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1Neuropediatrics Q2:07, Department of Woman and Child Health, Astrid Lindgens Childrens Hospital, Karolinska Institutet, S-171 76 Stockholm; 2Studies of Artificial Neural Systems, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm; and 3Neuropediatrics, Department of Woman and Child Health, Karolinska Institutet, S-171 76 Stockholm, Sweden
Submitted 22 October 2002; accepted in final form 8 February 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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We first propose a mathematical model incorporating muscles, hand mechanics, and the action of lifting an object. A simple control system sends motor commands to and receives sensory signals from the model. We identify three factors influencing the efficiency of the correction: the time development of the motor command, the delay between the onset of the grip and load forces (GF-LF-delay), and how fast the lift is performed. A sensitivity analysis describes how these factors affect the ability to prevent or stop slipping and suggests an efficient control strategy that prepares and corrects for an altered frictional condition.
We then analyzed fingertip grip and load forces (GF and LF) and position data from 200 lifts made by five healthy subjects. The friction was occasionally reduced, forcing an increase of the GF to prevent the object being dropped. The data were then analyzed by feeding it through the inverted model. This provided an estimate of the motor commands to the motoneuron pool.
As suggested by the sensitivity analysis the GF-LF-delay was indeed used by the subjects to prevent slip. In agreement with recordings from neurons in the primary motor cortex of the monkey, a sharp burst in the estimated GF motor command (NGF) efficiently arrested any slip. The estimated motor commands indicate a control system that uses a small set of corrective commands, which together with the GF-LF-delay form efficient correction strategies. The selection of a strategy depends on the amount of tactile information reporting unexpected friction and how long it takes to arrive. We believe that this technique of estimating the motor commands behind the fingertip forces during a precision grip lift can provide a powerful tool for the investigation of the central control of the motor system.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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) and friction (Saels et al. 1999). The grip force (GF) required (target GF) to avoid slips and dropping the object depends on friction (Johansson and Westling 1984b) and shape (Jenmalm and Johansson 1997) of the finger-object contact area. The CNS continuously monitors the current state of the lift and responds immediately to unforeseen events (Johansson and Westling 1984a). Of particular importance is the tactile information from local micro-slips (creeps) at the periphery of the finger-object contact area or from gross slips of the whole fingertip (Smith, 1993). The slips supply information about the texture and friction through activation of mechanoreceptors that, via the spinal cord, project supraspinally, e.g., to the primary somatosensory cortex (Salimi et al. 1999), and result in changes in firing frequency in the primary motor cortex (Boudreau and Smith 2001; Picard and Smith 1992a,b). Mechanoreceptors may, via spinal interneurons, drive motoneurons supplying the hand (McNulty et al. 1999). The information about the friction is crucial for adjusting the GF to avoid slip and, eventually dropping the object.
In this study, we focused on when the situation when an object that is more slippery than expected is lifted using a precision grip between the index finger and the thumb. Once the appropriate friction is detected, the fingertip forces have to be adjusted with a correcting motor command, here called correction profile, to avoid dropping the object. In the precision grip literature, there are traces of a repertoire of such correction profiles in the measured fingertip forces, both in response to unanticipated friction (Edin et al. 1992; Johansson and Westling 1984b) and in reaction to a sudden increase in the weight (Johansson and Westling 1988b). The time course of the correction profile is therefore considered to be one factor that influences how well the CNS manages to prevent slip or minimize the distance slipped. A second factor is the GF-LF-delay. This delay, evident in normal subjects, builds up a safety margin before the onset of the LF and makes the grip less sensitive to changes in frictional condition and to external perturbations in the LF. A third factor in how fast the LF increases in the load phase, i.e., between the start of the increase in the LF and the time at which the object lifts off. If an object is picked up slowly, i.e., the load phase duration is long, the fingers will slip less than in a fast lift. This is because the LF rate is lower for a slow lift and, hence, will cause a slower and shorter movement of the fingers at slip.
On the basis of the preceding considerations, the Correction Profile, the GF-LF-delay, and the Load Phase Duration are three candidates as factors, here called control parameters, that could influence the quality and the safety of the lift. The first goal in this study was to make a sensitivity analysis of these control parameters to indicate how and to what degree they affect the ability to prevent the occurrence of a slip and stop an ongoing slip. By using a neuro-biomechanical model of the precision grip, a systematic variation of the control parameters could be made that would not be possible in human experiments. The results suggest an optimal control strategy using the three parameters. This strategy is compared with data from human behavior obtained from similar experiments.
It has recently been suggested that signal-dependent noise in the motor command influences motor planning (Harris and Wolpert, 1998). By applying such noise to a model of the arm and choosing a trajectory that minimizes the variance in the final arm position, the theory accurately predicts the observed bell shaped velocity profiles of arm movements. This minimum-variance theory also predicts saccadic eye movements and the speed-accuracy trade-off described by Fitt's law. It is tempting to suggest that this unifying theory of movement control also applies to the control of fingertip forces. The fact that a precision grip lift task is characterized by bell-shaped fingertip force rate profiles and accurate precision of the target force (Johansson and Westling, 1988a) supports the possibility of an involvement of the minimum-variance theory. Hence, we investigate if signal-dependent noise could explain the selection of the correction profile.
Although previous studies of the precision grip have generated information about the processes controlling the human precision grip, data concerning the actual time development of the motor commands to the motoneuron pool are still lacking. The second goal was to explore these motor commands directly from human data using an inverted parameterized model; to the best of our knowledge, this would be for the first time. A similar well-established technique, called inverse dynamics, involves taking transforms of measured limb motions and exerted forces into joint torques, see Winters and Crago (2000) and, e.g., Chabran et al. (2001), but because no muscle dynamics are incorporated, no direct estimates of the motor commands are produced. If muscles were included, the model would have to be greatly simplified to be uniquely invertible. Instead, optimization techniques such as simulated annealing and genetic programming can indirectly estimate motor commands by optimizing a cost function representing, e.g., energy consumption (Ogihara and Yamazaki 2001), exerted force (Raasch et al. 1997) or commanded torque change (Nakano et al. 1999) even though the model is not uniquely invertible. However, these optimized motor commands are not estimated directly from human performance. Thus we have chosen a lumped parameter neuromuscular model that is simple enough to be invertible. We use the inverted model to estimate the neural motor commands during a precision grip lift task. The assumptions necessary to make this possible, and the implications they may have on the result are discussed.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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The model consists of three main components: control, hand, and object (see Fig. 1). The control component generates the motor commands for the GF and LF. It receives friction and slip information from the hand and can introduce a Correction Profile that updates the target GF to match the new frictional condition.
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Great care has been taken to preserve important biomechanical factors in the model, especially the limiting characteristics of the system, such as the force-velocity component of the muscle and the neuronal conduction delays in the peripheral nervous system. Other factors have been simplified, e.g., the number of joints and muscles. The model components are outlined in detail in the following text.
CONTROL COMPONENT. The control component generates two output signals, neural GF (NGF) and neural LF (NLF), representing the motor commands to the motoneuron pool. These signals are input to the hand component of the model, which generates the corresponding GF and LF. The control component started each lift with a motor command that mathematically can be described by
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is a time constant affecting the speed of the muscle contraction. The LFT was set to 2.9 N, which was 10% above the force needed to overcome the gravitational force. The GFT was set to 2 N, which matched the expected friction of the sandpaper and included a 50% slip margin as seen elsewhere for humans (Forssberg et al. 1995).
Correction Profiles. Different Correction Profiles could be utilized to correct for the unexpectedly slipper contact area, replacing the ongoing anticipated NGF. We focused on four Correction Profiles that were functionally and biologically plausible, see Fig. 3. Correction Profile 1 used the same filter as in Eq. 1 but with the correct target GF matching the new friction. We assumed that a change to the correct target GF would be a simple way for the control component to correct the GF. Because the Correction Profile was introduced during an ongoing lift, the time constant GFwas recalculated for Profile 1 to match the time of the lift-off. Correction Profile 2 was a step change to the new GF target. This was a faster correction than the first one, yet a simple action to generate. Profile 3 was characterized by a sharp overshoot followed by a slow decrease to the new target GF. It corresponds to the GF response seen when reacting to a sudden increase in LF (Cole and Abbs 1988; Fagergren et al. 2000; Johansson and Westling 1988b). Profile 4 started with a 10-ms burst of maximum neural activity (NGF = 1) and continued as profile 1. A similar burst of neuronal activity is evident in the primary motor cortex of the monkey in response to slipping caused by an external downward perturbation of the object (Boudreau and Smith 2001; Picard and Smith 1992b). The NLF was unaffected by the correction profiles.
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HAND COMPONENT. In humans, the precision grip involves a complex biomechanical machinery of about 15 different muscles (Valero-Cuevas et al. 1998). During the early years of childhood, these muscles are coordinated to act in synergy (Forssberg et al. 1991; Hepp-Reymond et al. 1996). In the model, the synergy of these muscles are used to generate GF and LF independently.
The hand component is the actuator, modeled as a rigid rod attached to a fixed point (wrist) around which the rod can rotate as a dorsal-ventral flexion/extension, see Fig. 2. This 1 degree of freedom (df) model received continuous control signals, mapping the NGF to an isometric GF, and the NLF to a torque that generates the vertical movement of the hand, resulting in the tangential LF through the friction at the finger-object contact area.
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Because all simulations starts with the hand a the contact-area, the GF is assumed to be isometric and is calculated by a second-order linear filter (Fagergren et al. 2000). It covers the dynamics from the motoneuron pool to the fingertip in contact with the object. It was derived by means of a system identification technique applied to data from human isometric precision grip experiments (see Fagergren et al. 2000). The characteristics of the transfer function dynamics are in agreement with experiments on human neuromuscular systems (Bigland-Ritchie et al. 1983; Buchthal and Schmalbruch 1970; Newton and Yemm, 1986; Thomas et al. 1990). Transfer functions of higher orders provide little or no improvement to the accuracy of isometric muscle models (Winters and Stark 1987). The GF is calculated by
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is the Laplace operator. The GFmax was arbitrarily set to 100 N based on the results in Armstrong and Oldham (1999) and the data in Fagergren et al. (2000) and represents the maximum voluntary contraction (MVC) in GF. The NGF is the motor command signal from the control system, ranging from -1 to +1. A delay of t
= 25 ms includes the 
-motoneuron conduction delay of 15 ms (Dengler et al. 1988) from the motoneuron pool to the motor endplate on the muscle and an electro mechanical delay of 10 ms (Johansson et al. 994) from the motor endplate to the production of mechanical work.
Because the fingertip LF is not isometric after the object has been lifted or during a slip, a more sophisticated model was used for generating the wrist movements and the consequent LF. Two antagonistic muscles, extensor and flexor, generated torque at the wrist joint. Together with a description of the passive dynamics of the joint, these muscles were described by nonlinear Hill-based lumped-parameter models (Winters and Stark 1985, 1987) that consisted of a first-order description of the neural-excitation dynamics, first-order active-state dynamics, and a torque generator with activation dependent force-length and force-velocity relationships, see APPENDIX A.
There is no unique solution for distributing the neural input to the flexor and extensor in the model. Hence, because the wrist movements and LFs were mainly directed upward, only variations in the neural drive to the extensor were considered. A small and constant neural input to the flexor, arbitrarily set to 1% of the maximal wrist torque, was assumed. The consequences of this assumption are discussed in the following text. Accordingly, the NLF refers to the motor command for the extensor muscle.
FRICTION MODEL. Friction arises when the fingertips move, or try to move, across the contact area. It opposes the motion that would occur in its absence, and its magnitude is equal to the tangential force that is applied. If the tangential force is large enough, a slip occurs, and the fingertips start to slide against the object. We assume that the maximum force of friction is µsGF, where µs is the coefficient of static friction when the relative motion between the hand and the object is zero. When a fingertip slides, the force of friction is µdGF in the opposite direction to the velocity. Experimentally, the friction decreases when the fingertips start to slide, and in the model, we assume that µd = 0.8 µs. In the model, a slip occurs when the force of friction is greater than µsGF or when the relative velocity between the hand and object is non-identical. This double condition accounts for the case when the GF is zero. The transition from slip to no slip occurs when the force of friction is less than µdGF and the relative velocity is zero. In each simulation, one of two predefined friction coefficients was selected, these being: sandpaper: µssp = 1.21, and silk: µssi = 0.35, (Johansson and Westling 1984b).
OBJECT COMPONENT. The object component simulates a rigid object in a Newtonian mechanistic environment. The object sits on a surface and can be lifted, given the appropriate GF and LF. The object has two flat vertical contact areas that are parallel. With the aim of minimizing the degrees of freedom (DOF), the object can only move along the arc outlined by the fingertips (1 DOF). The Newtonian mechanistic equations describing the object position and the forces acting in the object are dependent on the current state of the object, i.e., whether the object is in contact with the table or not and whether sliding occurs or not (see APPENDIX A). The weight of the object was set to 300 g.
Sensitivity analysis
A sensitivity analysis of the Correction Profile, GF-LF-delay, and Load Phase Duration compared how they affected the ability of the control system to correct for an unexpectedly slippery contact area. While two of these parameters were held constant, a simulation was run for each of four variations of the third parameter. This was repeated for all combinations of the three parameters. Normal subjects lifting a common object weighing 200 g use a GF-LF-delay of 43 ± 12 ms and a Load Phase Duration of around 280 ± 120 ms (Forssberg et al. 1991). Thus the investigated GF-LF-delays and Load Phase Durations were 20, 40, 60, and 80 ms and 200, 300, 400, and 500 ms respectively.
Two simulations were run for each combination of the parameters. First, we measured how each parameter affected the ability of the control system to stop the ongoing slip. This was indicated by the slip distance when the Correction Profile was introduced 55 ms after the start of the slip, which is a normal latency for this type of correction (Edin et al. 1992) (note that 25 ms, for signal transmission and force development, must be added to this latency when compared with correction latencies based on finger tip forces).
In a second simulation, we measured how each parameter affected the ability to prevent a slip from occurring. This was done by finding the latest time at which the Correction Profile could be introduced and still preventing slip from occurring. This time defined the neural correction window (NCW) as the time window spanning from the first possible moment that the slippery surface could be detected, i.e., at finger contact, to the latest possible time to activate the correction profile and still preventing slip to occur. If the correction profile was introduced within this time window, then slip was prevented, and if it was introduced after this time window, then a slip occurred.
Variance analysis
To test how signal-dependent noise in the NGF affects the accuracy of the GF, a variance analysis was set up using the four Correction Profiles. White noise with a mean of zero and a SD proportional to the NGF amplitude, was added to the NGF. The noisy NGF, NGFw, was generated using
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Human grip experiments
Five healthy, right-handed subjects (2 women and 3 men, 24–48 years old) participated in the present study. The subject sat in a chair resting the right forearm on a stable support, 15 cm above the table surface. A vacuum pillow was molded around the arm to keep the arm in the same position throughout the experiment. The object was picked up between the tip of the index finger and the thumb by an ulnar-radial extension of the hand around the wrist joint. A curtain blocked the vision of the object limiting the sensory information to tactile and proprioceptive input. Prior to the experiments (3–5 min) the subjects washed their hands with soap and water. All subjects practiced prior to the experiment, so that they were well acquainted with the two different textures that was altered between in the experiments. The Ethical Committee of the Karolinska Hospital has approved the study (Dnr 02-170).
APPARATUS. A specially designed instrumented object of 300 g with replaceable finger-object contact areas was used. Two flat contact areas with different textures (sandpaper and silk) were used to alter the frictional condition. The position of the object, the index finger and the thumb was recorded at 40 Hz by a magnetic transducing three-dimensional motion tracking system, FASTRAK(R), with a horizontal and vertical resolution of 0.15 and 0.3 mm, respectively. The fingertip forces were measured individually at the two contact areas, using silicon strain gauges (ATI F/T transducers) providing six components of force and torque each sampled at 1 kHz (1 ms), with a resolution of 0.005 N.
EXPERIMENTAL DESIGN. The subjects were instructed to lift the object about 5 cm above the table. Each subject carried out a series of 40–46 such trials at 10 to 15-s intertrial intervals. In all but seven of the trials, the contact area was sandpaper. To ensure that the subjects targeted the fingertip forces for sandpaper (Forssberg et al. 1995; Johansson and Westling 1984b), there were between 2 and 10 sandpaper trials before each silk trial. The two first sandpaper trials in each series and after a silk trial were removed because initial adjustments to the sandpaper surface was not the focus of the study.
PARAMETER DEFINITIONS. Markers defining specific events were set in each trial by visual inspection of the data records. The markers indicating the onset of the GF and LF were determined by the aid of an algorithm using the first and second derivative of the forces, as in (Birznieks et al. 1998). The following parameters, where the finger contact defined time t = 0, were calculated from the markers and were measured for each finger and all trials. 1) tg, the time at which the increase in the GF was initiated, here called the contact phase duration. 2) GFg, GF at tg. 3) di, the initial sliding distance, defined as the total distance of the path described by the finger relative the object from the initial finger contact to tg. 4) t1, time at which the increase in the LF is initiated. 5)LF1, LF at t1. 6)GF1, GF at t1. 7)FR1, force ratio (defined as GF1/LF1) at t1. 8) tg1 time between tg and t1 (the GF-LF-delay). 9) to, time at which the object is lifted off. 10) GFo, GF at to. and 11) t1o, time form t1 to to (load phase duration).
For trials where the object slipped, additional parameters were measured as follows: 1) ts, the time at the start of the slip, 2) ts, the slip duration, i.e., the time from the start to the end of the slip, 3) ds, the slip distance, 4) vs, the slip velocity, defined as ds/Ts, 5) tE1, the time from the start of the slip to the first excitatory response in NGF (E1), 6) tI1, time from the start of the slip of the first inhibitory response in NGF (I1), 7) tE2, time from the start of the slip to the second excitatory response in NGF (E2), and 8) tE1-2, time from tE1 to tE2.
A combination of kinematic and kinetic data was used to determine the slip events. The six force channels had a higher time resolution than the motion tracking system, therefore an alternative method was used to mark the start and stop times of the slip events. The six force channels were used to calculated the center of pressure (COP) on the finger-object contact area (see formulas in, e.g., Barnes and Berme, 1994). There was a fast change in COP when a slip occurred. Therefore the COP was used to mark the start and stop of the slip events in time with an estimated precision of ±10 ms. Only slip trials where both fingers slipped simultaneously (<50 ms apart) were included in the analysis. The position data from the motion system was then used to measure the slip distance as the difference in relative position between the object and the fingertip. The compliant motion of the vertically loaded pulp was slow compared with the motion at slip. This was clearly seen when comparing normal sandpaper trials with the slips in silk trials, Fig. 9.
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ESTIMATION OF THE MOTOR COMMANDS. Before calculating the estimated motor commands, NGF and NLF, the digitized fingertip force and position data were run through an eighth-order zero lag Butterworth low-pass filter. This was a necessary procedure because the inverted models were sensitive to high-frequency noise. Force data were filtered with a cut-off frequency at 40 Hz and position data at 8 Hz. The NGF was estimated by feeding the measured GF through the inverted GF model. The NLF was estimated by feeding the measured LF and finger position data through the inverted LF model. The estimates NGF and NLF was then run through an eighth-order zero lag Butterworth low-pass filter with the cut-off frequency at 100 Hz.
STATISTICAL METHODS. Before a statistical method was chosen all included variables were tested to determine if they were normal distributed (Kolmogorov-Smirnov) and if the variances were homogeneous (Levene's test). If both these tests were nonsignificant, ANOVA was accepted. Otherwise, alternative tests were chosen as described in the following text. We used the Tukey honestly significantly different (HSD) test for post hoc ANOVA analyses, which were only performed if the main effect was significant. Linear nonparametric correlation was used (Spearman rank order) because the residuals for some of the combinations of the included variables were not normally distributed. The level of probability selected as statistically significant was P < 0.05, and unless otherwise indicated, population estimates are presented in the form of means ± SD values. Unless otherwise stated, all statistical analyses were processed in the Statistica software (version 6.0, Statsoft, Tulsa, OK).
The null hypothesis that initial slide distance, di, the time at GF onset, tg, the GF at LF onset, GF1, the force ratio at LF onset, FR1, the GF-LF-delay, tg1, and the Load Phase Duration, t1o, were equal for sandpaper and silk trials was tested. Because the variances and covariances of the data differed between groups, repeated-measures mixed model ANOVA was used. A group effect of surface texture (sandpaper or silk) was tested, while taking a subject effect into account. A separate analysis was performed for each variable and each finger and was performed by the PROC MIXED procedure in the statistical analysis SAS/STAT software (version 8.2, SAS Institute, Cary, NC).
The hypothesis that the probability of slipping is affected by initial slide distance, di, time at GF onset, tg, GF at LF onset, GF1, force ration at LF onset, FR1, and GF-LF-Delay, tg1, was also tested. Only silk trials were included in this analysis. The response variable was binary (slip = yes/no), the measurements repeated and within subject, therefore we used generalized logistic regression in which each variable is dichotomized based on the subject's median value, and a regression is performed on the two classes rather on the variable values. The generalized logistic regression was performed by the GENMOD procedure in the SAS/STAT software.
As a complement to the regression analysis, linear correlation analysis controlling for subject was performed on each combination of the same variables. Apparent correlations due to mean differences between subjects were compensated for by subtracting the subject mean value for each of the variables.
The response in NGF and NLF to a slip was analysed by repeated-measured ANOVA. Specific events in the NGF and NLF response defined time points at which the median value of a 5-ms window were collected from each trial, see Fig. 8D. These median values were then used to analyze main effects of three repeated-measures factors: subject (4 levels, 1 of the subjects did not slip and was therefore not included in this analysis), finger (2 levels, index finger and thumb), and time (6 levels for NGF and 2 for NLF). Planned comparisons between the points were used.
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The null hypothesis that oscillations between 8 and 10 Hz are equal in power compared with surrounding frequencies, 5–7 and 11–13 Hz, was tested by repeated-measures ANOVA. For each trial, the power of the frequency components from a discrete Fourier transform of the NGF was calculated. The median power for the frequency components fi within the 8 to 10-Hz band (7.5 
fi < 10.5) defined the independent variable P8–10, whereas the median power for the surrounding frequencies (4.5 fi < 7.5 and 10.5 fi < 13.5) defined the independent variables P5–7 and P11–13, respectively. These median values were then used to analyze main effects of three repeated-measures factors: subject (4 levels, 1 of the subjects did not slip and was therefore not included in this analysis), type of trial (3 levels: sandpaper, silk without slip and silk with slip), and frequency band (3 levels: 5–7, 8–10 and 11–13).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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The results from the sensitivity analysis are shown in Figs. 4 and 5. All 4 x 4 x 4 combinations of the three control parameters were examined, but for displaying purposes only a subset of 4 + 4 + 4 are presented in the figure, i.e., in Fig. 4A, the GF-LF-delay is 40 ms and the Load Phase Duration is 300 ms, in Fig. 4B, a Load Phase Duration of 300 ms is used together with Correction Profile 2, and in Fig. 4C, a GF-LF-delay of 40 ms is used together with Correction Profile 2. Profile 2 was chosen because it was not affected by the variations in GF-LF-delay and Load Phase Duration. The GF-LF-delay of 40 ms and the Load Phase Duration of 300 ms represent the mean values obtained for normal subjects.
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The first test investigated the ability to stop a slip and was preformed by measuring the slip distance (top). Clearly, all three parameters affected the slip distance. The sharper the Correction Profile, i.e., the higher frequencies it contained, the earlier it stopped the slip, see Fig. 4A. Correction Profile 4 was the most efficient (slip = 1.9 mm) because it produced the fastest increase in the GF. In contrast, the slow Correction Profile 1 slipped 9.9 mm. It was concluded that the ability to stop an ongoing slip improved with the presence of higher frequency components in the Correction Profile because sharp increase in the input signal resulted in a steeper increase in the output GF. The GF-LF-delay affected the slip distance as shown in Fig. 4B. An increase in the GF-LF-delay from 20 to 80 ms increased the slip distance from 3.4 to 6.4 mm. This is because the slip margin is greater for a longer GF-LF-delay. Consequently, for a long GF-LF-delay, the LF and the LF rate were higher when the slip started than for a short GF-LF-delay, which resulted in a greater acceleration of the finger at slip. The Load Phase Duration influenced the slip distance as seen in Fig. 4C. A slow lift with a Load Phase Duration of 500 ms slipped only 2.0 mm, whereas a fast lift with a Load Phase Duration of 200 ms slipped 8.7 mm.
The second test was to investigate the ability to prevent a slip. This was done by measuring the neural correction window (NCW, see METHODS). The three control parameters influenced the NCW in different ways. As the Correction Profile became sharper, i.e., contained higher frequencies, it could be introduced later and still prevent a slip, see Fig. 5A. Profiles 2–4 had a NCW of 46–48 ms, whereas profile 1 only had a 26-ms window, requiring a fast reaction to completely prevent slip. Hence by using Correction Profile 2, 3, or 4, more time for sensory information processing is made available before the correction profile must be introduced. The GF-LF-delay had the strongest influence of all three parameters on the efficiency of prevent slipping, see Fig. 5B. A 60-ms increase in the GF-LF-delay (from 20 to 80 ms) increased the NCW by 115 ms (from 7 to 122 ms). The Load Phase Duration had almost no effect on the NCW as shown in Fig. 5C.
Variance analysis
The results of the variance analysis of the four Correction Profiles with signal-dependent noise is shown in Fig. 6. The variance obviously reflects the time course of the Correction Profiles because the noise was proportional to the signal. Accordingly, Correction Profile 1 produced the smallest variance. Though profile 4 had the highest NGF peak amplitude, the duration of that peak was sufficiently short to allow a fast decrease of the variance down to the level of profile 1 by 
200 ms, followed by profiles 2 and 3 at 400 and 900 ms, respectively. In other words, profile 4 regained the precision in GF faster than profiles 2 and 3.
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Human grip experiments
The trials from the human grip experiments was divided into two groups: sandpaper trials, for which no correction was necessary, and silk trials, where a correction was necessary to not drop the object. The silk trials could be divided further into nonslip trials where an early correction successfully prevented slip, and slip trials where a gross slip triggered the correction. All slips occurred before lift-off.
When comparing sandpaper trials and silk trials, no significant differences between the early parameters before the load phase were found: contact phase duration (tg), GF-LF-delay (tg1), GF at LF onset (GF1), and force ratio at LF onset (FR1). This indicates that the subjects followed the task and always set the motor programs to match the sandpaper surface, even for the silk trials. However, the initial slide distance of the thumb were significantly longer for silk [di = 4.3 ± 0.5 (SE) mm] than for sandpaper (di = 1.9 ± 0.6 mm), P = 0.043. This is natural because the finger tip slides more easily on silk than on sandpaper. The index finger was not significant but showed a strong tendency, P = 0.073, in the same direction (silk: di = 2.7 ± 0.7 mm, sandpaper: di = 1.0 ± 0.2 mm). Later into the lift, the Load Phase Duration in silk trials were significantly longer [t1o = 316 ± 53 (SE) ms] than sandpaper trials (t1o = 158 ± 17 ms), P = 0.048, for the thumb. Also here, the index finger was not significant but showed a tendency, P = 0.102 (silk: t1o = 345 ± 57 ms, sandpaper: t1o = 212 ± 27 ms).
If all trials were set the same, why did some silk trials contain a slip and others not? The best precursor for a slip was the initial slide distance di, which significantly affected the probability for a slip (P = 0.0043 and P = 0.0001 for index finger and thumb, respectively). The longer the initial slide distance, the greater the probability for preventing a slip. This is a clear indication that early information about the surface condition is gathered during the initial contact between the finger and the object and immediately used to tune the parameters of the motor command. The second best precursor was the GF-LF-delay (tg1), which affected the probability for a slip significantly (P = 0.0011), but only at the thumb. The longer the tg1 the greater the probability for preventing a slip.
Further the correlation analysis showed that the GF-LF-delay tg1 was positively correlated with the initial slide distance di (r = 0.34, P = 0.020 and N = 48), see Fig. 7. This suggests that the longer the initial slide distance the more evidence is received by the CNS indicating a new friction, and that to delay the LF onset is a strategy that is used to prevent slipping, as proven efficient in the sensitivity analysis.
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ESTIMATED MOTOR COMMANDS. In the sandpaper trials, the subjects lifted the object normally in agreement with what others have reported, e.g., (Johansson and Westling 1984a; Forssberg et al. 1991). The motor output was set in advance and executed in a feed forward manner, as indicated by the step increase of the NGF to the correct 2N target, shown in Fig. 8A. This is expected in a correctly programmed lift. Note that the NGF leads the GF by 25 ms due to the -motoneuron conduction delay of 15 ms (Dengler et al. 1988) and a neuromechanical delay of 10 ms (Johansson et al. 1994), see Eq. 2. Hence, the NGF starts to increase before the GF. Because NGF only codes for the isometric GF generation, the NGF is quite similar to the GF. The NLF has a more complex function, see Fig. 9A because it also codes for the lifting movement. This is clearly seen in the figure as the NLF initially leads the LF and then shifts at lift-off to lead the change in position.
In the non-slip silk trials, there was an early switch to a new motor command. The estimated NGF, plotted in Fig. 8B, shows a change in target GF from 2 N (for sandpaper) to 6 N (appropriate for silk). In these trials, the new friction was detected early, and a shift to the correct NGF together with a longer Load Phase Duration formed a simple and yet efficient correction strategy. This agrees well with the change in grip force rate seen at the first target GF, in other studies, e.g. (Johansson and Westling 1984a). Careful examination of single trials, see Fig. 9, D–F, revealed mainly three different ways in how NGF was corrected: D as a one-step increase, i.e., correct at the onset of the GF, E as a two-step increase where the first step aimed at 2 N and the second at 6 N, and F as a combination of D and E with the initial step aimed at 2 N followed by a multipeak increase until the correct GF was achieved. However, there were no clear cut borders between D, E and F, rather a great variance indicated a sliding scale.
A quite different correction strategy was executed when a slip occurred. A sharp burst in NGF was evident 44 ± 18 ms, after the start of the slip, see Fig. 8, C and D. The amplitude in NGF was significantly higher at the burst than at the start of the slip, P = 0.0499. The amplitude in NLF seemed to decrease after the start of the slip (52 ± 23 ms), but that decrease was not proven significant. However, by visual comparison of the median NLF in sandpaper, non-slip and slip trials, Fig. 8, A–C, there is a plateau in the NLF slope in slip trials, just after the start of the slip, that is not found in the sandpaper or non-slip trials. The small NLF plateau in sandpaper trials appears at lift-off and can therefore not explain the plateau in slip trials that appears before lift-off. This indicates that the increase in NLF is halted at slip and continued when the slip stops. By applying these NGF and NLF actions together, the control system can efficiently stop a slip. After the sharp burst in NGF there was a clear decrease in NGF, 76 ± 18 ms after the start of the slip, P = 0.028. Around 100 ms after the sharp burst (99 ± 19 ms), a second and stronger burst was evident in the NGF. This was a correction to the new target GF. A single trial correction is shown in Fig. 9C. Note that the delays and times referring to the NGF above are 15 ms less than the corresponding electromyography (EMG) signal due to the -motoneuron conduction delay (see Eq. 2). The duration of a slip never exceeded 200 ms (min = 45, median = 87, max = 113 ms). Data indicated that the second burst was coupled to the first burst rather than to the start of the slip. The variance of the delay between the first and the second burst was 42% less than the variance of the delay between the start of the slip and the second burst. The delay between the first and the second burst is equivalent to a 10-Hz oscillation in the motor command.
Interestingly enough, in the averaged data, a small increase was evident in the NGF already at 20 ms after the onset of slipping, indicating a spinal component, see Fig. 8D. However, repeated-measures ANOVA did not give a significant result when comparing the small increase with its immediate surrounding local minimum at 11 and 29 ms, respectively.
The fourier analysis of the NGF showed a main effect of frequency [F(2,78) = 12, P < 0.001], and the post hoc analysis revealed that the 8 to 10-Hz component was 25% stronger than the 5 to 7-Hz component, P = 0.0001, and 7% stronger then the 11 to 13-Hz component, P = 0.0083. There was a main effect of subject [F(3,39) = 4.1, P < 0.012], indicating intra subject differences in the 5 to 13-Hz frequency band. There was also a main effect of type of trial [sandpaper, non-slip and slip, F(2,39) = 42, P < 0.001], and the post hoc analysis showed that the total power of all the frequency bands (5–13 Hz) was 15% stronger for non-slip trials, P = 0.0013, and 65% stronger for slip trials, P = 0.0001, compared to sandpaper trials. This follows naturally the demand for increased grip force in the silk trials. An interaction effect between frequency and type of trial [F(4,78) = 4.9, P < 0.01] was also found in which the post hoc analysis showed that all three frequency bands was significantly higher in slip trials than in sandpaper trials, but only the 8 to 10-Hz and the 11 to 13-Hz bands when compared to the non-slip trials. This indicates that the slip trials contained stronger 8 to 13-Hz components than the non-slip trials even though the grip force demand was the same in all silk trials. In detail, the Fourier analysis of the NGF data showed a 46% higher 8 to 10-Hz component [N2] for the slip trials than for the non-slip trials, P = 0.029, and a 55% higher 11 to 13-Hz component, P = 0.003. This supports the above timing of the second burst being a 10-Hz frequency component following the first burst, rather than being triggered by the start of the slip.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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GF-LF-delay, a powerful parameter for preventing slip
The sensitivity analysis clearly suggests that increasing the GF-LF-delay efficiently prevents slip, by increasing the NCW. The result from the human experiments shows that the GF-LF-delay is made longer in trials in which the CNS receives more sensory input about the new friction. This suggests that the GF-LF-delay is a controllable parameter. The fact that the statistical evidence is stronger for the thumb than the index finger could be explained by the bigger contact area of the thumb (Kinoshita et al. 1997), thus generating more sensory input. A possible mechanical coupling between the initial slide distance and the GF-LF-delay could also have explained their correlation. To test this, an identical correlation analysis was performed on the sandpaper trials, but the result showed no correlation (r = 0.19, P = 0.18, and N = 52). Further, the time available to delay the onset of LF is sufficient for the CNS to react (t1 = 151 ± 69 ms for the sandpaper trials).
Because the sensitivity analysis suggests that the GF-LF-delay can indirectly tune the NCW, the GF-LF-delay can be expected to follow the development of the internal delays of the motor system (George and Taylor 1991; Müller et al. 1991), i.e., a short CNS delay permits a short GF-LF-delay. Indeed, the GF-LF-delay decreases during development and is the last parameter (of 8 investigated) to reach the level in adults (Forssberg et al. 1991). For children at 2 years of age, the GF-LF-delay is 120 ms, at 7 years, it is 60 ms, and for adults, it is 40 ms.
Furthermore, during digital anesthesia in normal adults the GF-LF-delay is prolonged and can last 0.5–1.0 s (Johansson and Westling 1984b). In conclusion, the GF-LF-delay, which seems to be controllable by the CNS, has the ability to compensate for internal feedback delays in the control system by building up a safety margin in the GF.
The sensitivity analysis showed that the distance slipped during a slow lift (long Load Phase Duration, Fig. 4C) is shorter than for a fast lift. We predict that the duration of the load phase is increased when lifting a fragile object or an object with small contact areas that limit the sliding range before losing contact, but studies investigating this issue have yet to be done. Unlike the GF-LF-delay, the Load Phase Duration shows no correlation with development (Forssberg et al. 1991) for patients with CP (Eliasson et al. 1991) or patients with Parkinsons disease (Gordon et al. 1997). As evident from Fig. 5C, the NCW did not change much with the Load Phase Duration. This shows that the Load Phase Duration was not a means by which the NCW could be increased. However, the data in our study clearly show a prolonged load phase for silk trials, indicating that a decrease in the LF drive are used to regain the safety margin.
Burst in motor command efficiently stops a slip
In the sensitivity analysis, profile 4 was the most efficient because the slip distance was 30% shorter than the second best profile and it had one of the longest NCWs. In addition, the variance analysis suggested profile 4 as the precision was regained earlier than for profiles 2 and 3. Indeed, the human data confirmed the use of a sharp burst as in profile 4. A similar burst is also seen in neurons in the primary motor cortex in the monkey in reaction to a sudden load perturbation causing a slip (Boudreau and Smith 2001; Picard and Smith 1992b).
The burst response is also found in other parts of the human motor system. When reacting to a sudden perturbation in posture, a sharp burst in EMG activity is evident (Gilles et al. 1999; Nashner, 1977; Ogiso et al. 2002; Shultz et al. 2000; Wilder et al. 1996), followed by the maintenance of a new equilibrium if necessary. The burst characteristic is also found in the visual system. The correcting motor command to a retinal slip in smooth-pursuit tasks is characterized by an initial sharp burst. It is most apparent for cortical neurons but is also evident for more downstream brain stem and cerebellar neurons (Takemura et al. 2001). The muscular and sensory anatomy of the land is certainly very different from the occulomotor system, but the task of stopping a sliding motion across a sensory area is very similar. Accordingly, this could be a general strategy of the motor system to efficiently correct for unexpected sensory events.
Our data showed strong oscillations 10 Hz in the NGF after the correcting burst. Oscillating motor output has been observed in several frequency bands including 10 Hz for isometric conditions (for a review on this topic, see e.g., McAuley and Marsden, 2000). Recent simulations of a pool of biophysically realistic motoneurons, show that the force output increases with increased synchronization at the input (Baker et al. 1999). This would indeed facilitate the fast increase in grip force needed to rapidly stop a slip.
What do the estimated motor commands code for?
In the normal sandpaper trials, the motor command for LF changes characteristics at lift-off, see Fig. 9A. Before lift-off, when there are no wrist movements, isometric muscle dynamics low-pass filter the NLF in the same way as for the NGF. After lift-off the change in wrist angle shortens the extensor muscle. Simplified, because the force-length and -velocity components weaken the shortening muscle, the NLF has to increase to maintain the moment of force at the wrist, see e.g. (Winters and Crago 2000). This phenomenon, where the motor command apparently changes coding form on modality to another, here from force to a mixture of position and velocity, is easily explained as a consequence of the need for the control system to overcome the nonlinear dynamics of the biomechanical system, as is so clearly demonstrated in Todorov (2000). A switch to an internal model of the new state, triggered by an expectation of a sensory event from the lift-off, is one explanation of how this could be accomplished.
Model and behavior suggests supraspinal control
Studies on cutaneomuscular reflex responses (Deuschl et al. 1995; Issler and Stephens 1983; Jenner and Stephens 1982) indicate a spinal latency of 30–50 ms, and a long latency of 55–75 ms with possible cortical involvement, for a review see Cruccu and Deuschl (2000). Triggered reactions (80–120 ms), which can be elicited from various receptors and act on associated musculature (Cargo et al. 1976; Johansson and Westling 1984b; 1988b; Schmidt and Lee, 1999), involve higher centers and fit well with the functional nature of the GF increase studied here.
One of the intentions of the sensitivity analysis was to indicate at what CNS level the control mechanism would have to reside in order to prevent slip. A spinal response would cover all four Correction Profiles, given a GF-LF-delay of 40 ms, see Fig. 5B. A long-latency response would cover Correction Profiles 2–4 given a GF-LF-delay of 40 ms, whereas profile 1 required a GF-LF-delay of 60 ms. A triggered reaction would cover all Correction Profiles with a GF-LF-delay of 60 ms. In conclusion, given the correct GF-LF-delay, the control mechanisms could reside at a cortical level and still perform a successful correction with any of the four profiles.
In the human experiments, the small early response seen in the averaged NGF for the slip trials, agrees with the short-latency spinal EMG response to a small skin and muscle stretch of the index finger (Macefield et al. 1996) and a mechanically stimulated receptive field (McNulty et al. 1999). The latency of the following sharp burst, also triggered by the start of the slip, is in agreement with the long-latency excitatory response seen in cutaneomuscular reflex experiments (see the discussion above and (Evans et al. 1990, 1991; Issler and Stephens 1983; Jenner and Stephens 1982)). The response latencies (43 ± 17 ms) for the burst in primary motor neurons in the monkey discussed in the preceding text (Bourdreau and Smith 2001; Picard and Smith 1992b) were similar to our data (44 ± 18 ms). This indicates that this burst involves neural substrates at a supraspinal level.
Phase-dependent control
The phenomena of phase dependent corrections in precision grip tasks was first described by Johansson and Westling (1984b). It has also been concluded from the present experiments that similar tactile input trigger different GF and LF responses in different phases of the lift. Slip information from the early part of the preload phase was used by the control system to take the decision to execute a suitable correction, i.e., to set a new target GF, delay LF onset and increase the Load Phase Duration (slow down the load force generation). In contrast, if slip information was received after the LF onset, a sharp burst in the NGF and a decay of the NLF increase were seen. This clearly indicates a state-dependent control system where the same sensory events, here mechanoreceptor activation caused by small slips, can be used to elicit different actions appropriate for the accomplishment of each phase. As suggested in the motor control theory outlined in Wolpert and Kawato (1998), these actions could be selected from a repertoire of learned motor programs on the basis of the current state of the system.
Novel technique of estimating motor commands
To invert the neuro-biomechanical model of LF generation with two unknown neural inputs (to the extensor and the flexor) and only one known output (LF), a minimum tonic drive to the flexor muscle was assumed while calculating the drive to the extensor muscle. This assumption had two implications for how the sensitivity results and the estimated NLF should be interpreted. First, the sensitivity analysis probably overestimated the slip distance due to the low-resisting force-velocity component of the flexor. However, the isometric phase before slip is unaffected by the assumption, leaving the NCW unaffected. Second, a fast wrist extension will lead to an underestimated NLF due to the low flexor resistance. This is of little importance here and does not affect the conclusions drawn.
One may argue that the model is too simple. However, as discussed in the preceding text the considerable agreement in our data with other studies supports our approach. First, the one-step increase in the NGF for the sandpaper trials agrees well with the bell-shaped force rate profiles in correctly programmed lifts. Second, the change in demand on the neural drive to the wrist muscles at lift-off clearly changed the NLF characteristics accordingly. Third, in the silk trials, the NGF indicated that it was preset for a friction appropriate to that of sandpaper. Fourth, the small spinal response and the sharp burst following a slip were evident in the NGF and the timing was plausible. Fifth, the small decrease reported in the LF rate following a slip was also seen in the NLF.
The model assumes that the muscles causing wrist rotation are isolated neurally and mechanically from those that generate grip force. Physiologically this is not the case and for fast wrist movements and brisk changes in isometric wrist load GF is indeed affected (Werremeyer and Cole, 1997). However, in a functional context, previous studies support this assumption by showing no or only minor crosstalk between GF and LF for slow wrist movements and moderate changes in isometric wrist load (Johansson and Westling 1984b; Werremeyer and Cole 1997).
The technique of using a model to estimate the motor commands directly from human force data has an advantage over surface EMG recordings. While some muscles are difficult or even impossible to record with surface EMG, the model captures changes in fingertip forces from all contributing muscles. This makes the technique extremely sensitive to small changes in the finger tip forces.
Conclusions
First, we proposed a mathematical model of the muscles, hand mechanics, and the lifting action of an object, and identified three factors influencing the sensitivity to altered friction. Simulations showed that one of these factors, the GF-LF-delay, provides a powerful means of preventing slip by increasing the NCW. Equivalent behavioral recordings showed that the GF-LF delay is indeed used to prevent slip. Second, using a new technique combining behavioral recordings and neuromuscular modelling, the motor commands behind the basic coordination of the fingertip forces in a precision grip lift are revealed for the first time. These motor commands are estimates of the neural drive to the motoneuron pool. The motor commands indicate a state-dependent control system that form efficient correction strategies by using a small set of corrective commands.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGMENTSREFERENCES |
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The motion of the hand and the object is based on Newton's 2nd law
 | (A1) |
 | (A2) |
Theta; the angular acceleration. The following subscripts are used: w, wrist; cm, center of mass of the hand; o, object; h, hand; and f, fingertips. These subscripts indicate the source of the variable rather than the origin of its coordinate system. The wrist joint is the origin in all equations. In the following text, 
is a position angle in radians, LF is the tangential force that is also the force of friction, GF is the grip force applied in the direction normal to the contact area, and r is a distance calculated from the wrist joint. The gravitational acceleration constant g is set to -9.81 m/s2. The hand and object interact via the force of friction between them. This nonlinearly coupled system is described by the following four states.
BEFORE LIFT-OFF, WITH NO SLIPPING. Hand and the object are still. Hence, the sum of momentum is zero.
 | (A3) |
 | (A4) |
 | (A5) |
 | (A6) |
 | (A7) |
Neuromuscular dynamics
The total momentum M at the wrist (w) joint is the sum of momentum from the passive (pass) viscoelastic wrist joint and from the flexor (flex) and extensor (ext) muscles
 | (A8) |
 | (A9) |
 | (A10) |
0, MXsh and MXsl are constants. Together with the torque-velocity unit, the contractile element (CE) is described as
 | (A11) |
is the length of the contractile element, and B is a function of joint position , neural input NCE and contractile element velocity 
. 
