^{1,a)}, K. Wachowicz

^{2}and D. A. Jaffray

^{3}

### Abstract

**Purpose:**

MR image geometric integrity is one of the building blocks of MRI-guided radiotherapy. In particular, tissue magnetic susceptibility-induced effects are patient-dependent and their behavior is difficult to assess and predict. In this study, the authors investigated in detail the characteristics of susceptibility (χ) distortions in the context of MRIgRT, including the case of two common MR-linac system configurations.

**Methods:**

The magnetic field distortions were numerically simulated for several imaging parameters and anatomical sites, i.e., brain,lung, pelvis (with air pockets), and prostate. The simulation process consisted of (a) segmentation of patient CT data into susceptibility relevant anatomical volumes (i.e., soft-tissue, bone and air/lung), (b) conversion of CT data into susceptibility masks by assigning bulk χ values to the structures defined at (a), (c) numerical computations of the local magnetic fields by using a finite difference algorithm, and (d) generation of the geometric distortion maps from the magnetic field distributions. For each patient anatomy, the distortions were quantified at the interfaces of anatomical structures with significantly different χ values. The analysis was performed for two specific orientations of the external main magnetic field (*B* _{0}) characteristic to the MR-linac systems, specifically along the *z*-axis for a bore MR scanner and in the (*x,y*)-plane for a biplanner magnet. The magnetic field local perturbations were reported in ppm. The metrics used to quantify the geometric distortions were the maximum, mean, and range of distortions. The numerical simulation algorithm was validated using phantom data measurements.

**Results:**

Susceptibility-induced distortions were determined for both quadratic and patient specific geometries. The numerical simulations showed a good agreement with the experimental data. The measurements were acquired at 1.5 and 3 T and with an encoding gradient varying between 3 and 20 mT/m by using an annular phantom mimicking the water-air and water-oil χ interfaces. For quadratic geometries, the magnitude of field distortion increased rapidly with the size of the inhomogeneity up to about 10 mm and then tended to plateau. This trend became more evident for materials with a larger Δχ relative to water. The simulations showed only a slight increase in the maximum distortion values when the*B* _{0} orientation was varied with regard to the shape of the χ inhomogeneity. In the case of patient anatomy, the largest distortion values arose at the air-soft-tissue interface. Considering the two MR-linac system configurations and comparing the field distortion values corresponding to all organ structures, the distortions tended to be larger for the biplanar magnet. The authors provide a reference table with ppm values which can be used to easily evaluate the geometric distortions for patient data as a function of *B* _{0} and the strength of the encoding gradient.

**Conclusions:**

The susceptibility distortions were quantified as a function of multiple parameters such as the χ inhomogeneity size and shape, the magnitude of*B* _{0} and the readout gradient, and the orientation of *B* _{0} with respect to the sample geometry. The analysis was performed for several anatomical sites and corresponding to two *B* _{0} orientations as featured by MR-linac systems.

The work was partly funded by the Grant Miller Cancer Research Grants, University of Toronto.

I. INTRODUCTION

II. METHODS

II.A. Numerical simulations and experimental validation

II.B. Patient data simulations

III. RESULTS

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- Medical imaging
- 23.0
- Magnetic susceptibilities
- 22.0
- Lungs
- 21.0
- Anatomy
- 16.0
- Magnetic fields
- 15.0

## Figures

The main steps in the data analysis workflow for the numerical simulations using patient data: (a) the volume contours of anatomical structures are delineated on the patient CT data and used as data input; (b) the contours are converted into 3D masks by assigning them bulk susceptibility values (e.g., soft-tissue, bone, air); (c) magnetic field simulations are performed (the inset shows a typical simulation output cross section for a lung patient); and (d) postsimulation data analysis-–distortion values are quantified for the contours representing the interface of anatomical structures defined at step (a).

The main steps in the data analysis workflow for the numerical simulations using patient data: (a) the volume contours of anatomical structures are delineated on the patient CT data and used as data input; (b) the contours are converted into 3D masks by assigning them bulk susceptibility values (e.g., soft-tissue, bone, air); (c) magnetic field simulations are performed (the inset shows a typical simulation output cross section for a lung patient); and (d) postsimulation data analysis-–distortion values are quantified for the contours representing the interface of anatomical structures defined at step (a).

Experimental validation of the numerical simulation algorithm. A cylindrical phantom, mimicking the water-air interface, was scanned on two different MR scanners (a) 1.5 and (b) 3 T with a wide range of frequency encoding gradient strengths. The simulation results are displayed at the inner water-air interface. The maximum ppm difference was 4.5. The orientation of *B* _{0} was along the *x*-axis and *G* _{ E } was set along the *y*-axis (image plane). The Dice similarity index for the simulation results versus experimental data was higher than 0.98 for all cases (slight variations due to changes in SNR). Please note the difference in the gradient strengths between the two image series for 1.5 and 3 T.

Experimental validation of the numerical simulation algorithm. A cylindrical phantom, mimicking the water-air interface, was scanned on two different MR scanners (a) 1.5 and (b) 3 T with a wide range of frequency encoding gradient strengths. The simulation results are displayed at the inner water-air interface. The maximum ppm difference was 4.5. The orientation of *B* _{0} was along the *x*-axis and *G* _{ E } was set along the *y*-axis (image plane). The Dice similarity index for the simulation results versus experimental data was higher than 0.98 for all cases (slight variations due to changes in SNR). Please note the difference in the gradient strengths between the two image series for 1.5 and 3 T.

Experimental validation of the numerical simulation algorithm. The phantom was prepared to resemble a water-oil interface, with the oil occupying the inner cavity. The phantom was scanned on a 1.5 and 3 T magnet with several frequency encoding gradient strengths. The simulation results are displayed at the inner water-oil interface. The maximum ppm difference was 0.3, which translated into negligible distortion values (within 0.2 mm) for all *B* _{0} and *G* _{ E } scenarios. The direction of *B* _{0} and *G* _{ E } was along the *x* and *y*-axis (image plane), respectively. The Dice similarity index for the comparison of simulation versus experimental data was better than 0.98 for all cases. Please note the difference in the gradient strengths between the two image series for 1.5 and 3 T.

Experimental validation of the numerical simulation algorithm. The phantom was prepared to resemble a water-oil interface, with the oil occupying the inner cavity. The phantom was scanned on a 1.5 and 3 T magnet with several frequency encoding gradient strengths. The simulation results are displayed at the inner water-oil interface. The maximum ppm difference was 0.3, which translated into negligible distortion values (within 0.2 mm) for all *B* _{0} and *G* _{ E } scenarios. The direction of *B* _{0} and *G* _{ E } was along the *x* and *y*-axis (image plane), respectively. The Dice similarity index for the comparison of simulation versus experimental data was better than 0.98 for all cases. Please note the difference in the gradient strengths between the two image series for 1.5 and 3 T.

Simulation results: susceptibility-induced field distortions dependence on the inhomogeneity size and composition. The outer compartment (diameter of 240 mm) of the annular phantom was assigned the χ water value. The material of the inner compartment was varied to mimic interfaces relevant to patient anatomy. The inset shows (a) the phantom geometry and simulation parameters, i.e., cavity size (diameter varied from 1 to 80 mm) and composition; (b) and (c) show the maximum ppm and the maximum range (difference between max and min values) of ppm values, respectively; (d) ppm offset relative to water.

Simulation results: susceptibility-induced field distortions dependence on the inhomogeneity size and composition. The outer compartment (diameter of 240 mm) of the annular phantom was assigned the χ water value. The material of the inner compartment was varied to mimic interfaces relevant to patient anatomy. The inset shows (a) the phantom geometry and simulation parameters, i.e., cavity size (diameter varied from 1 to 80 mm) and composition; (b) and (c) show the maximum ppm and the maximum range (difference between max and min values) of ppm values, respectively; (d) ppm offset relative to water.

Simulation results: the maximum distortion values, derived from ppm values using Eq. (1), as a function of *B* _{0} and *G* _{ E } for different air cavity sizes, i.e., the water-air interface of the cylindrical phantom presented in Fig. 4.

Simulation results: the maximum distortion values, derived from ppm values using Eq. (1), as a function of *B* _{0} and *G* _{ E } for different air cavity sizes, i.e., the water-air interface of the cylindrical phantom presented in Fig. 4.

Susceptibility effects dependence on the inhomogeneity shape and its relative orientation relative to *B* _{0}. The outer and inner compartments of the annular phantom were assigned the χ of water and air values, respectively. The inset shows (a) the phantom geometry and simulation parameters, namely, cavity shape (from ellipse to circle) and *B* _{0} orientation (parallel and perpendicular); (b) the maximum ppm values for two cavity sizes, i.e., 5 and 10 mm.

Susceptibility effects dependence on the inhomogeneity shape and its relative orientation relative to *B* _{0}. The outer and inner compartments of the annular phantom were assigned the χ of water and air values, respectively. The inset shows (a) the phantom geometry and simulation parameters, namely, cavity shape (from ellipse to circle) and *B* _{0} orientation (parallel and perpendicular); (b) the maximum ppm values for two cavity sizes, i.e., 5 and 10 mm.

Susceptibility-induced *B* _{0} perturbations maps for the two MR-linac system configurations in the case of a typical brain patient anatomy. Column (a) displays the simulation results for *B* _{0} along *z*-axis for the bore-type magnet, and column (b) shows the results for the biplanar magnet configuration with *B* _{0} along *y*-axis [in the (*x*,*y*)-plane].

Susceptibility-induced *B* _{0} perturbations maps for the two MR-linac system configurations in the case of a typical brain patient anatomy. Column (a) displays the simulation results for *B* _{0} along *z*-axis for the bore-type magnet, and column (b) shows the results for the biplanar magnet configuration with *B* _{0} along *y*-axis [in the (*x*,*y*)-plane].

Susceptibility-induced *B* _{0} perturbations maps for the two MR-linac system configurations in the case of a lung patient. The simulation results are in column (a) for *B* _{0} along *z*-axis as in a bore magnet configuration, and in column (b) for the biplanar magnet with *B* _{0} along *y*-axis [in the (*x*,*y*)-plane].

Susceptibility-induced *B* _{0} perturbations maps for the two MR-linac system configurations in the case of a lung patient. The simulation results are in column (a) for *B* _{0} along *z*-axis as in a bore magnet configuration, and in column (b) for the biplanar magnet with *B* _{0} along *y*-axis [in the (*x*,*y*)-plane].

## Tables

The field distortion simulations results for anatomical structures with significantly different susceptibility values in the case of several anatomical sites. The distortions were quantified in terms of maximum, mean, and range of field fluctuations. The corresponding geometric distortions for 0.5 and 3 T are given, assuming an encoding gradient strength of 5 mT/m [see Eq. (1)]. *B* _{0} is along *z*-axis as for a typical bore-type MR scanner.

The field distortion simulations results for anatomical structures with significantly different susceptibility values in the case of several anatomical sites. The distortions were quantified in terms of maximum, mean, and range of field fluctuations. The corresponding geometric distortions for 0.5 and 3 T are given, assuming an encoding gradient strength of 5 mT/m [see Eq. (1)]. *B* _{0} is along *z*-axis as for a typical bore-type MR scanner.

Simulation results (same metrics as in Table I) for the case of *B* _{0} along y-axis [in the (*x,y*)-plane]. This is the *B* _{0} configuration for a biplanar MR scanner.

Simulation results (same metrics as in Table I) for the case of *B* _{0} along y-axis [in the (*x,y*)-plane]. This is the *B* _{0} configuration for a biplanar MR scanner.

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