Dear Robin,
Not sure whether I understand this correctly, so let's make sure: You would want the microtime onset to reflect that point in time that was also reflected by the reference slice during slice timing. The microtime resolution should be reasonably large, but it doesn't have to reflect the number of slices acquired (and there is no particular reason why it should).
Example 1: In case the reference slice is the temporally middle slice (e.g. slice #47 in a scheme 1, 3, 5, 7,... 47, 2, 4, 6, 8, ... 46, which is the 24th slice of the temporal sequence then), then you would want the microtime onset to be 24/47 * microtime resolution, or that term rounded to the nearest natural number.
Example 2: In case the reference slice is chosen based on some spatial reflections (e. g. if you want that slice to be the reference that covers a certain anatomical structure), say slice #7 (which would be the 4th slice acquired out of the 47), then microtime onset should be 4/47 * microtime resolution, or that term rounded to the nearest natural number.
With regard to microtime resolution, assume one part of the trials to be be synchronised with TR onset, another part might occur 10 ms after TR onset, and another 20 ms afterwards. Now assume that these trials always result in a BOLD response perfectly matching the shape of the canonical HRF. The microtime resolution controls the temporal resolution of the on-off boxcar function, and onsets and durations are discretised into microtime units (the length is defined by TR / microtime resolution). Depending on microtime resolution and TR all onsets might be treated as if synchronised with TR onset (because one part is synchronised anyway and the others are rounded to the nearest time bin, which corresponds to TR onset). Only with a high microtime resolution you can ensure that the information is preserved and that the predicted values differ.
Now in practise, you will probably not detect a difference between trials with slightly different trial onset, as the BOLD response does not exactly match the shape of the canonical HRF, as there is lots of noise, as you have a limited number of trials and scanning time, ... but the limitation is not due to TR per se. Even if the TR were long you would still expect a slightly different BOLD signal.
Best
Helmut
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