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As mentioned in this answer, it's possible to generate an fMRI BOLD signal from neurotransmitter consumption. What equation would be appropriate for this use?

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  • $\begingroup$ The BOLD signal depends on the ratio between oxygenated and deoxygenated blood and the haemodynamic response function reflects this. Oxygen is not a neurostransmitter. It has a metabolic role in that it delivers potential energy to the cell, but the oxygen found in the blood does not take part in synaptic transmission, except as NO, CO and in compounds (e.g. -OH). I am not sure I understand why you are asking this. What is your research question? $\endgroup$ – noumenal Jul 28 '16 at 22:29
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    $\begingroup$ @noumenal my research question is to relate the metabolic role of oxygen to neurotransmitter consumption $\endgroup$ – Seanny123 Jul 29 '16 at 0:25
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The simplest equation for getting a BOLD signal from neurotransmitter that I could find was in "Tracing Problem Solving in Real Time: fMRI Analysis of the Subject-paced Tower of Hanoi", which itself references many other publications where it was used:

$$H(t)= m \times(t/s)^a\times e^{-(t/s)}$$

The parameters $s$, $a$ and $m$ don't have an explicit meaning. Heuristically, from the text:

$m$ is the magnitude of the response and $s$ is a time scale. The function peaks at time $a \times s$. The parameter a determines the shape of the function such that the larger $a$ is the more narrowly the function will be distributed around its peak.

So it seems you have to fit it to some previous data in the area you're trying to generate data from before it can be used.

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It is not clear what neurotransmitter you are interested in, but one model that relates the PET ligand affinity to the cerebral blood volume (CBV) from fMRI looks like this:

enter image description here

Source: Neurovascular coupling to D2/D3 dopamine receptor occupancy using simultaneous PET/functional MRI

You can find several studies, which try to relate neurotransmitters with oxygen consumption. Google made the following suggestions to me:

In addition to PET, of special interest is the technique MRS using the same type of scanner that is used for fMRI:

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