# Long-Term Stability of Gradient Characteristics Warrants Model-Based Correction of Diffusion Weighting Bias

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. DWI Phantom

^{−3}mm

^{2}/s) [20]. For all scanners, this ADC value was expected to be measured at a magnet isocenter, where magnetic field gradients are linear, and thus served as a universal reference (REF) value (Figure 1A,C,D, horizontal line) independent of scanner room temperature.

#### 2.2. MR Imaging Protocol

^{2}); acq/recon matrix = 200 × 200/256 × 256; number of slices = 15; slice thickness = 5 mm; TR/TE = at least 10 s/as short as possible (<150 ms); number of averages = 2; b-values = 0, 750, and 1500 (s/mm

^{2}); bandwidth/pixel (frequency-encoding) = 1500–2500 (Hz); and fat suppression was not used. Each b > 0 DWI was acquired using three diffusion gradients (${G}_{x}$, ${G}_{y}$, ${G}_{z}$) applied along the primary magnet axes to characterize individual gradient channels.

^{2}image along phase encode direction. No appreciable effect of concomitant fields [2] was expected for DSE using sagittal SI scans. An additional experiment with dial-in chronic shim gradient up to 0.1 mT/m was performed on Sys3 [23] to assess the maximum associated incremental impact on the ADC bias, for comparison to the measured chronic shim gradients on all the systems.

#### 2.3. Spatial ADC Measurements

#### 2.4. Theoretical Spatial ADC Based on GNL Model

^{−3}mm

^{2}/s). Spatially different theoretical ADCs were generated at various ROIs locations (e.g., Figure 1C, dashed curves) to which the measured spatial ADCs were compared. The measured locations were inferred from DICOM tags, and table offsets were accounted for if existing: On Sys5 and Sys6, an inferior offset of 1.3 cm was present for all measurements; an anterior offset of 2.3 cm was detected for Sys6; and a superior offset of 2.5 cm was observed for Sys1 and 2 for a single time point.

#### 2.5. Data Analysis

## 3. Results

#### 3.1. Temporal Variations in Spatial ADC Measurements

#### 3.2. ADC Measurements from SSE and DSE

#### 3.3. RMS Comparison of ADC Measurements

## 4. Discussion

_{0}shimming that introduced residual or chronic B

_{0}shim gradients [21] that were measured in this work. Our studies [23] with controlled chronic gradients demonstrated that the gradients observed in this study did not contribute to b-value errors by more than 5%. Furthermore, larger measured chronic gradients along SI correlated with the observation of higher temporal ADC variability, suggesting prevalent shim contribution to the temporal measurement errors.

_{0}map of the object, the presence of the residual shim gradients can be quantified and factored into an ideal GNL model by proportional spatial shifts and fractional offsets with respect to the isocenter.

## 5. Conclusions

## 6. Patents

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**An example of ice-water spatial-dependent (i.e., right-left (RL) offsets in gray and superior-inferior (SI) offsets in orange) apparent diffusion coefficient (ADCs) measured for the ${G}_{y}$ gradient channel (

**A**) and ${B}_{0}$ shim gradients (

**B**) on a 1.5T MR scanner. Fitted ADCs (ribbons corresponding to temporal mean ± SD) from longitudinal studies were compared with a predicted (dashed curves) system-specific gradient nonlinearity (GNL) model in (

**C**), and their relative differences normalized by an ADC reference (solid horizonal line) of 1.1 × 10

^{−3}(mm

^{2}/s) are shown in (

**D**). Mean ADC measurements within regions of interest (ROIs) (e.g., cyan circles in A-inset) are plotted as a function of RL and SI offsets, respectively, with error-bars corresponding to a standard deviation within an ROI. Dashed horizontal lines denote ± 5% deviations from the reference ice-water ADC value.

**Figure 2.**Spatial variations (colored ribbons representing temporal mean ± SD) of fitted ice-water apparent diffusion coefficient (ADCs) measured from longitudinal studies are shown as a function of a horizontal offset (light colors) and along the magnet bore (dark colors) for six different MR systems (Sys1-6) in (

**A**–

**F**), using three individual gradient channels ${G}_{x}$ (red), ${G}_{y}$ (green), and ${G}_{z}$ (blue). Solid and dashed horizonal lines mark an ice-water ADC reference and its ± 5% deviations.

**Figure 3.**Temporal variations of spatial apparent diffusion coefficient (ADC) profiles (colored ribbons representing temporal mean ± SD) measured using single spin echo (

**A**–

**C**) and double spin echo (

**D**–

**F**) pulse sequences for a single MR system (Sys 1), compared to the gradient nonlinearity (GNL) model (dashed black curves) for three physical gradient channels, i.e., ${G}_{x}$ (red), ${G}_{y}$ (green), and ${G}_{z}$ (blue). Solid and dashed horizonal lines mark an ADC reference and its ± 5% deviations.

**Figure 4.**Root-mean-squared (RMS)% deviations (within ±18 cm), normalized by an ice-water apparent diffusion coefficient (ADC) reference (REF), are shown for predicted system model gradient nonlinearity (GNL) versus REF (red bars), GNL versus temporal mean fit (green bars), and temporal fit SD (blue bars) for trace ADCs, measured for horizontal offsets (

**A**) and along the magnet bore (

**B**) for six studied MR systems (Sys1-6, the error bars denote the largest RMS% observed among three physical gradient channels on a specific MR system, see Table 1).

**Table 1.**Summary of spatially averaged $\%RMS{D}_{i}$ ($i=REF,EXP,TMP$) for horizontal (RL) and along-the-bore (SI) offsets of three physical (x, y, z) gradient channels and the trace (t) from six studied gradient platforms (Sys1-6).

Sys | Grad | RL | SI | ||||
---|---|---|---|---|---|---|---|

REF | EXP | TMP | REF | EXP | TMP | ||

1 | x | 23.7 | 1.9 | 4.2 | 26.1 | 7.8 | 3.8 |

y | 8.7 | 8.3 | 1.3 | 24.7 | 4.2 | 2.3 | |

z | 1.3 | 1.2 | 0.6 | 12.2 | 3.4 | 2.5 | |

t | 11.2 | 2.9 | 1.4 | 20.9 | 3.2 | 2.2 | |

2 | x | 5.8 | 3.7 | 3.2 | 13.0 | 5.6 | 2.5 |

y | 2.3 | 2.5 | 1.4 | 13.1 | 11.9 | 4.2 | |

z | 0.4 | 2.5 | 1.1 | 3.9 | 7.0 | 6.5 | |

t | 2.6 | 1.9 | 1.1 | 10.0 | 7.9 | 3.7 | |

3 | x | 4.6 | 2.1 | 1.0 | 13.3 | 2.1 | 1.3 |

y | 2.1 | 0.7 | 1.0 | 13.2 | 2.4 | 1.1 | |

z | 1.1 | 0.6 | 0.9 | 9.6 | 0.6 | 2.0 | |

t | 2.6 | 0.5 | 0.9 | 12.0 | 0.6 | 1.2 | |

4 | x | 4.6 | 1.1 | 1.0 | 13.2 | 1.5 | 0.9 |

y | 2.1 | 0.2 | 0.8 | 13.1 | 1.4 | 1.1 | |

z | 1.1 | 0.2 | 0.8 | 9.6 | 4.3 | 3.0 | |

t | 2.6 | 0.4 | 0.8 | 12.0 | 1.9 | 1.1 | |

5 | x | 5.6 | 2.5 | 1.0 | 16.8 | 7.6 | 3.8 |

y | 3.7 | 0.7 | 0.5 | 16.8 | 4.1 | 3.3 | |

z | 1.6 | 1.1 | 1.8 | 13.5 | 11.1 | 4.8 | |

t | 3.6 | 0.5 | 0.8 | 15.7 | 6.6 | 2.9 | |

6 | x | 11.5 | 2.1 | 1.2 | 22.5 | 5.1 | 1.5 |

y | 5.3 | 1.8 | 1.3 | 22.2 | 6.8 | 3.2 | |

z | 3.3 | 1 | 0.4 | 9.7 | 8.6 | 2.6 | |

t | 6.7 | 1 | 0.8 | 18.2 | 6.7 | 2.3 |

**REF**, reference,

**EXP**, measured;

**TMP**, temporal;

**RL**, right to left;

**SI**, superior to inferior;

**1**–

**6**, gradient system number;

**RL**, right-left;

**SI**, superior-inferior;

**Sys**, system;

**Grad**, gradient channel.

**Table 2.**Summary of cross-system variations (excluding Sys2) in spatial $\%RMS{D}_{i}$ ($i=REF,EXP,TMP$) of gradient-channel metrics listed in Table 1.

Grad | x | y | z | t | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSD | REF | EXP | TMP | REF | EXP | TMP | REF | EXP | TMP | REF | EXP | TMP | |

RL | Median | 5.6 | 2.1 | 1 | 3.7 | 0.7 | 1 | 1.3 | 1 | 0.8 | 3.6 | 0.5 | 0.8 |

Min | 4.6 | 1.1 | 1 | 2.1 | 0.2 | 0.5 | 1.1 | 0.2 | 0.4 | 2.6 | 0.4 | 0.8 | |

Max | 23.7 | 2.5 | 4.2 | 8.7 | 8.3 | 1.3 | 3.3 | 1.2 | 1.8 | 11.2 | 2.9 | 1.4 | |

SI | Median | 16.8 | 5.1 | 1.5 | 16.8 | 4.1 | 2.3 | 9.7 | 4.3 | 2.6 | 15.7 | 3.2 | 2.2 |

Min | 13.2 | 1.5 | 0.9 | 13.1 | 1.4 | 1.1 | 9.6 | 0.6 | 2 | 12 | 0.6 | 1.1 | |

Max | 26.1 | 7.8 | 3.8 | 24.7 | 6.8 | 3.3 | 13.5 | 11.1 | 4.8 | 20.9 | 6.7 | 2.9 |

**REF**, reference,

**EXP**, measured;

**TMP**, temporal;

**RL**, right to left;

**SI**, superior to inferior;

**Grad**, gradient channel.

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**MDPI and ACS Style**

Pang, Y.; Malyarenko, D.I.; Wilmes, L.J.; Devaraj, A.; Tan, E.T.; Marinelli, L.; Endt, A.v.; Peeters, J.; Jacobs, M.A.; Newitt, D.C.;
et al. Long-Term Stability of Gradient Characteristics Warrants Model-Based Correction of Diffusion Weighting Bias. *Tomography* **2022**, *8*, 364-375.
https://doi.org/10.3390/tomography8010030

**AMA Style**

Pang Y, Malyarenko DI, Wilmes LJ, Devaraj A, Tan ET, Marinelli L, Endt Av, Peeters J, Jacobs MA, Newitt DC,
et al. Long-Term Stability of Gradient Characteristics Warrants Model-Based Correction of Diffusion Weighting Bias. *Tomography*. 2022; 8(1):364-375.
https://doi.org/10.3390/tomography8010030

**Chicago/Turabian Style**

Pang, Yuxi, Dariya I. Malyarenko, Lisa J. Wilmes, Ajit Devaraj, Ek T. Tan, Luca Marinelli, Axel vom Endt, Johannes Peeters, Michael A. Jacobs, David C. Newitt,
and et al. 2022. "Long-Term Stability of Gradient Characteristics Warrants Model-Based Correction of Diffusion Weighting Bias" *Tomography* 8, no. 1: 364-375.
https://doi.org/10.3390/tomography8010030