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ORIGINAL ARTICLE
Year : 2018  |  Volume : 14  |  Issue : 1  |  Page : 184-195

Investigation of the dose perturbation effect for therapeutic beams with the presence of a 1.5 T transverse magnetic field in magnetic resonance imaging-guided radiotherapy


1 Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing; Department of Radiation Physics, Harbin Medical University Cancer Hospital, Harbin, China
2 Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics; Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Nanjing, China
3 Department of Radiation Physics, Harbin Medical University Cancer Hospital, Harbin, China
4 Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China
5 Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA

Date of Web Publication8-Mar-2018

Correspondence Address:
Prof. Xiaobin Tang
Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing
China
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jcrt.JCRT_1349_16

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 > Abstract 

Background: Magnetic resonance imaging (MRI)-guided radiotherapy is a promising image-guided cancer radiotherapy method. For MRI-guided radiotherapy, the proper energy of a therapeutic beam is important for beam-designing processes, and the magnetic-induced dose perturbation would be mainly influenced, especially the perturbation surrounding the tissue–air or air–tissue interfaces. Thus, it was necessary to investigate the impact of beam energy from photon, proton, and carbon ion beams on the magnetic-induced dose perturbations.
Materials and Methods: Using a phantom of a water-air-water structure, the dose distributions were calculated with or without the presence of a 1.5 T uniform magnetic field through GEANT4. Based on the calculated doses, magnetic-induced dose perturbations were then obtained. For investigating the effects of beam energies on magnetic-induced dose perturbations, low-, middle-, and high-beam energies were adopted for each beam type.
Results and Discussion: For photon beams, the dose perturbations were increased as the beam energies increased. At the up water–air interface, the maximum perturbations exceeded 50%. Near the edge of the radiation field, perturbations of 5%–20% were achieved. For proton and carbon ion beams, their Bragg peaks were shifted from original positions, and the shifting distances were increased with the increased beam energies. However, no evident magnetic-induced dose perturbations were noted at the up water–air interface and bottom air–water interface for all the beam energies. To some extent, this study provided references for assessing the effects of beam energies on magnetic-induced dose perturbations, especially the perturbations around the air cavities inside cancer patients.
Conclusion: In MRI-guided cancer radiotherapy, the dose perturbation effects for therapeutic beams are relatively obvious, and the beam energies of therapeutic beams have large impacts on the magnetic-induced dose perturbations with the presence of a 1.5 T transverse magnetic field.

Keywords: Beam energy, cancer radiotherapy, dose perturbation, GEANT4, magnetic field


How to cite this article:
Shao W, Tang X, Bai Y, Shu D, Geng C, Gong C, Guan F. Investigation of the dose perturbation effect for therapeutic beams with the presence of a 1.5 T transverse magnetic field in magnetic resonance imaging-guided radiotherapy. J Can Res Ther 2018;14:184-95

How to cite this URL:
Shao W, Tang X, Bai Y, Shu D, Geng C, Gong C, Guan F. Investigation of the dose perturbation effect for therapeutic beams with the presence of a 1.5 T transverse magnetic field in magnetic resonance imaging-guided radiotherapy. J Can Res Ther [serial online] 2018 [cited 2021 Jun 24];14:184-95. Available from: https://www.cancerjournal.net/text.asp?2018/14/1/184/226737


 > Introduction Top


Magnetic resonance imaging (MRI) has been proposed in image-guided radiotherapy (IGRT) because MRI may play an important role in minimizing the margins between clinical and planning target volumes. The high soft-tissue contrast images of patient's anatomies obtained through MRI imaging could be applied as the basis for real-time tumor tracking and tumor motion prediction.[1],[2],[3],[4],[5]

To date, MRI-linac hybrid (MRL) devices have been proposed by medical physicists because of important roles of MRI in IGRT practice. However, increased doses were noted at tissue–air and air–tissue interfaces in the application of MRL devices.[6],[7] This phenomenon known as electron return effect was resulted from the deflections of secondary electron paths under magnetic fields, while photon beams cross tissue–air or air–tissue interfaces. The doses in the organ-at-risk (OAR) can be increased by this kind of effect. Hence, the dose perturbation caused by magnetic fields (DPMF) should be investigated for MRI-guided radiotherapy. DPMF was a metric which was established to estimate the dose distribution variations in the presence of magnetic fields.

For photon beams, previous phantom studies demonstrated that the magnetic-induced dose perturbations were ranged from 28% to 106% for different magnetic field strengths and phantom geometries.[7],[8],[9] The effects of magnetic field strengths, geometric parameters, and phantom structures have been extensively explored. Besides, some clinical case studies were performed to assess the dose perturbations in MRI-guided photon therapy.[10],[11],[12],[13],[14],[15] However, photon beam energies were rarely considered as an important factor related to magnetic-induced dose perturbations. For proton beams, the effects on magnetic-induced beam deflections and dose perturbations have been observed.[16],[17] Clinical case studies were performed to explore the effects of a 1.5 T magnetic field on the dose distribution.[18],[19] However, the dose perturbations caused by the electron return effect at the tissue–air and air–tissue interfaces have not yet been explored for the proton energies larger than 90 MeV. For carbon ion beams, there were hardly any studies on the DPMF. This study mainly investigated the effects of beam energies on the magnetic-induced dose perturbation, especially the perturbation caused by electron return effect around the air cavities inside cancer patients.

In this study, a virtual phantom of a water-air-water structure was adopted in the dose calculation. It aimed to analyze the effects of beam energies on the magnetic-induced dose perturbations surrounding tissue–air and air–tissue interfaces. Dose distributions with or without the presence of a 1.5 T uniform magnetic field were calculated for photon, proton, and carbon ion beams using GEANT4. Magnetic-induced dose perturbations were then derived from the calculated dose distributions. To investigate the effects of beam energies, three levels of beam energies (low, middle, and high energies) were selected and simulated for the investigated beam types (photon, proton, and carbon ion beams). The calculated dose perturbations were illustrated for all the investigated beam types and energies along the central beam axis, respectively. Based on the calculated dose perturbations, dose perturbation comparisons were performed between photon, proton, and carbon ion beams. The volume outside radiation fields, which received extra irradiations, was calculated and analyzed in the 1.5 T magnetic field. To some extent, the results of this study provided beneficial references for estimating the dose perturbations surrounding the air cavities inside patients in MRI-guided cancer radiotherapy.


 > Materials and Methods Top


Monte Carlo (MC) particle transport codes have been widely applied in dose calculations.[20],[21],[22],[23],[24],[25],[26] In this study, GEANT4[27] was applied to calculate the dose distributions in the absence and presence of the 1.5 T magnetic field. The modular physics comprised in GEANT4 was employed. A two-layer water phantom and three types of therapeutic beams (photon, proton, and carbon ion beams) were included in the MC dose calculation. The production threshold of 0.7 mm was adopted for fulfilling the MC simulation tasks.

Geometry setup

In this study, water was selected as the tissue equivalent material in the MC geometry modeling. For investigating the dose perturbation effects around the interfaces, a virtual water phantom comprising a centrally placed air gap was adopted to calculate the dose perturbations at water–air and air–water interfaces [Figure 1]. The uniform 1.5 T magnetic field was set along the negative Z-axis to simulate the magnetic field surrounding cancer patients in MRI-guided radiotherapy. For obtaining high-resolution dose distributions, 2-mm dose-scoring voxels were applied in most cases.
Figure 1: Geometry setup of the two-layer water phantom

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Beam configuration

Unlike previous studies, this work emphasized on the impacts of beam energies on magnetic-induced dose perturbations. Thus, 4, 8, and 15 MV beam energies were selected for the photon beams; 90, 115, and 140 MeV for the proton beams; 170, 215, and 260 MeV/u for the carbon ion beams. The energy spectrums of the investigated photon beams [Figure 2] were obtained through the MC simulation of an Elekta linac. The proton and carbon ion beams were deemed as monoenergetic. The field size of the investigated beams was 5 cm × 5 cm
Figure 2: Photon spectra at 4, 8, and 15 MV

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Dose perturbation caused by magnetic fields

DPMF was defined as the dose variation in the presence of magnetic fields. Thus, DPMF was deemed as a metric to evaluate the dosimetric impact of magnetic fields generated by MRI devices. The DPMF from a specified beam under the 1.5 T magnetic field can be calculated as



Where (xi, yi, zi) was the geometry center location of a specified dose-scoring voxel, D (xi, yi, zi)1.5T was the calculated dose in the presence of the 1.5 T magnetic field, and D (xi, yi, zi)0T was the calculated dose in the absence of magnetic fields.

Extra irradiated volume outside the radiation field

In practical radiotherapy, the outside-field dose should be as low as possible to protect normal tissues of cancer patients. However, the transportation paths of charged particles were bended by Lorentz force under magnetic fields in MRI-guided radiotherapy. Hence, a physical quantity denoted as “extra irradiated volume” (EIV) was proposed to evaluate the outside-field volumes receiving extra irradiations in the presence of the 1.5 T magnetic field. For a specified radiation field, EIV was determined by summing the volumes of the outside-field dose-scoring voxels with DPMF values larger than the predefined threshold. The equation for calculating EIV values could be written as



Where i was the index of an outside-field dose-scoring voxel and V(i)voxel was the volume of the dose-scoring voxel with the index i. The subscript named “threshold” was a predefined DPMF threshold. The dose-scoring voxel was included to calculate the value of EIV using Eq. 2, only when the DPMF value of the voxel was greater than or equal to the value of threshold.


 > Results Top


Dose distributions of the photon beams

For the investigated photon beams, the calculated dose results comprised a series of three-dimensional dose matrixes, but merely the two-dimensional dose distribution planes were plotted for better understanding. The dose distributions in the x-y plane crossing the central beam axis are displayed in [Figure 3], [Figure 4], [Figure 5]. To avoid confusion between the in-water and in-air doses, the calculated dose distributions were converted to energy deposition distributions.
Figure 3: Energy deposition distributions for 4 MV photon beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 4: Energy deposition distributions for 8 MV photon beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 5: Energy deposition distributions for 15 MV photon beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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In general, dose perturbations were apparently observed under the 1.5 T magnetic field, and the dose perturbations mainly appeared at the water–air and air–water interfaces. First, [Figure 3]b, [Figure 4]b, and [Figure 5]b present with high-dose regions at the up water–air interface compared with that of [Figure 3]a, [Figure 4]a, and [Figure 5]a. The maximum interface dose reached up to about 130% at bottom surface of the up water layer for the 15 MV photon beam. Second, the regions with increased doses near the up water–air interface were enlarged with the increasing photon beam energies. Third, the outlines of the two-dimensional dose distributions were reshaped by the 1.5 T magnetic field, and dose increases were observed in the voxels outside the radiation field.

Dose perturbation caused by magnetic fields distributions of the photon beams

Based on the calculated doses, three-dimensional DPMF distributions were calculated with Eq. 1. To achieve a simple expression, only the two-dimensional DPMF distributions in the x-y plane along the central beam axis were plotted [Figure 6]. Compared with the dose distributions in [Figure 3], [Figure 4], [Figure 5], these DPMF illustrations offered more detailed quantitative information of the magnetic-induced dose perturbations under the 1.5 T magnetic field.
Figure 6: Dose perturbation caused by magnetic fields distributions for the (a) 4 MV, (b) 8 MV, and (c) 15 MV photon beams

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As illustrated in [Figure 6], the dose increase regions with about 50%–70% DPMF values appeared at the water–air interfaces of the up water layer for the 4, 8, and 15 MV photon beams. These regions were enlarged with increased beam energies. Near the left field edge, there was a dose decrease of 10%–20%. The coverage areas of the dose decrease regions were increased with increased beam energies, and the corresponding DPMF values of these regions reached a minimum of about 20% for the 15 MV photon beam as plotted in [Figure 6]c. Near the right field edge, the dose increases of about 10%–40% dose were observed. These dose-increase regions were gradually expanded as the beam energies increased, while the corresponding DPMF values of these regions reached a maximum of about 40% for the 15 MV beam as illustrated in [Figure 6]c. Moreover, dose decreases of about 10%–20% were founded at the air–water interface of the bottom water layer. These regions with decreased doses were enlarged as the beam energies increased, and the corresponding DPMF value reached a minimum of nearly 20% for the 15 MV beam as shown in [Figure 6]c.

Calculated extra irradiated volume values for the photon beams

With Eq. 2, the EIV values were calculated for the 4, 8, and 15 MV photon beams at 5%, 10%, 20%, 40%, and 70% threshold DPMFs. The calculated results are listed in [Table 1].
Table 1: Extra irradiated volume (extra irradiated volume*) values for the 4, 8, and 15 MV photon beams

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The results [Table 1] suggested that the calculated EIVs were mainly depended on the photon beam energies and threshold DPMFs. First, the calculated EIVs were increased with the increased beam energies for a specified threshold DPMF. By regarding the EIV of the 15 MV beam as 100%, the EIVs of the 4 MV photon beam were merely 30.1%, 33.3%, 10.6% at the DPMFs threshold of 5%, 10%, and 20%, respectively. Second, the calculated EIVs were rapidly decreased with the increased threshold DPMFs for a certain beam energy. This finding indicated that the numbers of dose-scoring voxels with relatively large DPMFs (e.g., 20% or 40%) were much less than those with small DPMFs (e.g., 5%).

Dose distributions of the proton beams

For the proton beams, the energy deposition distributions in the x-y plane along the central beam axis are plotted in [Figure 7], [Figure 8], [Figure 9].
Figure 7: Energy deposition distributions for the 90 MeV proton beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 8: Energy deposition distributions for the 115 MeV proton beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 9: Energy deposition distributions for the 140 MeV proton beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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These red regions in [Figure 7], [Figure 8], [Figure 9] represented the Bragg peaks of the proton beams. As illustrated in [Figure 7]b, [Figure 8]b, and [Figure 9]b, magnetic-induced lateral deflections were observed for the investigated proton beams in the presence of the 1.5 T magnetic field. The Bragg peaks shifted away from their original positions. Approximately, the shifting distances of Bragg peaks were increased from 2 cm to 3 cm as the beam energies increased. Unlike the photon beams, no obvious magnetic-induced dose perturbations were observed at the up water–air or bottom air–water interfaces for the proton beams.

Dose perturbation caused by magnetic fields distributions of the proton beams

The three-dimensional DPMF distributions of the investigated proton beams were calculated with Eq. 1. The two-dimensional DPMF distributions in the x-y plane along the central beam axis are plotted in [Figure 10].
Figure 10: Dose perturbation caused by magnetic fields distributions for the (a) 90 MeV, (b) 115 MeV, and (c) 140 MeV proton beams

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As shown in [Figure 10], dose decrease regions were observed inside the radiation field, and dose increases were mainly located outside the radiation field. Dose perturbations hardly occurred at the up water–air or bottom air–water interfaces for the proton beams. At a depth of the Bragg peaks, there were nearly 90% dose increases outside the radiation field and 90% dose decreases inside the radiation field. These dose perturbation regions were enlarged with the increased proton beam energies. As the depth decreased, the dose perturbations were gradually decreased until the minimum perturbations were achieved at the air–water interface of the up water layer.

Calculated extra irradiated volume values for the proton beams

The EIVs of the 90, 115, and 140 MeV proton beams were calculated for the 5%, 10%, 20%, 40%, and 70% threshold DPMFs with Eq. 2. The calculated results of EIVs are listed in [Table 2].
Table 2: Extra irradiated volume (extra irradiated volume) values for the 90, 115, and 140 MeV proton beams

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The positive EIVs indicated that the outside-field voxels were involved in the proton irradiations under the 1.5 T magnetic field. As listed in [Table 2], the calculated EIVs were increased with the increased proton beam energies for a specified threshold DPMF. By referring the EIV of the 140 MeV proton beam as 100%, the EIVs of the 90 MeV beam were 22.1%, 19.4%, 18.8%, 17.3%, and 17% for the 5%, 10%, 20%, 40%, and 70% threshold DPMFs, respectively. The calculated EIVs were rapidly decreased with the increased threshold DPMFs for certain proton beam energy. Thus, the volumes with relatively large DPMFs (e.g., 40% or 70%) were much less than those with small DPMFs (e.g., 5%).

Dose distributions of the carbon ion beams

The two-dimensional energy deposition distributions of the investigated carbon ion beams in the x-y plane along the central beam axis are plotted in [Figure 11], [Figure 12], [Figure 13].
Figure 11: Energy deposition distributions for the 170 MeV/u carbon ion beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 12: Energy deposition distributions for the 215 MeV/u carbon ion beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Figure 13: Energy deposition distributions for the 260 MeV/u carbon ion beam in the presence of (a) 0 T and (b) 1.5 T magnetic fields

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Lateral deflections of the carbon ion beams were observed in the presence of the 1.5 T magnetic field, and the Bragg peaks (red regions) were moved from their original positions because of magnetic-induced deflections of carbon ions [Figure 11], [Figure 12], [Figure 13]. The Bragg peak shifting distances were slightly increased with the increased beam energies. Like the proton beams, no obvious dose perturbations were observed at the up water–air and bottom air–water interfaces. The low-dose regions below the Bragg peaks of the carbon ion beams were noted, because of the secondary fragments generated by the interactions between the carbon ion beams and the bottom water layer.

Dose perturbation caused by magnetic fields distributions of the carbon ion beams

The three-dimensional DPMF distributions were calculated with Eq. 1. The two-dimensional DPMF distributions in the x-y plane along the central beam axis are plotted in [Figure 14].
Figure 14: Dose perturbation caused by magnetic fields distributions of the carbon ion beams with (a) 170 MeV/u, (b) 215 MeV/u, and (c) 260 MeV/u beam energies

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No obvious dose perturbations were observed at the up water–air and bottom air–water interfaces [Figure 14]. Up to 90% dose increases were observed outside the radiation field accompanying the dose decreases inside the radiation field. The coverage areas of the dose perturbation regions enlarged with the increased energies of the investigated carbon ion beams

Calculated extra irradiated volume values for the carbon ion beams

The EIVs were calculated for the 170, 215, and 260 MeV/u carbon ion beams at the 5%, 10%, 20%, 40%, and 70% threshold DPMFs. The calculated EIV values are listed in [Table 3].
Table 3: Extra irradiated volume (extra irradiated volume) values for the 170, 215, and 260 MeV/u carbon ion beams

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As listed in [Table 3], the calculated EIVs were mainly depended on the beam energies and threshold DPMFs. For a certain threshold DPMF, the calculated EIVs were increased with the increased beam energies [Table 3]. Referring the EIV of the 260 MeV/u beam as 100%, the EIVs of the 170 MeV/u beam were 17.2%, 16.9%, 20.1%, 27%, and 47.3% for the 5%, 10%, 20%, 40%, and 70% threshold DPMFs, respectively. As the threshold DPMFs were increased, the calculated EIVs were gradually decreased for certain beam energy. The volumes with relatively large DPMFs (e.g., 40% or 70%) were much less than those with small DPMFs (e.g., 5% and 10%).


 > Discussion Top


MRI is a promising technique which can be applied in real-time image-guided cancer radiotherapy. The potential magnetic-induced dose perturbations need to be investigated while high magnetic fields would be introduced by an MRI device during cancer radiotherapy. This paper demonstrated the characteristics of the magnetic-induced dose perturbations for photon, proton, and carbon ion beams in MRI-guided radiotherapy. The calculated dose perturbations were compared with that of published results.[8],[9],[10],[17] In this paper, we mainly focused on the relation between beam energies and magnetic-induced dose perturbations in MRI-guided radiotherapy, which was not studied in detail in the previous works.

Dose perturbation caused by magnetic fields analysis and comparison

Dose decrease regions were found near the left field edge for the 4, 8, and 15 MV photon beams [Figure 7]. This phenomenon was mainly originated in the secondary electron disequilibrium, while the electrons left the left field edge and migrated toward the right field edge. The average electron range of the 15 MV beam was larger than those of the 4 and 8 MV beams. As the beam energies increased, more secondary electrons were departed from the adjacent regions of the left field edge. Thus, the dose decrease regions enlarged as the beam energies increased.

Near the right field edge, secondary electrons left the radiation field and brought out the dose-increase regions along the right field edge under the 1.5 T magnetic field. In general, the secondary electrons of the 15 MV beam traveled longer distances than those of the 4 and 8 MV beams. More secondary electrons fled from the right radiation field for the 15 MV beam. The coverage areas of these regions were increased with the increased beam energies. Thus, there were more volumes outside the right radiation field to be irradiated by the magnetic-deflected electrons for the photon beams with relatively high energies, which would make adverse effects on the OAR surrounding radiation fields.

Near the water–air interface of the up water layer, dose increases of about 45%–68% were noted for the 4, 8, and 15 MV photon beams. For the 1.5 T magnetic field, the DPMF results of this study were in good agreement with the published data (40%–60%).[8],[9],[10] As the beam energies increased, the dose-increase regions were enlarged because of the increased secondary electron ranges of the investigated photon beams.

Near the water–air interface of the bottom water layer, dose-increase regions were noted with 15%–30% DPMFs. These regions were gradually expanded with increased beam energies because the photon intensities and secondary electron ranges were increased with the increased beam energies.

Near the air–water interface of the bottom water layer, the dose decrease regions with about 10%–20% DPMFs were observed. If there was no magnetic field, the secondary electrons emitted from the water–air interface of the up water layer could reach the air–water interface of the bottom water layer. However, these electrons re-entered into the up water layer under the 1.5 T magnetic field and did not reach the air–water interface of the bottom water layer. Thus, the dose decrease regions were brought out by the electron shortage due to the electron return effect. Furthermore, these regions were also enlarged with the increased beam energies because the average electron ranges were increased when the beam energies were increased.

For the ion beams (proton and carbon ion beams), the most serious dose perturbations were observed surrounding the Bragg peaks. Unlike the photon beams, the ion beam itself carried electric charges, and its transportation path was deflected at the presence of the 1.5 T magnetic field. As a result, the Bragg peaks of the ion beams were shifted from the original positions. At a depth of the Bragg peaks, Bragg peak shifting resulted in nearly 90% dose increases outside the radiation field and 90% dose decreases inside the radiation field. The ion beams hardly showed any dose perturbations at the up water–air interface and bottom air–water interface. Thus, the dose perturbations induced by the electron return effect almost could be neglected for the ion beams. Approximately, the dose perturbation results of this study for the 90 MeV proton beam coincided with the published data.[17]

Dose perturbation caused by magnetic fields differences between the photon and ion beams at the up water–air interface

The calculation results of this study indicated that the ion beams showed almost negligible dose increases at the water–air interface of the up water layer. This phenomenon can be analyzed by the energy spectrums and fluences of secondary electrons which penetrated through the water–air interface of the up water layer. Hence, the energy spectrums of the penetration electrons for the investigated beams at the water–air interface of the up water layer were calculated with GEANT4. The calculated results were beneficial to explain why the dose perturbations can be ignored for the investigated ion beams at the up water–air interface. To ensure that consistent criteria were applied for all the calculated energy spectrums of penetration electrons, the water doses at the water–air interface of the up water layer in the radiation field were maintained equal for all the investigated beams. All the calculated electron fluences were normalized by the maximum electron fluence of the energy spectrum for the 4 MV photon beam.

As plotted in [Figure 15], the maximum electron intensities of the 4, 8, and 15 MV photon beams were decreased with the increased beam energies. For the secondary electrons of the 4 MV beam, the electron intensity peaked at about 0.5 MeV, which was the largest relative intensity among the energy spectrums of the investigated photon beams. The proportion of high-energy electrons with energies larger than 2 MeV was increased with the increased photon beam energies. These results can explain the phenomenon that the magnetic-induced dose perturbations were increased with the increased photon beam energies at the water–air interface of the up water layer.
Figure 15: Calculated spectra of the penetration electrons for the 4, 8, and 15 MV photon beams

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As shown in [Figure 16], the electron fluences of the proton beams were increased with increased proton beam energies. The maximum fluence was observed at about 20 keV for the 140 MeV proton beam. The electron fluences of the proton beams were much less than that of the photon beams. Thus, relatively low-dose perturbations were found at the water–air interface of the up water layer for the proton beams compared with that of the photon beams. The secondary electron energies of the carbon ion beams were ranged from 0 to 0.7 MeV [Figure 17]. These electrons were mainly clustered at about 0.3 MeV, and the maximum relative electron fluence was about 0.08 for the 260 MeV/u carbon ion beam. The electron fluences of the carbon ion beams were much less than that of the photon beams. Thus, the interface dose perturbations caused by these electrons could be ignored to some extent.
Figure 16: Calculated spectra of the penetration electrons for the 90, 115, and 140 MeV proton beams

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Figure 17: Calculated spectra of the penetration electrons for the 170, 215, and 260 MeV/u carbon ion beams

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Extra irradiated volume analysis and comparison

In general, EIV was applied to quantify the outside-field volumes receiving extra irradiations in the presence of magnetic fields. Hence EIVs should be as small as possible.

For the photon beams, the calculated EIVs were decreased with the increased threshold DPMFs for specified beam energy. This result indicated that the numbers of the dose-scoring voxels with relatively small DPMFs were more than those with large DPMFs. Near the intersection of up water–air interface and right field edge, the dose-increase regions with the highest DPMFs (40%) were generated by the air-to-water returning electrons and magnetic-induced runaway electrons in water. These regions were enlarged with the increased photon beam energies because the secondary electron energies of the investigated photon beams were increased with the increased photon beam energies. Furthermore, the calculated EIVs were reduced to nearly zero at the 70% threshold DPMF. This phenomenon implied that only part of the secondary electrons fled from the radiation field, and a considerable part of the electrons still stayed and deposited energies inside the radiation field.

Like photon beams, the calculated EIVs of the ion beams were decreased with the increased threshold DPMFs and increased with the increased ion beam energies. DPMF values reached up to nearly 90% outside the radiation field. This result was achieved because the Bragg peaks of the ion beams were shifted from the radiation field and then deposited energies outside the radiation field.

The calculated EIVs of the proton beams were much larger than those of the carbon ion beams. For the 5% threshold DPMF, the EIV of the 140 MeV proton beam was approximately three times larger than that of the 260 MeV/u carbon ion beam [Table 2] and [Table 3]. This phenomenon was originated in the differences of lateral deflections between the proton and carbon ion beams at the presence of the 1.5 T magnetic field. At the 70% threshold DPMF, the proton beams also showed much larger EIVs compared with the carbon ion beams because the Bragg peak shifting displacements of the proton beams were larger than that of the carbon ion beams.

Lateral deflection difference between the proton and carbon ion beams

Supposing the range of a specified charged particle was R0 in water, then the magnetic-induced lateral deflection (d) of the charged particle at traveling distance s could be expressed as [28]



Where α and p were constants; q was the charge of the charged particle; E0 was the initial energy of the charged particle; m was the rest energy of the charged particle; and E(s) was the remaining energy at traveling distance s, where



For the proton and carbon ion beams, the energies were completely deposited at the depth of the Bragg peaks, and E(s) was zero. Thus, the lateral deflection of the Bragg peak could be expressed as



Given Eq. 5, it was calculated that the Bragg peak shifting of the proton beams was about two times larger than that of the carbon ion beams, while the ranges of the protons were equal to those of the carbon ions. This notion explained why the carbon ion beams have much smaller EIVs compared with that of the proton beams.

Future work

The study revealed the effects of beam energies on magnetic-induced dose perturbations at tissue–air and air–tissue interfaces. To some extent, the results could facilitate the estimation of the dose perturbations surrounding the air-gaps in cancer patients in MRI-guided cancer radiotherapy. In the future, it would be necessary to perform clinical case studies to investigate the practical manifestation of the characteristics obtained in this work.


 > Conclusions Top


In this study, the magnetic-induced dose perturbations were calculated in MRI-guided cancer radiotherapy with the photon, proton, and carbon ion beams. More importantly, the effect of beam energies on the dose perturbations was investigated for the three investigated beams types. On the basis of the results of this study, the following guidelines were recommended for MRI-guided radiotherapy.

For the 4, 8, and 15 MV photon beams, the magnetic-induced dose perturbations reached about 45%–68%. In practice, this increase may harm the OARs surrounding the air cavities inside cancer patients. Therefore, therapeutic beams should not pass through the air cavities inside patients during MRI-guided photon radiotherapy to eliminate the electron return effect at tissue–air and air–tissue interfaces. The doses were increased by approximately 5%–10% at the air–water interface of the up water layer. This phenomenon was almost unavoidable for the photon beams. Photon beams with relatively high energies have relatively large EIV values. Thus, photon beam energies played an important role in the magnetic-induced dose perturbations and thus should be seriously considered in MRI-guided photon radiotherapy.

For the 90, 115, and 140 MeV proton beams, the Bragg peaks were shifted from the radiation field under the 1.5 T magnetic field. The shifting distances of the proton beams were increased as the proton beam energies increased. Compared with the carbon ion beams, the Bragg peak shifting distances of the 170, 215, and 260 MeV/u carbon ion beams were much smaller with the same prescribed range. Unlike photon beams, the proton and carbon ion beams were not associated with evident magnetic-induced dose perturbations at the water–air and air–water interfaces. For a specified threshold DPMF, the EIVs of the proton and carbon ion beams were gradually increased as the beam energies increased. Hence, beam energies should be seriously considered to reduce the outside-field volumes receiving extra irradiations in MRI-guided proton or carbon ion radiotherapy.

Financial support and sponsorship

This work was supported in part by National Natural Science Foundation of China (Grant No. 11475087, 11605117, and 11775064); in part by the National Key Research and Development Program (Grant No. 2016YFE0103600); in part by the Project supported by the National Key Research and Development Program (Grant No. 2017YFC0107700); in part by the Funding of Jiangsu Innovation Program for Graduate Education (Grant No. KYLX16_0352); in part by the Education Department of Heilongjiang Province (Grant No. 12521425); and in part by the Priority Academic Program Development of Jiangsu higher education institutions.

Conflicts of interest

There are no conflicts of interest.

 
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    Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17]
 
 
    Tables

  [Table 1], [Table 2], [Table 3]



 

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