Respiratory Control and the Onset of Periodic Breathing

MACSI, University of Limerick, Limerick, Ireland OCIAM, Mathematical Institute, University of Oxford, Oxford, UK

^⋆ Corresponding author. E-mail: andrew.fowler@ul.ie

Abstract

We analyse a reduced version of the Grodins et al. control model [14] of respiration involving only CO₂, and show that it can be dramatically simplified by the use of judicious approximations. In particular, we show that the conceptual basis of the popular model of Mackey and Glass [20] is at odds with the important transport processes of the Grodins model. Despite this, a realistic approximation of the Grodins model yields a Mackey-Glass type model with almost the same criterion for the onset of Cheyne-Stokes breathing.

While the reduced Grodins model does apparently provide a realistic mechanism for instability, consideration of the buffering effect of the blood-brain barrier appears to make it unlikely. We conclude that a realistic physiological model of Grodins type to explain Cheyne–Stokes breathing is not yet in place, and raise the question whether the bicarbonate buffering system has a rôle to play.