Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014Issue dedicated to Michael Mackey
|Page(s)||39 - 57|
|Published online||07 February 2014|
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: firstname.lastname@example.org
We analyse a reduced version of the Grodins et al. control model  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  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.
Mathematics Subject Classification: 92C50
Key words: periodic breathing / respiratory control / Cheyne-Stokes respiration / delay equation
© EDP Sciences, 2014
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