**5.4. Models for the potentials recorded at the skin surface**

Models for the potentials recorded at the skin surface usually follow the convolutional approach, that is, they try to find a 'weighting function' that provides the potential recorded at any point on the surface of the skin above the active fiber and caused by an elementary current source at the fiber. First of all, a geometric model of the muscle has to be defined, which might accommodate the existence of several tissue layers with different electrical properties (conductivities and capacitances). Together with the 'weighting function', a source function of the distribution of current sources in the fiber, such as one of those proposed for the single fiber case (Rodríguez et al, 2012), has to be used. Apart from the infinite homogeneous volume conductors, one of the first approximations for modeling the geometry of the muscle was the semi-infinite structure, which divides the complete (infinite) space into two parts separated by the skin plane: one with finite conductivity representing the muscle tissue, and one with zero conductivity, representing the other side of the skin plane (Merletti et al, 1999).

Muscle tissue presents higher conductivity in the direction longitudinal to the fibers than in the perpendicular direction. To include this behaviour into EMG models a new coefficient was included in the formulation of the 'weighting function': the anisotropy ratio (ratio between conductivities in the longitudinal and perpendicular directions) (Merletti et al, 1999). The effects of fat and skin layers, that have different electrical properties (conductivity and capacity), have also been incorporated into some models (Farina, 2001), (Block, 2002; Lowery 2002). The fat layer is normally considered isotropic, with conductivity appreciably lower than the muscle. Skin has a laminar structure with a highly resistant stratum corneoum and a deeper granular tissue with higher conductivity. However, it is normally modelled as a simple layer with homogeneous conductivity, although there is not general agreement about the values of skin conductivity ), (Block, 2002; Lowery 2002). The effects of these layers have been studied through simulation; relative to models which only include one or two layers, multi-layer models generate potentials with peak amplitudes closer to those found in real recordings.

An important step forward in the construction of more elaborated EMG models is the inclusion of finite limb geometries. Cylindrical muscle models have been developed by several authors (Gootzen, 1989; Roeleveld, 1997; Farina, 2004) in which the fibers run parallel to the cylinder axis. But, fibers may also run radially within a cylindrical geometry, for example, in the anal sphincter (Farina, 2004) or have different fiber-pinnation angles (Mesin, 2004). More complicated geometries, which include bones and vessels, have also been included in the models (Mesin, 2008). As the geometrical structure and composition of layers of the EMG model is made more complicated, defining and solving the electrical equations of the problem becomes more difficult. Iterative computational approaches such as the finite-element method (FEM) or boundary element method (BEM) are called for. In (Lowery, 2002) a FEM model with cylindrical geometry was devised for a muscle. This included the muscle tissue, fat and skin layers and a bone, all of them with specific conductivities. Similarly, a FEM model with a realistic geometry taken from magnetic resonance images of a particular subject's muscle was also modelled (Lowery, 2004). Simulated signals from both models were compared to real EMG data from electrical stimulation of the upper arm. Both models presented similar features with regard to peak amplitude and power spectrum mean frequency as functions of the recording position. However, the more realistic model (Lowery, 2004) provided action potential shapes closer to those actually recorded (Lowery, 2002).

Finally, the effects of the surface EMG electrodes potentials should also be included in the model. In general, placing an electrode on the skin surface does not alter the potential field. This is due to the relatively high impedance "seen" by the conductor tissue, which is, in turn, due to the electrochemical double layer formed between the metal of the electrode and the tissue. The potential recorded by the electrode is then the average potential in the surface covered by the electrode (McGill, 2004). Analytical or numerical procedures may be used to calculate this average either in the spatial domain (Dimitrov, 1998; Merletti, 1999) or in the spatial frequency domain (Farina, 2004).

#### **5.5. Conclusions and open research lines**

Computational Intelligence in Electromyography Analysis – 28 A Perspective on Current Applications and Future Challenges

motor process.

trapezius muscle.

*5.3.4. Modeling the common drive* 

plane (Merletti et al, 1999).

synchronization is not appreciably affected.

**5.4. Models for the potentials recorded at the skin surface** 

that either rate coding or synchronization could provide output data fit to the real data and that either of these two strategies, or a combination of the two, could be involved in the

A different model was proposed by Kleine et al. (2001), who slightly modified Matthews' firing rate model to introduce synchronization in a controlled way. In essence, the noisy input component is divided into two parts, one which is common to other MUs in the pool and one that is unique and independent of the other MUs. Simulation of SEMG signals correctly predicted the findings observed experimentally in isometric contractions of the

Jiangs' physiological model for modeling the generation of MN firing trains also enables the simulation of common drive (Jiang, 2006). In the example explored (Fig. 9), there are independent MN inputs that determine their excitabilities (Iapp1 and Iapp2). When these inputs are given a common oscillating signal, emulating interneural or afferent signals reaching the two MNs, their firing rates exhibit a clear correlation (common drive), although

Models for the potentials recorded at the skin surface usually follow the convolutional approach, that is, they try to find a 'weighting function' that provides the potential recorded at any point on the surface of the skin above the active fiber and caused by an elementary current source at the fiber. First of all, a geometric model of the muscle has to be defined, which might accommodate the existence of several tissue layers with different electrical properties (conductivities and capacitances). Together with the 'weighting function', a source function of the distribution of current sources in the fiber, such as one of those proposed for the single fiber case (Rodríguez et al, 2012), has to be used. Apart from the infinite homogeneous volume conductors, one of the first approximations for modeling the geometry of the muscle was the semi-infinite structure, which divides the complete (infinite) space into two parts separated by the skin plane: one with finite conductivity representing the muscle tissue, and one with zero conductivity, representing the other side of the skin

Muscle tissue presents higher conductivity in the direction longitudinal to the fibers than in the perpendicular direction. To include this behaviour into EMG models a new coefficient was included in the formulation of the 'weighting function': the anisotropy ratio (ratio between conductivities in the longitudinal and perpendicular directions) (Merletti et al, 1999). The effects of fat and skin layers, that have different electrical properties (conductivity and capacity), have also been incorporated into some models (Farina, 2001), (Block, 2002; Lowery 2002). The fat layer is normally considered isotropic, with conductivity appreciably lower than the muscle. Skin has a laminar structure with a highly resistant stratum corneoum and a deeper granular tissue with higher conductivity. However, it is normally

A general perspective of EMG modeling has been displayed together with a description of the anatomical and functional physiological aspects, in which the described models are grounded. This panoramic view comprises models for the space and size distribution and architectural organization of MUs in the muscle; a view of the hierarchical organization of the motor control; models for the principal MU activation and firing strategies for muscle force production: MU recruitment, 'rate coding', MN synchronization and the 'common drive'; and models for the generation of potentials at electrodes placed on the skin surface. Experimental research works sustaining evidences for the theories and concepts described in the chapter have also been included.

EMG Modeling 31

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The research effort in modeling and simulating EMG signals in the last three decades has been paramount including both analytical as well as numerical orientations. The degree of complexity and detail has also run parallel to these developments with the aim of recreating the physiological EMG generation system on one hand and the temporal and spectral features of real EMG signals on the other hand. However, there is still room for improvement in several aspects:

