Topological and phenomenological classification of bursting oscillations

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.     

Oscillations in a collapsed-tube analog of the brachial artery under a sphygmomanometer cuff

To determine whether self-excited oscillations in a Starling resistor are relevant to physiological situations, a collapsible tube conveying an aqueous flow was externally pressurized along only a central segment of its unsupported length. This was achieved by passing the tube through a shorter and wider collapsible sleeve which was mounted in Starling resistor fashion in a pressure chamber. The tube size and material, and all other experimental parameters, were as used in our previous Starling resistor studies. Both low- and high-frequency self-excited oscillations were observed, but the low-frequency oscillations were sensitive to the sleeve type and length relative to unsupported distance. Pressure-flow characteristics showed multiple oscillatory modes, which differed quantitatively from those observed in comparable Starling resistors. Slow variation of driving pressure gave differing behavior according to whether the pressure was rising or falling, in accord with the hysteresis noted on the characteristics and in the tube law. The results are discussed in terms of the various possible mechanisms of collapsible tube instability, and reasons are presented for the absence of the low-frequency mode under most physiological circumstances.