Background: Paired cerebral blood flow (CBF) measurement is usually acquired before and after vasoactive stimulus to estimate cerebrovascular reserve (CVR). However, CVR may be confounded because of variations in time-to-maximum CBF response (t_max) following acetazolamide injection. With a mathematical model, CVR can be calculated insensitive to variations in t_max, and a model offers the possibility to calculate additional model-derived parameters. A model that describes the temporal CBF response following a vasodilating acetazolamide injection is proposed and evaluated.

Methods: A bi-exponential model was adopted and fitted to four CBF measurements acquired using arterial spin labelling before and initialised at 5, 15 and 25 min after acetazolamide injection in a total of fifteen patients with Moyamoya disease. Curve fitting was performed using a non-linear least squares method with a priori constraints based on simulations.

Results: Goodness of fit (mean absolute error) varied between 0.30 and 0.62 ml·100 g^-1·min^-1. Model-derived CVR was significantly higher compared to static CVR measures. Maximum CBF increase occurred earlier in healthy- compared to diseased vascular regions.

Conclusions: The proposed mathematical model offers the possibility to calculate CVR insensitive to variations in time to maximum CBF response which gives a more detailed characterisation of CVR compared to static CVR measures. Although the mathematical model adapts generally well to this dataset of patients with MMD it should be considered as experimental; hence, further studies in healthy populations and other patient cohorts are warranted.