If you conduct fMRI experiments then you'll have at least a basic understanding of the cascade of events that we term neurovascular coupling. When the neuronal firing rate increases in a patch of brain tissue, there is a transient, local increase of the cerebral blood flow (CBF). The oxygen utilization remains about the same, however. This produces a mismatch in the rate of oxygen delivered compared to the rate of oxygen consumption. The CBF goes up a lot while the oxygenation usage increases only slightly. Hence, there is a decrease in the concentration of deoxygenated hemoglobin in the veins draining the neural tissue region, in turn reducing the degree of paramagnetism of these veins that yields a signal increase in a T2*-weighted image. The essential point is that it's blood delivery - changes in CBF - that provides the main impetus for BOLD contrast.
How is blood pressure related to CBF?
The average CBF in a normal adult brain is typically maintained at around 50 ml of blood per 100 g of brain tissue per minute (50 ml/100g/min). The average number, while useful, represents considerable spatial and temporal heterogeneity across the brain. The typical CBF in gray matter is approximately double that in white matter, and there is significant variation across each tissue type arising from tight metabolic coupling. (See Note 1.)
At the local level, blood delivery to tissue is controlled by smooth muscles on the walls of arterioles and capillaries. The degree of vessel dilation, relative to that vessel's maximum possible dilation, is called its tone - the vascular tone. There are mechanisms to expand or constrict the smooth muscles, changing the local blood flow in order to maintain the tight local coupling of CBF to metabolic demand while protecting the vasculature and the tissue against damage that might arise with systemic changes in the blood supply from non-neural mechanisms. The totality of these processes is referred to as cerebral autoregulation. More on the non-neural factors later.
This is all very well, but there is something important missing from this picture. We have neglected to consider so far that the force of blood pumped out of the heart creates a pressure gradient across the arteries and the veins, with the tissue providing a resistance in between. It's this pressure gradient that causes the blood to flow. In fact, simple electrical circuits are a convenient model here. For those of you more familiar with electron flow than blood flow, we can think of the CBF as an analog of electrical current, the pressure difference as a voltage and, naturally enough, the tissue's resistance to flow mimics an electrical resistance. Thus we get:
CBF = CPP / CVR
where CPP is the cerebral perfusion pressure, the net pressure gradient - the driving force - that generates perfusion of brain tissue, and CVR is the cerebrovascular resistance. The CVR is the sum total of all mechanisms exerting control over the vascular tone at a particular location. It isn't easily estimated without detailed knowledge of the processes that might be active. The neurovascular coupling pathways contribute to CVR, for example.