Calculation of extracellular potentials produced by an inclined muscle fibre at a rectangular plate electrode

Generally the anatomy of muscles is rather complex, and the fibres have various inclination angles within the muscles. We suggest a fast and reliable way to calculate extracellular potentials produced at a point or rectangular plate electrode by a muscle fibre of finite length with an arbitrary inclination. A muscle fibre was considered to be a linear timeshift-invariant system of potential generation. Then, similar to the fibre without inclination, the extracellular potential produced by an inclined fibre was represented as the output signal of the system; it was calculated as the convolution of the input signal and impulse response. Irrespective of the inclination, the input signal of the system was the first temporal derivative of the intracellular action potential. The impulse response of the system differed for the fibres with inclination. This required a new method of analytical integration over the rectangular electrode area. The approach provides a chance to simulate and analyze motor unit potentials or F-, H- or M-responses produced by muscles of complicated anatomy (circum-pennate or complex pennate type) at electrodes of actual size and location in normals and patients with neuro-muscular disorders.