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Neural Averaging in Motor Learning

¹Department of Psychology, McGill University, Montréal, Québec, Canada; and ²Haskins Laboratories, New Haven, Connecticut

Submitted 17 July 2006; accepted in final form 28 September 2006

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
The capacity for skill development over multiple training episodes is fundamental to human motor function. We have studied the process by which skills evolve with training by progressively modifying a series of motor learning tasks that subjects performed over a 1-mo period. In a series of empirical and modeling studies, we show that performance undergoes repeated modification with new learning. Each in a series of prior training episodes contributes such that present performance reflects a weighted average of previous learning. Moreover, we have observed that the relative weighting of skills learned wholly in the past changes with time. This suggests that the neural substrate of skill undergoes modification after consolidation.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
The ways in which skills depend on past learning have been examined in a number of recent studies (Brashers-Krug et al. 1996; Caithness et al. 2004; Shadmehr and Brashers-Krug 1997; Walker et al. 2003). These studies have used variants of a procedure known as an ABA design where A and B are often opposite patterns of force applied to the hand by a robotic device. In these experiments, subjects learn task A and then following a variable interval, they learn task B. Subjects are then re-tested on task A to assess retention of initial learning. The interval between A and B is manipulated to investigate the time course of consolidation of task A learning. Some studies suggest that once consolidated, skills are not affected by further learning. Evidence for this idea comes from studies in which the learning associated with task A was retained provided that the interval between A and B was sufficiently long [more than 5 h (Brashers-Krug et al. 1996; Shadmehr and Brashers-Krug 1997)]. In contrast, other recent work suggests that new learning can displace original learning (Caithness et al. 2004; Walker et al. 2003). Evidence suggests that when A and B involve opposite patterns of force, learning B interferes with the retention of A regardless of whether the interval between A and B is 5 min, 1 day, or 1 wk. This suggests that consolidated skills, even those learned long ago, can be disrupted by new learning.

In the present study, we have tested the hypothesis that performance reflects a combination of past learning and that skills are neither fixed after consolidation nor displaced with new learning. Support for the idea that motor learning reflects a neural averaging of previous learning comes from studies that have explored generalization of learning across the workspace (Malfait et al. 2005). In these studies, subjects learned to make movements in each of two workspace locations. Different patterns of force were applied to the hand in each location. Performance at a location intermediate to the two training areas could be predicted in modeling studies based on a spatial average of the commands learned at the flanking locations. It has also been shown that for movements to benefit from earlier training, they must be made in areas of the workspace intermediate to previously trained movement directions, where spatial averaging of prior learning is possible (Gandolfo et al. 1996). This generalization falls off sharply for movements outside of these boundaries. These studies and others (Gharamani and Wolpert 1997) suggest that motor skills learned separately in different spatial locations can be combined. Here we have tested whether a combinatorial process also applies to the development of skills over time.

We designed two experiments in which subjects were tested a number of times over an extended period. This allowed us to track performance as it evolved with repeated training. In experiment 1, we left delays of either 24 h or 1 mo between training sessions to allow for consolidation of learning. In experiment 2, subjects trained on two consecutive days followed by delays of 2 or 10 days prior to final testing. Results suggest that consolidated skills are modifiable, but they are not entirely replaced by new learning. Instead performance reflects a combination of prior learning that changes with time.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Subjects

Eighty-nine young adults (48 females, overall mean age ± SE, 22.51 ± 0.38 yr) took part in the experiments described below. 48 and 41 subjects participated in experiments 1 and 2, respectively. The McGill University Ethics Review Board approved all procedures. Subjects were right-handed and neurologically healthy and had normal or corrected vision.

Apparatus

Subjects made movements while holding the handle of a two-joint robotic device (InMotion2, Interactive Motion Technologies, Cambridge, MA) that allows movements in the horizontal plane. An air sled supported the arm during movement and eliminated friction. Torque motors connected to the shoulder and elbow joints of the robot applied forces (see following text) to subjects' hands during movement. Sixteen-bit optical encoders (Gurley Precision Instruments, Troy, NY) sensed the robot's (and hence the subject's) joint angles. Data were sampled at 400 Hz and stored off-line for later analysis.

Experimental task

In each experimental session, subjects made movements to a set of five targets (Fig. 1A). The targets were 3 cm in diameter and were arranged around the upper arc of a circle with a radius of 15 cm. The starting position was defined by shoulder and elbow angles of 45° and 90° relative to the frontal plane and the upper arm, respectively. Subjects were told to observe the workspace and wait for a target to be illuminated before moving. After waiting at the start position for 1,000 ms, subjects were required to move to a pseudorandomly selected target within 500 ± 50 ms and to stay within its boundaries for an additional 750 ms. Visual and auditory cues informed subjects about the duration of each movement, after which the robot brought the hand back to the start position.

View larger version (14K): [in this window] [in a new window]   FIG. 1. Robotic device, force fields, and experimental protocol. A: subjects made movements to targets arranged in a semi-circle about the hand. B: robotic device was programmed to apply velocity-dependent forces to the hand in 5 directions relative to the direction of movement (a straight out movement is shown as an example). The size of the arrows schematically represents the force magnitude as it scales with velocity. C: subjects in experiment 1 were tested in 4 sessions over a 1-mo period. The colors shown identify each group in Figs. 1–4.

The robot was programmed to apply forces to the hand that were dependent on instantaneous movement velocity. Force, f_x and f_y, was applied according to the equation

where x and y are the lateral and sagittal directions, _x and _y are movement velocity, c = 15 N · s · m^–1 and defined the direction of force relative to the direction of movement (see following text and Fig. 1B).

Procedure

We performed two experiments. In the first experiment, subjects were tested a number of times over a 1-mo period. This allowed us to track performance as it evolved with repeated training. On each of 4 sessions, subjects made movements to five targets while holding the handle of a robotic device that was programmed to apply forces to the hand that varied with movement velocity (see Fig. 1A). We left delays of either 24 h or 1 mo between training sessions to allow for consolidation of learning. During session 1, subjects familiarized themselves with the task and no forces were applied. One day later in session 2, subjects were divided into five groups (n = 8 for each group) and each made movements in one of the force-fields depicted in Fig. 1B. Two of these fields pushed the hand laterally ( = 0° and = 180°); an assistive field, acted in the direction of movement ( = 90°); two other fields had assistive and lateral components, resulting in forces that acted at 45° to the direction of movement ( = 45°, assistive + clockwise and = 135°, assistive + counter-clockwise). A sixth group of control subjects (n = 8) did not make movements during session 2. One day later in session 3, all subjects made movements in a lateral field that pushed the hand in a counter-clockwise (CCW) direction relative to the direction of movement ( = 180°). This allowed us to determine the effect of session 2 training on session 3 performance. Approximately 1 mo later [session 4: mean delay 34.3 ± 7.2 (SD) days], to test the effect of the entire training history, subjects returned to make movements in a clockwise (CW) field that pushed the hand in a direction opposite to the session 3 field ( = 0°). Figure 1C summarizes the experimental protocol. Four of the 48 subjects tested in experiment 1 did not return for session 4 testing. Subjects made 100 movements each session. For each individual, testing sessions occurred at approximately the same time of day.

In the second experiment, we randomly selected the direction of load in each of two training sessions. By examining how performance on a final test session varied as a consequence of the wide variety of training histories, we could directly test the idea that performance reflects a combination of past learning. In this experiment, session 1 (familiarization) was followed immediately by session 2 training. For session 2, the field was chosen randomly from the five used in experiment 1. For session 3 (24 h later), the training field was again chosen randomly. This resulted in 25 possible combinations of session 2 and 3 training fields. During session 4 (after a 2- or 10-day delay), subjects were tested in a clockwise lateral field ( = 0° relative to the direction of movement). For the 2- and 10-day delay conditions, we ran 25 subjects (all combinations) and 16 subjects (a subset of the combinations), respectively.

Measures and statistics

Hand position data were numerically differentiated and then low-pass Butterworth filtered at 20 Hz to generate velocity profiles. Movement start and end were scored at 5% of peak tangential velocity. To assess movement curvature, we computed a measure of perpendicular error (PE), which is defined as the signed distance at maximum velocity from the vector linking movement start and end positions. We computed PE at the moment of peak velocity to assess movement curvature prior to any voluntary response to the load applied by the robot. We also computed initial angular deviation (the angle between the vectors linking start and end, and start with the point of maximum tangential velocity) and found results similar to those reported here. Throughout, we use the term performance to refer to movement path error in the lateral direction (PE).

Statistical tests were conducted using ANOVAs and were followed by post hoc Tukey comparisons where appropriate. In experiment 1, we divided subjects (48 in total) into groups of eight on the basis of the field in which they were trained during session 2. To compare session 2 performance for the different directions of load application, we performed an ANOVA on movement curvature (PE). We compared PE for movements 6–25 (the 2nd-5th movement to each of 5 targets; the 1st movement to each target was excluded). We also compared the unsigned PE at the end of training (movements 91–100) to assess the extent to which the magnitude of final error differed between groups. Since the assistive loads did not curve movements laterally but instead applied force in the direction of movement, we also examined movement velocity profiles. We computed the difference between time-normalized velocity profiles for movements made in force fields and those made to the same target in the absence of load (Malfait et al. 2005). We used the sum of squared differences as a dependent measure of the force fields' effect on velocity, and performed ANOVAs to determine whether velocity profiles changed over the course of training and whether final movements (91–100) were still affected by the force field.

To determine whether learning with assistive loads is retained over time in a fashion comparable to that observed with lateral loads, we examined the effects of training with assistive loads on movement duration. Our rationale for choosing this measure was that assistive loads affect timing along the intended trajectory, rather than error in the lateral direction. Since training with assistive loads was limited to session 2, our analysis focused on session 3 performance with or without previous training with assistive loads. Specifically, we examined the duration of the initial movement segment (1.0 cm from movement start) to preclude possible voluntary correction for the load. We examined the first 5 movements and used an independent samples t-test to compare session 3 movement durations for naïve subjects with those of subjects who trained in an assistive load in session 2.

For session 3 and session 4 we computed mean movement curvature (PE) for movements 6–25. We also computed PE for the final training movements in session 3 (91–100). Using ANOVA and post hoc comparisons, we assessed the dependence of movement curvature on the field in which subjects trained during session 2. For subjects that trained in the same lateral counter-clockwise field for both session 2 and session 3, we tested whether initial session 3 performance (movements 6–25) was facilitated relative to final session 2 performance (movements 91–100) by performing a paired-samples t-test.

We performed a further set of analyses to determine whether the rate of learning was affected by the direction of movement. For each of the five fields, we used repeated measures ANOVAs to examine whether adaptation rate varied across the 5 targets in the workspace. For these analyses we focused on movements 6–25.

In experiments 1 and 2, we used regression analyses to determine the relationship between performance on the test session and subjects' previous training histories. In experiment 1, we evaluated the dependence of initial session 3 curvature (PE for movements 6–25) on the five fields learned during session 2. We decomposed the loads experienced in the five fields into their lateral and assistive components and used each to predict performance in the counter-clockwise lateral field that subjects learned during session 3. The analyses reported here focus on how session 3 performance was affected by the lateral strength of the force fields. No relationship was found between performance with lateral loads in session 3 and assistive loads in session 2.

We used regression again in experiment 2. We assessed the dependence of initial session 4 curvature (after 2- or 10-days of rest) on the loads experienced during session 2 and session 3. This allowed us to determine whether session 4 performance could be accounted for by either session 2 or session 3 alone or both training sessions in combination. For these analyses, we decomposed both the session 2 and session 3 fields into lateral and assistive components. We carried out a regression in which session 4 performance (PE) was assessed as a linear combination of session 2 and session 3 training. The coefficients of terms representing the lateral loads experienced during session 2 and session 3 were used to estimate the relative effects of session 2 and session 3 training on session 4 performance. No relationship was found between session 4 performance and the assistive loads experienced during session 2 and session 3.

Statistical tests of differences in regression weights between the 2-day and the 10-day delay were conducted using the bootstrap function BOOTSTRP in Matlab (The Mathworks, Natick MA). We repeated each regression 100 times and performed an independent samples t-test on resulting weights.

Simulations

For simulations we used a model of planar two-joint arm movement (Gribble et al. 1998) based on the -version of the equilibrium point hypothesis (Feldman 1986). According to the model, movement and muscle co-contraction result from neural input that takes the form of time-varying shifts in the threshold muscle length for motor neuron recruitment (). Motor neuron activation depends on the difference between actual and threshold lengths as specified in the equation

In this equation, A is positive or zero, l is the actual muscle length, is the centrally specified threshold length for motor neuron activation, µ is a constant specifying the dependence of threshold length on velocity, dl/dt is the rate of change of muscle length and d is a constant reflex delay. Muscle force, F, is generated in proportion to motor neuron activation according to the exponential function

where each muscle's force generating ability varies with its cross sectional area, . The model includes six muscles: biceps long head and triceps lateral head at the elbow, pectoralis and deltoid at the shoulder, and biceps short head and triceps long head spanning both joints. Passive muscle stiffness also contributes to total muscle force.

The coordinated control of muscle s results in movement and muscle co-activation. We assume that movements are produced by time-varying shifts in the limb's equilibrium trajectory (and in the associated muscle s), where each point on the trajectory is given by the set of s that minimizes total muscle force. The co-contraction command is defined by a separate set of shifts that act to increase muscle force in the most equal proportions without changing net joint torque. As in Gribble et al. (1998), for purposes of these simulations the co-contraction command is defined initially in force space and hence its units are N and specify average muscle force. The vector in space associated with this muscle force in statics is used as the co-contraction command.

Force field adaptation was simulated using a learning algorithm in which the equilibrium trajectory and associated muscle s are adjusted on a trial-by-trial basis in proportion to the difference between desired and actual trajectories (see Gribble and Ostry 2000 for details). In particular, we assumed that commands were updated on the basis of squared position error, such that large errors led to large adjustments in the modeled motor commands while small errors resulted in small adjustments. These adjustments were scaled by a constant such that differential rates of adaptation could be modeled. Control signals were thus updated according to the following equation

where is a vector of changes to muscle threshold length which reflect position error. This vector is summed on a trial-by-trial basis with the vector of muscle threshold lengths, , that was used to produce movements on the preceding trial. The position error is calculated as the time-varying difference between centrally-specified and actual muscle lengths, and l. The parameter d_nm is a constant that time-advances the position error vector by an amount corresponding to the neuromuscular delay, and r is a gain parameter that scales the rate with which squared position error is minimized. In the modeling studies described below we varied rate and co-contraction parameters to best fit the empirical data (Table 1). We found similar results in a set of simulations in which these parameters were held constant.

We began with session 1 by simulating movements in the absence of load. This generated five sets of modeled control signals (one for each movement direction) that compensated for the dynamics of the arm and produced straight-line movements. For session 2 we used the five sets of final session 1 control signals as initial commands for movements in each of the five force fields. For session 3 and session 4, initial commands for each movement direction were based on a weighted average of the control signals for that direction from preceding sessions. For each movement direction, the modeled control signals were averaged according to the following equation

where ₁ and ₂ are time-varying vectors of threshold muscle lengths associated (in this example) with session 1 and session 2 training, w₁ and w₂ are the relative weights for each session, and _evg is the vectorally averaged control signal. To obtain initial commands for session 3, session 1 and session 2 control signals were weighted 20%/80% (according to the 2-day delay group in Fig. 5B). The same weightings were used for all movement directions. To select weightings for session 4, we performed a number of simulations in which weights for session 2 and session 3 ranged from 0%/100% to 100%/0%. We then computed the sum of squared differences between actual and simulated session 4 performance. Based on this analysis, session 2 and session 3 control signals were weighted 50%/50% to produce initial commands for session 4.

View larger version (14K): [in this window] [in a new window]   FIG. 5. Motor learning reflects a weighted combination of previous training. A: for both 2- and 10-day delays, regression showed that session 4 performance depended on a weighted average of the lateral loads learned during session 2 and session 3. B: as the delay between training and testing increased from 2- to 10-days, the relative influence that session 2 and session 3 training had on session 4 performance shifted toward equivalence. Bars depict the relative influence of each session (mean ± SE, derived from bootstrap tests).

	RESULTS

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View larger version (34K): [in this window] [in a new window]   FIG. 2. Empirical and modeled performance for session 2. A: initial movements made in the 5 fields during session 2. For each group, 2 movements representative of the mean curvature for movements 6–25 are shown. Curvature was consistent with the direction of loads applied by the robot. B: change in movement curvature over the course of session 2 training. Movements straightened with training during session 2. C: change in velocity profiles over the course of session 2 training. With training, differences between velocity profiles for movements made in force fields and those of movements made in the absence of load decreased. D: simulated movements in the 5 force fields were initially curved but straightened as modeled control signals were updated to account for position error (compare with B).

View larger version (25K): [in this window] [in a new window]   FIG. 3. Performance during session 3: effects of session 2 training ranged from facilitation to interference. A: initial movements in a counter-clockwise (CCW) lateral field: Movement curvature depended on the field in which subjects were trained during session 2.For each group, 2 movements representative of the mean curvature depicted in C are shown. B: change in movement curvature over the course of session 3 training. C: initial curvature (average PE for movements 6–25, highlighted by the horizontal gray bar in B) differed depending on the field in which subjects trained during session 2. Facilitation, interference and effects in between were observed. D: regression revealed that session 3 performance could be predicted on the basis of the lateral loads learned during session 2. E: simulated movements show a pattern similar to that observed empirically (compare with B). The simulations used a weighted average of final sessions 1 and 2 control signals (20%/80%) as initial movement commands for session 3. F: initial curvature (PE) for simulated movements 6–25 (highlighted by the horizontal gray bar in D, compare with C).

Subjects returned one month later (session 4) to be tested in a clockwise field that pushed the hand laterally in a direction opposite to that in session 3 (mean 34.3 ± SD 7.2 days). Movements during session 4 were initially curved in a direction that was consistent with the clockwise load (Fig. 4A) and straightened over the course of training (Fig. 4B). The initial movement curvature differed depending on subjects' training history (P < 0.001, Fig. 4C).

View larger version (24K): [in this window] [in a new window]   FIG. 4. Session 4 performance reflects both sessions 2 and 3 learning. A: initial movements in a clockwise (CW) lateral field. For each group, 2 movements representative of the mean curvature depicted in C are shown. B: change in movement curvature over the course of session 4 training. C: initial curvature (average PE for movements 6–25, highlighted by the horizontal gray bar in B) differed depending on training history. D: simulations in which initial session 4 commands were an equally weighted average (50%/50%) of the final sessions 2 and 3 control signals (compare with B). E: initial curvature (PE) for simulated movements 6–25 (highlighted by the horizontal gray bar in D, compare with C).

We tested whether the adaptation rate was affected by the direction of movement. We found no systematic effects of movement direction on rate of learning. Out of 20 possible combinations (5 force field directions X 4 sessions), only 3 showed a dependence of adaptation rate on movement direction (P < 0.05).

We designed a second experiment that directly tested the idea that performance reflects a combination of prior skill learning. In this experiment we randomly varied each subject's training history and assessed the effects on later performance. The study involved an initial familiarization session, two subsequent training sessions separated by 24-hours and a final test session. For each of the two training sessions (session 2 and session 3) the training field was selected randomly from the five shown in Fig. 1B, resulting in 25 possible training sequences. During session 4, subjects were tested in a field that perturbed the hand laterally in the clockwise direction. Two separate experiments followed this basic procedure, with either a 2-day or 10-day delay between the training sessions and final session 4 testing.

Subjects' training histories (session 2 and session 3 learning) strongly influenced initial performance in the final test session (Fig. 5A, P < 0.001 for both the 2-day and 10-day delays, 91.1% and 80.4% of variance accounted for, respectively). Session 4 performance could be predicted on the basis of both session 2 (P < 0.001, P < 0.05 for the 2-day and 10-day delays) and session 3 (P < 0.001 for both delays) training. Session 3 training had a stronger influence on session 4 performance, but its relative effect decreased (P < 0.01 using bootstrap tests) as the interval between the training and testing sessions grew from 2 days to 10 days (Fig. 5B). Representations of skill thus involve a weighted average of past training that changes over time.

Computational modeling of neural averaging in motor learning

We carried out simulation studies using a computer model of two-joint arm movement and our results were consistent with the idea that performance reflects a weighted combination of past training. Control signals in the model were updated on a trial-by-trial basis based on the difference between the desired and actual trajectory on the most recent movement trial (Gribble and Ostry 2000). This iterative adjustment of modeled neural commands permits compensation for externally applied loads.

In the simulation studies the model was trained over four successive "sessions" to mirror the experimental manipulation. For the initial training session (simulated session 1), we modeled movements in the absence of external load. This resulted in modeled control signals that produced straight movements to each of the five targets and effectively compensated for the mechanical behavior of the two-joint arm.

To simulate session 2, we modeled movements in the presence of each of the five fields depicted in Fig. 1B, using the final session 1 control signals as initial commands for session 2. Like in session 2 of our experiment, the five fields resulted in movements whose curvature was consistent with the externally applied load. As control signals were updated on the basis of position error this curvature was eliminated as it was in our experimental subjects (compare Figs. 2B and 2D). Velocity profiles were also altered by the presence of load but returned to normal with training. The iterative procedure resulted in five different sets of modeled control signals (one for each movement direction in each field) that reflected learning at the end of simulated session 2.

For session 3, we modeled movements in a lateral field that pushed the hand in a counter-clockwise direction. Initial performance during session 3 depended on what the model learned previously. By using a weighted vector average of the final session 1 and session 2 control signals (20% session 1 and 80% session 2) as initial session 3 commands we observed effects that were similar to those obtained empirically during session 3 of the experiment (compare Figs. 3B and 3E, 3C and 3F).

Session 4 simulations involved movements in a field that pushed the hand laterally in a clockwise direction. We used a weighted vector average of the control signals generated during session 2 and session 3 (50% session 2, 50% session 3) as initial commands for session 4 (see following text). We found that the model produced a pattern of performance similar to that observed empirically during session 4 (compare Fig. 4B and 4D, 4C and 4E). This suggests that the training history affected session 4 performance and skills reflect weighted combinations of the control signals learned on previous training episodes.

Figure 6 shows that a weighted average of session 2 and session 3 control signals best accounts for the pattern of performance observed empirically. When the final control signals from session 2 alone (Fig. 6A) or session 3 alone (Fig. 6C) were used as initial commands for session 4, performance was not well simulated. Instead, error between actual and simulated session 4 performance was minimized (Fig. 6D) when initial control signals comprised an equally weighted combination of final session 2 and session 3 commands (Fig. 6B).

View larger version (38K): [in this window] [in a new window]   FIG. 6. A combination of session 2 and session 3 control signals provide the best simulation of session 4 performance. A: predicted session 4 movement curvature when initial commands comprised final session 2 control signals. Black outlines show empirical session 4 performance (as in panels B and C). B: predicted movement curvature when initial commands were an equal combination of final session 2 and session 3 control signals. C: predicted curvature when initial commands comprised final session 3 control signals. D: error between empirical and simulated session 4 performance was minimized by using an equal weighting of session 2 and session 3 control signals as initial values on session 4. Session 4 performance associated with small letters a–c is shown in panels A–C.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

Much recent research on learning and memory has focused on the idea that after recall, memories are labile and subject to displacement. Reactivated memories can be displaced by interfering events such as disruption of cellular protein synthesis (Kleim et al. 2003; Nader et al. 2000) and also appear to be displaced by new learning (Caithness et al. 2004; Walker et al. 2003). The present studies point to a further possibility, that original learning is not replaced by new learning but rather that old and new learning are combined at a neural level and that subsequent performance is mediated by this neural average. Consistent with this idea, when subjects complete multiple training episodes, one can observe a continuum of effects that range from facilitation to interference. When training episodes repeat the same sensorimotor mapping, the two training sessions facilitate each other. When training episodes involve opposite sensorimotor mappings, interference results and on later testing performance is no different from naïve. In between these extremes, training sessions produce a range of effects on one another from partially facilitating to partially interfering. Thus when a range of sensorimotor mappings is examined, a gradation of effects results that is not consistent with the idea that new learning simply displaces old. Rather it suggests that the neural substrate of skill is a combination of previous training.

Recent studies have also shown that consolidation does not permanently fix learning within the brain. Studies have shown that during periods of sleep after training, skills improve (Walker et al. 2002) and neural activation patterns shift location (Walker et al. 2005). These studies highlight that there is substantial "off-line" processing of learning after consolidation. Here we report a complementary result. As the delay between the end of training and final performance increases, the relative influence of each training session on final performance shifts toward equivalence. These changes in relative weighting suggest that the neural substrate of skill can change after consolidation of learning.

A number of studies have reported that subjects can learn two different fields simultaneously and independently access both encodings. This has been observed after extensive training (Krouchev and Kalaska 2003) or when each field is tied to a particular posture (Gandolfo et al. 1996) or other contextual cues (Osu et al. 2004) [note, however, that in some cases these arbitrary cues are insufficient (Gandolfo et al. 1996)]. Other cues, such as temporal separation, are not useful (Karniel and Mussa-Ivaldi 2002). Here we have shown that subjects do not have separate access to the learning associated with individual training sessions even when the fields involved orthogonal mappings between state of the limb and perturbing force. Instead, later performance was affected by a weighted combination of past learning. The situations in which the nervous system can separately access prior learning seem to involve information beyond the different forces each field involves. Perhaps, by engaging processing elements related to more cognitive or conceptual abilities, these cues allow the nervous system to categorize new learning as a component of one skill without affecting others.

Our modeling studies produced results that closely matched the performance of experimental subjects. For session 4, the best match was produced when the rate of adaptation was slower and muscle co-contraction was elevated relative to the previous three sessions. Although the source of this effect is unclear, previous research has shown that when subjects encounter environments the mechanical properties of which vary, they respond by elevating limb impedance (Takahashi et al. 2001). In the present study, it is possible that having learned different force fields on sessions 2 and 3 may have resulted in increased limb stiffness on session 4. At the same time, it should be emphasized that the overall pattern of results in our modeling studies is not dependent on the particular values for co-contraction and learning rate. As noted in the preceding text, we found similar results in a set of simulations in which these parameters were held constant.

	GRANTS

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This research was funded by National Institutes of Health Grants HD-048924 and DC-04669, Le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT), and Natural Sciences and Engineering Research Council of Canada.

	ACKNOWLEDGMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
The authors thank P. Gribble and K. Nader for comments and G. Houle, M.-È. Lacasse, and J. Godin for technical support.

	FOOTNOTES

 
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Address for reprint requests and other correspondence: D. J. Ostry, Dept. of Psychology, McGill University, 1205 Dr. Penfield Avenue, Montréal, Québec H3A 1B1, Canada (E-mail: ostry{at}motion.psych.mcgill.ca)

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