*4.1.3. Motor end-plate zone, fiber diameter, and initiation of depolarization*

Electrophysiologically, the motor end-plate is the region where the motor end-plate potential is generated, hence where the intracellular action potential of the muscle fiber starts. Thus, the relative longitudinal position of the motor end-plates of the set of muscle fibers belonging to a single motor unit is determinant in the synchronization of the single fiber action potentials. In addition, there will be different times for the initiation of the depolarization of the different motor end-plates, depending on the length of the axonal sprout innervating it. Besides, SFAPs will propagate at different conduction velocities through the muscle fiber, mainly dependent on muscle fiber diameter. All these factors (spatial configuration of end-plates, initiation of depolarization, and muscle fiber conduction velocity) affect synchronization of the SFAPs contributing to the MUP, and ultimately this will affect the shape, amplitude, and duration of recorded MUPs.

Neuromuscular junctions tend to reside in the middle part of muscle fibers, as the connection is established while a muscle fiber is still growing in both directions. The threedimensional reconstruction of the motor end-plate zones leads to a two-dimensional membrane lying in the muscle volume. Measurements show that the width of this membrane, which corresponds to the variability in the longitudinal position of the individual motor end-plates, ranges between 6 and 10 mm in the *biceps brachii* (Aquilonious et al, 1984).

Muscle fiber conduction velocities can be measured *in situ* (Stålberg, 1966) and have a normal distribution of values for the whole of a given muscle. It is assumed that conduction velocity is directly proportional to fiber diameter, with histological analyses also showing a normal distribution for the diameters of muscle fibers.

Finally, a delay in the initiation of depolarization is caused by two factors: the axonal propagation delay, which is clearly dependent on the length of the axonal terminal branch and its propagation velocity; and the neuromuscular junction transmission delay, which has an average value, but also some variability (the "jitter").

#### **4.2. Models for the motor unit cross section**

The first computational muscle architecture models found in the literature were restricted to the simulation of a single motor unit. In essence, if individual motor units are modeled, of the triad: MUFN, MUTA, and MUFD, two quantities can be arbitrarily fixed, while the third will be a subsidiary quantity. After considering the dimensions and number of fibers of the motor unit, the models must deal with the placement of the individual MUFs within the MUT, in order to follow a certain spatial distribution.

Computational Intelligence in Electromyography Analysis – 14 A Perspective on Current Applications and Future Challenges

glycogen-depletion technique.

et al, 1984).

likely correspond to the holes observed in glycogen-depletion studies. Hence these results seem to agree with the long-range distribution findings in non-human vertebrates by the

Electrophysiologically, the motor end-plate is the region where the motor end-plate potential is generated, hence where the intracellular action potential of the muscle fiber starts. Thus, the relative longitudinal position of the motor end-plates of the set of muscle fibers belonging to a single motor unit is determinant in the synchronization of the single fiber action potentials. In addition, there will be different times for the initiation of the depolarization of the different motor end-plates, depending on the length of the axonal sprout innervating it. Besides, SFAPs will propagate at different conduction velocities through the muscle fiber, mainly dependent on muscle fiber diameter. All these factors (spatial configuration of end-plates, initiation of depolarization, and muscle fiber conduction velocity) affect synchronization of the SFAPs contributing to the MUP, and

*4.1.3. Motor end-plate zone, fiber diameter, and initiation of depolarization* 

ultimately this will affect the shape, amplitude, and duration of recorded MUPs.

normal distribution for the diameters of muscle fibers.

an average value, but also some variability (the "jitter").

**4.2. Models for the motor unit cross section** 

MUT, in order to follow a certain spatial distribution.

Neuromuscular junctions tend to reside in the middle part of muscle fibers, as the connection is established while a muscle fiber is still growing in both directions. The threedimensional reconstruction of the motor end-plate zones leads to a two-dimensional membrane lying in the muscle volume. Measurements show that the width of this membrane, which corresponds to the variability in the longitudinal position of the individual motor end-plates, ranges between 6 and 10 mm in the *biceps brachii* (Aquilonious

Muscle fiber conduction velocities can be measured *in situ* (Stålberg, 1966) and have a normal distribution of values for the whole of a given muscle. It is assumed that conduction velocity is directly proportional to fiber diameter, with histological analyses also showing a

Finally, a delay in the initiation of depolarization is caused by two factors: the axonal propagation delay, which is clearly dependent on the length of the axonal terminal branch and its propagation velocity; and the neuromuscular junction transmission delay, which has

The first computational muscle architecture models found in the literature were restricted to the simulation of a single motor unit. In essence, if individual motor units are modeled, of the triad: MUFN, MUTA, and MUFD, two quantities can be arbitrarily fixed, while the third will be a subsidiary quantity. After considering the dimensions and number of fibers of the motor unit, the models must deal with the placement of the individual MUFs within the

**Figure 5.** Representation of a simulated motor unit including the most relevant anatomical and physiological factor to reproduce the architecture and physiology of the motor unit.

The first motor unit model (Griep et al, 1978) was proposed in order to study the properties of the motor unit potential (MUP) by means of computer simulation. Other researchers, (Miller-Larsson, 1980; Gath and Stålberg, 1982; Hilton-Brown et al, 1985), were concerned with the modeling of fiber density and spatial distribution of muscle fibers of a single motor unit, in order to determine the influence of architectural changes produced by neuromuscular disease on clinical electrophysiological recordings. Other single motor unit models have been developed more recently. Other studies (Nandedkar et al, 1988; Stålberg and Karlsson, 2001) proposed a muscle model to study the correlation between anatomical parameters and MUP signals by means of simulations, allowing the study of the MUP variations under different pathological conditions such as denervation and re-innervation.

Two main approaches are used to model the spatial distribution of MUFs: random location and random selection from a muscle fiber grid. In the first approach, a number of MUFs are placed following a given spatial distribution, usually normal or uniform. In the second approach, a predefined grid of evenly distributed muscle fibers is created, and a number of them are selected to be innervated by the motor unit under simulation.
