Motion Correction of Multi-b-value Diffusion-weighted Imaging in the Liver

Rationale and Objectives

Motion artifacts are a significant source of error in the acquisition and quantification of parameters from multi-b-value diffusion-weighted imaging (DWI). The objective of this article is to present a reliable method to reduce motion-related artifacts during free-breathing at higher b-values when signal levels are low.

Materials and Methods

Twelve patients referred for magnetic resonance imaging of the liver underwent a clinical magnetic resonance imaging examination of the abdominal region that included DWI. Conventional single-shot spin-echo echo planar imaging acquisitions of the liver during free breathing were repeated in a “time-resolved” manner during a single acquisition to obtain data for multi-b-value analysis, alternating between low and high b-values. Image registration using a normalized mutual information similarity measure was used to correct for spatial misalignment of diffusion-weighted volumes caused by motion. Registration error was estimated indirectly by comparing the normalized root-mean-square error (NRMSE) values of data fitted to the biexponential intra-voxel incoherent motion model before and after motion correction. Regions of interest (ROIs) were selected in the liver close to the surface of the liver and close to internal structures such as large bile ducts and blood vessels.

Results

For the 12 patient datasets, the mean NRMSE value for the motion-corrected ROIs (0.38 ± 0.16) was significantly lower than the mean NRMSE values for the non–motion-corrected ROIs (0.41 ± 0.13) ( P < .05). In cases where there was substantial respiratory motion during the acquisition, visual inspection verified that the algorithm markedly improved alignment of the liver contours between frames.

Conclusions

The proposed method addresses motion-related artifacts to increase robustness in multi-b-value acquisitions.

In biological tissues, microscopic motion detected by diffusion-weighted imaging (DWI) includes both diffusion of water molecules, influenced by the structural components of the tissue, and microcirculation of blood in the capillary network (perfusion). When the diffusion sensitivity parameter, referred to as the b-value, is low, microperfusion causes rapid signal decay. To separate microperfusion effects from tissue diffusion in DWI studies, Le Bihan proposed the intravoxel incoherent motion (IVIM) biexponential model .

Several studies have applied an IVIM non-monoexponential model to characterize diffusion in tumors of the body . Application of the IVIM model, however, has been hindered by the presence of bulk motion and physiologic motions such as respiration. DWI is sensitive to both molecular displacement and the mean length of blood perfusion within the capillary network, both of which are of the order of tens of microns . However, body motion can produce displacements of the order of several millimeters, causing severe artifacts that interfere with calculation of DWI parameters.

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Materials and methods

Biexponential Model for Diffusion

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s(b)=S(0)⋅[(1−f)⋅exp(−b⋅D)+f⋅exp(−b⋅D∗)] s

(

)

(

)

⋅

[

(

−

)

⋅

exp

(

−

⋅

)

⋅

exp

(

−

⋅

∗

)

]

where D is the slow component of diffusion which describes true diffusion of extravascular water molecules, D* is the perfusion coefficient, f is the perfusion fraction, and S(b) S

(

) and S(0) S

(

) are the signal measured in each individual voxel in the DWI with diffusion sensitivity of b and 0, respectively. To estimate diffusion parameters with this model, diffusion signal is measured for a large number of b-values, ranging from very low (<200 s/mm 2 ) to high (>200 s/mm 2 ).

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Magnetic Resonance Imaging Data Acquisition

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Motion Correction of Multi-b-value DWI

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Phase 1

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Phase 2

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Image Registration: Three-dimensional Affine Transformation

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NMI(X,Y)=H(X)+H(Y)H(X,Y) N

(

)

(

)

(

)

(

)

where X is the reference (or source image) and Y is the target image. The quantities (and H(Y) H

(

) ) are the standard entropy definition entropy functions given by:

H(X)=−∑ip(i)⋅logp(i) H

(

)

−

∑

(

)

⋅

log

(

)

where p(i) p

(

) is the marginal probability distribution and H(X,Y) H

(

) is the joint distribution function given by:

H(X,Y)=∑ijp(i,j)⋅logp(i,j)p(i)⋅p(j) H

(

)

∑

(

)

⋅

log

(

)

(

)

⋅

(

)

where p(i,j) p

(

) represents the probability estimated using the (i,j) (

) joint histogram bin of the image pixel values of the reference and source image. The joint probability density functions describe the probability that a pair of values, one from each image in the comparison, occurs at the same spatial location. When two image volumes are matched, their mutual information is maximized. Affine transformation in three dimensions was used to register DW images in each acquisition. Three-dimensional (3D) affine transformation describes a global space warping with 12 degrees of freedom. The 3D affine transformation of a point x=(x,y,z)T x

(

)

T can be written as :

A(x)=A⋅x+T A

(

)

⋅

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A=R(,,ψ)⎡⎣⎢1SyxSzxSxy1SyzSxzSyz1⎤⎦⎥⎡⎣⎢Sx000Sy000Sz⎤⎦⎥ A

(

)

[

]

[

]

where R(,,ψ) R

(

) is a 3 × 3 rotation matrix, given by:

R(,,ψ)=⎡⎣⎢1000cos−sin0−sincos⎤⎦⎥×⎡⎣⎢cos0−sin010sin0cos⎤⎦⎥⎡⎣⎢cosψsinψ0−sinψcosψ0001⎤⎦⎥ R

(

)

[

cos

−

sin

−

sin

cos

]

[

cos

sin

−

sin

cos

]

[

cos

−

sin

cos

]

and {Sx,Sy,Sz} {

} are scale factors in three orthogonal directions, and {Sxy,Sxz,Syz,Syx,Szx,Szy} {

} are 3D shear parameters in the XY, XZ, YZ, YX, ZX, and ZY directions.

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Statistical Analysis

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NRMSE=1xdata,max−xdata,min∑Ni=1(xdata,i−xmod,i)2N−−−−−−−−−−−−−√ N

−

∑

(

−

)

where xdata,i x

i is the (pre- or post-registered) data and xmod,i x

i is the (pre- or postregistered) biexponential fit, and N is the number of voxels in the ROI. NRMSE is expressed as a percentage, where lower values indicate less residual variance. The NRMSE of each ROI for each patient was calculated and was regarded as an indirect measure of the ability of the registration algorithm to correct for motion. The nonparametric Wilcoxon signed-rank test was used to test statistical significance between pre- and postregistered NRMSEs. A P value of .05 or less was defined as significant.

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Results

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Table 1

The Mean NRMSE of Data Fitted to the Biexponential IVIM Model Value before Motion Correction and after Motion Correction for the 12 Patient Datasets

Subject NRMSE before Motion Correction NRMSE after Motion Correction 1 0.61 0.59 2 0.65 0.64 3 0.43 0.44 4 0.35 0.36 5 0.61 0.60 6 0.32 0.16 7 0.34 0.27 8 0.27 0.27 9 0.36 0.35 10 0.35 0.33 11 0.40 0.37 12 0.28 0.17 Average ± SD 0.41 ± 0.13 0.38 ± 0.16

IVIM, intra-voxel incoherent motion; NRMSE, normalized root-mean-square error; SD, standard deviation.

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Discussion

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Acknowledgments

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References

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Motion Correction of Multi-b-value Diffusion-weighted Imaging in the Liver

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

Biexponential Model for Diffusion

Magnetic Resonance Imaging Data Acquisition

Motion Correction of Multi-b-value DWI

Phase 1

Phase 2

Image Registration: Three-dimensional Affine Transformation

Statistical Analysis

Results

Discussion

Acknowledgments

References

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