Dear Yusuf,
> since there isn't a 0-back between each other condition
You don't need a 0-back block each time another block was presented. Typically you would want to have equal numbers of blocks for the different types of n-back, possibly also some fixation blocks or intervals (which are not mandatory though). Assuming you don't have any fixation blocks/periods you might
1) want to go with 3 explicitely defined conditions 1-, 2-, 3-back, leaving 0-back unmodelled. Activation during 0-back would "serve" as a baseline, and the modelled regressors would account for changes in activation relative to this baseline. You could then test for activations during any of the modelled conditions relative to the baseline with simple contrasts like [1 0 0], e.g. 1-back (> baseline), or set up differential contrasts like [-1 1 0] to e.g. test 2-back > 1-back.
2) You could also explicitely model 0-back, which might lead to overparameterization of the model. This is not necessarily a problem, but you have to take care when setting up/interpreting contrasts, see Pernet (2014, Front Neurosci, "Misconceptions in the use of the General Linear Model applied to functional MRI"). Note that Pernet refers to simple box-car / stimulus "on-off" functions (if anything but 1, 2, 3-back is 0-back then three regressors are sufficient). As you would convolve the box-car function with the HRF, also the 0-back regressor, this would be less of an issue in your case, but nonetheless relevant to consider. In short, you shouldn't set up any simple contrasts like [1 0 0 0] (e.g. testing for 0-back) but just differential contrasts like [-1 1 0 0] (e.g. 1-back vs. 0-back, which should be very close to the simple contrast [1 0 0] from 1) ).
In general you wouldn't go with a completely random presentation, but with some additional restrictions, e.g. sequences/cycles consisting of one block for each of the four conditions, and only within the sequence the presentation of 0, 1, 2, 3 is random. This ensures that the temporal gap between two blocks of the same type is similar across conditions, which is relevant due to high-pass filter aspects (leaving aside psychological issues, a random presentation might result in e.g. several successive blocks of 3-back, which might lead to frustration).
> only an event related design model be valid
I assume you came up with event-related due to missing fixation blocks. Turning to an event-related design does not necessarily solve the issue, as in n-back, the time course of an event-related regressor is often (very) similar to a block regressor (due to rather short inter-trial intervals and limited/no jitter). However, as stated above, missing fixation blocks is unproblematic. It just means that you won't be able to look at 0-back (or another of the three conditions in case you chose one of them to reflect baseline activation).
However, you can model an *experimental* block design with event-related regressors in *the GLM* (e.g. separate regressors for correct and incorrect trials, taking into account trial-specific reaction times, ...). If you haven't planned so from the beginning I wouldn't turn to event-related regressors though, as usually, one would have tried to optimize the design in certain ways then (e.g. jitter). Depending on paradigm it might also be likely that event regressors are not capable to properly model the underlying activations (e.g. working memory aspects that are not directly coupled to the stimulus presentation), but as stated, it also does not necessarily mean that you are incapable, as the time course of the event-related regressor might be very close to a block regressor depending on design.
Best
Helmut
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