Brain functional connectivity (FC) invariance and variability under timeseries editing (timeset operation)

Functional connectivity (FC) is defined by temporal correlations between pairwise timeseries signals, thus inheriting the correlation invariance property. In this report, we look into FC properties under versatile timeseries manipulations, as classified into cardinality-preserved or -reduced timeset operations. We show the effect of timeset operations on brain FC mapping by task-evoked and resting-state fMRI experiments through two data analysis methods: seed-based correlation analysis (SCA) and independent component analysis (ICA). The FC invariance and variability were numerically assessed by a spatial correlation (scorr) of a newly generated FC map after timeset operation against a reference of FC map with the original time setting. In the fingertapping task fMRI experiment, the FC invariance under cardinality-preserved timeset operation was verified with a fingertapping motor function (MOT) extracted by SCA (scorr = 1) and by ICA (scorr >0.98). Under timeset deletion editing, ICA yielded more FC variability (scorr <1) than SCA. Similar FC variability behavior was observed with resting-state fMRI experiments. In conclusion, brain FC mapping (networking) is theoretically invariant to arbitrary timepoint reordering during timeseries data preprocessing, and it is generally variant to timepoint reduction editing except for legitimate downsizing as governed by Nyquist sampling theorem and compressive sensing theory.