Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements

Abstract

Purpose: Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements.

Methods: All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations.

Results: Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems.

Conclusions: The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients.

Figure 1

Schematic of proposed ADC correction workflow. Dashed outline marks one-time procedure to obtain corrector maps for a specific MRI scanner. This is followed by description of allowed correction routes for a DWI scan to remove ADC bias.

Figure 2

Effect of gradient nonlinearity on spatial non-uniformity of diagonal (a–c) versus off-diagonal (d–f) elements of b-matrix over FOV = 300×300×300mm is illustrated for DWI gradients along “Z”-LAB (a,d), “Z”-OVP (b,e), and corrected “Z”-OVP (c,f). Spatial dependence is represented by color gradient at boundary planes (X=150mm, Y=150mm, Z=−150mm) and spherical slice through the FOV. Color-bars to the right of each 3D-map provide the scale for depicted b-values (s/mm²). The unbiased (uniform) b-value corresponds to 1010 (a), 755 (b) and 1510s/mm² (c) at isocenter. The deviation from uniformity is visually estimated by the color gradient scale away from isocenter. The color gradient of the corrected map (c) preserves all spatial non-uniformity information of (b) to remove nonlinearity bias via Eqs.[4,5]. The residual non-uniformity error, Eq.[2], of b-matrix is represented by the spatial bias and relative scale of the off-diagonal b-elements (d–f).

Figure 3

Comparison of measured spatial bias for ADC (a,b) for isotropic ice-water phantom) to the model (c,d) in case of LAB-DWI gradients plotted for three separate directions (dashed, dotted curves) and the trace (solid curve): (a,c) SI offset; (b,d) LR offset. Dotted horizontal lines mark 5% deviations from reported ADC ≡ 1.1×10⁻³mm²/s value of water (36) at 0 °C (solid line). Error bars for the measured trace ADC correspond to a standard deviation over 10 mm diameter circular ROI (approx. 90 pixels). Spatial non-uniformity bias away from isocenter exceeded experimental measurement errors.

Figure 4

Corrected versus uncorrected ADC gray-scale maps for 60 image slices (6×10 tiles) through FOV = 300×300×300 mm³ for (a) isotropic media FA=0 and (b) an arbitrary diffusion-tensor orientation with FA=0.9. Gray color-bar scale is 10⁻³ mm²/s. ADC non-uniformity bias is depicted by deviation from true (uniform model) ADC ≡ 1×10⁻³mm²/s across FOV.

Figure 5

(a) corrected (dark) versus uncorrected (light grey) error histograms (scaled to maximum pixel number) for four FAs and 2510 uniform diffusion-tensor orientations within FOV = 300×300×300mm; (b) total correction efficiency (%RMSE) as a function of FA for all pixels within FOV averaged over 2510 diffusion tensor orientations for LAB (gray circles) versus OVP (black circles) DWI. Squares illustrate baseline efficiency without bias correction.