Assessment of bias for MRI diffusion tensor imaging using SIMEX

Abstract

Diffusion Tensor Imaging (DTI) is a Magnetic Resonance Imaging method for measuring water diffusion in vivo. One powerful DTI contrast is fractional anisotropy (FA). FA reflects the strength of water's diffusion directional preference and is a primary metric for neuronal fiber tracking. As with other DTI contrasts, FA measurements are obscured by the well established presence of bias. DTI bias has been challenging to assess because it is a multivariable problem including SNR, six tensor parameters, and the DTI collection and processing method used. SIMEX is a modem statistical technique that estimates bias by tracking measurement error as a function of added noise. Here, we use SIMEX to assess bias in FA measurements and show the method provides; i) accurate FA bias estimates, ii) representation of FA bias that is data set specific and accessible to non-statisticians, and iii) a first time possibility for incorporation of bias into DTI data analysis.

Fig. 1

Flow chart of steps to create SIMEX Estimated Bias and True Bias maps. Variables refer to terms defined explicitly by equations in the Theory section.

Fig. 2

(A) Exploratory SIMEX plots of simulated FA_M.C. as a function of SNR for three voxels from the simulated observed data. 1000 Monte Carlo simulations were averaged for each ${\overline{\text{FA}}}_{\text{M}.\text{C}.}$. The FA_obs is the point at the highest SNR value (SNR = 35:1). An upward bias with decreasing SNR is observed for all three voxels. (B) FA_M.C.(ω) and the extrapolation fit for three voxels in the observed data set. The x-axis for extrapolation is ω ~1/SNR and the fit is extrapolated to ω = −1. The ideal FA_SIMEX (blue triangles) represents the extrapolated FA_SIMEX value if the true bias was correctly estimated.

Fig. 3

Simulated outcomes for SIMEX at several SNR values. ${\overline{\text{FA}}}_{\text{obs}}$ values for each SNR value (circles) were calculated starting from a voxel in the simulated truth data. The ${\overline{\text{FA}}}_{\text{obs}}$ values are shown with the standard deviation (error bars) from 1000 simulations run at each SNR value. 100 observations at each SNR value were randomly chosen for SIMEX. The median FA_SIMEX values (triangles) are shown with the standard deviation(error bars). The median value was chosen due to the decreased robustness of only 100 simulations.

Fig. 4

(A) The ‘ground truth’ FA map (FA_truth) of the slice selected for data analysis. (B) The True Bias map for an SNR of 35:1 is compared to (C) the absolute value of the Estimated Bias at SNR = 35:1. The absolute value difference map was calculated from the raw bias data (not the difference in the absolute values). For a significant majority of voxels the True Bias is positive and the Estimated Bias is greater than the True Bias.