Figure 2.13: . . . from the previous page: of simulated monopolar surface po- tential produced by a single fiber placed A), B) just below the skin(0mm deep in the muscle); C), D) 4mm deep in the muscle; E)10mm deep in muscle and F)just below the skin(0mm deep in the muscle). For A), C) IED=5mm and B), D) IED=7mm, and for panels E) and F) IED=15mm. Spatial images were obtained at propagation phase(t2, see figure 2.11). Detection system was con-
sidered to cover 127×127mm2
2.9
Spatial distribution (over the skin) of a simulated mo-
tor unit action potential (space-time and frequency
domain)
The issue of aliasing in skin potentials produced by a motor unit (MU) is discussed in this section. This case is more general than aliasing of just a single fiber. In reality, the number of motor units per muscle in human may range from about 100 for a small hand muscle to 1000 or more for large limb muscles (3).
The size of a MU depends on the function of the muscle and can contain from 10 to over 3000 muscle fibers1 . No significant difference is reported between the estimated number of Biceps Brachiis muscle fibers of young (253000) and old (234000) men (6). Muscle fiber number can be estimated by dividing the maximal area of the muscle (e.g. Biceps Brachii) which can be determined by magnetic resonance imaging (MRI) by the mean fiber area of that muscle determined in a muscle biopsy (6). With reference to the Biceps Brachii, a single MU may innervate on average 150 fibers. Considering 250,000 muscle fibers in Biceps Brachii, therefore, the muscle includes approximately 3300 MUs2.
To study the aliasing in a simulated MU, 150 fibers were simulated using the model developed by Farina and Merletti (5). The fiber length was considered 125mm (60mm as lower and 65mm as upper semi-fiber length). Buchthal and colleagues estimated from electrophysiological evidence in the Biceps Brachii that an average MU innervation zone (IZ) is longitudinally spread over a distance roughly equal to 10% of the fiber length (7). For simulation, the IZ spread was set to 10mm. The skin potentials were simulated as monopolar. Two motor units were simulated individually. One with rather small
1
www.biology.kenyon.edu/coursces/biol09/EMG/EMG.htm
2. EMG AMPLITUDE INDICATORS IN SPACE AND TIME
motor unit territory (radius =2mm) place 2mm deep in the muscle. The second motor
unit is a large motor unit with 15mm radius in a circular territory with the center placed at 15.5mm deep into the muscle. Figure 2.14 shows the geometry of the model (motor unit with 15mm territory radius) and the parameters that were used in this
study. Similar to the single fiber simulation study presented in the previous section, the spatial distribution of skin potentials at four instantaneous times (t1, t2, t3, and t4)
were studied (t1 to t4are corresponding to 1.5ms, 2.4 ms, 8.8ms, and 16.6ms after start
of depolarization respectively). These times were chosen by visual inspection of the detected signal from the electrode placed at the center of detection grid and are related to the action potential at depolarization, repolarization, first end of fiber and second
end of fiber. Figure 2.15 shows the simulated skin potential sampled by electrodes with IED=1mm, 5mm, 10mm, and 15mm.
Figure 2.16 show one cycle of the amplitude spectrum in space for sampling frequency
200, 100, and 67 samples/m (i.e. IED=5, 10, and 15mm respectively) with harmonics spaced by 1.0/0.128=7.81 cycles/m of simulated skin potentials (monopolar detection) produced by a single motor unit (see also figure 2.14).
For the IED = 15mm (see figure 2.16 panel ”C”) the presence of aliasing can be seen
for all selected times corresponding depolarization, repolarization, first and second end of fiber. The aliasing is getting worse as the IED increases.
2.9 Spatial distribution (over the skin) of a simulated motor unit action potential (space-time and frequency domain)
Figure 2.14: Geometry of the model up) 3-D view and bottom) top view that is used for simulating a single MU including 150 fibers, which are uniformly distributed in the motor unit territory. Specific parameters can be found in
2. EMG AMPLITUDE INDICATORS IN SPACE AND TIME
Figure 2.15: Distribution of the simulated monopolar surface potential from a motor unit including 150 fibers uniformly distributed in a circular territory (radius=15mm), the most superficial fiber among 150 fibers was placed 0.5mm deep in the muscle (skin thickness 1 mm, subcutaneous tissue thickness: 3mm). The action potential are at a), e), i), m) start of depolarization(t1); b), f ), j), n)
during depolarization(t2); c), g), k), o) during the first end of fiber effect(t3);
d), h), l), p) at the second end of fiber effect(t4). a), b), c), and d) are
relating to inter electrode distance(IED)=1mm. Panels e), f ), g), and h) are for IED=5mm; panels i), j), k), and l) are for IED=10mm; panels m), n), o), and p) are for IED=15mm. The detection system covers 128×128mm2
in all images. q)Simulated action potential generated by the model shown in figure 2.14 and detected by the electrode over the neuromuscular junction. Four different instant times, when the surface potential images were plotted, indicate start of depolarization (t1), during depolarization (t2= t1+ 2.5ms),
during first (t3 = t1+ 13ms) and second (t4= t1+ 16ms) end of fiber effect
2.9 Spatial distribution (over the skin) of a simulated motor unit action potential (space-time and frequency domain)
Figure 2.16: One cycle of the magnitude of the 2-D Fourier transform (up to sampling frequency) for spatial distribution of simulated monopolar surface potential produced by a single motor unit . . . continued on the next page...
2. EMG AMPLITUDE INDICATORS IN SPACE AND TIME
Figure 2.16: . . . from the previous page: including 150 fibers uniformly dis- tributed in a circular territory 15mm radius, 15.5mm deep in the muscle, at 4 different instant times (t1, t2, t3, t4-see figure 2.15-panel ”q”) with reference to
the action potential time generation (t1) are represented. The simulated skin
potentials (128×128mm2) were sampled at A) 200 samples/m (IED=5mm), B)
100 samples/m (IED=10)mm, and C) 67sampls/m (IED=15mm). The spatial domain plots are shown in figure 2.15.