# Retrospective Motion Artifact Reduction by Spatial Scaling of Liver Diffusion-Weighted Images

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Implicit Weighted Averaging

#### 2.2. Spatial Scaling for the Reduction of Motion-Induced Signal Loss

#### 2.2.1. Rejection Process

#### 2.2.2. Spatial Scaling of Average Diffusion-Weighted Images

#### 2.3. Data Acquisition

^{2}, voxel size of $(3\times 3\times 4)$ mm

^{3}; 60 slices with 0.4 mm gap; b-values of $b=(0,\phantom{\rule{0.166667em}{0ex}}50,\phantom{\rule{0.166667em}{0ex}}300,\phantom{\rule{0.166667em}{0ex}}600)\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}/\mathrm{mm}}^{2}$ with 2, 1, 2, and 6 repetitions, respectively; and 3 diffusion encoding directions for $b>0\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}/\mathrm{mm}}^{2}$. All scans were respiratory triggered with a fixed trigger delay of 200 ms.

#### 2.4. Image Reconstruction and Analysis

#### 2.4.1. ADC Comparison

#### 2.4.2. Clinical Evaluation

- Overall image quality: the gross appearance of the whole image volume;
- Liver homogeneity: the contrast between the signal of the liver parenchyma of the left lobe versus the right lobe;
- Perceived signal-to-noise ratio (SNR): the visual perception of the noise performance;
- Quality of lesion detection: the possibility to distinguish healthy liver parenchyma from lesions.

#### 2.4.3. Statistical Evaluation

## 3. Results

#### 3.1. Repetition and Voxel Rejection

#### 3.2. Spatial Scaling of Average DWI

#### 3.3. Quantitative ADC Measurement

^{2}/s only after applying the proposed method. This range is indicated in the plot by the cyan square. The slope of a linear regression between the left and right liver ADC values is closer to 1 for the proposed method: with 0.72 as compared to 0.55 with the standard method. Also, the Pearson-r correlation coefficient is greater for the ADC maps using the proposed method: with $r=0.75$ for the proposed and $r=0.63$ for the standard averaging method. The greater r-value indicates a higher linear correlation between the left and right liver lobes after applying the proposed algorithm. The ALRs of the individual patients with the proposed algorithm applied are significantly different from those of the standard averaged data set ($p<0.001$).

^{2}/s to $1.80\pm 0.08\times {10}^{-3}$ mm

^{2}/s. The ADC reduction is not statistically significant ($p=0.31$). Figure 8b plots the mean ADCs in the paraspinal muscles of all patients with the standard averaging and proposed methods. The linear regression with a slope close to 1 is rotated by a small amount from the $y=x$ line, indicating a slight trend towards smaller ADCs.

#### 3.4. Radiological Reading

## 4. Discussion

^{2}/s) [34,65,66]. Other studies also showed that reducing the bias in the liver with post-processing methods is possible [29,41,44]. Moreover, for the whole cohort of patient data, a trend towards a more homogeneous liver was observed, as reflected by a slope closer to 1 for the regression comparing left and right liver ADCs. The significant change in ADC in the right liver lobe can be attributed to motion affecting this area, albeit to a lesser extent than the left liver lobe [23]. Thus, the proposed method reduces the signal-loss artifact due to all kinds of motion and not only the cardiac-motion-induced signal loss in the left liver lobe. Additionally, the proposed method never decreases the signal compared to the standard averaging method and is likely to increase it, especially for higher b-values, leading to a corresponding reduction in ADC. However, in the paraspinal muscle, where motion is minimal, the ADC of the proposed method is not significantly different from the ADC of the standard averaging method.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADC | Apparent Diffusion Coefficient |

ALR | Apparent diffusion coefficient liver Lobe Ratio |

DW | Diffusion-Weighted |

DWI | Diffusion-Weighted (magnetic resonance) Imaging |

EPI | Echo-Planar Imaging |

FOV | Field Of View |

MCDE | Motion-Compensated Diffusion Encoding |

MRI | Magnetic Resonance Imaging |

ROI | Region Of Interest |

SNR | Signal-to-Noise Ratio |

TE | Echo Time |

T2 | T2 relaxation time |

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**Figure 1.**(

**a**) Six repetitions of respiratory-triggered diffusion-weighted images (DWIs) with a b-value of $b=600\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}/\mathrm{mm}}^{2}$ for three different diffusion directions that show different patterns of motion-induced signal-loss artifacts. The location of the left liver lobe is circled in red for each repetition. Some repetitions, like number 12, show global signal loss, while more often, local signal loss in the left liver lobe is observable, e.g., repetition 15. The local signal loss is incoherent and unpredictable between repetitions. (

**b**) A sum of magnitudes of the 18 repetitions yields the diffusion-weighted (DW) image on the left that displays an inhomogeneous liver with evidently higher values in the right liver lobe. Apparent diffusion coefficient (ADC) mapping calculated using the motion-affected DWIs results in a inhomogeneous appearance of ADC in the liver.

**Figure 2.**The two-step algorithm takes repetitions of one slice and one b-value as input. DW images in different directions are treated as additional repetitions. The sum of intensities of all voxels in each repetition is compared to a threshold ${{t}_{z}}^{\left(\mathrm{rep}\right)}$ for repetition rejection. Subsequent low-pass filtering blurs the images to consider that motion artifacts tend to affect patches of the image in the voxel rejection step. Spatially dependent thresholding on the filtered images determines whether a voxel is rejected. The spatially dependent weights ${w}_{z,i}(x,y)$ are computed on low-pass-filtered data by dividing the intensity of each repetition by the maximum intensity projection across all repetitions. Weights that exceed a value of 0.8 are set to 1. The resulting DW image is found by scaling the sum across repetitions of the magnitude of non-rejected voxels with the spatially dependent scaling factor ${W}_{z}(x,y)$ according to Equation (4).

**Figure 3.**(

**a**) The sum of intensities of one slice across all repetitions can vary substantially between repetitions. The red line marks the threshold under which slices get rejected. (

**b**) The rejected slice at repetition number 12 suffers from severe global signal loss, while some other repetitions suffer from local signal loss.

**Figure 4.**(

**a**) The magnitude values of two voxels across all repetitions (excluding the previously rejected slice at repetition number 12) are shown for two exemplary voxels. The rejection threshold indicated by the red line and background depends on the spatial location. (

**b**) Slices at repetitions 4 and 11 before and after the voxel rejection are shown with rejected voxels indicated in dark red. The colored arrowheads point to the voxels evaluated in (

**a**) with their colors matching the color of the plots in (

**a**). Repetition number 4 does not suffer from signal dropout, and consequently, no voxels inside the liver are rejected. Repetition number 11 suffers from signal loss, and patches of voxels are rejected.

**Figure 5.**Two representative weight maps calculated with Equation (9) for the b600 diffusion-weighted images. Lower weight values reflect higher signal loss and mainly localize to the left liver lobe.

**Figure 6.**Average DWIs at b-values of $b=600\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}/\mathrm{mm}}^{2}$ and corresponding ADC maps with the standard averaging and proposed methods. (

**a**) An increase of intensity inside the left liver in the DW image in the top row for the proposed method compared to the standard averaging is observable, leading also to a more homogeneous appearance of the liver in the ADC images in the bottom row. (

**b**) Another in vivo data set visualizes the ability of the proposed method to reduce signal loss in the left liver lobe in DWIs and to reduce the artificial overestimation of ADC. The lesion on the left side of the liver, which is marked with the red arrow, has improved visibility and is better defined in the DW image and particularly in the ADC image.

**Figure 7.**(

**a**) A comparison of ADCs in the nine Couinaud liver segments reveals that ADCs in segments I, II, and III are overestimated the most, but they also they show the greatest correction to lower values after using the proposed method. ADCs of the segments of the right liver experience smaller changes toward lower values after using the proposed method, although they are significant. (

**b**) The average ADC for all patients in the left liver is reduced by 38.2%, while in the right liver, the reduction is only 17.6%. This results in a more homogeneous liver appearance using the proposed method: with an ADC liver lobe ratio (ALR) of 1.13 ± 0.53 for the proposed method but 1.33 ± 0.47 for the standard method. (

**c**) The comparison between left and right liver is plotted for all patients. The cohort of ADCs from the proposed method is notably more dense and shifted towards the lower left corner and inside the cyan square that indicates the range of ADCs of healthy liver parenchyma. Linear regression of both these cohorts yields a steeper slope that is closer to 1 for the ADCs using the proposed method.

**Figure 8.**(

**a**) The mean ADC in the back muscle changes from $1.82\pm 0.08\times {10}^{-3}$ mm

^{2}/s to $1.80\pm 0.08\times {10}^{-3}$ mm

^{2}/s. The change is statistically insignificant. (

**b**) The shift towards smaller ADCs can also be observed when comparing the whole cohort of patients with standard averaging and the proposed method. The linear regression of the plot has a slope of 0.96.

**Table 1.**The mean ADCs over all subjects are reduced in every Couinaud liver segment. The p-values of differences in ADCs between standard averaging and the proposed methods in the different liver segments all show statistical significance.

Liver Segment | ADC_{standard} [mm^{2}/s] | ADC_{proposed} [mm^{2}/s] | p-Value |
---|---|---|---|

I | 1.97 ± 0.35 | 1.71 ± 0.36 | 9.0 × 10${}^{-20}$ |

II | 2.25 ± 0.33 | 1.82 ± 0.33 | 2.5 × 10${}^{-19}$ |

III | 1.87 ± 0.27 | 1.60 ± 0.28 | 1.3 × 10${}^{-12}$ |

IVa | 1.70 ± 0.25 | 1.48 ± 0.25 | 1.7 × 10${}^{-13}$ |

IVb | 1.58 ± 0.22 | 1.43 ± 0.23 | 1.2 × 10${}^{-8}$ |

V | 1.43 ± 0.23 | 1.32 ± 0.24 | 5.9 × 10${}^{-9}$ |

VI | 1.42 ± 0.18 | 1.31 ± 0.18 | 2.4 × 10${}^{-5}$ |

VII | 1.54 ± 0.20 | 1.40 ± 0.21 | 3.8 × 10${}^{-4}$ |

VIII | 1.51 ± 0.23 | 1.38 ± 0.24 | 8.4 × 10${}^{-6}$ |

**Table 2.**Radiological reading scores for all patient data sets for the standard and proposed methods in four categories. Liver homogeneity scored significantly better, showing an improvement in 24 out of 67 cases ($p=0.05$). Improvements in the other three categories were not statistically significant.

Image Quality | Liver Homogeneity | Perceived SNR | Lesion Detection | |
---|---|---|---|---|

Better | 1 | 24 | 13 | 3 |

Same | 66 | 39 | 48 | 25 |

Worse | 0 | 4 | 6 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Raspe, J.; Harder, F.N.; Rupp, S.; McTavish, S.; Peeters, J.M.; Weiss, K.; Makowski, M.R.; Braren, R.F.; Karampinos, D.C.; Van, A.T.
Retrospective Motion Artifact Reduction by Spatial Scaling of Liver Diffusion-Weighted Images. *Tomography* **2023**, *9*, 1839-1856.
https://doi.org/10.3390/tomography9050146

**AMA Style**

Raspe J, Harder FN, Rupp S, McTavish S, Peeters JM, Weiss K, Makowski MR, Braren RF, Karampinos DC, Van AT.
Retrospective Motion Artifact Reduction by Spatial Scaling of Liver Diffusion-Weighted Images. *Tomography*. 2023; 9(5):1839-1856.
https://doi.org/10.3390/tomography9050146

**Chicago/Turabian Style**

Raspe, Johannes, Felix N. Harder, Selina Rupp, Sean McTavish, Johannes M. Peeters, Kilian Weiss, Marcus R. Makowski, Rickmer F. Braren, Dimitrios C. Karampinos, and Anh T. Van.
2023. "Retrospective Motion Artifact Reduction by Spatial Scaling of Liver Diffusion-Weighted Images" *Tomography* 9, no. 5: 1839-1856.
https://doi.org/10.3390/tomography9050146