on his/her MVC performance, mechanical variables were normalized by time and amplitude. For time normalization, (1) each individual half-cycle was considered to be of 100% duration, (2) the data were interpolated to obtain points for every 1% of the half-cycle duration; thus each interpolated data set of each half-cycle included 101 points. For amplitude normalization, the moment of force was normalized by each subject’s target peak moment, (0.1 × MVC_I × 0.045) N m. The finger forces were normalized by 0.1 × MVC_I N. Variance of moment/force was normalized by [(0.1 × MVC_I × 0.045) N m]² and (0.1 × MVC_I N)², respectively. Using normalized data, average time profiles of force, moment of force, and variance were computed across the accepted 20 SU–PR/PR–SU half-cycles for each subject separately.

Agonist and antagonist moment of force

The way the moment production task was set, two pairs of fingers (IM and RL) acted as opponents since IM always produced moment of force into PR and RL always produced moment of force into SU. This means that at each phase of the cycle, one of the finger pairs produced moment of force against the required direction. We computed Agonist moment (M_AG) as the moment produced to meet the moment production task requirement and Antagonist moment (M_ANT) as the moment produced in the direction opposite to the required moment. When the subjects were required to produce the total moment into PR, moments generated by the IM forces added up to M_AG, while moments generated by the RL forces produced M_ANT. The role of the two finger pairs switched when the subjects had to produce the total moment into SU, IM produced M_ANT, while RL produced M_AG.

UCM analysis

The analysis was performed in the framework of the UCM hypothesis (Scholz and Schöner 1999; reviewed in Latash et al. 2002c). The hypothesis assumes that the controller organizes co-variation among elemental variables to stabilize a certain value of a performance variable (F_TOT or M_TOT in our study). Individual finger forces co-vary in a non-task-specific fashion because of the phenomenon of enslaving, i.e., unintended force production by fingers when other fingers of the hand produce force (Li et al. 1998; Zatsiorsky et al. 2000). Hence, the first step was to convert the data sets from time series of finger forces to time series of elemental variables, force modes that can be, at least hypothetically, modified by the controller one at a time.

Force modes were defined similarly to the previous studies (Latash et al. 2001; Scholz et al. 2002). Briefly, single-finger force ramp trials were used to compute the enslaving matrix E for each subject. The entries of the E matrix were computed as the ratios of the change in the force of each finger to the change in the total force over the ramp duration. The E matrix was used to compute changes in the vector of hypothetical independent commands to fingers (force modes, m) based on finger force changes.

Further analysis was done for each subject as follows:

After time normalization, for each 1% time sample, t_i, in each half-cycle the average vector of force modes, m_AV was computed. Then, for each half-cycle j, the deviation (Δm_j) between m_j and m_AV was computed. Variance of the Δm_j data set was then computed along a direction orthogonal to the UCM computed for the average value of F_TOT at that time slice (force-stabilization hypothesis) and for the average value of M_TOT (moment-stabilization hypothesis). We will refer to these indices as V_ORT-F and V_ORT-M, respectively. This was done using the Raleigh fraction:

$$V_{\text{ORT}}=\frac{{\mathbf{J}}_{m}cov(\mathbf{m}){\mathbf{J}}_{\text{m}}^{\text{T}}}{{\mathbf{J}}_m{\mathbf{J}}_m^{\text{T}}}=\frac{\mathbf{J}{\mathbf{E}}^{-1\text{T}}{\mathbf{E}}^{-1}cov(\mathbf{f}){\mathbf{E}}^{-1\text{T}}{\mathbf{E}}^{-1}{\mathbf{J}}^{\text{T}}}{\mathbf{J}{\mathbf{E}}^{-1\text{T}}{\mathbf{E}}^{-1}{\mathbf{J}}^{\text{T}}},$$ (2)

where J is a Jacobian matrix relating small changes in modes (J_m) or forces (J) to changes in the selected performance variable, total force or total moment, cov(m) is the covariance matrix in the mode space for the demeaned sets of vector m, cov(f) is the covariance matrix in the finger force space for the demeaned sets of vector f, and T is the sign of transpose. For force-stabilization hypothesis, J = [1, 1, 1, 1], while for moment-stabilization hypothesis, J = [d_I, d_M, −d_R, −d_L], see Eq. 1. Note that Js are written as vector-rows. J_m can be computed as: J_m = JE^−1T, where E^−1T is the transpose of the E inverse.

V_ORT reflects the amount of mode variance in the data set that corresponds to a change in the selected performance variable. The difference between the total amount of variance (V_TOT) and V_ORT corresponds to variance that does not affect the average value of the performance variable. We will address this variance as V_UCM (variance within the uncontrolled manifold): V_UCM = V_TOT − V_ORT. Note that the finger mode space is four-dimensional, V_ORT lies along a one-dimensional sub-space, while V_UCM lies in a three-dimensional sub-space. Therefore, to compare the amounts of variance per dimension, the following index was used:

$$\mathrm{\Delta }V=\frac{(V_{\text{UCM}}/3-V_{\text{ORT}})}{V_{\text{TOT}}/4}.$$ (3)

Normalization by the total amount of variance per dimension (V_TOT/4) was used to compare the data across subjects who could show different amounts of the total variance. Note that positive values of ΔV correspond to proportionally higher V_UCM than V_ORT. Hence, values ΔV > 0 may be interpreted as a reflection of a multi-mode synergy stabilizing that performance variable. If ΔV = 0, this means that the amount of variance per dimension is the same in directions that correspond to a change in the selected performance variable and those along directions that keep the variable unchanged. ΔV < 0 may be interpreted as covariation among changes in finger modes contributing to a change in the selected performance variable or destabilizing it (cf. Bienaymé equality theorem, Loève 1977).

Statistical analysis

Standard methods of parametric statistics were used. Each half-cycle was divided into four equal phase-intervals: Δφ₁, Δφ₂, Δφ₃, and Δφ₄ (See Fig. 2). The four intervals were chosen based on pilot data analysis as an optimal approach that allows to both explore within-a-cycle differences and keep the number of levels of this factor reasonably low. Mixed-effects analysis of variance (ANOVA) was used with factors: half-cycle (SU–PR vs. PR–SU, two levels), phase-interval (Δφ₁, Δφ₂, Δφ₃, and Δφ₄, four levels), index (ΔV_F vs. ΔV_M, two levels), and subject (12 levels). Tukey’s honest significant difference tests and pair-wise contrasts were used to further analyze significant effects. Data expressed in percent were subjected to z-transformation before using parametric methods of analysis.

Fig. 2.

Total moment of finger forces (M_TOT, thick solid lines) and total finger force (F_TOT, thin dashed lines) averaged across 12 subjects with standard error bars in the SU–PR half-cycle (left panel) and PR–SU half-cycle (right panel). M_TOT was normalized by each subject’s target peak moment (0.1 × MVC_I × 0.045 N m), and F_TOT was normalized by 0.1 × MVC_I N. The time axis indicates phase (one half-cycle duration equals 100%). Dashed vertical lines show four phase-intervals, Δφ₁, Δφ₂, Δφ₃, and Δφ₄ within each half-cycle

Results

General patterns of the total force and total moment

All the subjects were able to follow the rhythm specified by the metronome and change their total moment of force (M_TOT) such that it oscillated between the PR and SU target levels within the specified error margin after one or two cycles. For both SU–PR and PR–SU half-cycles, subjects reached relatively constant levels of peak SU and PR M_TOT, which was, on average, 0.2 ± 0.1 N m. Their average total force (F_TOT) was somewhat higher when they reached the SU peak of M_TOT than when they reached the PR peak of M_TOT, 13.4 ± 4.8 and 11.9 ± 4.6 N, respectively.

Figure 2 shows the time profiles of the total moment (M_TOT, thick solid line with standard error bars, left Y-axes) and of the total force (F_TOT, thin solid line with standard error bars, right Y-axes) averaged across 20 half-cycles each and further across subjects. Time axis indicates phase (one half-cycle equals 100%). Both M_TOT and F_TOT were normalized by time and amplitude, as described in the Methods; the error bars show standard errors across subjects. The total force showed a cyclic change with higher values observed close to peak SU M_TOT (Fig. 2). This pattern was confirmed by a three-way ANOVA, half-cycle (SU–PR vs. PR–SU) × phase-interval (Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject. There was a main effect of phase-interval [F_(3,77) = 10.3; P < 0.001]. Post-hoc Tukey’s tests indicate that F_TOT at Δφ₁ was significantly higher than at the other three phase-intervals (Δφ₂, Δφ₃, and Δφ₄) (P < 0.005). There were no other significant effects.

Patterns of force and moment variability

Variance time profiles of M_TOT (V_M) and of F_TOT (V_F) were computed across 20 SU–PR/PR–SU half-cycles at each 1% of the normalized time and for each subject. V_M was strongly modulated within a half-cycle with a peak in the middle of each half-cycle, about the time when the rate of M_TOT (dM/dt) was the highest, V_F showed no obvious modulation.

Figure 3 presents V_F (panels a, b) and V_M (panels c, d) time series averaged across the 12 subjects with standard error bars. The abscissa axis shows the phase in percent. Both V_F and V_M were normalized as described in the Methods. Panels a and c present V_M and V_F for the SU–PR half-cycle, and panels b and d present V_M and V_F for the PR–SU half-cycle.

Fig. 3.

Time profiles of the variance (V_M) of the total moment (panels a, b) and the variance (V_F) of the total force (panels c, d) computed across 20 SU–PR/PR–SU half-cycles and further averaged across subjects with standard error bars. V_M and V_F for the SU–PR half-cycle are displayed in panels a and c, and those of PR–SU half-cycle are displayed in panels b and d. V_M and V_F were normalized by (0.1 × MVC_I × 0.045 N m)² and (0.1 × MVC_I N)², respectively. The time axis shows normalized phase (one half-cycle equals 100%)

The peak value of V_M was on average 0.0025 and 0.0021 N² m² in the SU–PR and PR–SU half-cycles respectively, while its average value, observed when M_TOT approached its peaks, was 0.001 N² m² in both half-cycles. These results were confirmed by a three-way ANOVA of V_M, half-cycle (SU–PR vs. PR–SU) × phase-interval Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject. There was a main effect of phase-interval [F_(3,77) = 14.93; P < 0.001]. Post-hoc Tukey’s tests indicate that V_M at both Δφ₂ and Δφ₃, the two phase-intervals when M_TOT approached zero, were significantly higher than at the other two phase-intervals (Δφ₁ and Δφ₄) (P<0.005). There were no other significant effects.

In contrast, V_F shows a more monotonic pattern during each half-cycle. On average, V_F decreased from 10.2 ± 11.9 to 6.7 ± 5.2, when M_TOT into SU peaks changed into PR peaks. Note that in panels c and d of Fig. 3, the Y-axis shows normalized V_F (see the Methods). This V_F pattern has been confirmed by a three-way ANOVA, half-cycle (SU–PR vs. PR–SU) × phase-interval Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject. Phase-interval showed a main effect, F_(3,77) = 2.79; P < 0.05. The post-hoc Tukey’s tests confirmed that V_F at Δφ₁ when the moment was close to its peak value into SU was significantly higher than at Δφ₄ when the moment approached its PR peaks (P < 0.05).

To investigate the relation between V_M and dM/dt, we also evaluated the cross-correlation function between V_M and dM/dt as follows: (1) For each subject, dM/dt was computed for each half-cycle and then averaged over 20 SU–PR/PR–SU half-cycles; (2) The correlation function was computed for each subject separately between V_M computed across the half-cycles and the averaged dM/dt; (3) The average peak correlation coefficient (R_PEAK) and the average time lag (Δt) of R_PEAK were computed across subjects; and (4) z-transformation was run on R_PEAK values before across-subjects analysis. The average R_PEAK was 0.84 (z-score = 2.57 ± 0.58) and the average Δt was 1.67% for the SU–PR half-cycle; the averaged R_PEAK was 0.62 (z-score = 1.48 ± 3.33) and the averaged Δt was 8.75% for the PR–SU half-cycle.

Agonist and antagonist moments

This part of analysis addressed the apparently detrimental moment of force production by pairs of fingers that acted against the required direction of M_TOT. Assuming the midpoint of each half-cycle as the M_TOT transition point from PR to SU and from SU to PR, M_AG and M_ANT were computed for each half-cycle and for each subject. Then M_AG and M_ANT were averaged across the 20 SU–PR/PR–SU half-cycles for each subject separately and further averaged across the 12 subjects at each 1% of the phase. Finally, these data were analyzed over each phase-interval. The phase profiles of averaged M_AG (stripe bars) and M_ANT (checked bars) with standard error bars (across subjects) are shown in Fig. 4. The amplitudes of M_AG and M_ANT were normalized as described in the Methods.

Fig. 4.

Time profiles of the agonist moment (M_AG, the striped bars) and antagonist moment (M_ANT, the checked bars) averaged over each phase-interval (Δφ₁, Δφ₂, Δφ₃, and Δφ₄) and further across subjects (with standard error bars). Both M_AG and M_ANT were normalized by the target peak moment (0.1 × MVC_I × 0.045 N m). The dashed vertical line indicates the SU–PR (left panel) and PR–SU (right panel) half-cycles. The time axis shows normalized phase (one half-cycle equals 100%)

For both SU–PR and PR–SU half-cycles, an increase in the magnitude of M_TOT was always accompanied by a drop in M_ANT. This drop was, on average, over 28%. This observation has been confirmed by a two-way phase-interval (Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject ANOVA on M_ANT. There was a main effect of phase-interval [F_(3,81) = 14.46; P < 0.001]. The post-hoc Tukey’s tests confirmed that M_ANT increased when the total moment approached zero: there were significant differences between M_ANT at Δφ₁ and Δφ₂/Δφ₃, and also between Δφ₄ and Δφ₂/Δφ₃ (P < 0.001).

Moment production by individual fingers

Earlier studies have suggested the mechanical advantage hypothesis (Buchanan et al. 1989; Prilutsky 2000; Zatsiorsky et al. 2002; Shim et al. 2004a), which states that effectors (muscles or digits) with longer lever arms contribute more to the total rotational action as compared to effectors with shorter lever arms. In our study, two fingers (I and M) produced PR moments (M_PR) while two other fingers (R and L) produced SU moments (M_SU). Note that I and L finger forces had moment arms that were three times longer than those for M and R fingers and, therefore, I and L fingers could be expected to produce over 50% of the total moment into PR and SU, respectively.

To test this hypothesis, we computed the percentage of the PR moment produced by I finger (M_I_PR) and the percentage of SU moment produced by the L finger (M_L_SU) in both SU–PR and PR–SU half-cycles. M_I_PR and M_L_SU were averaged over each phase interval and then further averaged across subjects. Figure 5 shows the averages with standard error bars. Over the whole cycle, both M_I_PR and M_L_SU contributed more than 50% of the M_PR and M_SU, respectively.

Fig. 5.

Average percentage contribution of the index finger force to the total PR moment (M_I_PR, upper panel, checked bars) and of the little finger force to the total SU moment (M_L_SU, bottom panel, striped bars) averaged over each phase-interval and over the 12 subjects (with standard error bars). Note that the index finger acted as an antagonist when M_TOT was into SU, and it acted as an agonist when M_TOT was into PR. The time axis shows normalized phase (one half-cycle equals 100%)

Note that when the task required PR (SU) moment generation, I and M fingers produced M_AG (M_ANT) while R and L fingers produced M_ANT (M_AG). Figure 5 shows that M_I_PR monotonically increased in both half-cycles when the task required a change in M_TOT from SU to PR, and the I finger contribution to PR moment was particularly high when I finger acted as agonist finger (M_TOT close to PR peaks). This pattern was confirmed by a three-way, half-cycle (SU–PR vs. PR–SU) × phase-interval Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject, ANOVA on M_I_PR. Prior to running this analysis, M_I_PR values were converted into z-scores. There was a main effect of phase-interval for M_I_PR [F_(3,77) = 176.86, P < 0.001]. The post-hoc Tukey’s test indicated a significant difference between each pair of phase-interval (P < 0.001). M_I_PR was significantly higher over the phase-intervals when I finger produced M_AG (Δφ₃ and Δφ₄) than when it produced M_ANT (Δφ₁ and Δφ₂). Besides, there was also a main effect of half-cycle [F_(1,77) = 11.29, P < 0.005], which reflected significantly higher M_I_PR over the SU–PR half-cycle than over the PR–SU half-cycle (P<0.005).

In contrast, the profile for M_L_SU was flat. The contribution of L finger was constant (about 75%) whenever L finger acted as an agonist finger or as an antagonist finger. This observation was confirmed by a one-way of phase-interval ANOVA on M_L_SU [F_(3,11) = 0.04, P > 0.9].

Uncontrolled manifold analysis

To remind (see the Methods), this analysis quantified two components of the total variance, V_UCM and V_ORT, in the space of hypothetical command signals to fingers (finger modes). The V_UCM component reflects co-varied changes in signals to fingers across trials that keep an average value of a performance variable, either total force or total moment, constant. The V_ORT component reflects variations in signals to fingers that change the performance variable. We performed analysis with respect to two performance variables, F_TOT and M_TOT at each percentage of normalized time samples. A normalized index (ΔV) (Figs. 6, 7, panels c, d) of the difference between V_UCM and V_ORT was computed in such a way that its positive values could be interpreted as multi-finger synergies stabilizing that particular performance variable.

Fig. 6.

Time profiles of two components of the total variance of M_TOT, V_UCM (thick solid lines) and V_ORT (thin dashed lines), in the SU–PR (a) and PR–SU (b) half-cycles. Time profiles of ΔV_M for the SU–PR (c) and PR–SU (d) half-cycles. Note that ΔV_M was always positive. The time axis shows normalized phase (one half-cycle = 100%). Standard errors across subjects are shown

Fig. 7.

Time profiles of V_UCM (thick solid lines) and V_ORT (thin dashed lines), in the SU–PR (a) and PR–SU (b) half-cycles. Time profiles of ΔV_F in the SU–PR (c) and PR–SU (d) half-cycle. Averaged across subjects data are shown with standard error bars. Time axis indicates phase (one half-cycle equals 100%). Note the negative ΔV_F values over both half-cycles

Figures 6 and 7 illustrate the indices of variance, V_UCM, V_ORT, and ΔV for M_TOT and F_TOT, respectively, averaged across all the subjects with standard error bars. In the top panels, the thick solid line shows V_UCM, and the thin solid line refers to V_ORT. Panel a corresponds to the SU–PR half-cycle and panel b corresponds to the PR–SU half-cycle. Panels c and d show ΔV data for the two half-cycles, respectively.

The subjects were able to stabilize the time profile of the total moment by co-varied changes of commands to individual fingers as reflected by positive ΔV_M values over both half-cycles (Fig. 6, panels c, d). In contrast, the index of total force stabilization, ΔV_F stayed negative over both half-cycles (Fig. 7, panels c, d). Both ΔV_F and ΔV_M indices increased when M_TOT approached high PR values and decreased with M_TOT approached high SU values. Note the higher V_ORT values for both M_TOT and F_TOT when M_TOT approached its peak SU value as compared to the values when M_TOT approached its peak PR value. These changes are to a large degree responsible for the modulation of ΔV within the half-cycles.

For statistical analysis, we used a four-way index (ΔV_F vs. ΔV_M) × half-cycle (SU–PR vs. PR–SU) × phase-interval (Δφ₁, Δφ₂, Δφ₃, and Δφ₄) × subject ANOVA on ΔV. There was a main effect of phase-interval, F_(3,168) = 4.09, P < 0.01. The post-hoc Tukey’s test confirmed that both ΔV indices over the phase-interval when M_TOT was close to PR peaks (Δφ₄) were significantly higher than when M_TOT was close to SU peaks (Δφ₁) (P < 0.05). Besides, there was also a main effect of index [F_(1,168) = 98.11, P < 0.001] reflecting the significantly higher ΔV_M as compared to ΔV_F.

Discussion

The study has produced both expected and unexpected results. Our main hypothesis has been confirmed: there were multi-finger synergies stabilizing the time profile of the total moment of force as reflected by the positive values of the ΔV index throughout both half-cycles of moment production. As such, these findings corroborate the earlier reports on moment stabilization in both force and moment production tasks (Latash et al. 2001, 2004; Scholz et al. 2002; Zhang et al. 2006). Our second hypothesis has, however, been refuted: the total force produced by the fingers was not stabilized. Actually, commands to fingers (finger modes) showed predominantly positive co-variation across trials that could be viewed as contributing to total force variability. In earlier studies, such patterns of finger force co-variation were referred to as “the fork strategy”, that is using the fingers as the prongs of a fork rather than exploiting the flexibility of the hand design (Latash et al. 2002a; Scholz et al. 2003). We have also observed substantial differences in finger coordination during the production of PR and SU moments of force. Further, we discuss implications of these results for the control of the rotational hand action.

Multi-finger synergies stabilizing rotational hand action

Most studies of finger interaction have focused on the production of adequate gripping force (Johansson and Westling 1984; Flanagan and Wing 1995; Burstedt et al. 1999; Santello and Soechting 2000; Nowak and Hermsdorfer 2005). Only a handful of studies explicitly addressed the rotational action by the hand (e.g., Johansson et al. 1999; Latash et al. 2004). In particular, studies of finger force co-variation across static tasks withholding an object have suggested that the control of the hand action can be represented as a superposition of two processes, the control of the gripping action and the control of the rotational action (Shim et al. 2003, 2004a, 2005; Zatsiorsky and Latash 2004; Zatsiorsky et al. 2004). As such, hand control seems to obey the principle of superposition introduced in robotics (Arimoto et al. 2000, 2001); according to this principle, some complex tasks performed by a set of effectors may be more efficiently controlled if they are decomposed into sub-tasks that have their own controllers with no interference with each other. In all those studies, however, the production of a particular moment of force was an implicit task component, and the magnitude of the moment was not changed during the trial.

To our knowledge, the current study is only the second that analyzed multi-finger synergies when the subjects are required explicitly to produce a particular time profile of the total moment. The first study (Zhang et al. 2006) has shown that when the subjects are asked to follow a template with the signal corresponding to the total moment of force, they show multi-finger synergies stabilizing the total moment across trials but not synergies stabilizing the total force. That study could be criticized, in particular because over the trial duration, all the subjects showed a steady increase in the total force suggesting that, with respect to force production, the process was non-stationary.

We overcame those shortcomings in the current study. The moment-stabilizing synergies were very similar across the two experiments, while the index of force stabilization (ΔV_F) dropped into more negative values in the current study. We can conclude that in pressing tasks, there are no synergies stabilizing the total force unless this is explicitly required by the task. In contrast, synergies stabilizing the rotational action are present in tasks that explicitly require the production of a time profile of the total moment of force as well as in tasks that require the production of a time profile of the total force (cf. Latash et al. 2002a, b; Scholz et al. 2002). The observation of task-specific independent modulation of the indices of moment-stabilizing and force-stabilizing synergies based on the same set of elemental variables may be viewed as supporting the principle of superposition.

As mentioned in the Introduction, our current study addresses multi-finger synergies at the lower level of a hypothetical control hierarchy (Arbib et al. 1985; MacKenzie and Iberall 1994) involved in hand actions. The task we used in the study can be criticized as artificial, in particular because it did not involve the thumb. Most everyday manipulation tasks involve the thumb, which may affect interactions among the fingers. For example, an earlier study has shown that indices of finger inter-dependence show substantial quantitative changes across conditions that involve and do not involve the thumb (Olafdottir et al. 2005). Although that study did not quantify indices of multi-finger synergies, its findings suggest that such synergies may be modified by thumb involvement. Hence, our current data will have to be confirmed in more natural tasks involving the thumb.

Rotational efforts into pronation and supination

Reports on differences in the production of maximal torques in PR and SU have been inconsistent (Timm et al. 1993; Gallagher et al. 1997; Shim et al. 2004b; Matsuoka et al. 2006). To be safe, the magnitude of the target peak moment of force in our study was purposefully set at a relatively low value to both avoid fatigue and make sure that it was easy for the subjects to produce the required range of the moment magnitudes in both PR and SU. Nevertheless, we observed substantial differences in several indices of finger interaction during the production of PR and SU moments of force.

The subjects produced significantly higher moments of force by fingers acting against the required moment direction during SU efforts. Such excessive antagonist moment production may be viewed as a sign of worse finger coordination; higher antagonist moments during maximal moment production tasks were reported for elderly subjects as compared to younger subjects (Shim et al. 2004b). This excessive antagonist moment production was accompanied by higher total forces produced in SU phases of the main task and higher indices of force variability (possibly related to the well known relation between force and force variability; reviewed in Newell 1991).

Worse control of moments of force into SU has also been supported by indices of both moment- and force-stabilizing synergies (ΔV_M and ΔV_F) that were significantly lower during SU efforts than during PR efforts. In other words, the subjects showed weaker moment-stabilizing synergies during SU efforts, while finger mode co-variation showed stronger total force destabilization.

These results may partly reflect the differences in the degree of individuation of the human fingers. In particular, unintended force production (enslaving) is the smallest in the index finger and higher in the ring and little fingers (Li et al. 1998; Zatsiorsky et al. 2000; Lang and Schieber 2004). Note, however, that enslaving effects were taken into account in our analysis of multi-finger synergies that used not finger forces but finger modes as elemental variables.

More flexible control of the IM finger pair has also been reflected in our analysis of the percentage of the total moment into PR and SU generated by the fingers with the longer moment arms (I and L). According to the mechanical advantage hypothesis (Buchanan et al. 1989; Prilutsky 2000; Zatsiorsky et al. 2002), these fingers were expected to produce most of the moment in PR and SU, respectively. This was indeed true. However, L finger produced about the same percentage of the total SU moment irrespectively of the required moment direction, i.e., when it acted as an agonist and when it acted as an antagonist. In contrast, I finger produced close to 90% of the total PR moment when it acted as an agonist but only about 60% of the total PR moment when it acted as an antagonist.

The observed differences in the control of SU and PR efforts should be viewed as preliminary. The experiment involved moment production in only one-hand configuration (prone), which could have by itself affected the results (Matsuoka et al. 2006).

Variability and synergies

Most researchers would probably agree that motor variability is not just “noise” but a potentially important phenomenon, a window into the organization of the control processes in the brain (reviewed in Newell and Corcos 1993; Davids et al. 2005). In particular, studies of motor variability have allowed introducing an operational definition of synergies as neural organizations that tend to reduce variability of important performance variables by organizing co-variation at the level of elemental variables (reviewed in Latash et al. 2003, 2004). However, having a strong synergy does not by itself mean that variability of a corresponding performance variable will be low; similarly, a performance variable can be precisely specified without any synergy. Our results can be used to illustrate this point.

The index of variability of the main performance variable, the total moment of force showed a time profile that was quite different from that of the index of the corresponding synergy (ΔV_M). Variance of the total moment of force peaked at a time when the rate of change of the total moment was maximal. This can be interpreted as a consequence of a timing error in specification of this performance variable (Goodman et al. 2005). However, the index of moment stabilization, ΔV_M showed a peak close to the time of peak PR moment and was minimal close to the time of peak SU moment, when the rate of moment change was close to zero. In contrast, variance of the total force peaked when the index of force-stabilizing synergy, ΔV_F was minimal (close to peak SU moment), as expected from the model of Goodman and colleagues. A tentative interpretation of these observations is that the controller overcomes the naturally expected variation in the strength of a synergy with the rate of change of the corresponding performance variable and avoids destabilization of that variable, but only for performance variables that are explicit or implicit task components.