Biomedical Engineering Reference
In-Depth Information
monitors the feedback torque U
c
(
t
) for the error signal. U
n
is calculated from the
desired trajectory 2
d
and the synaptic weights Xby
U
n
= ' (
d
2
2
d
/dt
2
,
d
2
d
/
dt
, 2
d
,X).
[4]
The inverse model is trained during motor control using a feedback motor com-
mand as the error signal. The feedback controller transforms the trajectory error
into the motor-command error. The shape of the
m
-dimensional vector function
' depends on the type of neural network that actually constitutes the feedfor-
ward controller. The vectors U, U
c
and U
n
are
m
-dimensional, the vectors 2
d
and
2 are
n
-dimensional, and X is an
l
-dimensional vector. The synaptic modifica-
tion rule providing the plasticity of the feedback-error-learning scheme is repre-
sented in a general form as
d
X/
dt
= (0U
n
/0X)
U
U
c
.
[5]
Aside from the theoretical considerations, the authors (34) relate their compo-
nents to neural circuits, as proposed in a review by Allen and Tsukahara (3). For
the limb as the controlled object the association cortex provides the desired tra-
jectory 2
d
, which is sent via pontine nuclei to the lateral cerebellum and simul-
taneously to the motor cortex. Via transcortical loops the motor cortex is
informed about the realized trajectory 2. From the difference 2
d
- 2, motor
cortex neurons act as feedback controllers and calculate the negative feedback
command
u
fb
(corresponding to U
c
(
t
) in the model), which is sent to motor cortex
output neurons. A copy of this signal is sent as an error signal to inferior olive
neurons, evoking complex spikes in cerebellar Purkinje cells. The output of the
corticonuclear complex is the feedforward motor command
u
ff
(corresponding to
U
n
(
t
) in the model), which is sent via the dentate nucleus and the thalamus to the
motor cortex. Summation of
u
ff
and
u
fb
is performed in the motor cortex, forming
the final motor command
u
descending the corticospinal tract.
The corresponding assumption with the climbing fiber response as the error
signal coincides well with suggestions derived from our experimental observa-
tions (7,38). An inverse model, inverting the inputs and outputs of the controlled
object, results in an ideal feedforward controller also able to perform transfor-
mation of coordinates. The necessity for such a transformation was suggested by
Pellionisz and Llinas (56), who provided corresponding algorithms. The model
assumes that sensorimotor learning and transformation of coordinates occur ini-
tially in the cerebral cortex. The resulting movement is clumsy and produces a
motor command error that is sent by the climbing fiber activity to the cerebel-
lum, where procedural learning then occurs. Such a model allows adaptive
modification of the vestibulo-ocular reflex, the adaptive control for posture and
locomotion and learning control for voluntary movements (34).
