Weight Sensitivity of Temporal SNR Metrics in multi-echo fMRI

Purpose In multi-echo fMRI (ME-fMRI), various weighting schemes have been proposed for the combination of the data across echoes. Here we introduce a framework that facilitates a deeper understanding of the weight dependence of temporal SNR measures in ME-fMRI. Theory and Methods We examine two metrics that have been used to characterize ME-fMRI performance: temporal SNR (tSNR) and multi-echo temporal (metSNR). Both metrics can be described using the generalized Rayleigh quotient (GRQ) and are predicted to be relatively insensitive to the weights when there is a high degree of similarity between a metric-specific matrix in the GRQ numerator and a metricindependent covariance matrix in the GRQ denominator. The application of the GRQ framework to experimental data is demonstrated using a resting-state fMRI dataset acquired with a multi-echo multi-band EPI sequence. Results In the example dataset, similarities between the covariance matrix and the metSNR and tSNR numerator matrices are highest in grey matter (GM) and cerebrospinal fluid (CSF) voxels, respectively. For representative GM and CSF voxels that exhibit high matrix similarity values, the metSNR and tSNR values, respectively, are both within 4% of their optimal values across a range of weighting schemes. However, there is a fundamental tradeoff, with a high degree of weight sensitivity in the tSNR and metSNR metrics for the representative GM and CSF voxels, respectively. Geometric insight into the observed weight dependencies is provided through a graphical interpretation of the GRQ. Conclusion A GRQ framework can provide insight into the factors that determine the weight sensitivity of tSNR and metSNR measures in ME-fMRI. ### Competing Interest Statement The authors have declared no competing interest.