Estimating hemodynamic stimulus and blood vessel compliance from cerebral blood flow data

Several key brain imaging modalities that are intended for retrieving information about neuronal activity in brain, the BOLD fMRI as a foremost example, rely on the assumption that elevated neuronal activity elicits spatiotemporally well localized increase of the oxygenated blood volume, which in turn can be monitored non-invasively. The details of the signaling in the neurovascular unit during hyperemia are still not completely understood, and remain a topic of active research, requiring good mathematical models that are able to couple the different aspects of the signaling event. In this work, the question of estimating the hemodynamic stimulus function from cerebral blood flow data is addressed. In the present model, the hemodynamic stimulus is a non-specific signal from the electrophysiological and metabolic complex that controls the compliance of the blood vessels, leading to a vasodilation and thereby to an increase of blood flow. The underlying model is based on earlier literature, and it is further developed in this article for the needs of the inverse problem, which is solved using hierarchical Bayesian methodology, addressing also the poorly known model parameters.