A mathematical simulation of the hyperneas of metabolic CO2 production and inhalation

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.