A planar elliptical model of cardio-vagal hysteresis

The state-dependent portion of cardio-vagal baroreflex control is called baroreflex hyteresis: we observe hysteresis when RR interval and carotid diameter depend on both the direction and value of arterial pressure. The elasticity of arterial walls, as well as the responsiveness of central command reset controls the real-time pattern of neural outflow, which is indirectly measured by RR interval in humans. We model the state-dependent relationship among pressure, vessel diameter and heart rate as a three-dimensional planar ellipse. Two-dimensional projections of this ellipse provide motion direction and quantify hysteresis between mechanical (pressure-diameter), neural (diameter-heart rate), and integrated baroreflex (pressure-heart rate) components. A convenient measure for the magnitude of hysteresis is the ratio of the semi-minor and semi-major axes of the best fitting ellipse. This ratio is given a sign according to the direction of its motion. The signed sum of the hysteresis ratio for vessel mechanics and central neural control reliably predicts cardio-vagal hysteresis. Using this relationship, we can quantify the relative importance of neural versus mechanical contributions to integrated baroreflex responses.