Solution to a Mathematical Model of Cheyne-Stokes Breathing

Cheyne-Stokes Breathing (CSB) often occurs in patients with congestive heart failure and may be a prelude to death. A similar phenomenon is very common in healthy premature infants, but excessive CSB has been correlated with sudden infant death.  It follows that mathematical theories of CSB are of great interest. Our goal is predictive monitoring of patients in intensive care: by applying mathematical-physiological theories to respiratory data, we hope to extract parameters (time-delays, feedback coefficients, loop gain, etc.), and then to seek patterns in the behavior of these parameters that occur prior to -- and are reasonably predictive of -- important clinical events. Here we develop and present solutions to a mathematical theory that may extract new information from respiratory signals.