AJP - Regulatory, Integrative and Comparative Physiology, Vol 235, Issue 5 265-R278, Copyright © 1978 by American Physiological Society
A mathematical simulation of the hyperneas of metabolic CO2 production and inhalation
W. S. Yamamoto
Mathematical models of the CO2 responsive controller for ventillatory
responses to CO2 inhaled and to CO2 introduced in the perpheral tissues are
formulated in the context of a controlled system that is a compartmented
tissue system with a lung undergoing breathing movements. Equations
representing the system are either ordinary difference-differential
equations or algebraic equations. If the controller contains three
components simulating, respectively, a proportional controller with a set
point, a mechanism sensitive to trans-membrane CO2 gradients, and a
mechanism responsive to the autocovariance difference in arterial carbon
dioxide tension (PaCO2) about 1.2 s apart; and if the neural tissues
produce CO2 as a result of their own activity (positive feedback), the
entire system responds to metabolic production of CO2 by increasing
ventilation in proportion to metabolism while maintaining a constant PaCO2.
The same system responds to inhaled CO2 mixtures with ventilation
increasing in proportion to increases in PaCO2. The behavior of the model
is used to postulate a spatiotemporal hypothesis for the humoral component
of respiratory regulation of CO2 exchanges.
