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It depends on whether you're doing group comparisons.

If you're doing this study to compare the two groups---say, all men on one scanner, all women on the other; or, healthy volunteers on one scanner, patients on the other---then the effect of group and the effect of scanner are completely confounded, and there's no solution.

On the other hand, if there are no such groupings that you want to study, then it's OK because the effect of scanner isn't confounded with anything of interest.