We define cerebral vascular reactivity (CVR) as the ratio of the change in blood oxygen level-dependent (BOLD) magnetic resonance imaging (MRI) signal (S) to an increase in blood partial pressure of CO₂ (PCO₂): % Δ S/Δ PCO₂ mm Hg. Our aim was to further characterize CVR into dynamic and static components and then study 46 healthy subjects collated into a reference atlas and 20 patients with unilateral carotid artery stenosis. We applied an abrupt boxcar change in PCO₂ and monitored S. We convolved the PCO₂ with a set of first-order exponential functions whose time constant τ was increased in 2-second intervals between 2 and 100 seconds. The τ corresponding to the best fit between S and the convolved PCO₂ was used to score the speed of response. Additionally, the slope of the regression between S and the convolved PCO₂ represents the steady-state CVR (ssCVR). We found that both prolongations of τ and reductions in ssCVR (compared with the reference atlas) were associated with the reductions in CVR on the side of the lesion. τ and ssCVR are respectively the dynamic and static components of measured CVR.