%0 Journal Article
%@ 1402-9251
%A Stirling, James
%A Zakynthinaki, MarĂa S.
%D 2008
%F upm:2533
%I Atlantis Press
%J Journal of Nonlinear Mathematical Physics
%K Stirling, heart rate time series, exercise intensity, physiological.
%N 3 supp
%P 396-406
%T The point of maximum curvature as a marker for physiological time series
%U http://oa.upm.es/2533/
%V 15
%X We present a geometric analysis of the model of Stirling. 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.