Determination of Neuronal Action Potential Amplitude based on Multidimensional Differential Geometry

Arrangements are described for determining a physiological characteristic of the auditory pathway (as whole or selected parts such as an inner ear). Electrical stimulation pulses are delivered to inner ear neural tissue and corresponding tissue response signals are developed by measuring over time response of the auditory pathway to each electrical stimulation pulse, with each tissue response signal forming a response curve including at least one physiological landmark such as a local maximum and a local minimum. A multi-dimensional polynomial is fit over the tissue response signals, and calculation starting points are defined based on prominent physiologic landmarks such as a local maximum and a local minimum for one selected tissue response signal. A line of minimum principal curvature of the multi-dimensional polynomial over the plurality of tissue response signals that intersect the calculation starting points is calculated to determine a physiological characteristic of the auditory pathway.