positional output errors over each of the ten different
cycles performed by the subject. The average of the
output errors reflected the network’s ability to
extrapolate its results on samples that were not
directly included in the training set. After iteratively
testing different sigmoid activation functions for the
hidden layer of the network, numbers of epochs and
numbers of hidden neurons, the final configuration
of the network was determined.
The resulting network comprised seven hidden
neurons with the hyperbolic tangent as activation
function and the number of epochs was set to 50.
The reader is referred to previous publication
(Barzilay and Wolf, 2009) for a detailed explanation
on the setting of the network’s architecture.
2.3.2 Network with Kinematic and EMG
signals as Input
In the second step of this research, we added the
patient's biceps and triceps EMG signals to the input
of the network, such that the new exercise would be
designed with respect to the information on the
muscles of the subject as well as the knowledge on
the kinematic data of his limb.
The data provided by the electromyograms
contain useful information that can be deciphered by
signal processing. There are numerous ways
described in the literature to extract this information
from the EMG signal, including analysis in time or
frequency domains. We use the workflow described
in Hodges and Bui (1996) to compute the linear
envelope of the signal by processing it in the time
domain. The processed signal is needed at every
instant in our application and the processing time
has to be minimized, all the more since several
signals are needed simultaneously. We accelerated
this operation by using the processed signals from
the precedent instant and reduced the processing
time by approximately 96% (Barzilay and Wolf,
2011). This fast implementation allows providing
the subject with continuous visual feedback on his
own muscular performance during the training.
The same parameters that were described in
section 2.3.1 are used to evaluate the network, but
now in addition to the 3D curve, the desired EMG
performance specific to that trajectory should also be
designed. We therefore determined a few desired
cyclic trajectories for the limb of the subject and
recorded the EMG performances of a dozen of
healthy subjects. The average of this set of data is
then used as the desired EMG performance over a
specific trajectory, and fed as input to the neural
network together with the trajectory of the desired
kinematic performance.
The number of neurons in the hidden layer has
been set to 17, according to the evaluation criteria
which were previously used.
2.3.3 System Evaluation
The first network, described in section 2.3.1,
considers only the endpoint kinematics of the subject
and has obviously less physiotherapeutic interest
than the network involving the subject’s muscular
performance (section 2.3.2). Nevertheless, the
optimistic results (section 3.1 and Barzilay and
Wolf, 2009) suggested evidence of the feasibility of
modeling human motor control with neural networks
and brought us to expand the subject model to
include muscular performance as well.
From a therapeutic perspective, the muscles
activation of the patient is more significant than his
ability to accurately reproduce specific trajectories.
For that reason, we focus our efforts on minimizing
the error in the EMG performance, whereas the
kinematics error is considered more moderately.
Although the EMG signals are calibrated from
measurement of the maximal voluntary contraction
prior to the training, the signals’ amplitudes tend to
differ between different subjects. Furthermore, we
focus on the rhythmical patterns of the muscles more
than on the activation intensity. To do that, we
consider the error between the desired and actual
EMG performance in the frequency domain.
For the evaluation of the adaptive system, we
thus consider the root mean squared deviation, in the
frequency domain, between the desired EMG
performance and the smoothed EMG performance of
the subject. Each participant (n = 16) performed
motor training on two exercises: the patient-specific
exercise produced by the trained neural network
(adapted training), and a general exercise having for
trajectory the desired kinematic performance. The
latter resembles a standard physiotherapeutic session
where the physiotherapist demonstrates to the
patient, for example with his hand, the desired
gesture to reproduce (conventional training). The
primary criterion for the system evaluation was
defined as the ratio of the errors obtained in the
performances in both cases.
3 RESULTS
3.1 Network with Kinematic Input
The exercise trajectory, designed by the network,
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