Original Article Behavior EMG, electromyography; CW, clockwise; CCW,
counterclockwise; MPE, maximum perpendicular error; ANOVA, analysis of
variance. David W. Franklin, Neuromuscular Diagnostics, Department of Sport
and Health Sciences, Technical University of Munich, Germany
<EMAIL_ADDRESS>
# Feedback Gains modulate with Motor Memory Uncertainty

Sae Franklin  Institute for Cognitive Systems, Department of Electrical and
Computer Engineering, Technical University of Munich, Germany  David W.
Franklin  Neuromuscular Diagnostics, Department of Sport and Health Sciences,
Technical University of Munich, Germany

###### Abstract

A sudden change in dynamics produces large errors leading to increases in
muscle co-contraction and feedback gains during early adaptation. We
previously proposed that internal model uncertainty drives these changes,
whereby the sensorimotor system reacts to the change in dynamics by up
regulating stiffness and feedback gains to reduce the effect of model errors.
However, these feedback gain increases have also been suggested to represent
part of the adaptation mechanism. Here, we investigate this by examining
changes in visuomotor feedback gains during gradual or abrupt force field
adaptation. Participants grasped a robotic manipulandum and reached while a
curl force field was introduced gradually or abruptly. Abrupt introduction of
dynamics elicited large initial increases in kinematic error, muscle co-
contraction and visuomotor feedback gains, while gradual introduction showed
little initial change in these measures despite evidence of adaptation. After
adaptation had plateaued,there was a change in the co-contraction and
visuomotor feedback gains relative to null field movements, but no differences
(apart from the final muscle activation pattern) between the abrupt and
gradual introduction of dynamics. This suggests that the initial increase in
feedback gains is not part of the adaptation process, but instead an automatic
reactive response to internal model uncertainty. In contrast, the final level
of feedback gains is a predictive tuning of the feedback gains to the external
dynamics as part of the internal model adaptation. Together, the reactive and
predictive feedback gains explain the wide variety of previous experimental
results of feedback changes during adaptation.

###### keywords:

Human Motor Control, Muscle Co-contraction, Reaching Movement, Motor
Adaptation, Internal Modal, Feedback Gain Modulation, Visuomotor Feedback
Gains

##  1 Introduction

Humans have exceptional abilities to skillfully manipulate and interact with
objects in the environment. Our sensorimotor system constantly generates
appropriate signals to control our musculoskeletal system, based on a
prediction of the current dynamics. When these dynamics are stable and
repeatable, we use an internal model or motor memory to produce an efficient
and effective motion. When the external dynamics change, our sensorimotor
control system adapts rapidly to the environmental disturbances in a manner
that indicates a fundamental knowledge of the mechanics of the external world
[1, 2, 3]. Any sudden change in the environmental dynamics during a movement
causes large kinematic errors, leading to a rapid increase in muscle co-
contraction [4, 5, 6, 7]. This co-contraction increases limb stiffness, both
intrinsic [8, 9, 10] and reflexive contributions [11, 12], and acts to limit
the perturbing effects of the dynamics until the sensorimotor control system
is able to learn a motor memory or internal model that can predictively
compensate for these dynamics. Once this motor memory or internal model is
updated, this co-contraction is gradually decreased.

Large kinematic errors which occur during the initial stages of adaptation to
novel dynamics have also been shown to produce rapid increases in visuomotor
[13] and long latency stretch [14] feedback responses. We previously proposed
that this increase resulted from uncertainty in the internal model [13].
During initial adaptation, the sensorimotor system receives unexpected error
signals indicating that our current internal model no longer predicts the
environment accurately, and that it either needs to update our current motor
memory or select a new motor memory [15]. We suggest that along with co-
contraction, the sensorimotor control system also upregulates feedback gains
until the sensorimotor control system is able to relearn a new model that
predictively compensates for these dynamics. These feedback gains are a
reactive response to the internal model uncertainty to limit the perturbing
effect of the novel dynamics during this initial phase of adaptation. However,
even after adaptation to the new environment, these feedback gains are
upregulated compared to the null field levels and tuned to the environmental
dynamics [13, 16, 17]. That is, these feedback gains at the end of the
adaptation process appear to arise as the sensorimotor control system
regulates the gain of the feedback system as part of the adaptation process to
novel dynamics, resulting in this final predictive component of feedback
gains. We therefore suggested that there are two computational components of
increased feedback gains; a reactive response to model uncertainty and a
predictive response that is learned as part of the internal model [16].

Here we examine whether the initial reactive component of the increased
feedback gain is driven by internal model uncertainty or is simply learned as
part of the adaptation process by contrasting the adaptation to abrupt changes
in dynamics with the gradual introduction [18, 19, 20, 21, 22, 23, 24]. An
abrupt introduction to a novel force field causes large error signals, whereas
a gradual introduction to the same force field produces little or no error
signals. Large errors would indicate that our current internal model no longer
well predicts the environmental dynamics. In contrast, a gradual introduction
of the force field provides only small errors within the natural variability
of human reaching movements. As such, we predict that there will be little
change in the uncertainty associated with the internal model, thereby causing
little or no reactive increase in the feedback gains, despite adaptation
continuing throughout the exposure phase. Instead, we predict only a gradual
increase in the visuomotor feedback gains as the appropriate level of steady
state feedback gains is learned for the dynamics. Here, we test these
predictions by having participants adapt to both gradual and abrupt dynamics
while measuring their visuomotor feedback gains to visual motion of the hand
[25, 26, 27, 28, 29]. Understanding the role that errors, rate of
environmental change and internal model uncertainty have on the adaptation
process, especially on co-contraction and feedback gains, provides us with
important knowledge about structuring learning in sports, rehabilitation and
other motor skills.

##  2 Material and Methods

###  2.1 Experimental Setup

####  2.1.1 Participants

Twelve participants participated in the experiment (3 male and 9 female: aged
25.0 $\pm$ 4.4, mean $\pm$ SD). All participants were right-handed according
to the Edinburgh handedness inventory [30] with no reported neurological
disorders. Participants provided written informed consent, and the
institutional ethics committee approved the experiments. One additional
participant took part in the experiment, but was excluded from the final
analysis as the level of force field adaptation was 34.7% across both force
fields (CW and CCW) at the end of the exposure period. All other participants
achieved a mean above 60% across the abrupt and gradual adaptation protocols.
The exclusion of this participant as an outlier was confirmed using Grubb’s
test across the final fifteen blocks of exposure in both abrupt and gradual
conditions.

####  2.1.2 Apparatus

Participants grasped the handle of the vBOT robotic manipulandum [31] with
their forearm supported against gravity with an air sled (Fig. 1A). The
robotic manipulandum both generated the environmental dynamics (null field,
force field or channel), and measured the participants’ behavior. Position and
force data were sampled at 1KHz. Endpoint forces at the handle were measured
using an ATI Nano 25 6-axis force-torque transducer (ATI Industrial
Automation, NC, USA). The position of the vBOT handle was calculated from
joint-position sensors (58SA; IED) on the motor axes. Visual feedback was
provided using a computer monitor mounted above the vBOT and projected
veridically to the participant via a mirror. This virtual reality system
covers the manipulandum, arm and hand of the participant, preventing any
visual information about their location. The exact time that the stimuli were
presented visually to the participants was determined using the video card
refresh rate and confirmed with an optical sensor to prevent a time delay.
Participants performed right-handed forward reaching movements in the
horizontal plane at approximately 10 cm below shoulder level.

Figure 1: Experimental set-up. A: Participants grasp the robotic manipulandum
(vBOT) while seated and visual feedback is presented veridically using a top
mounted monitor viewed through a mirror so that it appears in the plane of
movement. The participant’s forearm is supported by an airsled. B:
Participants experienced either an abrupt (green) or gradual (blue) onset of a
velocity dependent force field in different sessions. C: Throughout the
experiment, on random trials visual perturbations (probe trials) were used to
examine the magnitude of the visually induced motor response. During these
trials, the hand (dark grey line) was physically constrained to the straight
path between the initial starting position and the final target using a
mechanical channel, such that any force produced in response to the visual
perturbation (blue or red dotted lines) can be measured against the virtual
channel wall (grey arrows) using the force sensor. D: In all trials except the
probe trials, the hand cursor (orange line) is shown to the participant
overlaid on the actual hand movement (black dotted line).

####  2.1.3 Setup

Participants were seated with their shoulders restrained against the back of a
chair by a shoulder harness. Movements were made from a 1.0 cm diameter start
circle centered approximately 28.0 cm in front of the participant to a 2.0 cm
diameter target circle centered 25 cm in front of the start circle. The
participant’s arm was hidden from view by the virtual reality visual system,
on which the start and target circles as well as a 0.6 cm diameter cursor used
to track instantaneous hand position were projected. Participants were
instructed to perform successful movements to complete the experiment. A
successful movement required the hand cursor to enter the target (without
overshooting) within 700 $\pm$ 75 ms of movement initiation. Overshoot was
defined as movements that exceeded the target in the direction of movement.
When participants performed a successful movement they were provided with
feedback as how close they were to the ideal movement time of 700ms (‘great’
or ‘good’) and a counter increased by one. Similarly, when they performed
unsuccessful movements they were provided with feedback as to why the movement
was not considered successful (“too fast”, “too slow” or “overshot target”).
Trials were self-paced; participants initiated a trial by moving the hand
cursor into the start circle and holding it within the target for 1000 ms. A
beep then indicated that the participants could begin the movement to the
target. The duration of the movement was determined from the time that the
participants exited the starting position until the time that participants
entered the target.

####  2.1.4 Electromyography

Surface electromyography (EMG) was recorded from two mono-articular shoulder
muscles (pectoralis major and posterior deltoid), two bi-articular muscles
(biceps brachii and long head of the triceps) and two mono-articular elbow
muscles (brachioradialis, and lateral head of the triceps). The EMG was
recorded using the Delsys Bagnoli (DE-2.1 Single Differential Electrodes)
electromyography system (Boston, MA). The electrode locations were chosen to
maximize the signal from a particular muscle while avoiding cross-talk from
other muscles. The skin was cleaned with alcohol and prepared by rubbing an
abrasive gel into the skin. This was removed with a dry cotton pad and the
gelled electrodes were secured to the skin using double-sided tape. The EMG
signals were analog band-pass filtered between 20 and 450 Hz (in the Delsys
Bagnoli EMG system) and then sampled at 2.0 kHz.

####  2.1.5 Probe trials to measure reflex gain

In order to assess reflex magnitude, visually induced motor responses were
examined using perturbations of the visual system similar to those previously
described [28, 13, 32, 33, 34] throughout the experiments. On random trials,
in the middle of a movement to the target, the cursor representing the hand
position was jumped perpendicular to the direction of the movement (either to
the left or to the right) by 2 cm for 250 ms and then returned to the true
hand position for the rest of the movement (Fig. 1C). During these trials, the
hand was physically constrained to the straight path between the starting
position and the target using a mechanical channel, such that any force
produced in response to the visual perturbation could be measured against the
channel wall using the force sensor. The mechanical wall of the channel was
implemented as a stiffness of 5,000 N/m and damping of 2Nm-1s for any movement
lateral to the straight line joining the starting location and the middle of
the target [35, 7]. As this visual perturbation was transitory, returning to
the actual hand trajectory, participants were not required to respond to this
visual perturbation to produce a successful trial. These visual perturbations
were applied perpendicular to the direction of the movement (either to the
left or the right). For comparison, a zero-perturbation trial was also
included in which the hand was held to a straight-line trajectory to the
target, but the visual cursor remained at the hand position throughout the
trial. The onset of the displacements occurred starting at 7.5 cm (30% of the
length of the movement). The perturbation trials were randomly applied during
movements in a blocked fashion such that one of each of the three
perturbations were applied within a block of twelve trials.

###  2.2 Experimental Paradigm

Our previous experiment suggested that the large feedback gains during initial
adaptation were due to the uncertainty in the internal model [13], however
this could not be dissociated from motor adaptation. Here we examine this
phenomenon in detail, by contrasting the adaptation to abrupt changes in
dynamics with the gradual introduction [20, 22]. In this experiment, we
examine the changes in the feedback gains while the reaching errors are
presented both physically and visually to participants. While participants
could not see their hands, a visual cursor (yellow circle) was presented which
corresponded to their hand location. With the exception of 250ms on the probe
trials in which this cursor was perturbed laterally by 2cm, the cursor always
matched the physical location of their hand in both x- and y-axes (Fig. 1D).

####  2.2.1 Experimental Protocol

Each participant performed two sessions, which were separated by a short
break, in a single day. On one session, a dynamical force field was abruptly
introduced (abrupt), while on the other session a directionally opposite force
field was gradually applied (gradual). The order of both sessions and the
force field directions were counterbalanced across participants. EMG
electrodes remained in place throughout the entire experiment. Before each
session, participants performed a practice of 61 null field trials in order to
familiarize themselves with the movement criteria. Throughout the experiment,
trials were arranged in blocks consisting of twelve trials; of which three
were probe trials (visual perturbation and mechanical channel) and nine were
normal reaching trials (null field or force field depending on the phase of
the experiment). These probe trials were used to assess both the visuomotor
feedback gain and the degree of learned force compensation. While lateral
movement in the random probe trials was constrained by the mechanical channel,
participants were free to move in any direction during all other trials. Each
session consisted of 4 phases. A single movement was always performed first in
any new phase such that a probe trial was never the first movement. First,
participants experienced the pre-exposure phase of 121 null field trials (10
blocks of twelve trials plus one initial trial). Next, the initial exposure
stage consisted of 361 force field trials (30 blocks plus one initial trial).
In the abrupt condition, the full force field was applied from the first
trial, whereas in the gradual condition the force field was scaled up from one
trial to the next over the 361 trials (Fig. 1B). The force field was a
velocity-dependent curl force field where the force in N (Fx, Fy) on the hand
was computed as:

$\displaystyle\left[\begin{array}[]{ccc}F_{x}\\\
F_{y}\end{array}\right]=b\left[\begin{array}[]{ccc}0&-1\\\ 1&0\\\ \end{array}\
\right]\left[\begin{array}[]{ccc}\dot{x}\\\ \dot{y}\\\ \end{array}\right]$ (7)

depending on the participants’ hand velocity ($\dot{x},\dot{y}$) [m/s] and the
scaling factor $b$ which was either 0.16 N/m/s (clockwise curl force field:
CW) or -0.16 N/m/s (counter-clockwise curl force field: CCW). Once the initial
exposure phase was completed, both groups of participants performed the final
exposure phase consisting of another 20 blocks of trials (241 trials).
Finally, participants experienced the post-exposure phase in which 10 blocks
(121 trials) of null field trials were performed. Participants were required
to take short breaks every 200 movements throughout the experiment. They were
also allowed to rest at any point they wished by releasing a safety switch on
the handle.

###  2.3 Analysis

Analysis of the experimental data was performed using Matlab R2019a. EMG data
were band-pass filtered (30 – 500Hz) with a tenth-order, zero phase-lag
Butterworth filter and then rectified. Position, velocity and endpoint force
were low-pass filtered at 40 Hz with a fifth-order, zero phase-lag Butterworth
filter. Statistics were performed in Matlab and JASP 0.14.1 [36]. Statistical
significance was considered at the p<0.05 level for all statistical tests.

####  2.3.1 Hand Path Error

The maximum perpendicular error (MPE) was used as a measure of the
straightness of the hand trajectory. On each trial, the MPE is the maximum
distance on the actual trajectory that the hand reaches perpendicular to the
straight-line path joining the start and end targets (errors to the left are
defined as negative and errors to the right are defined as positive). The MPE
was calculated for each non-probe trial throughout the learning experiment.

####  2.3.2 Force Compensation

In order to examine the predictive forces exerted by the participants
throughout the experiment, the forces against the channel walls on the probe
trials were used. On each trial, the amount of force field compensation was
calculated by linear regression of the measured lateral force against the
channel wall onto the ideal force profile required for full force field
compensation [37]. Specifically, the slope of the linear regression through
zero is used as a measure of force compensation. The ideal force field
compensation was estimated as the product of the y-velocity and the force
field scaling factor. In the null field, the ideal force field compensation is
based upon the compensation required in the curl force field [38]. Therefore,
values in the null force field before learning (pre-exposure phase) should be
close to zero. In the gradual curl force field, the force compensation on a
given trial was calculated based on the current strength of the force field at
this specific trial.

####  2.3.3 Electromyographic Activity

For plotting purposes, the EMG was adjusted to the mean value of EMG in the
null field trials prior to the force field exposure for each muscle of each
participant prior to averaging. To examine differences in the overall muscle
activity across the experiment, the integral of the rectified EMG data was
taken over 700 ms from 100 ms before movement start until 600 ms after
movement start. The EMG data was averaged across all trials in a block. The
EMG was normalized and then averaged across participants (but not across
muscles). To normalize for a particular muscle, a single scalar was calculated
for each participant and used to scale the muscle’s EMG traces for all trials
for that participant. The scalar was chosen so that the mean (across trials)
of the EMG data averaged over the whole experiment was equal across
participants (and set to the mean over all the participants). This puts each
participant on an equal scale to influence any response seen in the data. For
comparison across muscles, the EMG values were further scaled for each muscle
relative to the mean value in the pre-exposure phase (expressed as a
percentage value relative to the pre-exposure activity). The muscle activity
was further separated into the amount related to co-contraction and the amount
related to force production for each of the three muscle pairs. In order to
examine the amount of co-contraction, the minimum value of EMG between the two
muscles making up a muscle pair was determined and multiplied by 2 as both
muscles would contribute to the increased stiffness. The activation that would
correspond to the change in force was determined as the maximum muscle
activity of the two muscles of the muscle pair subtracted by the minimum of
the two muscle activities. Differences in these measures across the gradual
and abrupt conditions were examined using a t-test in Matlab.

####  2.3.4 Rapid Visuomotor Responses

Individual probe trials were aligned on visual perturbation onset. The
response to the right visual perturbation on probe trials was subtracted from
the response to the left perturbation on probe trials in order to provide a
single estimate of the motor response to the visual perturbation for each
block. To examine the feedback gain, we calculated the average post-
perturbation force over two intervals: the first corresponding to an rapid
involuntary response (180–230 ms) [28], and the second to a slower response
(230-300 ms) [32, 16]. To examine the electromyographic responses to the
visuomotor perturbations, the EMG traces were divided by the mean value of the
muscle activity in the null force field (pre-exposure) for that muscle in that
participant between -50 and 50 ms relative to the onset of the perturbation.
Muscular responses were considered over two intervals: 90-120 ms and 120-180
ms as in previous studies [33, 32, 39, 40].

####  2.3.5 Comparisons

In order to compare the final values after learning, the mean measures (MPE,
force compensation and visuomotor feedback gain) over the last 15 blocks in
the final exposure phase were contrasted between abrupt and gradual conditions
using frequentist repeated measures ANOVAs with a between subjects factor of
condition order using JASP 0.14.1. To complement the frequentist approach we
also perform equivalent Bayesian repeated measures ANOVAs using JASP 0.14.1.
Here we use the Bayes Factors $(BF_{10}$) to evaluate evidence for the null
hypothesis. In order to examine the after effects on the first block of trials
in the post-exposure phase for both MPE and force compensation, we subtracted
the mean values in the pre-exposure phase from the value of the first block in
the post-exposure phase. We then performed a paired t-test using Matlab to
examine any differences between the gradual and abrupt adaptation groups.
Significant differences were examined at the p<0.05 level.

##  3 Results

Participants performed forward reaching movements while grasping the handle of
a robotic manipulandum (Fig. 1A). Participants were then presented with either
an abrupt or gradual introduction of a velocity-dependent force field (Fig.
1B). Throughout the entire experiment we measured the feedback gains on random
trials by presenting the participants with a brief visual perturbation of a
hand cursor (to the right or left of the movement) while the physical hand was
mechanically constrained to move within a channel to the target, termed probe
trials, (Fig. 1C). On these probe trials we measured the lateral force
produced by the participant’s hand into the channel providing information both
about the learned predictive forces for compensating the force field and the
magnitude of the rapid visuomotor feedback gains. Throughout the experiment,
participants received visual feedback about their movement and the target via
a computer screen in the plane of movement (Fig. 1D).

###  3.1 Behavior

All participants adapted to both an abrupt and a gradual introduction of a
curl force field where both the order and the field direction were
counterbalanced across participants. After a short pre-exposure phase where
the initial trials were in the null field, a curl force field was applied
unexpectedly. In the abrupt condition this caused a large increase in the
kinematic error (Fig. 2A left, green). However, in the gradual condition, as
the strength of the curl force field is gradually increased, the kinematic
error (MPE) only slowly increased until the strength of the force field got
close to the final level (Fig. 2A right, blue). Once the force field reached
the final level, the MPE appeared to gradually reduce over the next twenty
blocks of trials. Interestingly, after the experiment had finished,
participants generally reported that they did not realize that a force field
had been applied, instead only that something different was being done to
their arm during these movements once they were halfway through the gradual
loading of the force field. Comparing with a repeated measures ANOVA the last
15 blocks in the final exposure phase (dark gray shaded area), the MPE in the
abrupt condition was not significantly different from that in the gradual
condition ($F_{1,10}=0.598,p=0.223;BF_{10}=0.845$) (Fig. 2A center bar graph)
and there was no between subjects effect of condition order
($F_{1,10}=0.984,p=0.345;BF_{10}=0.604$). For both groups, when the force
field was removed (post-exposure phase) the maximum perpendicular error
increased dramatically in the opposite direction to that of the force field
(Fig. 2A, left and right), but was reduced quickly over the subsequent blocks.
There was no significant difference between the kinematic after effects on the
first block of trials between the abrupt and gradual adaptation groups
($t_{11}=1.17,p=0.267$).

Figure 2: Comparison of adaptation between abrupt and gradual exposure to the
curl force fields. A: The mean (solid line) and standard error of the mean
(shaded region) of the maximum perpendicular error (MPE) of the hand
trajectory over the experiment. The sign of the MPE measurement from the CCW
force fields was flipped so that all errors produced by the force field were
shown to be positive. The gray shaded area (and darker green and blue colors)
indicate the period over which the curl force field was applied. The vertical
dotted line shows the time point at which the gradual force field was the same
strength as the abrupt force field. Dark gray shaded area indicates the last
15 blocks of the full force field exposure phase over which the final levels
of adaptation were compared. The center bar graph compares this final level of
MPE across the two force fields. The error bar represents the standard error
of the mean (s.e.m.). Each participant’s final value is shown with a point. A
light grey point indicates the CW force field whereas a dark grey point
indicates the CCW force field. The square indicates the first force field
experienced whereas the circle indicates the second time participants
experienced a force field. There were no significant differences between the
conditions. B: Force compensation level over the experiment as measured on the
channel trials. A value of 100% indicates perfect compensation for the force
field. Force compensation in the null field was quantified with respect to the
full force field value, so a value of 0 is expected. In the gradual condition,
as the force field is ramped up, the force compensation is expressed as a
percentage of the force field that has been applied to the participant at this
point in the experiment. Values plotted as in A. Similar levels of force
compensation were found for abrupt and gradual conditions with no significant
difference over the last 15 blocks of exposure.

Throughout the entire experiment, random trials were introduced in which
participants performed movements in a mechanical channel constraining their
hand to a straight movement to the target. Using these trials, we can estimate
the predictive force compensation as participants adapt to the dynamics (Fig.
2B) indicating the percentage of perfect adaptation to the force field. Note
that in the gradual condition, the percentage of adaptation is expressed as a
function of the current level of force field during the ramp phase.
Interestingly, the force compensation in the gradual force field adaptation
appears to start from 60-70% perfect adaptation from the beginning and stay
around this level throughout both the initial ramping phase and the later
constant phase. In both the abrupt and gradual conditions, participants showed
high levels of force compensation (over 70%) after they reached to 100%
strength of the force field (blocks 40-60). When comparing the final levels of
adaptation in the abrupt and gradual conditions (final 15 blocks of exposure
phase), we again found no significant difference (dark gray shaded area in the
figures) in the force compensation (Fig. 2B center) between the abrupt and the
gradual conditions ($F_{1,10}=0.962,p=0.350;BF_{10}=0.647$) and no between
subjects effect of condition order ($F_{1,10}=1.280,p=0.284;BF_{10}=0.536$).
Therefore, the final adaptation level of participants in the abrupt and
gradual conditions were similar, although the abrupt condition had a much
greater number of trials in which they were presented with the full magnitude
of the force field. In the post-exposure phase, there was also no significant
difference between the force compensation after effects on the first block of
trials between the abrupt and gradual adaptation groups
($t_{11}=0.276,p=0.788$).

###  3.2 Muscle Activity

Muscle activity (EMG) was recorded from six muscles and is shown separately
for the counter-clockwise (Fig. 3A) and clockwise (Fig. 3B) force fields. The
EMG values are normalized to the null field level for all muscles, and are
only shown here on the mechanical channel trials in which the force field is
not applied and no trajectory errors occur. In the abrupt condition (green),
all muscles increase their activity when the force field was first applied,
suggesting an initial large increase in co-contraction. However, the muscles
slowly reduced their activity as learning proceeded, eventually reaching a
plateau level late in adaptation. At the end of the exposure phase there are
high activity levels in the muscles compensating for the force field:
posterior deltoid and triceps longus for the CCW force field and pectoralis
major and biceps brachii for the CW force field. In the gradual condition
(blue), the muscle activity remained low throughout the early exposure period,
only gradually increasing and reaching a plateau towards the end of the
exposure phase. The final levels of muscle activity were similar between both
the abrupt and gradual conditions for both force fields. The similar levels of
final muscle activity were true for both the muscles compensating for the
force field, and those acting as stabilizers – increasing the co-contraction.
When the force field was suddenly removed (after block 60), there were further
increases of muscle activity, especially in the antagonist muscles – the
muscles that were not acting to compensate for the force fields (e.g.
posterior deltoid and triceps longus in the CW force field for a forward
movement). As the muscle activity on this (and subsequent figures) is obtained
from the channel trials, we would expect that most of the activity is pre-
planned and not a reaction to kinematic errors experienced on the specific
trial.

Figure 3: Comparison of muscle activity (EMG) across the experiment for abrupt
(green) and gradual (blue) exposure to curl force fields. Light blue and green
indicate values in the null field whereas dark blue and green indicate values
in the curl force field. Data is only from the randomly interspersed
mechanical channel trials where the curl force field was not applied.
Increasing extensor muscle activity is plotted in the downward direction. A:
Muscle activity (mean and s.e.m) during adaptation to the CCW curl force
field. Muscle activity was normalized for each of the six muscles to the mean
value in the pre-exposure phase before averaging across participants. EMG
values were calculated as the integrated muscle activity from -100 to 600 ms
relative to the start of the movement. Grey shaded region indicates the
exposure phase and the vertical dotted line indicates the point at which the
gradual force field is equal to the full force field value. B: EMG in the CW
curl force field. Across both force fields, high levels of muscle activation
were initially observed when the force field was introduced abruptly (green)
but not when introduced gradually (blue).

The temporal profile of muscle activity after adaptation was examined for both
the CCW and CW force fields (Fig. 4) on the channel trials, with the profile
of activity on the null field trials shown for comparison. As expected the
profile of muscle activity in the null field prior to either the abrupt or
gradual force field application is similar. After adaptation, we also find
similar temporal profiles of muscle activation for many of the muscles, but
with specific differences between the conditions. In particular, in the CCW
force field (Fig. 4A), there was a larger activation of the posterior deltoid
muscle in the abrupt condition, whereas there was a larger triceps longus
activation in the gradual condition. After adaptation to the CW force field
(Fig. 4B) it appears that there is a larger pectoralis major and triceps
longus muscle activation after the abrupt introduction of the force field,
whereas the gradual condition shows a slightly larger biceps brachii
activation. Therefore, across both force fields, the abrupt introduction of
the force field produced slightly higher activation of the shoulder muscles,
whereas gradual adaptation often recruited the biarticular muscles to a larger
degree. It is therefore possible that the specific pattern of large
directional errors in the abrupt conditions changes the overall recruitment
pattern of muscles even after adaptation.

Figure 4: Temporal profiles of muscle activity in the null force field and
after adaptation for the abrupt (green) and gradual (blue) conditions. Data is
only from the mechanical channel trials where the curl force field was not
applied. Increasing extensor muscle activity is plotted in the downward
direction. Prior to averaging across participants, the EMG has been smoothed
with a 50-point (25ms) smoothing function. A: EMG profiles in the CCW curl
force field. Null field activity (all 10 blocks in the pre-exposure phase)
prior to adaptation is indicated by the light green and light blue traces.
Final adaptation activity (all 20 blocks in the final exposure phase) is
indicated by the dark green and dark blue traces. Muscle activity has been
aligned to the start of the movement (0 s). Solid lines indicate mean across
participants and shaded regions indicate s.e.m. B: EMG profiles in the CW curl
force field.

The possibility that abrupt and gradual adaptation results in different
patterns of adaptation is very intriguing but difficult to test here without a
larger number of participants, as the participants adapted to both CW and CCW
force fields. Nevertheless, we can perform some exploratory analysis by
combining the CW and CCW force fields together. To do so, we combined the
appropriate muscles (considering the agonist or antagonist role of the muscle
in each force field). For example, the pectoralis major activity in the CW
force field and posterior deltoid in the CCW force field were combined, and a
t-test was used to contrast the mean level (over 100-500ms) in the abrupt and
gradual conditions. We found a significantly larger muscle activity for the
agonist shoulder muscle in the abrupt condition ($t_{22}=3.59,p=0.0016$) and a
significantly larger muscle activity for the agonist biarticular muscle in the
gradual condition ($t_{22}=2.27,p=0.0328$), but all other comparisons were not
significantly different (all $p>0.5$). However, it is important to clarify
that these statistics are exploratory and provide only weak support for this
difference in final muscle activation patterns.

Figure 5: Muscle activity in initial and final exposure to abrupt (green) and
gradual (blue) application of force fields. Data is only from the mechanical
channel trials where the curl force field was not applied. A: Initial exposure
(first 10 blocks in initial exposure phase) to abrupt force field elicits
large co-contraction in shoulder, biarticular and elbow muscles for both CCW
and CW curl fields. Muscle activity is calculated as increase relative to the
null field activity. Bars indicate mean ($\pm$ 95% confidence intervals)
integrated muscle activity from -100 to 600 ms from the start of the movement.
If the error bars do not overlap then this indicates a significant difference
at $p<0.05$. B: Final exposure (last 10 blocks in final exposure phase) shows
similar levels of change in muscle activity for both abrupt and gradual change
in dynamics. C: The co-contraction index and adaptation index of muscle
activity in the initial exposure. Bar indicates total values across the muscle
pairs ($\pm$ s.e.m.) and the colors indicate the relative contribution from
the shoulder muscles (dark colors), biarticular muscles (medium colors) and
elbow muscles (light colors). Values are across both the CCW and CW curl
fields. Statistics indicate result of t-test. D: The co-contraction index and
adaptation index of muscle activity in the final exposure periods.

Similar effects can be seen when we quantify the increases in EMG for both
initial and final exposure (Fig. 5). As expected, the abrupt condition
produced large increases in muscle activation for all six muscles (and
therefore increased co-contraction) during the initial exposure (Fig. 5A). In
contrast, only a small increase in muscle activity was seen initially in the
gradual condition. However, during the final exposure phase we see a similar
level of muscle activity in both abrupt and gradual conditions (Fig. 5B). Here
again the difference between the abrupt and gradual adaptation appears in our
experiment. Abrupt presentation of the force field appears to recruit higher
activation in the shoulder muscles whereas gradual adaptation recruited higher
levels of biarticular muscle activity. As error bars reflect the 95%
confidence intervals, some of these differences are significant. In order to
quantify the degree of co-contraction and adaptation in the experiments across
the gradual and abrupt conditions, we calculated the co-contraction and
adaptation indices (Fig. 5C and 5D). The co-contraction index is a simple
measure to capture the relative amount of activation in antagonistic muscle
pairs, whereas the adaptation index is designed to indicate the amount of
muscle activity in a specific direction (reciprocal activation) that might be
directed to compensate for the force field. In the initial exposure phase
(Fig. 5C), the co-contraction index was much higher in the abrupt condition
than in the gradual condition ($t_{11}=5.3314,p=0.0002;BF_{10}=135.15$). The
adaptation index was also higher in the abrupt condition
($t_{11}=4.1241,p=0.0017;BF_{10}=25.75$), but this difference was much smaller
(approximately twice the level). However, in the final exposure phase (Fig.
5D), there were no significant differences in either the co-contraction
($t_{11}=0.4797,p=0.6409;BF_{10}=0.317$) or adaptation
($t_{11}=0.9499,p=0.3625;BF_{10}=0.420$) measures. The difference in the
shoulder and biarticular muscle activity at the end of adaptation can again be
seen in the adaptation index measure (Fig. 5D, right), but does not show up in
the co-contraction index. Despite these differences, the overall muscle
activity levels were similar across both presentations of the dynamics.

###  3.3 Visuomotor Feedback Responses

Figure 6: Changes in visuomotor feedback gain during adaptation to abrupt
(green) and gradual (blue) curl force fields. A: Visuomotor feedback gains
during 180-230ms after the visual perturbation onset. Figure plotted as in
Fig. 2. B: Visuomotor feedback gains during 230-300ms after the visual
perturbation onset. Visuomotor feedback gains are measured on channel trials
where the curl force fields were not applied.

Throughout the abrupt and gradual experiments, the visuomotor feedback
responses were measured using probe trials in which the hand was constrained
to a mechanical channel, but a visual perturbation of the cursor position was
applied. The visuomotor feedback response was quantified over two intervals:
an early interval between 180 and 230 ms (Fig. 6A) and a later interval
between 230 and 300 ms (Fig. 6B). In both intervals the onset of the abrupt
change in dynamics produced a rapid increase in the visuomotor gain (green
traces) which then remained fairly high over the rest of the exposure phase,
with a possible slight decrease over learning as seen in previous work [13].
In contrast, when the curl force field was applied gradually, there was little
to no initial increase in the visuomotor gains, which instead gradually
increased over the whole exposure period and then plateaued as the full level
of force field was applied in the final exposure trials. Despite the very
different patterns of visuomotor gains during the learning phase, the
visuomotor gains in the last 15 blocks of the exposure phase were not
significantly different between the abrupt and gradual conditions in either
the early ($F_{1,10}=1.697,p=0.122;BF_{10}=0.922$; Fig. 6A bar plot) or late
intervals ($F_{1,10}=0.542,p=0.334;BF_{10}=0.537$; Fig. 6B bar plot). For both
cases, there was also no effect of condition order (early:
$F_{1,10}=0.409,p=0.576;BF_{10}=0.665$; late:
$F_{1,10}=0.531,p=0.519;BF_{10}=0.554$). Therefore, both conditions produced
the same final level of visuomotor gains regardless of the large difference in
kinematic errors during the adaptation. When the force field was removed
abruptly in both conditions, we see an initially high visuomotor gain that
decreased rapidly in these null field trials.

Figure 7: Comparison of final visuomotor feedback responses after adaptation
to the abrupt (green) and gradual (blue) curl force fields. A: Mean ($\pm$
s.e.m.) lateral force produced after rightward (solid lines), zero (dotted
lines) and leftward (dashed lines) visual perturbations across both CCW and CW
fields in the abrupt condition. Lateral force was adjusted by subtracting the
mean lateral force across all channel trials in each force field. B: Lateral
force in response to visual perturbations across both CCW and CW fields in the
gradual condition. C: Visuomotor responses (zero perturbation subtracted)
across both CCW and CW fields. Light grey shaded region indicates the early
visuomotor response interval (180-230 ms) while the dark grey region indicates
the late visuomotor response interval (230-300 ms). D: Lateral force produced
in response to visual perturbations after adaptation to the abrupt onset of
the CCW force field. E: Lateral force produced in response to visual
perturbations after adaptation to the gradual onset of the CCW force field. F:
Visuomotor responses in the CCW force field after abrupt and gradual
adaptation. G-I: Visuomotor force responses after adaptation to the CW force
field.

As previous studies have shown that movement kinematics can influence feedback
gains [41, 42], we also examined the peak velocities. The mean peak forward
velocities ($\pm$ std) were 74.08 $\pm$ 10.15 m/s in the gradual condition and
75.45 $\pm$ 10.71 m/s in the abrupt condition. To test for differences across
the adaptation period (early and late), we performed a repeated ANOVA. There
was no difference between abrupt and gradual ($F_{1,11}=0.495,p=0.496$), or
between early and late exposure phases ($F_{1,11}=1.919,p=0.193$), but there
was a significant interaction effect ($F_{1,11}=6.042,p=0.032$). However post-
hoc analysis found no differences between any of the conditions (all
$p>0.098$).

In order to contrast the visuomotor feedback gains at the end of the exposure
period we plotted the lateral hand force as a function of the time from
perturbation onset (Fig. 7) in these probe trials. The lateral force is the
force produced by the participant against the wall of the virtual channel. The
force produced after the abrupt introduction of the force field (Fig. 7A)
looks similar to that after the gradual introduction of the force field (Fig.
7B). When we subtract the zero-perturbation condition, we can see that the
visuomotor response is similar in both conditions, not only in the early and
late intervals but across the whole response (Fig. 7C). Participants in these
experiments adapted to both the CCW and CW force fields, so we also examined
the force response in each of these force fields separately (Fig. 7D-I). We
find similar lateral forces against the channel wall for both the abrupt and
gradual conditions in the CCW force field, but when we subtract the zero-
perturbation condition it looks as though the forces are slightly larger in
the gradual condition (Fig. 7F). In the CW force field, the lateral forces are
in the opposite directions, but here the comparison shows a similar response
in both abrupt and gradual conditions (Fig. 7I). One interesting point is that
the CCW and CW force fields require opposite adaptive forces which can be
clearly seen in the force traces (e.g. compare Fig. 7 D and G). In each force
field a perturbation in one direction would be resisted by highly active
muscles whereas in the other direction these muscles would have much lower
activation (e.g. Fig. 5). This would then be reversed in the opposite force
field. However, despite these differences the visuomotor force response is
roughly equal in both perturbation directions. To support this claim, we
compared the feedback force response to perturbations in the direction of the
force field to those opposite to the direction of the force field using a
t-test. We found no significant differences in either the early
($t_{22}=0.929,p=0.3629$) or late ($t_{22}=0.786,p=0.440$) intervals. This
result supports our previous results that visuomotor feedback responses do not
exhibit gain scaling [13, 16], at least at the level of force responses.

Figure 8: Visuomotor feedback responses in the pectoralis major muscle after
force field adaptation. A: Pectoralis major activity to leftward (dashed
lines), zero (dotted lines), and rightward (solid lines) visual perturbations
after abrupt adaptation to the CCW force field. Activity is scaled according
to the level of muscle activity in the null field (mean between -50 and +50 ms
prior to the perturbation time) which is represented by the dotted black line.
Shaded region indicates the s.e.m. B: Muscle activity after gradual adaptation
to the CCW force field. C: Muscle activity after abrupt adaptation to the CW
force field. D: Muscle activity after gradual adaptation to the CW force
field. E: Visuomotor responses (perturbation – zero perturbation) averaged
across the CCW and CW force fields for the abrupt (green) and gradual (blue)
conditions. Rightward perturbations (solid lines) produce an excitatory
response whereas leftward perturbations (dashed lines) inhibit the muscle
activity. Light grey and dark grey bars indicate the early (90-120 ms after
perturbation onset) and late (120-180 ms) visuomotor response time windows.
Bar plot quantify the responses over the early and late windows. Error bars
indicate 95% confidence intervals. F: Visuomotor responses averaged across
abrupt and gradual conditions to examine differences between the CCW (pink)
and CW (brown) force fields Figure 9: Visuomotor feedback responses in the
posterior deltoid muscle after force field adaptation. Responses plotted as in
Fig. 8 to leftward (dashed lines), zero (dotted lines), and rightward (solid
lines) visual perturbations. A: Posterior deltoid activity to leftward, zero,
and rightward visual perturbations after abrupt adaptation to the CCW force
field. B: Gradual adaptation to the CCW force field. C: Abrupt adaptation to
the CW force field. D: Gradual adaptation to the CW force field. E: Visuomotor
responses (perturbation – zero perturbation) averaged across the CCW and CW
force fields for the abrupt (green) and gradual (blue) conditions. Bar plot
shows responses over the early and late windows, with error bars indicating
95% confidence intervals. F: Visuomotor responses averaged across abrupt and
gradual conditions to examine differences between the CCW (pink) and CW
(brown) force fields.

Finally, we examined the muscle responses to the visual perturbation,
particularly those in the pectoralis major (Fig. 8) and posterior deltoid
(Fig. 9); the major muscles to correct lateral perturbations in this movement.
As the background load and muscle activity are different across force fields,
the muscle responses to the visual perturbation is shown separately for the
CCW and CW fields for both the abrupt and gradual conditions (Fig. 8A-D).
Visual perturbations produce clear excitation or inhibition of the muscular
activity. If we average across the two force fields we see that there are
similar responses in the pectoralis major in both the abrupt and gradual
conditions (Fig. 8E), with no differences across either the early or late
visuomotor response windows (error bars represent 95% confidence intervals).
If instead, we average across the abrupt and gradual conditions, we can
directly compare the muscular responses in the CCW versus the CW force fields
(Fig. 8E). Here again there were no differences across the temporal response
or within the early or late visuomotor response windows. That is, despite
differences in the background loads of the muscles, the visuomotor response at
the end of the learning the force fields were similar for both CCW and CW
force fields. Similar responses were observed in the posterior deltoid (Fig.
9). When averaged across the force fields, we found no differences in the
muscular responses between the abrupt and gradual conditions (Fig. 9E).
However, when averaging across abrupt and gradual conditions, we found
apparent differences in the muscular responses between the CCW and CW force
fields, although these differences were not statistically significant (Fig.
9F). Visual feedback responses may have exhibited small field-specific
differences across the abrupt and gradual fields (for example compare
posterior deltoid response in Figs. 9A and 9B). However, with only six
participants available for these specific comparisons, it is not possible to
examine these possible trends further in this study.

##  4 Discussion

The goal of this study was to examine whether internal model uncertainty
drives changes in the feedback gains during adaptation. In order to do this,
participants performed reaching movements where the environmental dynamics
were either changed abruptly (producing large kinematic errors) or gradually
(producing small kinematic errors). Abrupt changes in dynamics produced large
kinematic errors during the movements signaling that the internal model was
incorrect – which should increase internal model uncertainty. In contrast, a
gradual change in the dynamics produced only small kinematic errors and should
produce much lower uncertainty in the internal model. In the initial exposure
to the force fields, participants in the abrupt condition experienced large
kinematic errors, extensive muscle co-contraction, increased visuomotor
feedback gains, and a rapid increase in force compensation. In contrast,
participants in the gradual condition experienced little to no kinematic
errors, very little co-contraction and only small increases in the visuomotor
feedback gains. Despite this, the force compensation was maintained at around
70% of the applied force field throughout the initial exposure period, and was
associated with the respective changes in the muscle adaptation index.
Although there were large differences in the initial exposure phase,
participants in both abrupt and gradual conditions reached similar levels of
kinematic error, force compensation, co-contraction, muscle activity and
visuomotor feedback gains by the end of the exposure phase.

Here we claim that internal model uncertainty drives the changes in feedback
gains, rather than internal model inaccuracy. It is important to point out
that we do not have a specific measure of internal model uncertainty, and that
here we only manipulate it with increased errors through changes in the
environmental dynamics which also directly affects internal model accuracy.
Despite this, we believe that it is internal model uncertainty rather than
inaccuracy that drives these changes. First of all, we may have internal model
inaccuracy, but without errors indicating that this is the case, we predict no
increased feedback gains. For example, we can consider the first trial in the
exposure phase. There is initially high internal model inaccuracy as the
prediction is a null force field (but environment is a force field), but low
internal model uncertainty as the current model has accurately predicted all
the previous trials. Only after a large error has indicated that the internal
model is inaccurate, directly increasing internal model uncertainty, will we
find increased feedback gains. Moreover, we predict higher feedback gains if
the internal model uncertainty is high even if the internal model accuracy is
perfect on a given trial (for example as the external dynamics change on a
trial-by-trial basis). While we do not yet know any data supporting this
testable prediction, the effects are similar to the changes in grip force seen
during adaptation to changing force fields [43]. In this paper [43], Hadjiosif
and Smith showed that the grip force was much more sensitive to increased
variability in the strength of the force fields than in the size of the force
field, suggesting a connection between statistical confidence and the grip
force matching similar changes in co-contraction. Here we also find similar
changes in feedback gains which match their predictions. Our interpretation
that internal model uncertainty drives increases in feedback gains also
predicts that we would find a brief increase in feedback gains when the force
field was removed – initial washout trials – as we found in our previous work
[13]. However, there is no clear evidence of this effect in the current
manuscript, where the initial feedback gains in the post-exposure phase are
similar to those in the exposure phase (Fig. 6).

In this study we used a within-subject design, with a counterbalanced order of
presentation such that half of the participants experience the gradual
adaptation first and half the abrupt adaptation. A limitation of this design
is that participants have already experienced adapting to a force field upon
presentation of the second force field. This effect was limited by ensuring
that participants adapted to the opposite force field during the second
adaptation period (avoiding the effect of savings), and by having 303 null
field trials between the first adaptation and the second adaptation phases to
ensure sufficient washout. Moreover, there were no statistically significant
effects of experiment order. However, there are also important advantages to
this design. First of all, the amount to which each participant adapts to a
force field varies greatly, with some participants adapting almost fully and
others only partially [44, 45]. The repeated measures design allows us to
adjust for participant variability in the adaptation process. More importantly
this design allows us to keep the EMG electrodes on the participant to record
muscle activity in both gradual and abrupt conditions. Overall, this design
improves our sensitivity to any differences in the adaptation process without
requiring a large number of participants. Even though we only have 12
participants, limiting the effect of individual variance by having all
participants perform all conditions improves estimates of any effects.
However, counterbalancing the force fields means that most of the muscle
activity data is presented for six participants (CW and CCW separately), and
thereby limits our ability to statistically test these results further. Here
we have analyzed and presented EMG data normalized to the activity in the null
field as in our previous work [6, 13]. While this normalization technique
allows for clear comparison across different papers and experiments, it has
some limitations in the normalization between muscles. That is if one muscle
has very low levels of activation throughout the whole movement, this muscle
is more susceptible to increased noise. As with any summed measure of muscle
activity across muscles, care needs to be taken with interpretations of our
indexes of co-contraction and adaptation which sum activity across muscles.
However, these value along with the trial-by-trial and temporal patterns of
muscle activity for each muscle individually provide evidence that there are
similar levels of muscle activity after adaptation to both gradual and abrupt
changes in dynamics.

Many studies have compared gradual adaptation with abrupt adaptation to force
fields [18, 19, 20, 21, 22, 23, 24, 46]. It has been shown that the final
level of adaptation is similar regardless of whether the novel dynamics are
presented abruptly or gradually [18, 19, 24, 46]. Here we also found no
difference in the final level of kinematic error (MPE) or force compensation,
agreeing with these previous studies. It has been suggested that gradual
presentation of novel dynamics drives changes in the internal model of the
limbs dynamics rather than in the internal model of the tool (or robot) [20],
which could explain why the motor memory formed with gradual adaptation does
not transfer bimanually to the other limb [18]. Although it has been suggested
that gradual presentation produces better retention [21], more recent studies
have shown that the retention rates are similar, and that the biggest effect
on retention is simply the amount of training [46]. Nevertheless, as larger
errors are more likely to induce adaptation of a new motor memory [15] or
adapt a specific tool related motor memory [20], we might expect that there
are subtle differences in the properties of the motor memories that are formed
under these two different situations, such as the fact that gradually adapted
motor memories do not transfer across limbs [18].

Although earlier studies suggested that abrupt presentation of novel dynamics
is learned faster [21], more recently it was claimed that the learning rate in
abrupt and gradual dynamics is similar [24]. Milner and colleagues found that
while amplitude error decreased faster under abrupt conditions, the temporal
error or smoothness decreased faster under gradual conditions. Here we did not
compare the rate of adaptation under the two conditions, however the force
compensation calculated relative to the presented dynamics was consistently
70% of the applied force field throughout both the gradual increase of the
force field and the steady state phase. Under the abrupt change in dynamics,
the force compensation increased up to a similar level. Therefore, it appears
that under both conditions, the adaptation mechanism is able to incorporate a
similar level of the error to modifying the predictive force compensation.
Previous work has shown that the adaptation system is more sensitive to small
errors than larger errors [47, 48, 49, 50], which might suggest that gradual
dynamics would be learned faster. Here we have shown that the large errors
produced during abrupt onset of dynamics induces much higher levels of co-
contraction, which have been suggested to increase the speed of adaptation
[51]. It has been suggested that co-contraction might increase the rate of
adaptation by concentrating the adaptation within the range of state space in
which the dynamics must finally be learned [51], as participants learn
adaptation of dynamics as a function of the visited states rather than planned
states [52]. However, the small kinematic errors that occur during gradual
presentation of the force field also mean that participants are never
perturbed away from the region of state space to be learned. Thus, gradual
presentation could be learned just as quickly as abrupt presentation despite
the absence of co-contraction. The similar rates of adaptation under these
different conditions likely arises through trade-offs in the competing
mechanisms of co-contraction, error sensitivity, and nearness to the learned
state space.

Abrupt adaptation to novel dynamics has been shown to cause a large increase
in initial co-contraction which gradually reduces as the internal model is
gradually learned [4, 6, 7, 53]. This increase in co-contraction from errors
is so strong, that it has been shown as a response to an abrupt introduction
of a visuomotor rotation [54], despite the fact that co-contraction cannot
reduce this type of visual transformation errors. Here we also showed a large
initial increase in co-contraction when the dynamics were abruptly applied,
but little or no increase in co-contraction when the dynamics were only
gradually applied, even though both conditions show adaptation to the force
field in terms of force compensation and our EMG based adaptation index. This
suggests that it is the errors that drive these changes in co-contraction and
not the adaptation process. Despite these differences early in learning, we
found similar levels of co-contraction at the end of the exposure phase in
both conditions. Therefore, even when co-contraction is not induced through
large kinematic errors, co-contraction gradually builds up as part of the
adaptation process.

The final levels of muscle co-contraction were similar after both gradual and
abrupt adaptation to the dynamics, and clearly different from the levels of
co-contraction in the null force field as shown previously [55, 13]. However,
the actual pattern of muscle activation after adaptation may have varied
depending on the manner in which the dynamics were learned. However, here we
only have weak statistical support for these differences, so further
experimentation will be required to determine whether this difference is
consistent. In the abrupt condition participants tended to have higher
shoulder muscle activity, whereas in the gradual condition participants tended
to have higher biarticular muscle activity. We suggest two possible reasons
for these differences in the final pattern of muscle activation. First, it is
possible that abrupt onset of novel dynamics produces large errors, but these
errors can be clearly associated with a specific cause – the robot is
producing a disturbance which is perturbing specific muscles more than others
(in this case single joint shoulder muscles). The sensorimotor control system
therefore associates the errors with this novel task, forming motor memories
of the tool rather than the body [56, 20]. On the other hand, in the gradual
condition there are small continuous errors which reduce the task success [23]
but cannot be associated with any specific cause, inducing participants to
adapt their baseline or limb dynamics model [20, 15]. These small errors and
reduced task success may be signals of instability [57, 58] that drive
specific increases in biarticular muscle activation as these have specific
critical roles in limb stability [59, 60]. As there is extensive redundancy in
the arm muscles that could be used to compensate for the external loads of the
force fields, different conditions would drive different final adaptation
measures. The second possible explanation for these findings is that
adaptation occurs through a feedback error learning mechanism [61, 62, 63]. In
this case, different errors produce different sensory feedback signals which
are then incorporated into the feedforward motor command on the subsequent
trial. A different pattern of feedback responses would therefore result in a
different final pattern of muscle activity. Such a possibility could be
connected to potential different feedback responses in the different
environments that we were not able to examine with the current study as
discussed with Fig 9. That is, the first possibility suggests that large
errors directly select different models whereas consistent small errors may
signal instability leading to differential adaptation. In contrast, the second
possibility suggests that it is simply the different pattern of errors that
drives these differences. These two possibilities are not mutually exclusive,
so the different patterns of muscle activity could be driven by both. However,
further experiments are required to determine whether these results are a
general result of gradual versus abrupt adaptation or if they are specific to
the movement direction studied in this experiment. A consistent finding of
higher biarticular muscle activation would be important for use in
rehabilitation studies [64, 65, 66] where the goal is training new patterns of
muscle activity. Gradual adaptation in a split-belt treadmill has already
shown to generalize better to normal walking [67], and an associated increase
in stabilizing biarticular muscle activation could be an additional helpful
result of such training if this is a consistent finding.

Throughout the experiment, we assessed the gain of the visuomotor feedback
response using rapid perturbations of the visual representation of the hand
[25, 26, 27]. These visuomotor feedback gains demonstrate task modulation [29]
and are tuned to changes in the dynamics of the environment [16]. Our previous
work showed that early in learning novel dynamics (or when these dynamics are
suddenly removed) the visuomotor feedback gains are upregulated [13] and then
gradually reduce to a plateau after adaptation is completed. In the curl force
field, the final level of visuomotor feedback gain was higher than in the null
field, which was interpreted as adaptation to the increased uncertainty in the
curl force field. We hypothesized that this initial increase in feedback gains
was driven by increased uncertainty in the internal model of the dynamics
[13], causing large feedback gains similar to the increased co-contraction
seen in early adaptation [4, 6]. Here we tested this theory by having
participants adapt to abrupt and gradual force field presentations. As in our
previous work, the abrupt onset or removal of the force field elicited large
increases in feedback gains. However, when the force field was only applied
gradually these feedback gains remained low and only increased slowly to the
same plateau level after adaptation was complete. However, both the force
field compensation and adaptation index show that adaptation to the force
field already occurs early in gradual learning, demonstrating that this
initial upregulation of feedback gains is not just a side effect of
adaptation. Instead, we suggest that it represents a reactive increase in
feedback gains due to the uncertainty in the internal model as signaled by
large kinematic errors.

Feedback gains during adaptation have also been studied using stretch reflexes
[17, 14], although examining the changes in stretch reflex gains independent
of their gain scaling [68] is more difficult. By examining changes in the long
latency stretch reflex response for a movement direction in between two
movements in which force fields were learned, [17] showed that the long
latency stretch reflex increased slowly as learning occurred, paralleling the
slow increase in the visuomotor feedback gain that we found during gradual
adaptation. On the other hand, a recent study [14] found only initial
increases in the feedback gain during early learning, but no long-term changes
after complete adaptation. However, the perturbation to assess the feedback
responses was performed in the dwell period prior to the movement onset, so no
long-term upregulation of the feedback gain during this time period would be
needed for adaptation. Although this early increase in the feedback gains was
attributed to the fast process of a two-state model of motor adaptation [14],
we believe that the rapid increase in feedback gains, particularly as seen
here and previously [13], could be better described as a reactive increase in
response to error rather than as part of the adaptation process itself. This
is particularly likely for feedback gains seen prior to movement initiation
when little or no adaptation is ever found in the predictive force against the
channel wall [69, 46]. Further supporting our interpretation, we find
identical levels of visuomotor feedback gain to perturbations to the left or
right (see Fig. 7), even though adaptation as predicted by the fast process
shows a directionality according to the force field.

Figure 10: Schematic of feedback changes during adaptation to novel dynamics.
A: The pattern of feedback gain modulation during adaptation and de-adaptation
to changes in environmental dynamics. Increases in feedback gain occur when
the dynamics are changed (onset or offset), and the final level of feedback
gain after adaptation to the force field is different to that in the null
force field. B: We propose that the total feedback gain is comprised of the
reactive (purple) and predictive (blue) changes in feedback gains during
adaptation. The reactive feedback gains increase immediately in response to
large errors (model predictive errors) and gradually reduce as learning
occurs. The predictive feedback gains gradually increase (or decrease) during
adaptation as they are tuned to the environment.

Overall, feedback gains during adaptation to novel dynamics demonstrate a
clear pattern of modulation (Fig. 10A), with an initial rapid increase
associated with large kinematic errors, followed by a gradual reduction to a
new baseline level during the exposure. We suggest that this pattern is
actually composed of two complementary processes (Fig. 10B) which we term
reactive and predictive feedback gains [16]. Any large errors, signaling model
uncertainty, produce rapid increases in reactive feedback gains, which are
gradually reduced as learning occurs. We propose that after adaptation is
complete, these contribute little or nothing to the overall feedback
responses, where this pattern matches perfectly the changes found in a recent
paper [14]. However, throughout the adaptation process, feedback responses are
also learned and tuned according to the dynamics of the environment [16],
becoming predictive feedback gains which are part of the learned motor memory
to compensate for the force field [70, 71, 72, 73]. The time course of these
predictive change in the feedback gains matches well the changes seen in Cluff
and Scott [17] where no reactive responses were required as no errors were
experienced on these trials. These two contributions to the overall pattern of
feedback control would explain the different results found in a variety of
experiments [13, 17, 14]. Furthermore, we predict that each of these two
components would have different properties; reactive feedback gains are likely
to be broader in terms of temporal timing (before and after the movement)
whereas predictive feedback gains may be more likely to generalize spatially
to nearby movements similar to the generalization of predictive force [2, 74,
75].

Recent work examining sensorimotor control have suggested robust control as a
framework for explaining and interpreting human behaviour [76, 77, 78]. Robust
control would predict higher feedback gains with increased internal model
uncertainties, fitting well our current experimental results. Moreover, it has
been shown that each participant modulates feedback responses differently,
leading to the suggestion that each participant may fall along a continuum
between optimal and robust control [45]. It could be imagined that the
reactive feedback gains might correspond to a robust control policy that
attempts to provide stability despite internal model inaccuracies, and that
the predictive feedback gains could reflect a shifting of the control policy
to an energy efficient mode as the internal model accuracy is improved.
However, it is unclear whether such shifting control policies are needed to
explain the reactive and predictive feedback gains, and we do not examine
variations in the feedback responses across participants. Nevertheless, the
large up-regulation of feedback gains in response to large errors well matches
the predictions of robust control [45, 77].

Abrupt and gradual adaptation produce very different initial patterns of force
compensation, muscle activity, co-contraction and feedback gains, but finally
result in a similar pattern after adaptation despite the different time course
of errors. Although the final adaptation is similar, there still remain subtle
differences in terms of the pattern of muscle activity (Fig. 4&5) and
generalization [18]. However, the different patterns of visuomotor feedback
regulation allow us to separate out two components of feedback regulation:
reactive and predictive. Here we argue that internal model uncertainty drives
upregulation of the reactive feedback gains, and that adaptation tunes the
predictive feedback gains according to the environment.

## ACKNOWLEDGEMENTS

We thank Daniel Wolpert and James Ingram for support with the experimental
facilities.

## CONFLICT OF INTEREST

The authors declare no competing financial interests.

## DATA AVAILABILITY

Data and code for analysis is available at:
https://doi.org/10.6084/m9.figshare.12816086.v1

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