MODELING INSTABILITY IN THE CONTROL SYSTEM FOR
HUMAN RESPIRATION: APPLICATIONS TO INFANT NON-REM
SLEEP J. J. BATZELy AND H. T. TRANz
Abstract. Mathematical models of the human respiratory control system have been developed
since 1940 to study a wide range of features of this complex system. The phenomena collectively
referred to as periodic breathing (including Cheyne Stokes respiration and apneustic breathing) have
important medical implications. The hypothesis that periodic breathing is the result of delay in the
feedback signals to the respiratory control system has been studied since the work of Grodins et al.
in the early 1950's [36]. The purpose of this paper is to extend the model presented by Khoo et al.
[60] in 1991 to include variable delay in the feedback control loop and to study the phenomena of
periodic breathing and apnea as they occur during quiet sleep in infant sleep respiration at around
4 months of age. The nonlinear mathematical model consists of a feedback control system of ve
delay dierential equations. Numerical simulations are performed to study instabilities in the control
system and the occurence of periodic breathing and apnea in the above case which is a time frame
of high incidence of sudden infant death syndrome (SIDS).
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