Jiancheng Zhuang^{1}

The diffusion weighted images acquired with the multiband sequence or the Lifespan protocols shows a type of slice distortion artifact. This artifact is caused by the eddy currents, which can be induced by the diffusion gradient associated with either the current DW image or the previous DW images. The artifact can be corrected by a correction algorithm which includes the diffusion gradients from both the current and previous DW images.

DWI data were acquired using multiband sequence with the following parameters as in the Lifespan projects: TR = 3222 msec, TE = 89.2 msec, 197 diffusion gradient directions, 92 axial slices for whole brain coverage, MB factor as 4, and maximum b value as 2000 s/mm^2. One fBIRN phantom and two adults were scanned on a Siemens 3T Trio Prisma MRI system. To study the nature of this artifact, we changed the slice order from interleaved into ascending, and switch the phase encoding direction into AP, PA and RL in the DWI scans on the fBIRN phantom.

To correct the diffusion weighted images which already have this artifact, we apply an algorithm for correcting the eddy current distortions using the known diffusion gradients [2]. With the current diffusion gradient _{}G_{i} and the previous one G_{i-1} considered, the resulting distortion in translation D_{ti} from the alignment between the images of the i-th diffusion gradient and the 1st gradient can be calculated for i > 1 as Equation 1

$$D_{ti}=G_{i}\cdot T+\alpha G_{i-1}\cdot T-G_{1}\cdot T$$

where the vector T are the translations along the phase encoding direction induced by the corresponding unit changes in the x, y, and z gradients, and α is the decay factor of eddy current from G_{i-1} at the time point of i-th DW image.

Therefore, the three unknown elements of vector T can be calculated as Equation 2

$$T=(G'^{T}\cdot G')^{-1}\cdot G'^{T}\cdot D_{t}$$

where the rows of matrix G' are formed by $$$(G_{ix}+\alpha G_{i-1x}-G_{1x}, G_{iy}+\alpha G_{i-1y}-G_{1y}, G_{iz}+\alpha G_{i-1z}-G_{1z})$$$ for the i-th diffusion gradient.

Similarly, vectors S for the shear distortion and M for the the scaling (or magnification) distortion induced by a unit change of the x, y, and z components of the gradient can be calculated using Equations 3 and 4

$$S=(G'^{T}\cdot G')^{-1}\cdot G'^{T}\cdot D_{s} $$

$$M=(G''^{T}\cdot G'')^{-1}\cdot G''^{T}\cdot D'_{m}$$

where the G'' is formed as $$$(G_{ix}+\alpha G_{i-1x}-D_{mi}G_{1x}, G_{iy}+\alpha G_{i-1y}-D_{mi}G_{1y}, G_{iz}+\alpha G_{i-1z}-D_{mi}G_{1z}) $$$and $$$D'_{mi} = D_{mi} –1$$$ for i>1.

Given the model parameters for the distortions T, S, and M, the image distortions can be corrected by reverse application of these parameters to the distorted DW images.

[1] Feinberg, et al., PloS ONE: e15710, 2010.

[2] Zhuang, et al., JMRI: 1460, 2013.