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A hybrid scheme, combining image series and moment method has been utilized for the calculation of the intramuscular three-dimensional (3-D) current density (CD) distribution and potential field transcutaneously excited by an electrode array. The model permits one to study the effect of tissue electrical properties and electrode placement on the CD distribution. The isometric recruitment curve (IRC) of the muscle was used for parameter estimation and model verification, by comparison with experimentally obtained IRCs of functional electrical stimulation (FES)-activated quadriceps muscle of paraplegic subjects. Sensitivity of the calculated IRC to parameters such as tissue conductivity, electrode size, and configuration was verified. The resulting model demonstrated characteristic features that were similar to those of experimentally obtained data. The model IRCs were insensitive to the electrode size; however, the inclusion of the bone-fascia layer significantly increased the intramuscular CD and, consequently, increased the IRC slope. Of the different configurations studied, a four-electrode array proved advantageous because, in this case, the CD between the electrodes was more evenly distributed, providing better resistance to fatigue. However, due to the steeper linear portion of the IRC, this configuration suffered from a somewhat reduced controllability of the muscle.

The present work develops an analytical model that allows one to estimate the current distribution within the whole muscle and the resulting isometric recruitment curve (IRC). The quasistatic current distribution, expressed as an image series, i.e., a collection of properly weighted and shifted point-source responses, outlines an extension for more than three layers of the classical image theory in conductive plane-stratified media. Evaluation of the current distribution via the image series expansions requires substantially less computational time than the standard integral representation. The expansions use a unique recursive representation for Green's function, that is a generic characteristic of the stratification. This approach permits one to verify which of the tissue electrical properties are responsible for the current density distribution within the muscle, and how significant their combinations are. In addition, the model permits one to study the effect of different electrode placement on the shape and the magnitude of the potential distribution. A simple IRC model was used for parameter estimation and model verification by comparison with experimentally obtained isometric recruitment curves. Sensitivity of the model to different parameters such as conductivity of the tissues and activation threshold was verified. The resulting model demonstrated characteristic features that were similar to those of experimentally obtained data. The model also quantitatively confirmed the differences existing between surface (transcutaneous) and implanted (percutaneous) electrode stimulation.