Modeling cerebral blood flow and ventilation instability due to CO₂

A minimal model of cerebral blood flow and respiratory control was developed to describe hypocapnic and hypercapnic responses. Important nonlinear properties such as cerebral blood flow changes with arterial partial pressure of carbon dioxide ([Formula: see text]) and associated time-dependent circulatory time delays were included. It was also necessary to vary cerebral metabolic rate as a function of [Formula: see text]. The cerebral blood flow model was added to a previously developed respiratory control model to simulate central and peripheral controller dynamics for humans. Model validation was based on previously collected data. The variable time delay due to brain blood flow changes in hypercapnia was an important determinant of predicted instability due to nonlinear interaction in addition to linear loop gain considerations. Peripheral chemoreceptor gains above a critical level, but within normal limits, were necessary to produce instability. Instability was observed in recovery from hypercapnia and hypocapnia. The 20-s breath-hold test appears to be a simple test of brain blood flow-mediated instability in hypercapnia. Brain blood flow was predicted to play an important role with nonlinear properties. There is an important interaction predicted by the current model between central and peripheral control mechanisms related to instability in hypercapnia recovery. Posthyperventilation breathing pattern can also reveal instability tied to brain blood flow. Previous data collected in patients with chronic obstructive lung disease were closely fitted with the current model and instability predicted. Brain vascular volume was proposed as a potential cause of instability despite cerebral autoregulation promoting constant brain flow.NEW & NOTEWORTHY Prior models of brain blood flow and respiratory control have not focused on instability. Time varying time delay resulting from brain blood flow changes due to carbon dioxide (CO₂) and peripheral chemoreceptor gain were predicted to be important determinants of instability due to nonlinear interaction in addition to linear control loop gain. Time delay was assumed to be set by the ratio of brain arterial vascular volume and blood flow. This vascular volume was predicted to also significantly change with CO₂.