Hello there, just a quick update given new development, it seems that aCompCor might not only reduce the issue but fix it altogether, this is what is suggested in the followup paper of Eklund et al, Cluster Failure Revisited, where they tested ICA but not PCA regression of noise but they expect a similar enhancement to the false positive rate inflation :-)

* Eklund, A., Knutsson, H., & Nichols, T. E. (2019). Cluster failure revisited: Impact of first level design and physiological noise on cluster false positive rates. Human brain mapping, 40(7), 2017-2032.

Also another paper shown that modelling accurately the autocorrelation function greatly increases fMRI reliability, which suggests the fp inflation is mainly due to the autocorrelation function being either incorrectly modelled in some software packages and/or not enough regressed.

* Olszowy, W., Aston, J., Rua, C., & Williams, G. B. (2019). Accurate autocorrelation modeling substantially improves fMRI reliability. Nature communications, 10(1), 1220.

Best regards,
Stephen