A geometric view of signal sensitivity metrics in multi-echo fMRI

In multi-echo fMRI (ME-fMRI), two metrics have been widely used to measure the performance of various acquisition and analysis approaches. These are temporal SNR (tSNR) and differential contrast-to-noise ratio (dCNR). A key step in ME-fMRI is the weighted combination of the data from multiple echoes, and prior work has examined the dependence of tSNR and dCNR on the choice of weights. However, most studies have focused on only one of these two metrics, and the relationship between the two metrics has not been examined. In this work, we present a geometric view that offers greater insight into the relation between the two metrics and their weight dependence. We identify three major regimes: (1) a tSNR robust regime in which tSNR is robust to the weight selection with most weight variants achieving close to optimal performance, whereas dCNR shows a pronounced dependence on the weights with most variants achieving suboptimal performance; (2) a dCNR robust regime in which dCNR is robust to the weight selection with most weight variants achieving close to optimal performance, while tSNR exhibits a strong dependence on the weights with most variants achieving significantly lower than optimal performance; and (3) a within-type robust regime in which both tSNR and dCNR achieve nearly optimal performance when the form of the weights are variants of their respective optimal weights and exhibit a moderate decrease in performance for other weight variants. Insight into the behavior observed in the different regimes is gained by considering spherical representations of the weight dependence of the components used to form each metric. For multi-echo acquisitions, dCNR is shown to be more directly related than tSNR to measures of CNR and signal-to-noise ratio (SNR) for task-based and resting-state fMRI scans, respectively.