# Converging Proton Minibeams with Magnetic Fields for Optimized Radiation Therapy: A Proof of Concept

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Monte Carlo Simulations

^{9}proton histories were simulated for each setup to obtain a level of relative statistical uncertainty of less than 1% at each voxel throughout the distribution. The dose is scored in a water phantom of 10 × 10 × 30 cm

^{3}with a pixel dimension of 0.1 × 2 × 1 mm

^{3}.

#### 2.2. Simulation Geometry and Configurations

^{2}with a center-to-center (ctc) distance of 4 mm and with a slit tilt increasing linearly with the off-axis distance (0.025 degree per millimeter) to fit the beam divergence. In Configuration #2, a collimator with the same slit dimension, but with a larger ctc distance of 6 mm, is coupled with a 5-cm thick dipole placed after it to deviate the minibeams and ensure the same transverse dose distribution at the Bragg peak. The magnetic field in the dipole is uniform in space and directed towards the y direction. To converge the minibeams, the field intensity is increased with the off-axis distance of the irradiated slit (x1 in Figure 1) by correlating the dipole field value with the pencil beam spot x coordinate in TOPAS simulations. The minibeams are, thus, deflected towards the central z-axis with an angle at the dipole exit that increases with their off-axis distance. In Configuration #3, we used the same collimator as in Configuration #2, but we deflected the minibeams by applying a homogeneous magnetic field to the water phantom, in the same manner as with an MRI-guided treatment. As in Configuration #2, the magnetic field is directed in the y direction and its intensity increases with the x-position of the pencil beam spots.

#### 2.3. Magnetic Field Optimization

#### 2.4. SOBP Optimization

## 3. Results

#### 3.1. Monoenergetic Beams

#### 3.2. Spread-Out Bragg Peak

## 4. Discussion

^{3}[40]. However, fringe fields outside the deflection region were not taken into account in this study. Magnetic field in fringe field regions can produce additional proton deflection not only along the desired direction but also along the perpendicular direction, since other components of the magnetic field might not be negligible in this region [40]. For a more in-depth investigation of these approaches, future studies should integrate real field maps and assess to what extent fringe fields affect the proton trajectories and the magnetic field optimization strategy.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic drawing of the configurations of magnetic field and collimator used in the study.

**Figure 2.**Dose maps for a 150 MeV beam in the five analyzed configurations and the corresponding transverse profiles at the Bragg peak (bottom-right figure).

**Figure 3.**Transverse profile of the central minibeam for 150 MeV protons at the entrance of the water phantom and at a 7 cm depth.

**Figure 4.**(

**a**) Peak-to-Valley Dose Ratio (PVDR) as a function of depth and (

**b**) depth dose of the first central valley in the five analyzed configurations for three different proton energies.

**Figure 5.**Optimized spread-out Bragg peak in the three configurations. The figure shows the contributions of the individual Bragg peaks (colored continuous lines) to the total peak dose (black continuous line) on the central minibeam axis as well as the valley dose on the first central valley (dashed black line).

**Figure 6.**Peak-to-valley dose ratio as a function of depth (

**left image**) and depth-dose of the first central valley (

**right image**) in the three configurations.

**Table 1.**Intensity of the magnetic field optimized for the two configurations as a function of the slit off-axis distance and the beam energy.

Magnetic Field | Slit Off-Axis Distance (mm) | 100 MeV Beam | 150 MeV Beam | 200 MeV Beam |
---|---|---|---|---|

Configuration #2 | 6 | 0.5 T | 0.37 T | 0.279 T |

12 | 1 T | 0.74 T | 0.558 T | |

18 | 1.5 T | 1.105 T | 0.837 T | |

24 | 2 T | 1.475 T | 1.116 T | |

30 | 2.5 T | 1.84 T | 1.395 T | |

36 | 2.99 T | 2.21 T | 1.674 T | |

42 | 3.48 T | 2.575 T | 1.953 T | |

Configuration #3 | 6 | 0.883 T | 0.274 T | 0.121 T |

12 | 1.766 T | 0.548 T | 0.243 T | |

18 | 2.649 T | 0.822 T | 0.364 T | |

24 | 3.532 T | 1.096 T | 0.486 T | |

30 | 4.415 T | 1.37 T | 0.607 T | |

36 | 5.298 T | 1.644 T | 0.728 T | |

42 | 6.181 T | 1.918 T | 0.85 T |

Depth in Phantom | Configuration #1 | Configuration #2′ | Configuration #3′ | |
---|---|---|---|---|

100 MeV | Phantom entrance | 12.5 ± 0.1 | 15.6 ± 0.1 | 22.3 ± 0.2 |

3.8 cm | 5.07 ± 0.05 | 6.35 ± 0.06 | 9.18 ± 0.09 | |

7.5 cm (BP) | 1.22 ± 0.01 | 1.26 ± 0.01 | 1.30 ± 0.01 | |

150 MeV | Phantom entrance | 11.6 ± 0.1 | 15.1 ± 0.1 | 18.2 ± 0.2 |

3.8 cm | 6.42 ± 0.06 | 8.59 ± 0.09 | 10.4 ± 0.1 | |

7.5 cm | 2.20 ± 0.02 | 3.10 ± 0.03 | 4.09 ± 0.04 | |

12.5 cm | 1.03 ± 0.01 | 1.07 ± 0.01 | 1.12 ± 0.01 | |

200 MeV | Phantom entrance | 6.98 ± 0.07 | 9.22 ± 0.09 | 10.3 ± 0.1 |

3.8 cm | 5.91 ± 0.06 | 7.77 ± 0.08 | 8.71 ± 0.09 | |

7.5 cm | 3.24 ± 0.03 | 4.45 ± 0.04 | 5.21 ± 0.05 | |

12.5 cm | 1.21 ± 0.01 | 1.58 ± 0.02 | 1.89 ± 0.02 | |

15 cm | 1.05 ± 0.01 | 1.14 ± 0.01 | 1.27 ± 0.01 |

**Table 3.**Normalized weights ${w}_{i}$ obtained with genetic optimization of the 3 cm wide SOBP in the reference Configuration #1 and in the two configurations with magnetic fields and a dynamic aperture.

Weights w_{i} | 150 MeV | 154 MeV | 158 MeV | 162 MeV | 166 MeV |
---|---|---|---|---|---|

Configuration #1 | 0.104 | 0.140 | 0.202 | 0.263 | 1 |

Configuration #2′ | 0.141 | 0.171 | 0.210 | 0.275 | 1 |

Configuration #3′ | 0.167 | 0.190 | 0.248 | 0.338 | 1 |

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**MDPI and ACS Style**

Cavallone, M.; Prezado, Y.; De Marzi, L. Converging Proton Minibeams with Magnetic Fields for Optimized Radiation Therapy: A Proof of Concept. *Cancers* **2022**, *14*, 26.
https://doi.org/10.3390/cancers14010026

**AMA Style**

Cavallone M, Prezado Y, De Marzi L. Converging Proton Minibeams with Magnetic Fields for Optimized Radiation Therapy: A Proof of Concept. *Cancers*. 2022; 14(1):26.
https://doi.org/10.3390/cancers14010026

**Chicago/Turabian Style**

Cavallone, Marco, Yolanda Prezado, and Ludovic De Marzi. 2022. "Converging Proton Minibeams with Magnetic Fields for Optimized Radiation Therapy: A Proof of Concept" *Cancers* 14, no. 1: 26.
https://doi.org/10.3390/cancers14010026