An Electromyogram (EMG) is an electrical signal, which is measured from a skeletal muscle during voluntary and involuntary contractions. EMGs are useful in interpreting pathological states of the musculoskeletal system. In particular, EMGs offer valuable information concerning the timing of muscular activity and its relative intensity. Various EMG models have developed with many different purposes from a pure mathematical model to a pattern structure model [17,46]. Sophisticated EMG models are necessary to examine the effects of small changes in muscular morphology and activities [46]. Due to the crucial importance of EMG models, all factors in the model should be precise and accurate. Especially, an intracellular action potential (IAP) model, the starting point of an EMG model, should be precisely generated because of its importance as the main component for an EMG model. Generally, the Rosenfalck IAP model [75,89] has been used because of its computational simplicity [59,72,77]. However, the Rosenfalck IAP model oversimplifies a real IAP, which has been experimentally measured, and it results in mismatching amplitudes and time duration between a real and modeled IAP.
This research proposes a mathematical IAP model using a series of modified gamma and erlang probability density functions. The optimization of the proposed IAP model was conducted by several different numerical methods, namely Gauss-Newton, Steepest Descent, and Conjugate Gradient methods. These optimizing methods for the proposed muscle IAP model were validated by applying them to the experimental results of the Hudgkin and Huxley neuron action potential [11]. Due to the similarity in the mechanism of both nerve and muscle IAP generations, the validation shows that the methods and results are reasonably applied and obtained in the proposed muscle model, which for the first time incorporates properties that explain ion channel behavior in IAP generation
