Mathematics in Independent Component Analysis

264 Chapter 20. Signal Processing 86(3):603-623, 2006
(a)
s-EMG MU#2 MU#1
50 ms 0.5 mV
(b)
CNS
spinal cord
motor
unit
α-motoneurons
MU#2
( )
MU#1 ( )
Fig. 1. Electromyogram; (a) Example of a signal obtained from a surface electrode
showing the superposition of the activity of several motor units. (b) α-motoneurons
convey the commands from the central nervous system to the muscles. A motor unit
consists of an α-motoneuron and the muscle fibres it innervates.
2 Method
2.1 Signal origin and acquisition
The central nervous system conveys commands to the muscles by trains of
electric impulses (firings) via α-motoneurons, whose bodies are located in the
spinal cord. The terminal axons of an α-motoneuron innervate a group of
muscle fibres. A motor unit (MU) consists of an α-motoneuron and the muscle
fibres it innervates, Fig. 1(b). When a MU is active, it produces a train of
electric impulses called motor unit action potential train (MUAPT). The s-
EMG signal is composed of the weighted summation of several MUAPTs; an
example is given in Fig. 1(a).
2.1.1 Artificial signal generator
We developed a multi-channel s-EMG generator based on Disselhorst-Klug et
al.’s model [19], employing Andreassen and Rosenfalck’s conductivity parameters
[20], and the firing rate statistical characteristics described by Clamann
[21].
The volume conductor between a muscle fibre and the skin surface where the
electrodes are placed acts as a spatial low-pass filter; hence, a source signal
is attenuated in direct proportion to its distance from the electrode. Using
Griep’s tripole model [22], we can calculate the spatial potential distribution
3