Potential distribution and single-fibre action potentials in a radially bounded muscle model

Abstract

In modelling the electrical behaviour of muscle tissue, we used to employ a frequency-dependent volume conductor network model, which was infinitely extended in all directions. Equations in this model could be solved using a finite-difference approach. The most important restriction of this model was the fact that no boundary effects could be incorporated. Analytical models of muscle tissue normally do not have this disadvantage, but in those models the microscopic structure of muscle tissue cannot be taken into account. In the paper, we present a combined numerical/analytical approach, which enables the study of potential distributions and SFAPs in simulated microscopic muscle tissue in which the influence of the muscle boundary has been considered. We considered muscle models with radii of 1.5 mm and 10 mm. Both models were compared with an unbounded network model. In the model with a radius of 1.5 mm we varied the position of the active fibre relative to the muscle surface. It appeared that in most cases the presence of a boundary had a considerable effect on the potential distribution. An increase in the peak-to-peak value of the SFAP amplitude up to 300 per cent was noticed when the active fibre was positioned 500 microns beneath the muscle surface in a model with a radius of 1.5 mm.

A multiple-layer finite-element model of the surface EMG signal

“…These models have been predominantly based on analytical solutions for muscle fibers located in either finite or infinite volume conductors [1]- [6]. Analytical models, however, are limited to simple cylindrical or elliptical geometries and become increasingly difficult to handle as additional layers are incorporated.…”

“…To date, a limited number of models have considered the finite nature of the volume conductor in which the muscle fibers lie [3]- [6], [11]. Of these, only the models of Gootzen et al, [3] and Roeleveld et al, [5] have incorporated multiple layers of fat and skin tissue, although fat and skin layers have been included in a recent hemi-space model for planar geometries [12].…”

Finite element modeling of electromagnetic signal propagation in a phantom arm

“…Some studies have considered cylindrical volumes embedded in infinite volume conductors [14], [15]. Only a few studies have considered the finite dimensions of a cylindrical volume conductor [16]- [20]. These studies have shown that the boundary can have a significant impact on single fiber action potentials.…”

“…This could significantly affect the amplitude, as well as the phase and shape, of the EMG signal. Although some investigators have considered the effects of capacitance near the source [10], [20], [26], [27], none have included the permittivity of the tissue as a whole. A full electromagnetics model is necessary to quantify these effects and determine their significance.…”

“…Some researchers have modeled the action potential as a simple dipole [4], [15], and many groups have used a balanced tripole [5], [8], [9], [11], [19], [28], whereas others [6], [7], [13], [14], [20], [29] have used the more realistic analytic waveform described by Rosenfalk [30] and modified by Nandedkar and Stalberg [31]. The electric field will fall off more rapidly with a balanced tripole than with a dipole, resulting in less crosstalk around the limb.…”