Current Biology 20, 1763–1767, October 12, 2010 ª2010 Elsevier Ltd All rights reservedDOI 10.1016/j.cub.2010.08.049
Human Muscle Spindles
Act as Forward Sensory Models
Michael Dimitriou1,2and Benoni B. Edin2,*
1Computational and Biological Learning Laboratory,
Department of Engineering, University of Cambridge,
CB2 1PZ, UK
2Physiology Section, Department of Integrative Medical
Biology, Umea ˚ University, S-901 87 Umea ˚, Sweden
Modern theories of motor control incorporate forward
models that combine sensory information and motor
commands to predict future sensory states [1, 2]. Such
models circumvent unavoidable neural delays associated
with on-line feedback control . Here we show that signals
in human muscle spindle afferents during unconstrained
wrist and finger movements predict future kinematic states
of their parent muscle. Specifically, we show that the
discharges of type Ia afferents are best correlated with the
velocity of length changes in their parent muscles approxi-
mately 100–160 ms in the future and that their discharges
vary depending on motor sequences in a way that cannot
be explained by the state of their parent muscle alone. We
therefore conclude that muscle spindles can act as ‘‘forward
sensory models’’ : they are affected both by the current
state of their parent muscle and by efferent (fusimotor)
control, and their discharges represent future kinematic
states. If this conjecture is correct, then sensorimotor
learning implies learning how to control not only the skeletal
muscles but also the fusimotor system.
Muscle spindle discharges are determined by the current
kinematic state of their parent muscles and by efferent (fusi-
motor) commands related to a-motor commands; i.e., inputs
to muscle spindles are similar to those of forward sensory
models. We have used data obtained from published micro-
neurography recordings of afferents from muscles actuating
unrestrained wrist and finger movements [5, 6] to investigate
two additional requirements that must be met if muscle spin-
dles are to qualify as forward sensory models. First, spindle
discharges must predict future kinematic states. Second, the
fusimotor drive to muscle spindles should not be strictly
coupled to the skeletomotor drive of their parent muscle. For
ical state of an agonist muscle will depend on whether its
antagonist is relaxed or contracting.
Muscle Spindle Primary Afferents Predict Future Muscle
Given velocity (v) and acceleration (a), the velocity at some
future time, v(t + Dt), can readily be estimated as v(t) + a(t)$Dt;
the smaller the Dt, the better the estimate. Because type Ia
afferents encode both the first and second time derivatives
of the length of their parent muscles, i.e., v and a [5, 6], their
discharge should be best correlated with v at some time in
the future (i.e., Dt > 0) rather than with the instantaneous v
(i.e., Dt = 0). However, if the discharge rate of type Ia afferents
were dependent only on v and a, its correlation with future
velocities would never exceed that of v(t) + a(t)$Dt, and the
spindles’ prediction of future v would be a mere consequence
of their encoding properties. We therefore determined the
correlation between the actual velocity recorded at various
future times, v(t + Dt), and the ongoing type Ia ensemble
discharge rates at time t and compared this with the correla-
tion between the recorded v(t + Dt) and the estimated future
discharges is described in [5, 6]).
grasp and release objects of different sizes . As expected,
the correlation between type Ia ensemble discharges and the
velocity of their parent muscles increased with Dt, i.e., as the
interval between the ongoing discharge and the measured
velocity increased. The correlation was maximal for an
advance of 160 ms (Figure 1A; solid line with filled circles in
Figure 1B; r = 0.51 at Dt = 0 and r = 0.82 at Dt = 160 ms; p <
1024). More importantly, the correlation at Dt = 160 could not
be explained simply by the afferents’ velocity and acceleration
sensitivity because it was significantly higher than that
between the actual and the estimated future velocity (dashed
linein Figure 1B; r =0.82 versus 0.67; p <1024). This close rela-
tionship with future velocity was unique to type Ia afferents.
For instance, the correlation between velocity at Dt = 160
and the discharges of type Ib and type II afferents and
EMG signals at Dt = 0 was 0.18, 0.17, and 0.20, respectively.
Significant predictions of future velocity were also found
in type Ia discharges from the radial wrist extensor muscle
during a key-pressing task (Figure S1 in the Supplemental
Information; ) in which subjects made wrist and middle-
finger movements to sequentially press keys laid out in a
3 3 3 grid with a center key surrounded by eight others (Fig-
ure 2A, inset). The subject pressed the center key (‘‘5’’)
followed by a ‘‘target key’’ and then the center key again,
e.g., 5-2-5, 5-3-5, etc.
Signals in type II afferents in both the key-pressing and the
block-grasping tasks were well correlated with the velocity
of their parent muscles [5, 6]; in consequence, type Ia activity
also predicted future type II discharges (Figure 1D; r = 0.80,
p < 1024).
Muscle spindle type Ia afferents thus appear to predict
the rate of length change of their parent muscles some
120–160 ms in the future, i.e., better than expected from their
simultaneous encoding of velocity and acceleration.
The Drive to Muscle Spindles Is Not Strictly Coupled
to that of Their Parent Muscle
An indication that the fusimotor drive to spindles was some-
times decoupled from the drive to their parent muscle during
the key-pressing task  was target-specific discharge differ-
ences in periods with no obvious differences in kinematics or
EMG activity (Figures 2A–2C). Namely, afferent discharge
patterns were significantly different long before and after
subjects pressed the target key, whereas the EMG levels,
muscle length, and length changes were not. Because indi-
vidual afferents showed such differences, we reasoned that
it might be possible on the basis of their discharges to identify
the location of the fingertip during target key pressing. To this
location of the variable target keys: one used the discharge
rate of 37 spindle afferents from the ulnar and radial wrist
extensors (‘‘PLS-MS’’), and another combined the lengths of
the two wrist extensors, the velocities of their length changes,
and their EMG (‘‘PLS-LVE’’) to generate predictions (on how
the PLS models were created, see legend of Figure 2 and
If spindles only represented current muscle-state variables,
their predictions could at best match the predictive ability of
these variables. We therefore expected that the PLS-LVE
models would be superior to the PLS-MS models unless there
was a sequence-dependent fusimotor drive that significantly
affected spindle afferent discharges. The results were
unequivocal: the PLS-MS models generated good predictions
of the location of the variable target key in all phases of the
sequences (Figures 2D and 3). Indeed, the geometric centers
of the PLS-MS predictions were close to the actual x-y coordi-
nates of the target keys during all phases (Figure S2). More-
over, whereas PLS-LVE models generated fair predictions
only around the time the target key was pressed (Figures 2E
and 3; also Figure S2B), PLS-MS models made good
predictions both immediately before and after subjects
pressed the first and last ‘‘5’’ key, respectively, of the
sequences, i.e., during periods when the efferent drive to
and the mechanical state of their parent muscles were appar-
ently independent of the target key (Figure 2A).
The patterns of constant and variable errors across the
phases (Figure 3) could easily be explained for the PLS-LVE
models: the muscle states and EMG levels were practically
identical during early and late phases across the key
sequences, but they were markedly different around the
time when the target key of each sequence was pressed
(Figure 2A). Hence, whereas the afferents’ dependence on
the muscle states provided a plausible explanation for the
predictions around the time the target key was pressed,
muscle states could not explain the good predictions from
spindle discharges during early and late phases. Accordingly,
the variability of the afferents’ discharges across key-pressing
sequences could not be due to a strict coupling to either the
efferent drive to the parent muscles or their mechanical state.
We take this as evidence for sequence-dependent actions of
the fusimotor system on muscle spindles.
Although there is ‘‘. a kaleidoscope of functions, in which
proprioceptive feedback has been supposed to be involved’’
, muscle spindles have specifically been proposed to play
Figure 1. On-Line Prediction of Future States from the Discharge of Digital Extensor Muscle-Spindle Afferents during Block Grasping with the Thumb and
(A) The ensemble discharges of type Ia afferents (n = 13) plotted against the velocity of their parent muscles at the same time as the discharge (0 ms) and the
velocity at other times in the future. The ensemble discharge showed the maximum correlation with the velocity w160 ms in the future (r = 0.82).
(B) Correlation between type Ia ensemble discharge at time t and muscle velocity for time advances 0–400 ms, i.e., v(t + Dt); filled circles correspond to data
in (A). Also shown is the correlation between the actual v(t + Dt) and v(t) + a(t)$Dt, i.e., the best correlation expected if the spindle output were a mere conse-
quence of their velocity and acceleration sensitivity. At 160 ms, the r value obtained with the ensemble discharge was significantly higher than that obtained
with v(t) + a(t)$Dt (p < 1024).
(C) Auto-correlations of the muscle velocity and acceleration observed during the block-grasping task. Shaded areas in all panels correspond to 95% confi-
(D) Significantly higher correlations (p < 1024) were obtained between the observed ongoing ensemble type Ia discharges and the type II discharges 200 ms
in the future than between the observed ongoing ensemble type Ia discharges and the concurrent type II discharges.
Current Biology Vol 20 No 19
roles in feedback control and in the optimization and mainte-
nance of motor programs , as have forward models
[1, 2, 4, 10, 11]. Here we show that muscle spindles fulfill the
criteria set forth for neurophysiologically identifying a forward
sensory model : the inputs to the muscle spindles are the
current kinematic states of their parent muscle and efferent
commands related to the a-motor commands (viz., fusimotor),
and their output is an estimate of a future kinematic state.
erties for muscle spindles, they do suggest a novel role for g
Whether muscle spindles should be literally considered
forward models or not, it is easy to recognize the usefulness
of their velocity estimates, which are sufficiently advanced to
match the minimum delay, i.e., 80–100 ms, required for trajec-
tory corrections during reaching movements . However,
beyond reducing the computational requirements placed
on central structures, there is a good reason that evolution
would place forward sensory models within effectors: current
sensory states can be directly incorporated into predictions
rather than estimated by means of a probably less accurate
forward dynamic model . Predictive proprioceptive signals
can be useful in feedback control only when compared with
adesired state.Thedischarge ratesof cerebellar Purkinje cells
are related to limb position and velocity w100 ms in the future
, a finding promoted as evidence of the cerebellum’s role
Figure 2. The Discharge Rates of Muscle Spindle Could Not Be Explained by Just the Kinematic State and Efferent Drive to Their Parent Muscles
We used partial least-square analyses (PLS) to determine f such that Y = f(U), where Y corresponded to the x-y coordinates of the center of the sequence’s
created PLSmodels with Ucorresponding to thelengths ofthe ulnarand radialwrist extensor muscles, their velocities (i.e.,rate of change of muscle length),
and EMG levels (‘PLS-LVE’).For each phase 1–9 andkey press, two sets of 10,000 random vectors were generated. Each vector contained the predictedx-y
coordinates of the finger when it was pressing the target key of the sequence and either the simulated response of the 37 spindle afferents (PLS-MS) or the
deviation as those observed experimentally. We used one of the two sets to create a PLS model and the other to analyze the models’ predictions.
(A) Muscle length, velocity, and EMG for the ulnar (UWE, blue color) and radial (RWE, red color) wrist extensor during phase 1 and 4 depending on the key
pressed during phase 5 (mean 6 SD). There were practically no differences between the means in phase 1 (or phase 9, not shown) and those in phase 4.
(B and C) The mean 6 SEM (black lines and colored areas, respectively) of the discharge rate, EMG, length change, and velocity during the 100 ms period
immediately before subjects pressed the first ‘‘5’’ key (B) and after they pressed the last ‘‘5’’ key (C) in sequences with different target keys ‘‘X’’ as indicated
by the colors. For unit 33-04 (B), for instance, red color represents data from sequences with the target key ‘‘4,’’ and blue color represents data from
sequenceswith thetarget key ‘‘9.’’For thesesamplerecordsthedischarge rates andpatternswere significantlydifferentlongbeforeandlongaftersubjects
pressed the target key, whereas the EMG levels, muscle length, and changes in muscle length were not. Units 33-04 and 33-06 were type II afferents orig-
inating in the ulnar wrist extensor; unit 39-01 was a type Ia afferent originating in the radial wrist extensor.
The encircled numbers represent the mean predicted x-y coordinates of the fingertip during phase 5, i.e., when the participants pressed the target key of
a sequence. Note that good predictions were possible in all movement phases, indicating that the spindle discharges depended on the specific key-
(E) Good mean predictions from the muscle length, velocity, and EMG (PLS-LVE) of the finger-tip positions during phase 5 were only possible close to the
actual pressing of the target key.
Muscle Spindles Act as Forward Sensory Models
as a forward sensory model . A proposed site for
comparing proprioceptive and cerebellar signals is the inferior
olive  because it receives proprioceptive information from
the spinal cord and corollary information from the cerebellum.
If the proprioceptive and cerebellar systems are intimately
linked in their sensorimotor feedback roles, it should not be
surprising that cerebellar and sensory neuropathy patients
display similar motor deficits  and a distinct inability to
counter the effects of joint-interaction torques .
Sensorimotor control implies control of both skeletal
muscles and sensory inflow. Information about the current
state of an organism (posture, contractile properties, etc.)
and the results of its own actions are crucial for adequate
control. Indeed, there is abundant evidence that the CNS
controls afferent projections in general [18, 19], as well as
projections from muscle-spindle afferents in particular .
The teleological reason for independent fusimotor control,
i.e., via g rather than only b fusimotor neurons, has remained
unknown. So has the reason for the time-varying g activity
that has repeatedly been reported in acting animals .
However, if muscle spindles serve to instantiate forward
models, perhaps we can understand the operations of
complex segmental and intersegmental reflex pathways
conveying different afferentinputs fromvarioustissues tofusi-
of activating a limb muscle are not only a function of its own
onists as well as other limbs. We can only speculate on the
precise way in which the CNS controls g motor neurons for
this purpose. We expect, for instance, that the fusimotor drive
is sculpted by the widely converging inputs to fusimotor
neurons, including the outputs of the forward sensory models
instantiated by muscle spindles so that the muscle-spindle
afferents reflect future sensory consequences of movements.
We also expect that the CNS mechanisms governing the fusi-
motor drive are optimized through learning. Therefore, senso-
rimotor learning would imply learning to control both a and g
motor neurons given that the fusimotor system is engaged in
the orchestration of complex motor actions across multiple
muscles and joints. It would in fact make sense to decrease
the fusimotor drive during learning of new sensorimotor trans-
execution, it might be impossible to generate useful patterns
of fusimotor activity. This seems indeed to happen in humans
during tasks requiring novel sensorimotor transformations
. That a lack of inputs from spindle afferents might actually
improve behavior in such tasks is furthermore suggested by
the finding that deafferented patients, in contrast to normal
subjects, have no problems in mirror drawing, a task that
requires an unusual visuomotor transformation .
It has been proposed that, in addition to having a role in
feedback control, forward sensory models facilitate our sense
of self. The main evidence linking type Ia afferent responses to
conscious sensations is based on tendon vibration studies.
However, the illusions evoked by vibrating passive muscles
are slow and small in amplitude , depend on context ,
are easily eliminated by conflicting sensory inputs, and impor-
tantly, show significant latencies after the onset of vibrations
of passive muscles (often up to several seconds , although
values below 1 s have been recorded during active behaviors
). If the decoding of signals in type Ia spindle afferents,
on the other hand, relates to prediction of future rather
than current sensory states, stimulating them in isolation
may explain both the weak illusionary effects and the sizeable
In conclusion, we have shown that type Ia muscle-spindle
afferents predict the future kinematic state of their parent
muscle during active motor behaviors and have provided
evidence that the fusimotor output to the spindles is depen-
dent on motor sequences. Such uncoupling of fusimotor and
skeletomotor control is a fundamental property enabling
muscle spindles to operate as forward sensory models. Our
findings provide a plausible explanation for the extensive
CNS investment in the control of the muscle spindles and
a physiological basis for the lack of motor feedback instabil-
ities despite considerable neural delays, and they highlight
the importance of involving g motoneurones in theories of
Supplemental Information include Supplemental Experimental Procedures
and two figures and can be found with this article online at doi:10.1016/
This work was supported by the Swedish Research Council (projects 08667
and 2008-2863) and the 6th Framework Program of the European Union
(SENSOPAC, IST-001917). We are grateful for the many valuable sugges-
tions provided by P.B.C. Matthews, R.N. Lemon, and R.C. Miall on previous
versions of this manuscript.
Discharges Outperformed Those from Muscle
Kinematics and EMG
3. Predictionsfrom Muscle Spindle
(A and B) Constant (A) and variable (B) prediction
error of the PLS models based on muscle spindle
afferents (PLS-MS)and on
velocity, and EMG (PLS-LVE), respectively. Solid
lines represent median values; shaded areas
represent 50% of the distributions.
The spindle discharges were thus sufficiently
specific to each key-pressing sequence to allow
modeling of the target key of a sequence during
all its phases. Such predictions from the muscle
kinematics and the EMG were only possible in
phases close to the actual pressing of the target
key. This finding implies that the discharge of
muscle spindles was influenced not only by
sequence-dependent muscle states but also by
sequence-dependent fusimotor drive.
Current Biology Vol 20 No 19
Received: June 2, 2010
Revised: July 29, 2010
Accepted: August 24, 2010
Published online: September 16, 2010
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