I'll co-sign SubiculumCode's comment -- there's a lot of yelling about how bad fMRI is generally, which is not particularly fair to the fMRI research (or at least the better parts of it) or related to the argument.
The BOLD signal, the thing measured by fMRI, is a proxy for actual brain activity. The logic is that neural firing requires a lot of energy and so active neurons will being using more oxygen for their metabolism, and this oxygen comes from the blood. Thus, if you measure local changes in the oxygenation of blood, you'll know something about how active nearby neurons are. However, it's an indirect and complicated relationship. The blood flow to an area can itself change, or cells could extract more or less oxygen from the blood--the system itself is usually not running at its limits.
Direct measurements from animals, where you can measure (and manipulate) brain activity while measuring BOLD, have shown how complicated this is. Nikos Logathetis and Ralph Freeman's groups, among many others did a lot of work on this, especially c. 2000-2010. If you're interested, you could check out this news and views on Logathetis's group's 2001 Nature paper [1]. One of the conclusions of their work is that BOLD is influenced by a lot of things but largely measure the inputs to an area and the synchrony within it, rather than just the average firing rate.
In this paper, the researchers adjust the MRI sequences to compare blood oxygenation, oxygen usage, and blood flow and find that these are not perfectly related. This is a nice demonstration, but not a totally unexpected finding either. The argument in the paper is also not "abandon fMRI" but rather that you need to measure and interpret these things carefully.
In short, the whole area of neurovascular coupling is hard--it includes complicated physics (to make measurements), tricky chemistry, and messy biology, all in a system full of complicated dynamics and feedback.
The BOLD signal, the thing measured by fMRI, is a proxy for actual brain activity. The logic is that neural firing requires a lot of energy and so active neurons will being using more oxygen for their metabolism, and this oxygen comes from the blood. Thus, if you measure local changes in the oxygenation of blood, you'll know something about how active nearby neurons are. However, it's an indirect and complicated relationship. The blood flow to an area can itself change, or cells could extract more or less oxygen from the blood--the system itself is usually not running at its limits.
Direct measurements from animals, where you can measure (and manipulate) brain activity while measuring BOLD, have shown how complicated this is. Nikos Logathetis and Ralph Freeman's groups, among many others did a lot of work on this, especially c. 2000-2010. If you're interested, you could check out this news and views on Logathetis's group's 2001 Nature paper [1]. One of the conclusions of their work is that BOLD is influenced by a lot of things but largely measure the inputs to an area and the synchrony within it, rather than just the average firing rate.
In this paper, the researchers adjust the MRI sequences to compare blood oxygenation, oxygen usage, and blood flow and find that these are not perfectly related. This is a nice demonstration, but not a totally unexpected finding either. The argument in the paper is also not "abandon fMRI" but rather that you need to measure and interpret these things carefully.
In short, the whole area of neurovascular coupling is hard--it includes complicated physics (to make measurements), tricky chemistry, and messy biology, all in a system full of complicated dynamics and feedback.
[1] https://www.nature.com/articles/35084300