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.