The Point of Maximum Curvature as a Marker for Physiological Time Series

Abstract

We present a geometric analysis of the model of Stirling et al. [14]. In particular we analyze the curvature of a heart rate time series in response to a step like increment in the exercise intensity. We present solutions for the point of maximum curvature which can be used as a marker of physiological interest. This marker defines the point after which the heart rate no longer continues to rapidly rise and instead follows either a steady state or slow rise. These methods are then applied to find analytic solutions for a mono exponential model which is commonly used in the literature to model the response to a moderate exercise intensity. Numerical solutions are then found for the full model and parameter values presented in Stirling et al. [14].