A Method for the Analysis of AP Foot Convexity: Insights into Smooth Muscle Biophysics

Action potential (AP) profiles vary based on the cell type, with cells of the same type typically producing APs with similar shapes. But in certain syncytial tissues, such as the smooth muscle of the urinary bladder wall, even a single cell is known to exhibit APs with diverse profiles. The origin of this diversity is not currently understood, but is often attributed to factors such as syncytial interactions and the spatial distribution of parasympathetic nerve terminals. Thus, the profile of an action potential is determined by the inherent properties of the cell and influenced by its biophysical environment. The analysis of an AP profile, therefore, holds potential for constructing a biophysical picture of the cellular environment. An important feature of any AP is its depolarization to threshold, termed the AP foot, which holds information about the origin of the AP. Currently, there exists no established technique for the quantification of the AP foot. In this study, we explore several possible approaches for this quantification, namely, exponential fitting, evaluation of the radius of curvature, triangulation altitude, and various area based methods. We have also proposed a modified area-based approach (C_X,Y) which quantifies foot convexity as the area between the AP foot and a predefined line. We assess the robustness of the individual approaches over a wide variety of signals, mimicking AP diversity. The proposed (C_X,Y) method is demonstrated to be superior to the other approaches, and we demonstrate its application on experimentally recorded AP profiles. The study reveals how the quantification of the AP foot could be related to the nature of the underlying synaptic activity and help shed light on biophysical features such as the density of innervation, proximity of varicosities, size of the syncytium, or the strength of intercellular coupling within the syncytium. The work presented here is directed toward exploring these aspects, with further potential toward clinical electrodiagnostics by providing a better understanding of whole-organ biophysics.