Today, at our MRI group meeting, I had a sudden idea that led me to tune out most of the rest of the meeting, working out the idea. After getting all the intuitions down, I concluded that it was very likely that my idea had been had before -- it's clever, but not uniquely so. Talking with my officemate, he confirmed that the intuitions are not unique. This isn't the first time I've had this kind of thing happen.. The intuition:
==Sub-TR temporal resolution with MRI==Two of the characteristics of MRI are high spatial resolution and low temporal resolution. In MRI, data from thin slices of the brain are acquired in a particular, predictable sequence, with the entire studied area being sampled once per a factor called TR (measured in seconds). There is a linear relation between size of scanned area (number of slices) and minimum TR. My studies use a TR of 2, and retrieve 34 slices with the 24th slice oriented around the AC/PC line (a particular 2d surface defined by two geographical features in the brain). With a TR of 2 defining a single scan (meaning an entire set of slices in this context) in a trial, each trial has a set of experimental factors and is composed of a given number of scans. Trials are normally designed to be of an appropriate TR-length multiple so fixed points can be compared across all trials.
I believe we can get better temporal resolution in MRI by carefully designing the experiment and doing the analysis differently. If we had no factors in the experiment, and simply wanted to get better temporal resolution for a known factor, we could do so reliably if there were no between-trial factor by intentionally choosing an experiment that was not of a TR-length multiple, instead choosing one that (for example) had a remainder of .5*TR. The experiment would then cycle through 4 periods, capturing data from offsets equivalent of a TR a quarter of the actual TR. This is slightly complicated by the fact that TRs are built by sequence instead of a large snapshot, but this can be compensated for by grouping the actual timeslices into 4 buckets based on which of 4 equally positioned timepoints they're closest to (this is actually better than a non-TR-bucket approach which essentually blurs over the entire TR), and consider them to be 4 entities similarly rotating through the timespace rather than one large entity. To allow factors back into the experiment, we would create separate divisions for each permutation of factors, doing the reconstruction separately for each. We could measure how much we suffer from the assumption for between-trial-within-otherwise-equal-con
The 4, 2TR, .5 used as examples in the intuition are simply related to each other and easily substituted with other similarly related values to achieve different temporal resolutions, with the caveat that the greater TR is subdivided, the more scan time is needed in balance in order to keep the power of the experiment constant.
==Afternote==Apparently ideas similar to this can be found using a search for "MRI Jitter". I'm going to look into this a bit more -- although the idea is not unique to me, I feel a certain interest in seeing how far other people have run with it.