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J Neurophysiol 101: 816 – 823, 2009.
First published December 3, 2008; doi:10.1152/jn.91075.2008.
Inducing Any Virtual Two-Dimensional Movement in Humans by Applying
Muscle Tendon Vibration
Jean-Pierre Roll,1 Frédéric Albert,1 Chloé Thyrion,1 Edith Ribot-Ciscar,1 Mikael Bergenheim,2
and Benjamin Mattei1
1
Laboratoire de Neurobiologie Humaine, Unité Mixte de Recherche 6149 du Centre National de la Recherche Scientifique, Université de
Provence, Marseille, France; and 2Department of Surgery, Central Hospital Karlstad, Karlstad, Sweden
Submitted 24 September 2008; accepted in final form 25 November 2008
INTRODUCTION
Muscle proprioception along with vision and touch contribute to position sense and kinesthesia. Concerning proprioception, the muscle spindles feed the CNS with signals about
changes in the length of bearing muscles for both sensorimotor
and perceptual purposes (Cordo 1990; Edin and Johansson
1995; Gandevia 1996; Gandevia and Burke 1992; Jones et al.
2001; Radovanovic et al. 2002; Roll et al. 2000). However, it
remains unknown how the CNS collects the proprioceptive
feedback arising from all the muscles surrounding a particular
joint and how it integrates this information to build up a picture
of the movement being performed.
Neurosensory and psychophysical data have shed light on
these complex proprioceptive sensory codes and the associated
perceptual events. First, microneurography serves to record
feedback messages triggered in populations of afferents from
Address for reprint requests and other correspondence: J.-P. Roll, Laboratoire de Neurobiologie Humaine, UMR 6149 CNRS, Université de Provence,
Pôle 3C, Case B, 3 Place Victor Hugo, 13331 Marseille Cedex 03, France
(E-mail: [email protected]).
816
all the muscles surrounding a given joint in response to
two-dimensional movements performed under active and passive conditions (Bergenheim et al. 2000; Cordo et al. 2002;
Jones et al. 2001; Roll et al. 2000, 2004). In addition, the
“population vector model,” first used at the cortical level
(Georgopoulos 1982), was adapted to ensembles of somesthetic sensory neurons and to the particular anatomical and
physiological organization of the cutaneous and muscular systems (Aimonetti et al. 2007; Bergenheim et al. 2000; Jones
et al. 2001; Roll et al. 2000). Indeed, the muscle spindles merge
into a very homogeneous population inside the muscle that
bears them. These studies showed that each muscle spindle
responds only to a specific range of movement directions (the
Preferred Sensory Sector) and exhibits maximum sensitivity in
a specific direction (the Preferred Sensory Direction). When
moving away from this direction, the receptor’s activity is
decreasingly cosine tuned. The mean activity of a muscle
spindle population throughout a movement trajectory is represented by a “population vector.” The direction of this population vector is the Preferred Sensory Direction of a given muscle
(i.e., the average of the preferred sensory directions of all the
muscle spindles in that muscle), whereas its module is proportional to the mean firing rate. By taking the sensory activity
originating from all the muscles of a given joint, it was
demonstrated that the neurosensory sum vectors are highly
correlated with the movement vectors at any point of a given
trajectory (Albert et al. 2005, 2006; Bergenheim et al. 2000;
Jones et al. 2001). Consequently, each sum vector gives the
instantaneous direction and velocity of the ongoing movement
(i.e., its tangential velocity).
Moreover, muscle vibration activates the Ia muscle spindle in a
one-to-one ratio and induces illusions of movements in the 1- to
100-Hz frequency range (Burke et al. 1976; Goodwin et al. 1972;
Roll and Vedel 1982; Roll et al. 1989). Such a link between
sensory and kinesthetic events has been particularly attested by Ia
afferent feedback recordings during an ankle movement, which
evoked the illusion of the same movement when reapplied to the
participant via muscle vibration (Albert et al. 2006).
This corpus of data obtained at both neurosensory and perceptual levels (Albert et al. 2006; Bergenheim et al. 2000; Roll et al.
2000, 2004) led us to develop a model mimicking proprioceptive
inputs that can be used to induce any virtual two-dimensional
movement. Since the movement vectors describing the movement
trajectories are highly correlated with the neurosensory sum vecThe costs of publication of this article were defrayed in part by the payment
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Roll J-P, Albert F, Thyrion C, Ribot-Ciscar E, Bergenheim M,
Mattei B. Inducing any virtual two-dimensional movement in humans
by applying muscle tendon vibration. J Neurophysiol 101: 816 – 823,
2009. First published December 3, 2008; doi:10.1152/jn.91075.2008.
In humans, tendon vibration evokes illusory sensation of movement. We
developed a model mimicking the muscle afferent patterns corresponding
to any two-dimensional movement and checked its validity by inducing
writing illusory movements through specific sets of muscle vibrators.
Three kinds of illusory movements were compared. The first was induced
by vibration patterns copying the responses of muscle spindle afferents
previously recorded by microneurography during imposed ankle movements. The two others were generated by the model. Sixteen different
vibratory patterns were applied to 20 motionless volunteers in the absence
of vision. After each vibration sequence, the participants were asked to
name the corresponding graphic symbol and then to reproduce the
illusory movement perceived. Results showed that the afferent patterns
generated by the model were very similar to those recorded microneurographically during actual ankle movements (r ⫽ 0.82). The model was
also very efficient for generating afferent response patterns at the wrist
level, if the preferred sensory directions of the wrist muscle groups were
first specified. Using recorded and modeled proprioceptive patterns to
pilot sets of vibrators placed at the ankle or wrist levels evoked similar
illusory movements, which were correctly identified by the participants in
three quarters of the trials. Our proprioceptive model, based on neurosensory data recorded in behaving humans, should then be a useful tool
in fields of research such as sensorimotor learning, rehabilitation, and
virtual reality.
VIBRATION-INDUCED VIRTUAL MOVEMENTS IN HUMANS
tors (Albert et al. 2005, 2006; Bergenheim et al. 2000), we
decided here to use a procedure backward: each sum vector is
decomposed into a series of population vectors giving the mean
discharge frequency of the afferents in each muscle at any moment. These population vectors represent the oriented and
weighted contribution of each receptor population to the instantaneous coding of the ongoing movement.
We first compared the mean natural afferent patterns recorded microneurographically and the patterns generated by
the model. Second, we compared the illusory trajectories
evoked using our proprioceptive model with those induced at
ankle level by piloting the vibrators by means of prerecorded Ia
afferent patterns (Albert et al. 2006). Last, we investigated the
effectiveness of this model for another joint, the wrist.
General experimental setup
Three sets of vibration patterns were used to activate the tendon of
the main ankle and wrist muscle groups to induce the corresponding
illusory movement (see Fig. 1). The first one, experiment 1, reported
from Albert et al. (2006), presents the set of vibrations directly based
on the muscle spindle afferent responses previously recorded using
the microneurographic method. On the other hand, experiments 2 and
3 are specific to the present study and present the sets of vibrations
generated by the proprioceptive model at the ankle and wrist levels.
After experiencing the illusions, the participants were asked to
name the shape of the trajectory they had perceived before drawing it
on a digitizing tablet.
Experiment 1 was carried out on 10 healthy volunteers. Experiments 2 and 3 were each carried out on 10 healthy human volunteers
(5 males, 5 females). These participants were selected because they
previously experienced kinesthetic illusions during muscle tendon
vibration. All the participants gave their informed consent to the
procedure as required by the Helsinki declaration. This study was
approved by the local ethics committee (CCPPRB, Marseille I).
The participants were comfortably seated in an armchair, holding a
pencil in their right hand. The tip of the pencil was in contact with a
digitizing tablet. The participants had their legs in a standardized
relaxed position with both feet resting on stationary pedals. The left
ankle was kept at an angle of 90°. In experiments 1 and 2, five
electromagnetic vibrators (Vibralgic model, Electronic Conseil, Alès,
France) were fixed to adjustable devices so that the vibrators could be
positioned perpendicularly to the tendons of the left ankle joint
muscles with a pressure of about 0.5 N. In experiment 3, four vibrators
were fixed with the same pressure perpendicularly to the tendons of
the muscle groups of the right wrist joint. The heads of the vibrators
were 1 or 2 cm long, depending on the size of the tendon vibrated, and
were 0.6 cm in diameter. The vibration was delivered via two
multichannel electronic devices connected to high-power amplifiers
(pulse duration: 5 ms; amplitude: 0.25 mm peak to peak; Rematic,
St-Etienne, France). The vibration frequency (1–100 Hz) was controlled by a software program (LabVIEW 6i).
Computing the vibration patterns
The experimental procedures used to perform microneurographic recordings
and to determine vibration patterns mimicking Ia afferent activities
have been extensively described elsewhere (Albert et al. 2006; Roll
EXPERIMENT 1 USING MICRONEUROGRAPHIC RECORDINGS.
FIG. 1. Main stages in the experimental procedure. Experiment 1 (from Albert et al. 2006): the averaged muscle spindle afferent responses previously recorded
microneurographically in the main ankle muscle groups during a movement trajectory forming the letter “a” (TA, tibialis anterior; EHL, extensor hallucis longus;
EDL, extensor digitorum longus; PL, peroneus lateralis; GS, gastrocnemius soleus; TP, tibialis posterior muscles). Experiments 2 and 3: corresponding afferent
patterns generated by the proprioceptive model at ankle (experiment 2) and wrist level (experiment 3). These patterns were used to pilot the vibrators applied
to each corresponding muscle tendon. The participants had to recognize, name, and copy on a digitizing tablet each trajectory they perceived (bottom middle).
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METHODS
817
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ROLL ET AL.
To
compute the multipopulation patterns evoked by a specific movement
(previously written by the experimenter on a digitizing tablet as in
experiment 1), a set of mathematical transforms was applied to the
two-dimensional trajectory of each movement. These transforms were
drawn from the “population vector model” (Bergenheim et al. 2000;
Georgopoulos et al. 1982, 1988; Roll et al. 2000; Schwartz 1992,
1993). First, to smooth out the signal, we applied a low-pass filter (a
Hanning filter with a half-window of 0.05 s) to the limb trajectory
recorded. Second, the instantaneous tangential vector components of
the trajectory were determined every 200 ms using the formula ẋ(t) ⫽
[x(t ⫹ 1) ⫺ x(t ⫺ 1)]/2, and likewise for ẏ. This time window was
identical to the one used by Roll et al. (2004) to compute the afferent
inputs recorded in microneurography. At each time point, the instantaneous velocity vector was orthogonally projected onto the previously determined Preferred Sensory Direction of each muscle using
ជ 储 ⫽ 储 Vect
ជ 储 䡠 储 PSD
ជ 储 䡠 cos ␪. “Vect
ជ ” is the tangenthe formula: 储 Proj
EXPERIMENTS 2 AND 3 USING THE PROPRIOCEPTIVE MODEL.
tial velocity vector, “PSD” is the Preferred Sensory Direction of a
ជ ” is
given muscle, and ␪ is the angle between these two vectors. “Proj
the population vector representing the muscle spindle feedback from the
muscle under consideration. This projection allowed us to simulate the
cosine variations in the activity of the proprioceptive receptors of each
muscle. Based on microneurographic data, the Preferred Sensory Sector
of each muscle was chosen to be symmetric around the muscle’s Preferred Sensory Direction and to cover 180°. Figure 2 illustrates the
modeling procedure used.
The final step of modeling was to normalize the proprioceptive
input originating from each muscle in the same way as for the
microneurographic recordings, that is, with respect to the maximum
firing rate obtained in all the muscles tested. (This approach is under
Patent number 0.8/02242.)
Thus to generate vibratory patterns that effectively induce illusory
movements, all one needs to include in the model is the preferred
sensory directions of the main muscle groups. Since Bergenheim et al.
(2000) showed that the direction of vibration-induced illusions did not
differ significantly from the Preferred Sensory Direction of the vibrated muscle, determined microneurographically, we used the preferred sensory directions previously determined for the ankle in
Bergenheim et al. (2000) and for the wrist in Roll and Gilhodes
(1995). In these studies, after a vibration of 80 –100 Hz during 10 s for
J Neurophysiol • VOL
270°
GS
PL
TP
180°
0°
EDL
90°
FIG. 2. The modeling procedure. Here is how the proprioceptive model
determines the amplitude of each population vector, shown in heavy lines, for
one particular instantaneous movement direction (black vector). The instantaneous velocity vector was orthogonally projected onto the previously determined preferred sensory direction of each muscle (here for the main ankle
muscles: tibialis anterior [TA] ⫹ extensor hallucis longus [EHL] in blue;
extensor digitorum longus [EDL] in green; peroneus lateralis [PL] in orange;
gastrocnemius soleus [GS] in purple; tibialis posterior [TP] muscles in red).
The gray semicircle represents the 180° around the tangential velocity vector
in which the model computed sensory activities. Note that if the preferred
sensory direction of one particular muscle is not within an angle of 180°
around the instantaneous movement direction, the amplitude of this particular
vector will be null.
each muscle group, the participants were asked to indicate the direction of the illusion they perceived on a report sheet, on which only the
horizontal and vertical directions were given as indications. Since the
variability reported in these studies is low, we decided not to take it
into account in our modeling procedure. These directions for the ankle
are TA ⫹ EHL: 96°; EDL: 65°; PL: 316°; GS: 274°; and TP: 217°; for
the wrist they are Extensors: 90°; Flexors: 270°; Abductors: 0°; and
Adductors: 180°. The origin, zero degree, is set at 15 min on a clock
representation (see Fig. 2).
Muscle tendon vibration
The optimum position of each vibrator head was carefully determined by asking the participants to keep their eyes closed and to give
the direction of the perceived illusory movement during 10 s of 80-Hz
muscle tendon vibration. We checked whether this direction matched
the known preferred sensory direction.
The participants were asked to relax, keep their eyes closed, and to
focus on the illusory movement trajectory that the tip of the left foot
(experiments 1 and 2) or the right hand (experiment 3) was experiencing. Prior to the vibration, they were informed about the category
of movement that could be recognized, i.e., letters, numbers, or
geometrical shapes. Experimental vibratory patterns (experiment 1) or
modeled ones (experiment 2) inducing illusory movements forming
four letters (a, b, e, n) and four numbers (1, 2, 3, 8) were applied
randomly to the corresponding ankle muscle tendons of each participant. In experiment 3, modeled vibratory patterns evoking six letters
(a, b, e, n, u, v), six numbers (1, 2, 3, 6, 8, 9), and four geometric
shapes (circle, rectangle, square, triangle) were applied randomly to
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et al. 2004). In brief, for the microneurographic experiments, participants were seated in an armchair with their right foot placed on a
stationary pedal and their left foot attached to a movable pedal
connected to a computer-controlled machine. This machine imposed
two-dimensional movements on the ankle joint, making the tip of the
foot trace various graphic symbols mimicking the kinematic parameters of movements performed by the experimenter on a digitizing
tablet (see e.g. Roll et al. 2004).
During these imposed movements, the unitary activity of 55 muscle
spindle afferents was recorded microneurographically at the popliteal
fossea (for further details, see e.g. Bergenheim et al. 1999). Twelve of
these 55 afferents were located in the tibialis anterior (TA), 17 in the
extensor digitorum longus (EDL), 8 in the extensor hallucis longus
(EHL), 8 in the peroneus lateralis (PL), 8 in the gastrocnemius soleus
(GS), and 2 in the tibialis posterior (TP). From the data thus recorded,
the mean firing pattern of the muscle spindle population in each muscle
was determined during each movement. The proprioceptive input originating from each muscle was normalized with respect to the maximum
firing rate in all the muscles tested (between 0 and 100 Hz). In addition,
since the TA and the EHL tendons are anatomically too near each other
to be vibrated separately and since their afferent patterns were found to be
very similar, the responses from these muscles were averaged. The
spatiotemporal patterns obtained during the above-cited recording sessions were then used to pilot each of the five vibrators applied to the
TA ⫹ EHL, EDL, PL, GS, and TP muscle tendons.
VIBRATION-INDUCED VIRTUAL MOVEMENTS IN HUMANS
the corresponding wrist muscle tendons of each participant. Each
vibration sequence was repeated three times. After the three vibratory
sequences, the participants were asked to name the movement they
had just perceived and, immediately afterward, to copy this movement
by drawing it by hand on a digitizing tablet. They were requested to
pay special attention to the shape, velocity, and size of the illusory
trajectory perceived. The movement trajectory drawn by each participant was then sampled at 200 Hz and stored for further analysis.
Data analysis
Quantification of the kinesthetic illusions
The average shape of each sign drawn on the digitizing tablet was
determined from all the trajectories. These trajectories were first
normalized and then repositioned with a common starting point so that
visual comparisons could be made. The criterion used to determine
whether the participants recognized the illusory writing was correct
identification of each symbol.
Drawing up vectors describing the various types
of trajectories
Each of the four types of trajectories—Initial, Experimental, Model
Ankle, and Model Wrist Trajectories—was also described by series of
vectors giving the tangential velocity recorded during the same
successive 200-ms time windows. To compare the direction and
amplitude of each category of vectors, the vectors were normalized
and the trajectory points used to construct them were sampled at 2-ms
time steps.
TABLE
RESULTS
Model validation: the recorded and modeled afferent
patterns resembled each other
First of all, we tested the modeling procedure for the ankle
joint. From the modeled patterns, we could deduce at each time
point the population vectors representing the activity of each
population of muscle afferents and then reconstruct the movement vectors by summing the population vectors. Then these
population vectors were put head to tail to reconstruct a
trajectory. This trajectory correlated with the corresponding
Initial Trajectory used to compute the pattern. Table 1 gives the
correlation coefficients between these two kinds of trajectories.
After including in the proprioceptive model the preferred
sensory directions of each ankle muscle and calculating the
instantaneous vectors describing the tangential velocity of the
movement trajectories, it was possible to generate the afferent
pattern emitted by each of the muscles activating the joint. The
mean natural afferent patterns recorded microneurographically
(blue traces) are compared in Fig. 3 with the patterns generated
by the proprioceptive model (red traces) for movement trajectories forming the letter “a” and the number “8.” The frequency
patterns were similar for both trajectories in most of the five
ankle muscles. A highly significant level of correlation (0.82)
was found between the natural and simulated patterns for
several letters (a, b, e, n) and numbers (1, 2, 3, 8) in each of the
five main ankle muscle groups. Only 4 of the 40 patterns
studied gave a level of correlation ⬍0.60 (see Table 2).
Recorded and modeled muscle spindle feedback patterns
evoked similar illusory movements when used to pilot sets
of vibrators
When the recorded and modeled afferent patterns were used
to pilot a set of vibrators applied to the five main ankle muscle
groups of motionless participants, all of them clearly perceived
illusory foot-tip movements in both cases. The shapes of the
illusory trajectories that the participants subsequently reproduced by hand on a digitizing tablet clearly resembled the
outlines of various letters and numbers. Figure 4 gives the
mean shapes of the trajectories drawn by all the participants.
The averaged reproduced trajectories were very similar to
those originally imposed on the foot, irrespective of whether
recorded or modeled afferent patterns were used as the stimuli.
To analyze to what extent the spatiotemporal parameters of
the two kinds of perceived illusory movements paralleled those
of the imposed movements, correlation analyses were carried
out on the direction and the amplitude of each group of vectors.
1. Correlation between vectors describing the initial and modeled trajectories
Letters
Direction
Initial Trajectories/Modeled Trajectories
Amplitude
Initial Trajectories/Modeled Trajectories
Numbers
a
b
e
n
1
2
3
8
Average
0.88
0.86
0.79
0.48
0.85
0.94
0.77
0.95
0.81
a
b
e
n
1
2
3
8
Average
0.90
0.91
0.91
0.71
0.92
0.95
0.80
0.83
0.87
Correlation coefficients were calculated for the ankle joint between vectors describing the Initial Trajectories (i.e., the movement trajectories imposed during
microneurographic recordings and used to compute the patterns) and those describing the Modeled Trajectories, built up from the muscle spindle feedback
generated by the model. Correlation coefficients were computed between the directions and the amplitudes of the various pairs of vectors.
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Four types of trajectories (“Initial Trajectories”; “Experimental
Trajectories”; “Model Ankle Trajectories”; “Model Wrist Trajectories”) were analyzed in this study. The “Initial Trajectories” are the
movement trajectories imposed during microneurographic recordings
and used to compute the patterns. In experiment 1, the “Experimental
Trajectories” were the participants’ drawings of the illusory movements they perceived in response to the vibration patterns based on
previous microneurographic recordings (for details, see Albert et al.
2006). In experiment 2, the “Model Ankle Trajectories” were the
participants’ drawings of the illusory movements they perceived in
response to the vibration patterns generated by the proprioceptive
model. Finally, in experiment 3, the “Model Wrist Trajectories” were
the subjects’ drawings of the illusory movements they perceived in
response to application to the wrist of the vibration patterns given by
the proprioceptive model.
To validate our modeling procedure we compared, for the ankle
joint, the vectors describing the Initial Trajectories with those built up
from the muscle spindle feedback generated by the model. The
effectiveness of our model was also tested by cross-correlations
performed between the average patterns resulting from microneurographic recordings of Ia activities and the patterns generated by the
proprioceptive model at ankle level.
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ROLL ET AL.
3. Recorded and modeled afferent patterns. The blue lines give the
natural mean frequency pattern of responses recorded microneurographically
in the 5 main muscle groups of the ankle joint (TA, tibialis anterior; EHL,
extensor hallucis longus; EDL, extensor digitorum longus; PL, peroneus
lateralis; GS, gastrocnemius soleus; and TP, tibialis posterior muscles) during
movements forming the number “8” and the letter “a.” The trajectories and the
X and Y coordinates of these 2 graphic signs are also shown (top). The red
lines give the frequency pattern generated by the proprioceptive model for the
movement trajectories forming the letter “a” and the number “8.” All the
patterns were normalized; the values ranged between 0 and 100 Hz.
Table 3 gives the correlation coefficients obtained when comparing the kinematic parameters of the Initial Trajectories with
those of the Experimental illusory Trajectories and Model
Ankle ones. The mean correlation coefficients obtained were
rdir ⫽ 0.85 and ramp ⫽ 0.90 in the first case and rdir ⫽ 0.84 and
ramp ⫽ 0.91 in the second case. In addition, the illusory
movements induced by applying the Experimental and the
Model Ankle patterns resembled each other, as shown by the
mean correlations obtained, i.e., rdir ⫽ 0.86 and ramp ⫽ 0.89
(third line).
The proprioceptive model can be applied to different joints
and to any virtual two-dimensional movements
To check the effectiveness of the proprioceptive model with
other joints, it was tested at wrist level. First, the values of the
preferred directions of the four wrist muscle groups were
included in the model. Second, we generated afferent patterns
corresponding to trajectories previously imposed on the foot
and to eight new trajectories: two letters (u and v), two numbers
(6 and 9), and four geometrical shapes (rectangle, square, triangle,
FIG. 4. Mean vibration-induced illusory movements. A: black lines give the
trajectories imposed to the participant’s foot during the microneurographic
recording of the muscle spindle activity, i.e., the trajectories used to generate
vibration patterns with the proprioceptive model at ankle and wrist level in the
case of 4 numbers (1, 2, 3, and 8) and 4 letters (a, b, e, and n). Gray lines give
the average trajectories drawn by all the participants under each experimental
condition (from top to bottom: “Experimental,” “Model Ankle,” “Model
Wrist”). B: as in A, but with other trajectories, which were studied only at the
wrist level (square, circle, triangle, rectangle: u, v, 6, and 9).
and circle). Here again, the participants were asked to actively
draw the illusory movements they perceived on a digitizing tablet.
Correlation analyses (see Table 4) showed that the kinematic
parameters of the Initial Trajectory and the Model Wrist Trajectory matched (rdir ⫽ 0.82; ramp ⫽ 0.86).
Figure 4 shows the similarities between the trajectories
initially drawn on the digitizing tablet and the corresponding
mean illusory trajectories induced at hand level using the
modeled vibration patterns. High correlations were also found
with the new trajectories tested at the wrist level (see Table 4).
Finally, participants were also able to recognize the illusory
trajectories in terms of graphic symbols. Indeed, before copying the illusory movements they perceived on a digitizing
tablet, the participants were asked to name the letters, numbers,
and geometrical figures formed by the illusory movement
trajectories they perceived. Table 5 gives the recognition rates
recorded under all the experimental conditions tested. The
participants identified the symbols correctly in three quarters of
the trials and there were no striking differences between foot
and hand level or between the illusory movements induced by
recorded afferent patterns and those generated by the proprioceptive model.
2. Correlation between the natural afferent patterns recorded microneurographically and the artificial patterns generated by the
proprioceptive model
TABLE
Letters
Numbers
Muscle
a
b
e
n
1
2
3
8
Average
TA ⫹ EHL
EDL
PL
GS
TP
Average
0.82
0.73
0.77
0.71
0.86
0.78
0.74
0.79
0.61
0.84
0.89
0.79
0.82
0.67
0.33
0.45
0.90
0.70
0.88
0.86
0.68
0.87
NaN
0.84
0.97
0.97
0.95
0.99
NaN
0.98
0.64
0.65
0.74
0.65
0.56
0.65
0.84
0.93
0.84
NaN
0.78
0.86
0.77
0.83
0.80
0.63
0.23
0.70
0.85
0.84
0.76
0.86
0.83
0.82
Correlation coefficients for various letters (a, b, e, n) and numbers (1, 2, 3, 8) in each of the five main ankle muscle groups (TA, tibialis anterior; EHL, extensor
hallucis longus; EDL, extensor digitorum longus; PL, peroneus lateralis; GS, gastrocnemius soleus; and TP, tibialis posterior muscles). NaN, not a number.
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FIG.
VIBRATION-INDUCED VIRTUAL MOVEMENTS IN HUMANS
TABLE
821
3. Correlation coefficients between vectors describing imposed and illusory ankle movements
Letters
Numbers
Direction
a
b
e
n
1
2
3
8
Average
Initial Trajectories/Experimental
Initial Trajectories/Model Ankle
Experimental/Model Ankle
0.80
0.83
0.88
0.74
0.68
0.79
0.99
0.93
0.94
0.93
0.90
0.91
0.85
0.90
0.88
0.79
0.82
0.84
0.91
0.84
0.86
0.80
0.84
0.83
0.85
0.84
0.86
Amplitude
a
b
e
n
1
2
3
8
Average
Initial Trajectories/Experimental
Initial Trajectories/Model Ankle
Experimental/Model Ankle
0.90
0.92
0.88
0.88
0.84
0.86
0.98
0.98
0.97
0.95
0.92
0.94
0.83
0.86
0.80
0.86
0.86
0.88
0.92
0.94
0.93
0.91
0.96
0.93
0.90
0.91
0.89
Vectors describing imposed movement trajectories (labeled “Initial Trajectories”) and those describing the illusory trajectories induced using either the
recorded afferent patterns (labeled “Experimental”) or the simulated afferent patterns (labeled “Model Ankle”) at the ankle level with different letters (a, b, e,
n) and numbers (1, 2, 3, 8). Correlation coefficients were computed between the directions and the amplitudes of the various pairs of vectors.
any point on a movement trajectory, the computed neural sum
vector fits well with the ongoing movement vector describing
the trajectory.
The adaptation by Bergenheim et al. (2000) of this “central
population vector model” to the sensory level requires considering the anatomical and physiological organization of the
muscular system. In particular, the sensory receptors merge
into a homogeneous population inside the muscle that bears
them (see Bergenheim et al. 2000; Fig. 4). Since all the sensory
receptors inside a muscle have an extremely close Preferred
Sensory Direction, this feature allows one to compute, for a
population of receptors, only one Preferred Sensory Direction
for a given muscle. Although the number of vectors to be
summed was limited and all the directions were not equally
represented, our proprioceptive model is highly effective, especially in view of the high correlation between the Initial
Trajectories and the trajectories reconstructed from the modeled afferent patterns.
The instantaneous neurosensory sum vector corresponds to
the sum of all the “population vectors” giving the weighted and
oriented contribution of the afferent feedback of each muscle to
the sensory coding of movement direction and velocity (Bergenheim et al. 2000; Ribot-Ciscar et al. 2002; Roll et al. 2000,
2004). Since the instantaneous tangent vectors describing the
trajectory correlate with the corresponding neurosensory sum
vectors (Albert et al. 2005, 2006; Roll et al. 2004), our
modeling consists in following the procedure backward: each
sum vector is decomposed into a series of population vectors
We chose to build our proprioceptive model according to the
functional properties of Ia afferent populations revealed
through recordings on humans performing movements. This
model accurately generates complex vibratory patterns, whose
frequencies mimic almost exactly those of the muscle spindle
feedback evoked by actual movements. These modeled vibratory patterns can be applied to sets of muscles to elicit virtual
two-dimensional movements. Another important feature of our
model is that it can be adapted to other joints if one specifies,
for a given posture, the preferred sensory direction of each
muscle group acting at a joint.
From movement trajectory to the corresponding
proprioceptive afferent feedback
The complex multimuscle proprioceptive coding of the spatial and kinematic parameters of any movement trajectory can
be described by a population vector model under both passive
and active conditions at both hand and foot levels (Albert et al.
2006; Bergenheim et al. 2000; Jones et al. 2001; Roll et al.
2004). Interestingly, this suggests that some general neuronal
coding principles previously found to pertain at the motor
cortical level responsible for motor command in monkeys
(Caminiti et al. 1990; Georgopoulos et al. 1984; Johnson and
Ebner 2000; Kalaska 1991; Schwartz and Moran 1999, 2000;
Schwartz et al. 1988) may also be relevant at the sensory level.
At these motor and sensory levels, this principle states that, at
TABLE
4. Correlation coefficients between vectors describing imposed and illusory wrist movements
Letters
Numbers
Geometric Shapes
Direction
a
b
e
n
u
v
1
2
3
6
8
9
䊐
E
ⵦ
Average
Initial Trajectories/Model Wrist
Model Ankle/Model Wrist
0.67
0.68
0.79
0.79
0.94
0.93
0.79
0.77
0.80
—
0.93
—
0.88
0.82
0.80
0.75
0.82
0.79
0.80
—
0.83
0.82
0.85
—
0.79
—
0.83
—
0.78
—
0.78
—
0.82
0.79
Amplitude
a
b
e
n
u
v
1
2
3
6
8
9
䊐
E
ⵦ
Average
Initial Trajectories/Model Wrist
Model Ankle/Model Wrist
0.74
0.73
0.84
0.80
0.97
0.96
0.85
0.84
0.84
—
0.88
—
0.85
0.85
0.85
0.80
0.88
0.86
0.89
—
0.91
0.89
0.90
—
0.86
—
0.87
—
0.84
—
0.83
—
0.86
0.84
Shown are vectors describing imposed movement trajectories (labeled “Initial Trajectories”) and those describing the illusory trajectories induced using the
afferent patterns simulated at the ankle level (labeled “Model Ankle”) and at the wrist level (labeled “Model Wrist”) with various letters (a, b, e, n, u, v), numbers
(1, 2, 3, 6, 8, 9), and geometrical shapes (square, circle, rectangle, triangle). Correlation coefficients were calculated on the directions and the amplitudes of the
various pairs of vectors. Note that no correlation coefficients are given for the letters “u” and “v”; the numbers “6” and “9”; or the four geometrical shapes studied
(square, circle, rectangle, triangle) between the ankle and wrist levels because these eight new trajectories were tested only at the wrist level.
J Neurophysiol • VOL
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DISCUSSION
822
ROLL ET AL.
TABLE
5. Recognition rates of graphic symbols
A
a
b
e
n
Average (Letters)
Experimental
Model Ankle
Model Wrist
80
60
30
50
90
80
90
90
80
90
80
60
78
80
63
1
2
3
8
Average (Numbers)
90
90
80
70
60
60
80
90
80
70
70
90
78
78
78
Experimental
Model Ankle
Model Wrist
B
u
v
6
9
䊐
E
ⵦ
60
60
70
90
80
60
100
90
Average
76
giving the mean discharge frequency of the afferents in each
muscle at any moment. In addition, the mean instantaneous
firing rate of each muscle spindle population is a cosine
function of the difference between the direction of the trajectory and the preferred sensory direction of the muscle (Bergenheim et al. 2000). The proprioceptive model therefore
generates the mean afferent patterns produced by each of the
muscles surrounding a given joint during a two-dimensional
movement trajectory. This was confirmed by the high correlations between the firing frequencies in the recorded and modeled afferent patterns.
In behavioral conditions, muscle spindle feedbacks evoked
by the performance of two-dimensional movements forming
letters or numbers were previously found to be specific to each
trajectory and perfectly reproducible when the same movement
was repeated (Albert et al. 2006; Roll et al. 2004). For a given
joint, the mean afferent feedback pattern can be determined as
a specific firing pattern, in which any increase in the frequencies corresponds to the stretching phases of the receptorbearing muscles. If all the sensory activities of the muscles
involved are taken together, one obtains what we have called
the “proprioceptive signature” of a given movement (Roll et al.
2004).
So this model constitutes a real methodological breakthrough, in that it gives access to these “proprioceptive signatures” evoked in humans by the execution of any two-dimensional movement. The only method available so far for this
purpose was the microneurographic method, a very demanding
and rather invasive procedure (Bergenheim et al. 1999; Vallbo
and Hagbarth 1968).
Both the recorded and modeled proprioceptive patterns
induced similar virtual two-dimensional movements
Since the afferent patterns generated by the model closely
paralleled those recorded in participants during actual movements, it was expected that using these two types of patterns to
pilot the set of vibrators would give rise to fairly similar
illusory movements. Before using the afferent patterns to pilot
a set of vibrators, it was first necessary to check the validity of
the method. In a recent study, we investigated whether an
afferent pattern previously recorded during an actual movement gave rise to a similar afferent pattern when reapplied to
a muscle tendon via vibration. The two firing patterns were in
J Neurophysiol • VOL
fact practically identical (Albert et al. 2006; Fig. 2). In addition, the illusory trajectories induced at the ankle level using
the two types of afferent patterns were very similar in terms of
the resulting shape and the instantaneous tangential velocity
(Albert et al. 2005).
When the proprioceptive model was applied to the wrist
after specifying the preferred sensory direction of each wrist
muscle group, the illusory trajectories induced at hand level
were also similar to those evoked at the ankle level. This
finding confirms that the model can be used to generate virtual
writing or drawing movements with various two-dimensional
trajectories at various joints.
The muscle spindle afferent patterns recorded and the modeled patterns applied via vibration gave rise to illusory trajectories forming symbols (letters, numbers, and geometrical
shapes) that were in both cases equally well recognized by the
participants. This point was checked by asking the participants
to name the letter, number, or geometrical figure formed by the
perceived illusory trajectory before copying it on the digitizing
tablet. No significant differences were observed between the
recognition rates obtained by the participants when natural
versus modeled afferent patterns were used (⬃75%). To determine how meaningful this ratio is, especially when the
participants had to recognize writing movements that did not
correspond to their own cursive writing, we compared it with
the recognition ratio (91%) when passively imposing the same
movements to the ankle of 10 subjects (F. Albert, C. Thyrion,
and J. P. Roll, unpublished observations).
Last, either for the active copy of a movement perceived by
a participant or its symbolic identification, one could question
the relevance of studying such standard and overlearned trajectories instead of more abstract shapes. The question arises as
to whether the participants reproduced their own writing or
drawing movement or carefully copied the illusory trajectories
they perceived. As reported by Albert et al. (2006) in Fig. 3C
the participants did not reproduce their own usual handwriting;
rather, they reproduced illusions of movement they perceived
while they were exposed to vibration. This was particularly
obvious for the number “8,” for which both the imposed and
reproduced trajectories started with an upward movement to
the left, whereas the usual writing trajectory of some of the
participants started with a downward movement to the left.
Further proof is brought by the lower correlation coefficients
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Mean rate of correct identification (recognition rate) of the graphic symbols tested in each experimental condition (A) and the new trajectories tested only at
the wrist level (B).
VIBRATION-INDUCED VIRTUAL MOVEMENTS IN HUMANS
GRANTS
This research was supported by grants from Agence Nationale de la
Recherche and Association Française de Lutte contre les Myopathies.
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between the vectors describing the reproduced and the usual
handwriting trajectories (Albert et al. 2006; Table 1).
These observations confirm the validity of the present
method that uses symbolic illusory movements. Indeed, these
movements can be recognized solely on the basis of proprioceptive afferent inputs (Albert et al. 2005, 2006; Roll et al.
1996; Viviani et al. 1997), even if other sensory modalities
certainly contribute to the recognition process in natural behavior (Bara et al. 2004; Collins and Prochazka 1996; Gordon
and Soechting 1995). To conclude, our proprioceptive model,
which is directly based on neurosensory data recorded in
behaving humans, can be used to generate the complex proprioceptive feedback patterns associated with the execution of
any two-dimensional movement. Its simplicity and accuracy as
a means of inducing virtual two-dimensional movements in
motionless participants make it a potentially valuable tool for
use in fields of research such as sensorimotor learning, patient
rehabilitation, and virtual reality.
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