An empirical characterization of the quality of DTI data and the efficacy of dyadic sorting

Metrics calculated from images acquired using the diffusion tensor imaging (DTI) technique possess a systematic bias that depends on signal-to-noise ratio (SNR). Dyadic sorting provides a simple method for remediating some of this bias within a region(s) of interest (ROI). Although this bias and its removal using dyadic sorting have been studied previously within a theoretical framework, one can employ precise geometric knowledge of microstructures to perform an empirical comparison between expected DTI results and those measured with a scanner. In this project, the biasing effect of low SNR (∼1-10) on DTI eigenvalues was measured directly using water-filled capillary structures of two different sizes, and the magnitude of the corrective effect of dyadically sorting eigenvector-eigenvalue pairs was characterized. Multiple DTI series were acquired for determining DTI metrics at eight unique SNR values, using T_R to vary signal intensity via T₁ contrast. Differences between the second and third eigenvalues, which should be equal for prolate geometry, ranged from ∼23% to 45% and from 19% to 41% for large and small inner diameter capillaries after sorting eigenvalues by magnitude, and ranged from ∼1% to 18% and from 1% to 4% after dyadic sorting. A high-resolution DTI series was used to observe the effect of ROI size on dyadic sorting. For restriction of diffusion on the scale of the small capillary at SNR∼18, an ROI with ≥50 pixels is adequate to determine fractional anisotropy to 99% accuracy, while larger ROI are required to resolve the two smaller eigenvalues to the same accuracy (∼330-390 pixels). At low values of SNR, the iteration of dyadic sorting is suggested to achieve good accuracy. A method for the incorporation of empirical measurements into a bias-correction map, which would be useful for characterizing uncertainty and for reducing systematic bias in DTI data, is introduced.