Mathematics in Independent Component Analysis

Chapter 20. Signal Processing 86(3):603-623, 2006 267
only resulted in the reduction of the amplitude of the final MUAPs. This does
not have any influence in our case, as the algorithms are not affected by the
general amplitude of the signals, only by their respective proportions, if at all.
The simulated electrode-array used to generate the mixed recordings had the
same dimensions and characteristics of the real one and was virtually located
20 mm apart from the endplate region, which had a thickness of 0.4 mm. X axis
corresponded to the length of the electrode, Y axis to the depth, and Z axis
to the fibres direction. The mean instantaneous firing rate of each MU was 20
firings/second (mean inter-pulse interval meanIPI of 50 ms), with a standard
deviation calculated following Clamman’s model as 9.1 · 10 −4 · meanIPI 2 + 4
[21].
The s-EMG signals were generated as followed; each muscle fibre composing
a firing MU generates an action potential following the moving tripole model
([24] and references therein); the final MUAP appearing in each channel is the
summation of those action potentials after applying the anisotropy coefficient
A and the fading produced by the media crossed by the signal ([19] and references
therein). Note that the model generally holds for any skeletal muscle.
However, some of the parameters (such as the fat layer and firing rate) were
chosen following the average, normal values of the biceps brachii [25].
A single such data set is visualized in Fig. 2. The eight-dimensional s-EMG
observations that have been generated from the five underlying MUAPTs are
shown in Fig. 2(a). Their locations are depicted in Fig. 2(b) and the mixing
matrix used to generate the synthetic data set (see Fig. 2(c)) is shown in
Fig. 2(d). We will use several (100) of these signals with randomly chosen
source locations in batch runs for statistical comparisons.
2.1.2 Real s-EMG signal acquisition
Fig. 3 shows the experimental setting for the acquisition of real s-EMG recordings.
The subject (after giving informed consent) sat on a chair and was
strapped to it with nylon belts as shown in Fig. 3(a). The subject’s forearm
was put in a cast fixed to the table, the shoulder angle being approximately
30 ◦ . To measure the torque exerted by the subject, a strain gauge was placed
between the forearm cast and the table fixation. An electrode array was placed
on the biceps short head muscle belly, out of the innervation zone, transverse
to the direction of muscle fibers, after cleaning the skin with alcohol and Skin-
Pure (Nihon Kohden Corp, Tokyo, Japan). The electrode array consists of
16 stainless steel poles of 1 mm in diameter, 3 mm in height, and 2.54 mm
apart in both plane directions that are attached to a rigid acrylic plate, see
Fig. 3(b). The poles of each bipolar electrode were placed at the shortest
possible distance to obtain sharper MUAPs.
6