Modeling instability in the control system for human respiration: applications to infant non-REM sleep

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 F.S. Grodins, J. Gray, A.I. Norins, R.W. Jones [J. Appl. Physiol. 1 (1954) 283–308] in the early 1950s. The purpose of this paper is to extend the model presented by M.C.K. Khoo, R.E. Kronauer, K.P. Strohl, A.S. Slutsky [J. Appl. Physiol. 53 (3) (1982) 644–659] 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 five delay differential equations. Numerical simulations are performed to study instabilities in the control system and the occurrence of periodic breathing and apnea in the above case which is a time frame of high incidence of sudden infant death syndrome (SIDS).