Peer-Reviewed Journal Details
Mandatory Fields
Fowler, AC
2014
January
Mathematical Modelling Of Natural Phenomena
Respiratory Control and the Onset of Periodic Breathing
Published
()
Optional Fields
periodic breathing respiratory control Ateyne-Stokes respiration delay equation STATE-SPACE MODEL CONTROL-SYSTEM MATHEMATICAL-ANALYSIS HEART-FAILURE STABILITY INSTABILITY
9
39
57
We analyse a reduced version of the Grodins et al. control model HA] 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 1201 is at odds with the important transport processes of the Grodins model. Despite this, a realistic approximation of the Grodius 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 role to play.
10.1051/mmnp/2011-9104
Grant Details