afni.nimh.nih.gov

Adding on to Peter's sage advice... NIFTI datasets can have slice timing information, but it's limited to a few "slice_code" types. See the link below for more info. The AFNI format is a little more flexible is slice timing types. And to complicate this a bit more, the AFNI extension can be included inside the NIFTI header.

[afni.nimh.nih.gov]