**4.3. Models of the physiological parameters affecting the temporal dispersion of a MUAP**

In all the above-mentioned models, muscle fiber conduction velocity, delay of initiation of depolarization, and longitudinal position of the motor end-plate are modeled as random variables from statistical distributions. It is important to note that, as individual motor units are being modeled, simulated distributions refer to the MUFs and not to all the fibers of the muscle bundle.

Muscle fiber diameter is modeled as a normally distributed variable with mean and standard deviation fixed to match corresponding values observed in real counterparts of the simulated muscle. Muscle fiber conduction velocity (MFCV) is modeled as a normally distributed variable, obtained from a linear transformation of the muscle fiber diameter. The most widely used relationship between fiber diameter and conduction velocity (Nandedkar and Stålberg, 1983) is:

$$\mathbf{v} = 3.7 + 0.05 \left( \mathbf{d} - 55 \right) \tag{10}$$

EMG Modeling 17

modeled. The electromyographist tries to bring the core closer to active fibers, producing sharp spikes in MUPs. In the corresponding model, the electrode is allowed to move 1 mm around the original insertion point in the longitudinal direction of the needle, and the position with the shortest distance to an active fiber is selected (Nandedkar et al, 1988;

In this section, the modeling of the electrical activity of a complete and functional muscle is described. After summarizing the principal anatomical and physiological characteristics of skeletal muscle, the different elements for building a model of a surface EMG signal generated by such a muscle are presented. Together with models of motor unit activity, discussed in the previous section, these elements comprise models for the architecture and geometric organization of the motor units within the muscle, models for the motor neuron

In order to better understand the anatomical and physiological scenario which the models should recreate, an overview of the arrangement of MUs within the muscle and of the

When trying to analyze a muscle's cross-section as a whole, overall statistics for the MUFN, MUTA and MUFD must be provided. We can think of the muscle cross-section as a tightly packed set of muscle fibers that are innervated by a smaller set of motoneurons. The innervation process, which determines the actual set of muscle fibers innervated by each motoneuron, defines the number and spatial distribution of the MUFs, hence the MUFN and

The MUFNs of the motor units in a muscle tend to distribute exponentially, with fewer motor units with lower MUFN and less motor units with higher MUFN. Indirectly, MUFN can be studied on the basis of the mechanical response of the muscle. Studies of the mechanical response of skeletal muscle support the idea that many factors influence the force production of a single motor unit, including the MUFN, the cross-sectional area of motor unit fibers, and the specific tension output for the different muscle fiber types. However, within motor units of a single type, the main factor determining force production is shown to be the MUFN (Bodine et al, 1987). This makes it reasonable to assume that MUFN is proportional to motor unit maximum tetanic tension (Fuglevand et al, 1993). All these findings support the use of maximum tetanic force estimation techniques in order to investigate the MUFN in humans, where glycogen-depletion techniques obviously cannot be applied. The relative MUFNs can be assessed by measuring the sizes of the electrical and mechanical responses of individual motor units when motor axons are excited by threshold

*5.1.1. Anatomical and architectural organization of the motor units in skeletal muscle* 

Hamilton-Wright and Stashuk, 2005).

**5. Modeling electrical activity of skeletal muscle** 

**5.1. Physiological aspects concerning muscle EMG** 

the MUTA, and, subsequently, the MUFD.

organization and strategies of the motor control is first provided.

pool activity, and models for the potentials recorded at the skin surface.

With v being the MFCV in m/s and d the muscle fiber diameter in μm. This equation assumes a linear relationship between both quantities, and a MFCV of 3.7 m/s for a muscle fiber diameter of 55 μm. Both these values are the central values of the corresponding distributions for the human *biceps brachii* muscle.

The delay in initiation of depolarization is usually modeled as a normal or uniform random variable, although in some cases its influence on simulation outcomes is assumed to be negligible and consequently it is not modeled and set to zero for all the muscle fibers.

Finally, the longitudinal position of the motor end-plates is modeled as a normal or uniform random variable, emulating the narrow width that the motor end-plate zone occupies within the longitudinal section of the muscle. Uniform distributions usually lead to overly complex MUPs, which seems to call for normal distributions. However, a specific model accounting for the motor unit fractions observed in scanning-EMG recordings, modeled the motor end-plates of small groups of motor unit fibers as narrower normal distributions with the mean of the distributions again distributed uniformly (Navallas and Stålberg, 2009). This model allows for a motor end-plate zone that is wider, whilst keeping the dispersion, and hence the MUP complexity, locally low.

### **4.4. Models of recording electrodes for intramuscular EMG**

Point recording models, which are accurate enough for the simulation of single fiber EMG recordings, must be extended in order to simulate other needle electrodes where electrode poles are not small enough to be considered as points. Two main approaches are available. One is the analytical approach, which requires calculation of the integrals in order to simplify the calculations (Nandedkar and Stålberg, 1983; Dimitrov and Dimitrova, 1998). The other is the discrete elements approach, where the poles are modeled as grids of points where the potentials are calculated individually, and lately averaged to give the potential of the pole. In the case of concentric needle EMG, two poles must be modeled: the core, which represents the active recording region; and the cannula, used as the reference potential. The core, which is a small plane elliptical region, can be directly modeled using either approach. The cannula, a cylindrical region, which averages the potential over a much broader region than the core, can be simplified as a one dimensional cable structure coincident with the needle axis. In the case of macro EMG recordings, the active area is the cannula itself, and the electrode may be modeled accordingly.

There are other effects related to the needle insertion procedure that can also be modeled. Whenever the needle electrode is inserted, fibers in the way of insertion can be displaced by the needle shaft. This effect, named "fiber ploughing", calls for an update in the fiber positions according to the displacement suffered. The electrode manipulation typically performed by an electromyographist while recording concentric needle EMG can also be modeled. The electromyographist tries to bring the core closer to active fibers, producing sharp spikes in MUPs. In the corresponding model, the electrode is allowed to move 1 mm around the original insertion point in the longitudinal direction of the needle, and the position with the shortest distance to an active fiber is selected (Nandedkar et al, 1988; Hamilton-Wright and Stashuk, 2005).
