Novel ideas for fast muscle action potential simulations using the line source model

Using a signal processing approach, we analyze the line source model for muscle action potential (AP) modeling. We show that the original model presents a tradeoff between violating the Nyquist criterion on one hand and using a discretization frequency that is unnecessarily high with respect to the bandwidth of the generated AP on the other. Here, we present an improved line source model that, compared to the original, allows a lower discretization frequency while retaining the accuracy by simply introducing a continuous-time anti-aliasing filter. Moreover, a transfer function form of the transmembrane current is presented that promote the use of sophisticated signal processing methods on these type of signals. Both continuous-time and discrete-time models are presented. We also address and analyze the implications of the finite length of the muscle fibers. Including this in the model is straightforward, owing to the convolutional form of the line source model, and is manifested by a simple transformation of the associated weighting function. AP modeling is discussed for the three different electrode models: the concentric needle electrode, the single fiber electrode, and the macro electrode. The presented model is suitable for modeling large motor units, where both accuracy and computational efficiency are important factors. To simplify the selection of the discretization interval, we derive what we call the cumulative cutoff frequency that provides an estimate of the required Nyquist frequency.