A framework for quality control and parameter optimization in diffusion tensor imaging: theoretical analysis and validation

Abstract

In this communication, a theoretical framework for quality control and parameter optimization in diffusion tensor imaging (DTI) is presented and validated. The approach is based on the analytical error propagation of the mean diffusivity (D(av)) obtained directly from the diffusion-weighted data acquired using rotationally invariant and uniformly distributed icosahedral encoding schemes. The error propagation of a recently described and validated cylindrical tensor model is further extrapolated to the spherical tensor case (diffusion anisotropy approximately 0) to relate analytically the precision error in fractional tensor anisotropy (FA) with the mean diffusion-to-noise ratio (DNR). The approach provided simple analytical and empirical quality control measures for optimization of diffusion parameter space in an isotropic medium that can be tested using widely available water phantoms.

Figure 1

Experimental demonstration and validation of the model presented on a water phantom at 3.0 T of the predicted theoretical relationship between the ROI standard error in RA_n and the inverse of the mean diffusivity-to-noise ratio. The plot shows the results of 24 different experiments acquired using Icosa21bpn scheme at different total number of images, N_ref, N_d, and N_e but constant b-factor (b-factor=600 s mm⁻²). The encoding scheme and ROI are also shown. The plot shows the Pearson correlation coefficient and the corresponding best fit and p values.

Figure 2

Experimental demonstration on a water phantom at 3.0 T of the relationship between the measured σ(RA_n) and the predicted values using our theoretical analysis [Eq. (10)]. The plot shows the results of 24 different experiments acquired using different subsets of Icosa21bpn scheme at different total number of images, N_ref, N_d, and N_e but constant b-factor (b-factor=600 s mm⁻²). The encoding scheme, ROI and _SNR0 estimation method are also shown (see brief description in the Methods). Notice that SNR₀ was estimated from the mean of two sets with N_ref=1, and variance in the difference images. The estimated mean diffusivity is consistent with known values at the estimated room temperature (See reference 1 for more details).

Figure 3

A bar plot comparison of the predicted versus measured mean diffusivity-to-noise ratio (DNR(D_av)) for different encoding subsets of the Icosa21b using different combinations of N_ref, N_d, and N_e but constant N_T=22. The data set was acquired at 1.5 T, with an SNR₀=60 (using one reference image or N_ref=1) and a b-factor = 820 s mm⁻². Notice the strong correlation between the measured and predicted values (r=0.986), the slight deviation of the measured from the predicted values is attributed to the computation of SNR₀, which may fluctuate for different images due to scanner stability (compare these results with the theory in Table 1 and Fig. 4).

Figure 4

Illustration of the empirical (theoretical) DT-MRI optimization results at equal time for an isotropic tensor (FA=0, D_av=0.0008 mm² sec⁻¹). The plots show the optimal κ_D and ξ_max=b_opt*D_av as function of ξ=b*D_av at constant total imaging time, N_T=22=N_ref+N_d*N_e (compare with Table 1 and Fig. 3) and for different combinations (N_ref, N_d*N_e) using different encoding schemes, XYZ, Icosa6, Icosa15, Icosa16 and Icosa21. The tensor eigenvalues λ_1,2,3=[0.0008, 0.0008, 0.0008] mm² sec⁻¹. Note that the maximum DNR is associated with the Icosa6 with N_ref=4, N_d=3. The increase in b_opt*D_av as N_d*N_e/N_ref deviates from the optimal theoretical ratio ~ 3.6 is also demonstrated.