Volume 49, Issue 3 p. 1853-1873
RESEARCH ARTICLE
Open Access

Integrated MRI-guided proton therapy planning: Accounting for the full MRI field in a perpendicular system

Lucas N Burigo

Corresponding Author

Lucas N Burigo

German Cancer Research Center (DKFZ), Heidelberg, Germany

National Center for Radiation Research in Oncology (NCRO), Heidelberg Institute for Radiation Oncology (HIRO), Heidelberg, Germany

Correspondence

Lucas N Burigo, German Cancer Research Center (DKFZ), Heidelberg, 69120, Germany.

Email: [email protected]

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Bradley M Oborn

Bradley M Oborn

Helmholtz-Zentrum Dresden-Rossendorf, Institute of Radiooncology - OncoRay, Dresden, Germany

Centre for Medical Radiation Physics (CMRP), University of Wollongong, Wollongong, NSW, Australia

Illawarra Cancer Care Centre (ICCC), Wollongong, NSW, Australia

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First published: 15 December 2021
Citations: 7

Abstract

Purpose

To present a first study on the treatment planning feasibility in perpendicular field MRI-integrated proton therapy that considers the full transport of protons from the pencil beam scanning (PBS) assembly to the patient inside the MRI scanner.

Methods

A generic proton PBS gantry was modeled as being integrated with a realistic split-bore MRI system in the perpendicular orientation. MRI field strengths were modeled as 0.5, 1, and 1.5 T. The PBS beam delivery and dose calculation was modeled using the TOPAS Monte Carlo toolkit coupled with matRad as the optimizer engine. A water phantom, liver, and prostate plans were evaluated and optimized in the presence of the full MRI field distribution. A simple combination of gantry angle offset and small PBS nozzle skew was used to direct the proton beams along a path that closely follows the reference planning scenario, that is, without magnetic field.

Results

All planning metrics could be successfully achieved with the inclusion of gantry angle offsets in the range of 8 $^{\circ }$ –29 $^{\circ }$ when coupled with a PBS nozzle skew of 1.6 $^{\circ }$ –4.4 $^{\circ }$ . These two hardware-based corrections were selected to minimize the average Euclidean distance (AED) in the beam path enabling the proton beams to travel inside the patient in a path that is close to the original path (AED smaller than 3 mm at 1.5 T). Final dose optimization, performed through further changes in the PBS delivery, was then shown to be feasible for our selection of plans studied yielding comparable plan quality metrics to reference conditions.

Conclusions

For the first time, we have shown a robust method to account for the full proton beam deflection in a perpendicular orientation MRI-integrated proton therapy. These results support the ongoing development of the current prototype systems.

1 INTRODUCTION

It is widely accepted in the radiotherapy community that due to the finite range of protons, just a few proton beams can be used to achieve substantially high dose conformation for irradiation of a deep-seated tumor. This reduces the overall dose to the surrounding normal tissue compared to photon beam irradiation.1 However, in practice, there are several uncertainties that lead to the use of large margins when defining the planning target volume (PTV) in proton therapy planning. These include the inherent sensitivity of dose calculations to tissue heterogeneities, range uncertainty, and the changing anatomy of the day during the fraction delivery. This may lead to a substantial increase of exposure for the normal tissues surrounding the tumor. Furthermore, the clinical target volume (CTV) dose coverage in intensity-modulated proton therapy (IMPT) can be drastically deteriorated due to patient misalignment, anatomy deformations, as well as interplay effects of organ motion and the dynamic beam delivery.2 For these reasons, proton therapy has continuously incorporated advanced imaging guidance techniques to monitor and respond to changes in the anatomy under treatment in comparison to the reference anatomy obtained with the computed tomography (CT) scan acquired for treatment planning. The combination of real-time MRI and proton therapy would, in principle, provide accurate soft tissue anatomical information, reducing the uncertainty in target localization.3

Future real-time adaptive MRI-guided proton therapy has been described at an overview level in at least two papers.4, 5 Various aspects of this future modality have been further studied and essentially derisked. Dose planning feasibility, considering just the impact of the magnetic field of the MRI surrounding the patient, has been modeled and shown to be successful.6-12 A comprehensive study on the performance of radiation detectors in magnetic fields with proton beams has recently been published with promising results.13 And finally, a proof of concept system exists in Germany.14, 15 However, online MRI-guided proton therapy will require significant technological development to integrate real time imaging, treatment planning, and beam delivery. In particular, it is essential to develop novel beam delivery techniques as the presence of the magnetic field of the MRI scanner affects substantially the proton beam path all the way from the far fringe field down to the imaging field.16, 17

In a previous study,18 we investigated in detail the adaptation strategies for IMPT planning and delivery in the presence of the full MRI magnetic field in-line with the beam direction. It was shown that simple corrections for beam delivery could largely account for the observed rotation of the beam profile in the beam eye view caused by the fringe and primary imaging magnetic field of the MRI scanner. A beam spot-based adaptation was demonstrated to achieve the same plan quality as obtained in the absence of the magnetic field.

More recently, a detailed simulation and experimental study was conducted, which used a proton beamline, coupled with a small research dipole magnet in a perpendicular configuration.19 This work demonstrated the feasibility of modified treatment planning to account for the localized near fringe and main 1 T magnetic field of a 12.5 cm pole gap dipole magnet. In their work, the particle source was located at 522 mm from the surface of the dosimetry phantom, and the magnetic field model covered a range up to 122 mm outside the phantom. Therefore, the deflection of the particle beam before arriving at the phantom surface was only considered over the final 122 mm of air above the phantom. For this particular experiment, this approach was possible due to the unique low fringe field of the research dipole magnet. It therefore still remains to predict the feasibility of delivering clinical proton pencil beam scanning (PBS) in the presence of full perpendicular orientation MRI magnet models.

In the current study, we investigate the necessary adaptations of the beamline and the pencil beam delivery for IMPT in the presence of the full MRI magnetic field when perpendicular to the beamline. In the simplest terms, the magnetic field of the MRI scanner acts to deflect the proton beam away from the isocenter of the MRI scanner. An adaptation is therefore required to the beamline geometry such that the proton beams travel through the original isocenter location after undergoing the deflection caused by the MRI scanner. The adaptation that is implemented in this work is that of a gantry offset combined with a small tilting of the PBS assembly around the scanning origin or virtual source location. The latter is akin to a head tilt or skew in a conventional Linac head, and similarly, results in an isocenter that tracks out a circular path around the true isocenter (i.e., if no skew was present). To assess the feasibility of this approach, several planning studies are performed and various dose metrics are calculated. These plans include a water phantom, and liver tumor and prostate cancer cases. The MRI model is based on a real split-bore system and is modeled as operating at 0.5, 1, and 1.5 T to cover a range of field strengths.

2 MATERIALS AND METHODS

2.1 Integrated MRI-proton beamline model

For this simulation-based study, a generic PBS assembly has been modeled as being integrated into a gantry that rotates around a split-bore MRI system. The MRI model is directly based on the 1 T MRI scanner from the Australian MRI-Linac Program system.24, 25 This MRI system has a 50-cm split-bore gap and so would readily facilitate proton beam delivery in the perpendicular orientation, as shown in Figure 1. A generic gantry ring is envisaged that would support a PBS nozzle to deliver beams directly through the MRI split-bore gap and with a common isocenter of the two components. Although not shown, various options could be possible to enable PBS delivery from any gantry angle while supporting the MRI system. Figure 1(c) shows an example of the impact that the MRI (1 T model) has on the transport of 150 MeV protons, namely, a lateral shift on the order of 100 mm at the MRI isocenter. Also shown in Figure 1(d) is the simple beamline modifications that are implemented to direct the proton beams through the patient at angles that are as close as possible to the case where no magnetic field is present. These modifications include an offset in the gantry angle (GO) coupled with a small PBS nozzle skew angle (SA) around the virtual point source. Superimposed in (c) and (d) are the paths of 150 MeV proton beams that outline the extents of a 30 × $\times$ 30 cm 2 $^2$ field size.

Details are in the caption following the image
Overview of the integrated perpendicular orientation MRI-proton therapy beamline model with a field strength of 1 T. (a) 3D view of the system depicting the split-bore MRI and beamline orientation. (b) Sideview showing the system. (c) Deflected paths of 150 MeV protons outlining a 30 × 30 $30\times 30$ cm 2 $^{2}$ field. (d) Example of a gantry angle offset combined with PBS nozzle skew around the virtual source location. The PBS components are also shown as IC (ion chamber), SM1 (scanning magnet 1), and SM2 (scanning magnet 2). The PBS nozzle skew and gantry offset angles are shown as SA and GO, respectively. In parts (c) and (d), the lines indicate the beam central axis without magnetic field (red), the 30 × 30 $30\times 30$ cm 2 $^{2}$ field size boundaries without magnetic field (green), and the 30 × 30 $30\times 30$ cm 2 $^{2}$ field size boundaries with magnetic field (blue)

2.1.1 Magnetic field model

A 3D magnetic field map was generated using a finite element model of the 1 T split-bore MRI scanner for the sake of modeling the static and spatially inhomogeneous magnetic fringe field. In the beamline setups considered in this study, the imaging magnetic field is always oriented in the superior-inferior direction and the proton beam is delivered perpendicular to the main imaging field direction. The overall effect is lateral beam deflection due to the Lorentz force causing the beam spots to shift in the direction mutually perpendicular to the beam and imaging field directions.

As the Lorentz force is proportional to the magnetic field strength, each MRI scanner model will lead to a unique impact on the beam delivery. In this study, we considered the split-bore MRI scanner with imaging field strengths of 0.5, 1.0, and 1.5 T. In particular, to generate the MRI field strength models from 0.5 and 1.5 T, the 3D magnetic field map from the 1 T split-bore MRI scanner was linearly scaled to generate the respective imaging strengths. Figure 2 shows the magnetic field component in the SI direction (scanner axis) along the beamline axis as well as the strength of the static magnetic field in the central plane of the MRI scanner perpendicular to the scanner axis. The 3D map was imported into the Monte Carlo (MC) transport simulations in TOPAS via a customized C++ extension to account for the transport of charged particles in the magnetic field.

Details are in the caption following the image
(Top) Profiles of the magnetic field component in the SI direction along the beam-line axis and (bottom) 2D magnetic field profile. The position of the vacuum window at −1500 mm, indicated by the dashed line, and positions of particle source (S) and isocenter (O), indicated by circles, are also shown

2.1.2 Monte Carlo proton beam model

A clinical quality MC proton beam model was implemented in TOPAS version 3.120 based on Geant4 toolkit version 10.3 with patch 01.21, 22 It models the beam optics at the vacuum exit window in the beam nozzle using an emittance-type source. This accounts for a realistic description of beam characteristics, including energy-dependent spot size, divergence, and energy spread. The beam optics parameters and beam energy spread were adopted from a data library distributed with the MC code MCsquare23 modeling an IBA universal nozzle at the University of Pennsylvania. Figure 3(a) shows the energy spread at beam exit window as a function of the nominal beam energy. Figure 3(b) shows the mean focus size as a function of distance to isocenter for four different energies. Figure 3(c) shows the depth-dose profiles for a selection of nine beam energies. The base data are required by the treatment planning system matRad to generate the set of proton pencil beams for IMPT planning.

Details are in the caption following the image
(a) Model of the energy spread as a function of nominal energy. (b) Mean beam focus size in air as a function of distance to isocenter (negative values correspond to being upstream the isocenter). (c) Subset of base data of depth-dose profiles in water

The default beamline (no magnetic field present) is modeled with a source-to-axis distance of 200 cm, see Figure 1(a). This setup is based closely on the previous work that modeled how a clinical PBS assembly would interfere with an MRI scanner and vice versa.17 In this design, it is important to note that the presence of the MRI scanner will not necessarily mean an increased source to isocenter distance, or loss of vacuum between the PBS and patient position. Figure 1 details the beamline scenarios when the MRI scanner is included. These will be described in greater detail in Section 2.2.1 below.

2.2 Beam delivery in magnetic field

The following sections describe a set of adaptations aimed at correcting the beam delivery in the presence of the MRI magnetic field. The irradiation in the absence of the MRI scanner is called the reference radiation.

Section 2.2.1 presents the setup considered for the MRI integration with the proton beamline including a nozzle skew angle for optimizing the field scanning area. In Section 2.2.2, we consider an adaptation of the gantry angle to achieve the most similar beam path in the patient as possible compared to the path in the absence of the magnetic field. Finally, Section 2.2.3 describes the spot-by-spot adaptation of the PBS (i.e., energy and scanning angles) to compensate for the proton beam deflection in the magnetic field. The goal of the individual spot corrections is to achieve an equivalent target coverage by the beam spots in the presence of the magnetic field, in comparison to the delivery in the reference conditions. By considering a gantry angle offset and the spot-by-spot corrections, differences in the dose distribution can be expected to be minimized after the plan is subjected to inverse planning optimization (see Section 2.3).

2.2.1 Adaptation of nozzle skew

Different scenarios for an MRI-integrated beamline setup are illustrated in Figure 1. Specifically, the scenarios include the case of reference irradiation setup with the beamline pointing toward the MRI isocenter (see Figure  1c), and the cases including a PBS skew angle as well as the PBS skew in combination with a gantry angle offset (see Figure  1d). Each of the scenarios are considered separately to discuss the implications of the setup on the scanning range and the potential of the gantry to address the beam path inside the patient.

Table 1 shows the offset of the beam spot at the MRI isocenter for a set of nominal beam energies and the three magnetic field strengths. For an unmodified beamline in the presence of the magnetic field, that is, with the beam aimed directly toward the MRI isocenter, the beam isocenter can no longer be defined in a classical way. Due to the offset resulting by the beam deflection, a gantry rotation around the MRI isocenter leads to the formation of a circular beam isocenter path centered at the MRI isocenter. The radius of this circular path increases with the magnetic field strength and decreases with the beam energy as illustrated by the offsets shown in Table 1.

TABLE 1. Offset of beam spot directed towards the MRI isocenter for unmodified delivery of the proton beam. The offset is estimated with respect to the spot position with identical beam delivery in absence of the MRI
Nominal energy B-field Spot position offset
[MeV] [T] [mm]
90 0.5 65.1
1.0 137.6
1.5 231.5
150 0.5 49.2
1.0 101.3
1.5 160.7
210 0.5 40.8
1.0 83.2
1.5 129.5

To minimize the radius of the circular isocenter path, the PBS can be adapted to partially account for the beam deflection prior to the injection of the proton beam in the magnetic field region. This allows to counteract the bending of the beam, defining an isocenter path closer to the MRI isocenter. As the scanning magnets alone may not be able to fully compensate for the deflection of the proton beam depending on their operational range, we considered a PBS skew angle to direct the beam toward a virtual point with an offset from the MRI isocenter in the opposite direction of the main beam deflection. This will effectively reduce the radius of the circular isocenter beam path. Figure 4 shows a comparison of the maximum field area available for scanning for beam energies of 67.9, 154.6, and 216.4 MeV that can be delivered using the reference beamline setup (i.e., without magnetic field) and two setups in the presence of the 1.5 T MRI scanner, namely, when delivered with an unmodified beamline and when applying a tilt of the PBS assembly (skew angle of 4.4 $^{\circ }$ ). The scanning range of the PBS system was obtained assuming a maximum nominal scanning field of 30 × 30 $30\times 30$  cm 2 $^2$ for the reference beamline. The results illustrate the outline of the nominal reference field inside a water phantom with the distal end of the pencil beam at the depth of the MRI isocenter. The source to surface distance (SSD) for each proton beam energy was adapted to account for the varying range. No correction was applied to the proton beam energy to compensate for the Bragg peak retraction in the presence of the magnetic field for the purpose of this illustration. In this example, the PBS skew setup can partially correct the beam spots offsets increasing the distance to the MRI isocenter that can be scanned in any direction.

Details are in the caption following the image
Maximum area available for scanning for (a) 67.9 MeV, (b) 154.6 MeV, and (c) 216.4 MeV proton beam delivery for the reference condition and in the presence of the 1.5 T magnetic field from the MRI scanner. The scanning field is shown in the beams eye view for an RL beam (beam along +X axis) with the horizontal scanning direction along the −Z axis and vertical scanning direction along the −Y axis. In the figure, the SI magnetic field is from left to right (−Z direction) resulting in the beam deflection pointing downward (+Y direction). The maximum scanning field without the PBS skew extends below outside of the displayed grid. The large deflection in the magnetic field results in the irradiation field to move significantly downwards when not tilting the PBS assembly. In addition, the horizontal dimension of the field size in the upper end is significantly reduced

The method for selecting the PBS skew angle for each MRI magnetic field was based on the angle that maximizes the minimum scanning distance from the MRI isocenter for the whole clinical beam energies. This was achieved by minimizing the maximum offset of the central beam spot as follows: first, for a given PBS skew angle, the distance of the central beam spot to the MRI isocenter is computed for the lowest and highest beam energies. Then, the largest distance to the MRI isocenter is selected as the offset for the given PBS skew angle. Finally, the PBS skew angle that minimizes the offset is selected.

2.2.2 Adaptation of gantry angle

Also considered is an adaptation of the gantry angle to minimize the difference of the beam path in the magnetic field with respect to the beam path in the reference irradiation. Figure 5 illustrates the paths of pencil beams delivered in different beamline setups hitting the same spot position in the target for the irradiation of the liver tumor in the reference condition and in the presence of 1.5 T magnetic field. The beam path when only tilting the PBS assembly strongly differs from the reference beam path due to the beam deflection resulted when traversing the fringe magnetic field before reaching the patient. Substantially different beam paths are expected even for the lower magnetic field strength of 0.5 T (results not shown). Therefore, B-field-optimized IMPT plans generated in the case of PBS skew cannot be expected to show equivalent dosimetric properties as the reference plan. However, when combining the PBS skew with a gantry offset, it is possible to modify the trajectory of the beam, and therefore, change the entry point in the patient. In the example shown in the figure, a gantry angle offset was chosen to achieve a beam path inside the patient similar to the reference LR field in the absence of the magnetic field. In this case, the path closely resembles the straight beam path of the reference beam. In such scenario, the optimization of the IMPT plans in the presence of the magnetic field may be expected to result in similar dosimetric properties as for the reference plan.

Details are in the caption following the image
Path of the distal pencil beam in the center of the irradiation field for the liver tumor in different beamline setups. Trajectories are shown for the case of the reference beam (magenta line), and two setups in the presence of 1.5 T magnetic field, namely, (i) the PBS skew with an angle of 4 . 4 $4.4^{\circ }$ (red line) and (ii) the PBS skew ( 4 . 4 $4.4^{\circ }$ ) combined with a gantry offset ( 27 $27^{\circ }$ ) (blue line). The heat map shows the component of the magnetic field along the superior–inferior direction and is used to illustrate the extension of the fringe magnetic field. The negative values in the far fringe field correspond to the field in the opposite direction
In particular, the offset of the gantry angle is applied to the beam prior to the spot-by-spot adaptation of the PBS as described below. To select the gantry angle offset, we evaluated the difference in the beam path using as a metric the average Euclidean distance (AED) of the beam path inside the patient volume with respect to the beam path in the reference condition and selected the gantry angle offset resulting in the minimum AED for the distal-most pencil beam in the center of the irradiation field (i.e., the spot at the center of the field under reference condition for the highest energy). More specifically, first, the pencil beam parameters for the spot at the center of the field for the highest energy are adapted using the method described below until the Bragg peak position matches with the Bragg peak position in the reference condition within 0.1 mm error, and then the AED between the reference beam path (straight line) and the path in the magnetic field is computed as follows:
  1. A set of n $n$ equidistant points { P i = ( x i , y i , z i ) | 1 i n } $\lbrace P_i = (x_i,y_i,z_i) | 1 \le i \le n\rbrace$ is selected along the line segment of the reference beam path inside the patient.
  2. For each point P i $P_i$ , a point P i $P^{\prime }_i$ in the deflected beam path in the magnetic field is selected so that the vector P i P i $\overrightarrow{P_iP^{\prime }_i}$ is perpendicular to the reference beam path.
  3. Finally, the AED is computed as the average of the length of the vectors P i P i $\overrightarrow{P_iP^{\prime }_i}$ computed using the Euclidean metric d ( P i , P i ) $d(P_i,P^{\prime }_i)$ :
    AED = 1 n i = 1 n d P i , P i = 1 n i = 1 n ( x i x i ) 2 + ( y i y i ) 2 + ( z i z i ) 2 . \begin{eqnarray*} \mbox{AED} &=& \frac{1}{n} \sum _{i=1}^n d{\left(P_i,P^{\prime }_i\right)}\nonumber\\ &=& \frac{1}{n} \sum _{i=1}^n \sqrt {(x_i-x^{\prime }_i)^2 + (y_i-y^{\prime }_i)^2 + (z_i-z^{\prime }_i)^2}. \end{eqnarray*}
In particular, n = 1000 $n=1000$ points were used to compute the AED.

The optimal gantry angle yielding the smallest AED depends on the specific irradiation scenario, that is, on the geometry of the irradiated volume and the position of the target volume. In addition, each pencil beam is characterized by a different path leading to different AED values. In this study, however, a fixed gantry angle offset per irradiation field (i.e., per beam direction) was applied instead of adapting the gantry angle on a spot-by-spot basis. In particular, the choice of AED for the distal-most pencil beam in the center of the irradiation was motivated by the fact that (i) the distal-most pencil beam has the longest beam path inside the patient and (ii) the distal pencil beams contribute more to the dose distribution.

2.2.3 Adaptation of pencil beam scanning

Following the motivation for the PBS skew angle above, each pencil beam composing the IMPT field needs to be directed to new virtual spot positions so that the protons, after magnetic deflection, end their path at the correct spot in the target volume. This adaptation process needs to be determined and applied to each individual pencil beam of the IMPT plan as the beam deflection is not necessarily uniform across all the beam spots (i.e., the MRI fringe field is 3D spatially variant). An algorithm was implemented to automate the adaptation of every parameter (energy and the two virtual scanning positions) for each pencil beam. It consists of the following steps:
  • Ad hoc pencil beam delivery correction for homogeneous medium: By means of MC transport simulations of individual pencil beams stopping in a homogeneous water phantom placed at the MRI isocenter (including the MRI field), a lookup table was created consisting of the inputs, namely, the pencil beam parameters (i.e., the horizontal and vertical spot scanning positions and beam energy), gantry angle offset, and magnetic field strength, and the corresponding 3D coordinate outputs of the Bragg peak position. The data are used to linearly interpolate the scanning pencil beam parameters as a function of the coordinates of the Bragg peak position in water. The interpolation of the lookup data in water provides a first-order estimation of the pencil beam parameters for delivering a given beam spot in the patient anatomy. The difference between the pencil beam parameters to the reference values (i.e., in the absence of magnetic field) for a given Bragg peak position in the target defines the horizontal and vertical shift of the scanning spot positions and the increment in the pencil beam energy.
  • Supervised regression model for pencil beam parameter adaptation in patient: An algorithm was implemented to tune the pencil beam parameters to minimize the error in the Bragg peak position with respect to the desired position in the reference irradiation condition to ensure complete target coverage. In practice, the pencil beam parameters are tuned until the error is below the arbitrary threshold of 0.1 mm. The algorithm is initiated with the first-order correction of the pencil beam parameters for homogeneous medium presented above. The algorithm then applies particle transport simulation of protons in the presence of the magnetic field to generate a dataset of pencil beam parameters and the corresponding Bragg peak positions in the patient. Then, the dataset is used to train a supervised regression model consisting of a multilayer perceptron (MLP) neural network that is applied to predict the pencil beam parameters for the desired Bragg peak positions. The actual Bragg peak positions for the predicted pencil beam parameters by the regression model are obtained through MC simulations and compared to the desired values. If the error is above the acceptance threshold, the data of the simulations are further used to retrain the regression model in order to fine tune the model until the predicted pencil beam parameters pass the acceptance criteria for the Bragg peak positions. It is important to note that the regression model is patient-specific, that is, it is trained for each patient case.

2.3 IMPT planning in the presence of a magnetic field

In the framework of this study, an interface was implemented between the MC proton beam model, including the modeling of the magnetic field and the algorithms for beam delivery adaptation, and the open-source research treatment planning system matRad26 developed at the German Cancer Research Center. The workflow for the treatment planning is summarized in Figure 6. It should be emphasized that with such an interface, the impact of the MRI scanner on the proton beam is only modeled through the MC simulation. Namely, the interface is used to apply the spot-by-spot adaptations required to achieve the desired spot position in the target as well as to compute the MC-based dose-influence matrix for inverse treatment planning. In the following, IMPT plans were generated for the reference conditions (without magnetic field) as well as in the presence of the magnetic field in order to investigate the feasibility of IMPT plan delivery in the presence of the static magnetic field of the MRI scanner and the potential degradation of the treatment plan quality.

Details are in the caption following the image
Treatment planning workflow in the presence of the magnetic field characterized by the additional steps for the hardware optimization facilitated by the Monte Carlo beam model and the external algorithms for the beam delivery adaptation

2.4 Case selection and treatment plan parameters

A set of treatment plans was analyzed accounting for the IMPT plan optimization in the reference condition and in the presence of the MRI scanner. The treatment plans include the irradiation of homogeneous water phantoms with extended target volumes at depths of 10, 15, and 20 cm (W10, W15, and W20 phantoms, respectively), as well as anthropomorphic geometries consisting of a liver tumor and a prostate cancer case. The patient data were obtained from the CORT dataset.27

Table 2 shows the treatment planning settings and the beam field configurations considered in this study. The water phantoms include the definition of a 5 × 5 × 5 $5\times 5\times 5$  cm 3 $^3$ CTV with a prescribed dose of 60 Gy and a PTV defined by axial and lateral CTV-PTV margins of 2.5 and 5 mm, respectively. In addition, a volume surrounding the PTV is defined as an OAR adjacent to the target volume with respect to the beam direction. In the case of the liver tumor, the PTV with a prescribed dose of 45 Gy is defined by an isotropic CTV-PTV margin of 6 mm. As for the prostate cancer patient, two PTV regions (PTV 56 $_{56}$ and PTV 68 $_{68}$ ) are defined with prescribed doses of 56 and 68 Gy. The PTV 68 $_{68}$ corresponds to a geometrical expansion of the prostate (6–15 mm margin, see Ref. [27]). In the following, the CTV for the prostate cancer case is considered as the volume of the PTV 68 $_{68}$ excluding the volume intersected by the bladder and rectum.

TABLE 2. Treatment plan parameters including site, treatment fields, number of fractions (FX), volume of interest (VOI) considered in the plan optimization, VOI type (target or OAR), VOI volume, optimization objective, reference dose and penalty. The treatment fields are specified using the following abbreviations: AP (anterior-posterior), LR (left-right), RL (right-left), RPO (right-posterior-oblique, gantry angle of 240°) and RAO (right-anterior-oblique, gantry angle of 300°)
Optimization settings
Site (treatment fields) FX VOI VOI type VOI volume [cm3] Dose objective Dose [Gy] Penalty
W10/W15/W20 phantoms (AP) 30

PTV

CTV

OAR

Target

Target

OAR

198.0

125.0

464.8

Squared deviation

Squared deviation

Squared overdosing

60

60

30

1000

1000

200

Liver

(RL, RPO-RAO)

10

PTV

CTV

Heart

Abdomen

Target

Target

OAR

OAR

156.5

87.7

743.0

43365.5

Squared deviation

Squared deviation

Squared overdosing

Squared overdosing

45

45

25

25

500

500

300

300

Prostate

(RL-LR)

34

PTV68(1)

PTV56(2)

CTV(3)

Pelvis

Bladder

Rectum

Target

Target

Target

OAR

OAR

OAR

182.8

256.3

132.7

18640.1

313.1

47.6

Squared deviation

Squared deviation

Squared deviation

Squared overdosing

Squared overdosing

Squared overdosing

68

56

68

30

50

50

1500

1000

1500

100

300

200

  • 1 Region of the PTV with planned reference dose of 68Gy.
  • 2 Region of the PTV with planned reference dose of 56Gy.
  • 3 Region of the PTV with planned reference dose of 68Gy not intersecting with the bladder or rectum.

For all plans, the longitudinal and lateral spot spacing were set to 3 mm. The IMPT plans were designed to achieve adequate dose coverage of V 95 % > 98 % $V_{95\%} &gt; 98\%$ and V 107 % < 2 % $V_{107\%} &lt; 2\%$ in the CTV by means of the minimization of the composite objective function defined as the sum of the objective functions for each volume of interest weighted by its respective penalty value. An in-depth discussion about the optimization procedure in matRad is provided elsewhere.26 Plans were evaluated with respect to physical dose only because considering the clinically used RBE of 1.1 would not affect the analysis presented in this study.

3 RESULTS

3.1 Beam delivery adaptation

3.1.1 PBS skew angle

The PBS skew angles that maximized the minimum scanning distance from the MRI isocenter (i.e., the area available for scanning) over the clinical beam energies considered in this study was determined as 1.6 $^{\circ }$ , 3.0 $^{\circ }$ , and 4.4 $^{\circ }$ for the magnetic field strengths of 0.5, 1.0, and 1.5 T, respectively.

This beamline modification still allows to deliver squared scanned field sizes as large as 20 × 20 $20\times 20$  cm 2 $^2$ in the presence of the 1.5 T magnetic field in the whole range of therapeutic proton beam energy considered in this study when considering the operational range of the scanning magnets for a maximum scanning field size of 30 × 30 $30\times 30$  cm 2 $^2$ in the reference conditions for a typical PBS system with a source to axis distance of 200 cm as used in this study (see Figure 4). At higher beam energies as well as lower imaging field strength, a larger area is available for scanning. Furthermore, larger scanning areas centered at the MRI isocenter are possible by selecting an optimal skew angle for a narrower beam energy interval.

3.1.2 Gantry angle offset

Table 3 summarizes the gantry angle corrections applied in treatment planning in the presence of the magnetic field using the PBS skew combined with the gantry offset. The gantry angle corrections correspond to the shift in the gantry angle necessary to minimize the AED between the pencil beam path for the distal-most pencil beam in the center of the irradiation field to the beam path of its corresponding pencil beam in the reference plan. The AED for the proximal-most and distal-most pencil beams in the center of the irradiation field are shown for comparison. A larger correction to the gantry angle is required for a higher magnetic field strength. The required gantry angle correction strongly depends on the depth of the target volume as clearly observed from the results obtained with the homogeneous water phantoms. Gantry angle corrections between 8 $^{\circ }$ and 29 $^{\circ }$ were necessary to minimize the AED in all the investigated cases.

TABLE 3. Gantry angle corrections and the respective average Euclidean distance (AED) of the pencil beam path in the patient volume for the proximal-most and distal-most pencil beams in the center of the irradiation field. Results are shown for the magnetic field strengths of 0.5, 1.0 and 1.5 T for the different irradiation fields considered in this study (see Table 2). The energy E0 of the corresponding proximal-most and distal-most pencil beams in the absence of magnetic field is shown for reference
Gantry angle Proximal Distal
Tumor site (treatment field) B-field [T] Ref. [deg] Correction [deg] E0 [MeV] AED [mm] E0 [MeV] AED [mm]

W10 phantom

(AP)

0.5

1.0

1.5

0

−9

−19

−29

93.4

0.7

0.9

2.1

134.7

0.6

0.7

1.0

W15 phantom

(AP)

0.5

1.0

1.5

0

−8

−17

−25

127.5

0.6

0.9

2.0

162.4

0.7

1.2

1.8

W20 phantom

(AP)

0.5

1.0

1.5

0

−8

−15

−23

156.2

0.7

1.1

1.5

187.2

1.1

1.8

2.6

Liver

(RPO)

0.5

1.0

1.5

240

−8

−17

−25

125.7

0.9

0.4

1.9

168.5

0.7

1.3

1.8

Liver

(RL)

0.5

1.0

1.5

270

−9

−18

−27

102.1

0.5

1.1

2.5

149.8

0.4

0.8

1.3

Liver

(RAO)

0.5

1.0

1.5

300

−9

−18

−28

95.6

0.8

1.7

2.2

144.9

0.4

0.8

1.2

Prostate

(LR)

0.5

1.0

1.5

90

−8

−16

−24

129.4

0.3

0.7

1.3

192.8

0.9

1.7

2.5

Prostate

(RL)

0.5

1.0

1.5

270

−8

−16

−24

127.5

0.4

0.7

1.4

191.4

0.9

1.7

2.6

3.1.3 Correction of pencil beam parameters

Figure 7 presents the histograms of the corrections applied to the pencil beam energies and the scanning spot positions for the water phantoms and the patient geometries for the different magnetic field strengths. The energy corrections for the water phantom are small due to the fact that the gantry angle offset together with the PBS skew angle largely restores the beam path inside the water phantom in the presence of the magnetic field in comparison to the path in the reference condition. As the phantom is homogeneous, the small curvature of the beam path inside the phantom in the presence of the magnetic field will not significantly affect the radiological depth, and therefore, only requires minor changes in the beam energy. This is not the case, however, for the patient anatomies where small curvatures might lead to the proton beam crossing voxels with significantly different radiological thickness that require larger energy corrections. The corrections for the horizontal spot scanning position are not negligible and increase at larger magnetic field strengths. Lastly, the corrections for the vertical spot scanning position are significant and highly dependent on the geometry with the necessary corrections depending on the target depth as demonstrated by the results for the water phantoms. In particular, for the homogenous water phantom, a high-frequency pattern in the corrections is observed resulting from the initial discrete energy selection for the longitudinal spot spacing in the IMPT plan. The corrections correlate well with the proton range in the phantom (see Figure 8a) and, because the phantom is homogeneous, these corrections are nearly the same across all axial slices. On the other hand, the same structure is not observed for the patient anatomies because the corrections are different for each axial slice.

Details are in the caption following the image
Histogram of corrections for the pencil beam energy and for the two pencil beam scanning directions for the (a) W10 phantom, (b) W15 phantom, (c) W20 phantom, (d) liver tumor irradiated with right–left fields, (e) liver tumor irradiated with two oblique fields, and (f) prostate cancer with two opposing fields. Results are shown for the magnetic field strengths of 0.5, 1.0, and 1.5 T with irradiation using the beamline setup of PBS skew combined with gantry offset with skew angles of 1 . 6 $1.6^{\circ }$ , 3 . 0 $3.0^{\circ }$ , and 4 . 4 $4.4^{\circ }$ , respectively. Vertical spot scanning position refers to the direction perpendicular to the magnetic field
Details are in the caption following the image
Corrections for the vertical pencil beam scanning spot position (i.e., in the direction perpendicular to the magnetic field). The corrections are shown for the case of 1.5 T magnetic field for the pencil beams with Bragg peak positions located in the central axial plane for (a) the W20 phantom, (b) liver tumor irradiated with RL field, and (c) for the LR and RL fields for the prostate cancer case

In order to better visualize the spatial dependence of the beam parameter adaptations, Figure 8 shows the required correction to the vertical spot scanning position (i.e., in the direction perpendicular to the imaging field) for the beam spots located in the central axial plane in the case of 1.5 T magnetic field. An inverse correlation can be clearly observed between the corrections and the range of the pencil beams. It results from the larger deflection during the traversal of the fringe fields for the pencil beams with lower kinetic energy, that is, lower range. Similarly, Figure 9 shows the corrections for the other spot scanning position (i.e., the scanning direction parallel to the magnetic field direction) for the beam spots located at the coronal and sagittal planes through the isocenter for the liver tumor irradiated with RL field and prostate cancer case, in the case of 1.5 T magnetic field. In this case, the results clearly show that the corrections for the respective scanning spot positions correlate with the position of the beam spot (i.e., the scanning angle) in the superior–inferior direction (i.e., in the direction of the magnetic field). In contrast to the observations with respect to the two spot scanning directions, the corrections for the beam energy are relatively much smaller and do not present a systematic correlation with the spatial position of the beam spots.

Details are in the caption following the image
Corrections for the horizontal pencil beam scanning spot position (i.e., in the direction parallel to the magnetic field). The corrections are shown for the case of 1.5 T magnetic field for the pencil beams with Bragg peak positions located in the central coronal and sagittal planes for (a) and (b) liver tumor irradiated with RL field and (c) and (d) for the LR and RL fields for the prostate cancer case, respectively

3.2 IMPT plan delivery in the presence of perpendicular magnetic field

Figures 10(a) and (b) show a comparison of the dose distributions in an axial plane for the reference IMPT plan for the W20 water phantom irradiated with a single AP field and the distorted dose distribution resulting by the uncorrected delivery of the reference plan in the presence of the 1 T magnetic field. The deflection in the fringe field leads to a complete miss of the target volume. Similar results were observed for all treatment plans and magnetic field strengths (results not shown). Due to the clearly poor target dose coverage, no quantitative dosimetric evaluations of the uncorrected delivery of the reference plans in magnetic field are reported. Figures 10(c) and (d) show the corresponding IMPT plans optimized in the presence of the 1 T magnetic field for the beamline setup with a PBS skew and the setup combining a PBS skew with a gantry offset, respectively. In both cases, the plans include the adaptation of the pencil beam parameters to achieve the same target coverage as in the reference plan. Comparison of the optimized dose distributions shows qualitatively the same target dose coverage for the reference IMPT plan and B-field optimized IMPT plans of the two adapted PBS setups. The results also highlight, however, that the beam path in the phantom is substantially different when applying a PBS skew only with respect to the beam path in the reference plan. This should be taken into account would an OAR be located adjacent to the beam path as in this example. On the contrary, the similar beam path observed between the reference plan and the plan generated when combining the PBS skew with the gantry offset should reduce such complications.

Details are in the caption following the image
2D dose distributions in axial plane for the W20 phantom irradiated with a single AP field for (a) reference condition (no B-field), (b) uncorrected delivery of reference plan in the presence of a perpendicular 1 T B-field, and B-field optimized plans with (c) PBS skew ( 3 $3^{\circ }$ ) and (d) PBS skew combined with gantry offset ( 15 $15^{\circ }$ )

In the following, the dose distributions for the IMPT plans in the reference condition are compared solely to the dose distributions of their respective IMPT plans optimized in the presence of the magnetic field from the MRI device in the case of the beamline setup of PBS skew combined with gantry offset. Figure 11 shows the results for the W10, W15, and W20 water phantoms. The curvature of the beam path inside the phantom can be easily observed for the deep target volume in the presence of the 1.5 T magnetic field. The curvature of the beam is responsible for significant changes in the lateral dose fall-off from surface to proximal SOBP, that is, in the region of normal tissues adjacent to the beam. In contrast, the dose distribution in the central part of the beam is equivalent in both plans as evidenced by the dose difference between the plans (see Panel (c) in Figure 11).

Details are in the caption following the image
2D dose distribution of optimized IMPT plans in axial plane for the W10/W15/W20 phantoms irradiated with a single AP field for (a) reference condition (no B-field), (b) in the presence of the perpendicular 1.5 T B-field (with optimized head skew and gantry offset applied), and (c) dose difference between the two plans

Figures 12 and  13 show the dose distributions in axial planes through the isocenter for the liver tumor irradiated with a single RL field and two oblique fields, respectively. The short range of the proton beam in the liver tumor irradiation leads to a small curvature of the beam path inside the patient because the beam delivery adaptation strategy optimizes the beam delivery to minimize the distance between the beam path in the magnetic field with respect to the reference IMPT plan. Due to the small beam curvature in this case, only minor dose differences in the lateral dose fall-off can be observed. The impact of the anatomical changes along the slightly different beam paths for the reference irradiation and the irradiation in the magnetic field is accounted for in the beam delivery adaptation strategy resulting in highly equivalent dose distributions in the two scenarios as qualitatively illustrated by the dose difference distributions (see Panel (c) of Figures 12 and  13).

Details are in the caption following the image
2D dose distribution of optimized IMPT plans in axial plane for the liver tumor irradiated with a single RL field for (a) reference condition (no B-field), (b) in the presence of the perpendicular 1.5 T B-field (with optimized head skew and gantry offset applied), and (c) dose difference between the two plans
Details are in the caption following the image
2D dose distribution of optimized IMPT plans in axial plane for the liver tumor irradiated with two oblique fields with (a) reference condition (no B-field), (b) in the presence of the perpendicular 1.5 T B-field (with optimized head skew and gantry offset applied), and (c) dose difference between the two plans

Figure 14 shows the dose distributions in axial plane through the isocenter for the prostate cancer irradiated with two opposing fields. In contrast to the liver tumor case, the target volume for the prostate cancer is located at a substantially larger depth. Therefore, the impact of the curvature of the beam path on the dose distribution can be more easily identified. In this case, the curvature for each beam is in the opposite direction. Again, as observed in the case of the water phantoms, the beam curvature causes a significant dose difference at the lateral dose fall-off, whereas the dose in the central beam path and in the target volume is equivalent between the two scenarios.

Details are in the caption following the image
2D dose distribution of optimized IMPT plans in axial plane for the prostate cancer irradiated with RL-LR fields with (a) reference condition (no B-field), (b) in the presence of the perpendicular 1.5 T B-field (with optimized head skew and gantry offset applied), and (c) dose difference between the two plans
Figure A.1 (in the Appendix) shows the dose-volume histograms for the liver tumor irradiated with the RL field and the prostate cancer case for the reference IMPT plans and the optimized plans in the presence of perpendicular 1.5 T magnetic field. The dose metrics in the CTV for the reference IMPT plans and the plans optimized in the presence of the magnetic field are presented in Table A.1 (in the Appendix). The IMPT plan optimization accounting for the beam deflection and the dose distributions in the presence of the magnetic field is able to generate the same target dose conformation as the reference IMPT plan. No significant changes on the dose metrics in the CTV are observed. A minor increase of the dose homogeneity with increasing magnetic field strength was observed for the liver tumor irradiated with RL field. Specifically, defining the homogeneity index (HI) as
HI = D 2 % D 98 % D 50 % . \begin{equation*} \mbox{HI} = \frac{\mbox{D}_{2\%}-\mbox{D}_{98\%}}{\mbox{D}_{50\%}} \mbox{.} \end{equation*}
HI decreases from 0.08 for the reference IMPT plan to 0.06 for the plan with 1.5 T magnetic field.

The dose metrics for the reference IMPT plans and the plans optimized in the presence of the magnetic field for selected OARs of the liver tumor and the prostate cancer are shown in Table A.2 (in the Appendix). The results show no substantial impact of the magnetic field on the dose metrics of all OARs evaluated. Specifically, the mean dose in the heart and the healthy part of the liver in the irradiation of the liver tumor case vary only slightly among the four different magnetic field conditions, whereas a small but systematic decrease of D 10 % $_{10\%}$ in the heart is observed at increasing magnetic field strength. In the prostate cancer case, a slight increase of the mean dose and D 50 % $_{50\%}$ can be observed in the bladder and the rectum with increasing magnetic field strength.

4 DISCUSSION

In this study, we have shown how the magnetic field from an MRI scanner will significantly deflect therapeutic proton beams away from the MRI isocenter in an integrated perpendicular orientation MRI proton therapy system with PBS delivery. Two simple beamline modifications have been explored to enable the proton beams to travel through the MRI isocenter after the magnetic deflection from the MRI scanner magnetic field. These beamline modifications, a simple gantry angle offset, and a small PBS nozzle skew (up to 4.4 $^{\circ }$ ) are readily feasible solutions for the MRI field strengths investigated. Once the proton beamline direction has been modified, the magnetic field of the MRI still gives rise to patient geometry specific changes in the locations of the Bragg peaks. From this point forward, the dose planning adaptations and optimizations need to be handled by the flexibility of the PBS system. Fortunately, the PBS process is inherently flexible as a large range of pencil beam energies and scanning positions are possible. In the current work, we have shown that once the gross pencil beam deflections are accounted for with the gantry offset and PBS nozzle skew, then the final changes required for a PBS pattern (patient treatment) are well within the possible range of deliverable spot parameters, as shown in Figure 7. We have shown this process successfully for a liver and a prostate cancer scenario, two examples of a tumor located deep within a patient body where there is overall stronger magnetic deflection amounts due to the longer path lengths of the proton beams in the body. The following sections discuss several other areas of this research and important considerations.

4.1 MRI model

The current study looks at using a 0.5–1.5 T air–core MRI system with a split bore. This has a far fringe field that has a direction opposite to the main MRI imaging field, as indicated in Figure 2. Hence, this sets up a small deflection of the proton beams in the opposite direction to the bulk deflection that requires correction. We note, however, that iron-yoked MRI systems (i.e., having a natural flux return yoke) will not have this feature of the far fringe field being opposite in direction. Thus, overall, there would be a stronger deflection of the proton beams for iron-yoked systems. This is obviously dependent on the field strength of the iron-yoked MRI scanners. Currently, we note that the maximum field strength of iron-yoked MRI systems with a split-bore design is around 0.56 T.28 The deflections at isocenter, as based on the data in Table 2, will be on the order of 65 mm for a 90 MeV proton beam in the air-cored MRI. Even if the deflection amount doubles in the iron-yoked design, these will be readily corrected by the gantry angle offset and PBS nozzle skew as described in this work.

4.2 PBS adaptation and IMPT planning

The IMPT planning in the presence of the MRI scanner requires major modifications to the treatment planning system to account for the proton beam deflection that significantly affects the position of the Bragg peak. In a previous work, Hartman et al. have shown the feasibility of IMPT planning in the presence of an uniform perpendicular magnetic field within a 35-cm radius distance from the gantry isocenter and no magnetic field beyond.9 By means of selecting appropriate PBS angles and energies, they were able to show that inverse treatment plan optimization yields dose distributions similar to the plans in the absence of the magnetic field. A large limitation of that work, however, is that it neglected the major proton beam deflection that results when traversing the far and near magnetic fringe fields.16, 17 As shown in the present study for a realistic 3D magnetic field modeling of the 1 T split-bore MRI system, a significant change in the beam path is observed outside of the patient volume that effectively translates into different beam geometry even after applying individual pencil beam adaptations to cover the target volume. We have shown for the first time that hardware adaptations including a head skew and a gantry angle offset, however, can be used to counteract the deflection of the proton beam in the fringe field in order to restore near the same beam path in the patient.

In this study, a research TPS was extended to apply a novel strategy for IMPT planning in the presence of fringe perpendicular magnetic field. In particular, the beam parameters for each individual pencil beam, characterized by the beam energy and the scanning spot positions at a transversal plane located at the isocenter, were adapted from their original values in the reference conditions without the magnetic field. The adaptation of the beam parameters was obtained in an automated process by applying machine learning techniques to model the relationship between the three-dimensional coordinates of the Bragg peak position inside the patient and the three-dimensional space of the beam parameters. This strategy allowed for positioning the Bragg peak inside the target volume as in the reference plan. The necessary corrections to the PBS parameters were observed to strongly depend on the patient anatomy as well as the spot position relative to the MRI isocenter.

IMPT plans were generated for a water phantom and patient anatomies including a liver tumor and prostate cancer for the reference condition and using the combination of gantry angle offset and PBS nozzle skew for the planning in the presence of the perpendicular magnetic field with imaging field strengths of 0.5, 1.0, and 1.5 T. In general, the results for the optimized IMPT plans in the presence of the magnetic field showed the same dose metrics as the reference plans, indicating that the plan quality was recoverable despite the presence of the MRI scanner.

The results of beam delivery adaptation for the IMPT plans with CTV at varying depths for the water phantom clearly illustrate the complexity of the corrections of the beam scanning parameters even in a simple situation of homogeneous medium. The beam delivery adaptation resulted in similar beam path inside the phantom that translated in dose distributions equivalent to the reference plan. The impact of the residual beam deflection inside the phantom, however, can still be observed as shown by the dose differences between the IMPT plan in the magnetic field and the reference plans. This effect would be of particular importance only when irradiating with an OAR directly adjacent to the beam path. Besides, only minor changes in the dose level is expected. Similar results are also observed for the IMPT plans for the liver tumor and the prostate cancer case. No quantitative difference of the dose distribution in the CTV was observed in all cases investigated.

The method for IMPT planning and beam delivery presented in this study only considered the simple scenario of static geometry, that is, the CT information was used to compute the necessary adaptations to the beam scanning parameters to accurately position the Bragg peak in the target volume. This study simply aimed to demonstrate that optimized IMPT plans in the presence of the MRI scanner can be obtained without any prejudice to the plan quality in comparison to the reference conditions when no magnetic field is present. Further studies should investigate the difficulties to obtain accurate anatomical information, adapt the beam delivery, and recompute the dose distribution in real time.

4.3 Nongantry horizontal beamline systems

Results of the current study can be somewhat translated to an equivalent nongantry horizontal proton beamline system, such as those used in research bunkers. In such configurations, however, the loss of the gantry means that treatment options are limited unless the patient is axially rotated to emulate a gantry rotation. We note, however, a recent study by Guerreiro et al.30 that demonstrates feasible dose planning for proton beam therapy with axially rotated patient, and previous work on a successful axially rotating couch system by Whelan et al.31 The transferability of the current study results is ultimately dependent on the orientation of the patient axis with respect to the MRI field direction and beamline axis. In the case of an MRI scanner with magnetic field oriented in the floor/ceiling direction, the deflection of the proton beams will be in a lateral direction, that is, parallel with the floor/ceiling planes. To emulate a gantry angle offset and PBS nozzle skew, the MRI system needs to be simply positioned off-axis with respect to the original MRI position. If the patient is positioned upright/standing and allowed to axially rotate, then the correction methods of the current study would be transferable. Otherwise, the patient is positioned along an axis that would be considered like a classical couch angle, resulting in different beam orientations. The current work did not consider couch angles primary because these are not envisaged as a possible feature of a gantry-based MR-integrated proton therapy system. To achieve a simple but flexible MRI offset, a mobile system would make the most sense. For example, the dedicated system presented by Schellhammer et al.14 would allow such flexibility. In the case of an MRI scanner with a horizontal field direction (i.e., parallel to the floor/ceiling planes), the case is slightly more complicated. The MRI scanner isocenter must be raised/lowered from the beamline horizontal axis. In this scenario, it would perhaps make most sense to raise the MRI scanner through a dedicated motorized hoist platform or similar. Again, if the patient is able to axially rotate, then the correction methods of the current work are possible.

4.4 General dosimetry considerations

One dosimetry area of this study has not been evaluated in detail, which is of the electron return effect (ERE) associated with proton beams.29 In this previous study, the ERE was found to contribute to a dose enhancement ratio up to 8% in exit surface or skin doses when in the presence of a 0.95 T magnetic field perpendicular to the proton beam direction. However, such dose enhancement was only observed directly at the vicinity of the tissue–air interface and averaged out significantly across the typical millimeter size voxels used for treatment planning. For our current study, no patient geometries were examined with suitable air cavities to demonstrate any of the negative dosimetry effects of the ERE. Future studies could focus on this topic by applying the same MC dose calculation in magnetic field and optimization methods that were used in this work.

Also of interest is the consideration of the imaging gradient fields of an MRI scanner. This has been studied in the past for a 0.56 T MRI system suitable for integration with a proton beamline.28 The obvious finding is that these gradient fields, in the order of 40 mT/m, are simply not strong enough to change the MRI main field to induce any additional significant perturbation of the proton beams.

5 CONCLUSIONS

The modeling work conducted in this study brings a robust set of data to support modified beam delivery and successful dose planning in MRI-guided proton therapy, in particular, when the MRI main field direction is perpendicular to the beamline axis. While previous studies have only considered the impact of the MRI imaging field, this work includes the full MRI field map that extends to encompass the far fringe fields and correspondingly how this changes the proton beam trajectory. A simple combination of a gantry angle offset between 8 $^{\circ }$ and 29 $^{\circ }$ and a PBS nozzle skew up to 4.4 $^{\circ }$ has been shown to account for the gross deflection of the proton beams before reaching the patient volume. Finally, dose planning will require patient-specific optimization within the inherent flexible nature of the PBS beam delivery system. This has been shown to be successful in the current work for clinical liver and prostate plans. The work ultimately supports the further development of integrated MRI-guided proton therapy which is currently being pursued by several groups around the world.

ACKNOWLEDGMENTS

We would like to acknowledge the technical support from the information technology core facility (ITCF) of the German Cancer Research Center.

We would also like to acknowledge the Australian MRI-linac Program Grant (NHMRC Grant No. 1132471) and the Cancer Council NSW (Grant No. 1128336).

Open access funding enabled and organized by Projekt DEAL.

    CONFLICT OF INTEREST

    The authors have no conflicts to disclose.

    APPENDIX A: DOSIMETRIC INDICATORS FOR THE TARGET AND OARs

    The plan quality indicators in the target volume for the reference IMPT plans and the B-field optimized IMPT plans in the case of the beamline setup of PBS skew combined with gantry offset are shown in Table A.1. The dose metrics for the OARs of the liver tumor case and the prostate cancer case are shown in Table A.2. In particular, the OARs evaluated for the liver tumor include the heart and the healthy part of the liver, while for the prostate cancer case, the bladder and the rectum were considered. The dose metrics include the mean dose, D mean $_{\rm {mean}}$ , D 50 % $_{50\%}$ , D 10 % $_{10\%}$ , and maximum dose, D max $_{\rm {max}}$ . The corresponding dose-volume histograms for the target and OARs of the liver tumor and prostate cancer case for the reference IMPT plan and the optimized IMPT plans in the presence of the 1.5 T magnetic field are shown in Figure A.1.

    TABLE A.1. Plan quality indicators (D98%, D50%, D2%, V95%, V107%) in the CTV for the W10 phantom, W15 phantom, W20 phantom, liver tumor and prostate cancer. Results are shown for the reference plan (indicated by B-field of 0 T) and the optimized IMPT plans in the presence of the perpendicular magnetic field from the MRI scanner. The IMPT plans in the presence of the magnetic field were generated using the gantry angle and beam spot delivery correction of pencil beams prior to plan optimization. The statistical errors of the plan quality indicators are smaller than the last significant digit
    Tumor site (treatment fields) B-field [T] D98% [Gy] D50% [Gy] D2% [Gy] V95% [%] V107% [%]

    W10 phantom

    (AP)

    0.0

    0.5

    1.0

    1.5

    57.8

    57.8

    57.8

    57.8

    59.8

    59.8

    59.8

    59.8

    60.5

    60.6

    60.6

    60.5

    100.0

    100.0

    100.0

    100.0

    0.0

    0.0

    0.0

    0.0

    W15 phantom

    (AP)

    0.0

    0.5

    1.0

    1.5

    57.6

    57.6

    57.6

    57.7

    59.8

    59.8

    59.8

    59.8

    60.4

    60.4

    60.4

    60.5

    100.0

    99.9

    99.9

    99.8

    0.0

    0.0

    0.0

    0.0

    W20 phantom

    (AP)

    0.0

    0.5

    1.0

    1.5

    57.4

    57.4

    57.4

    57.5

    59.8

    59.8

    59.8

    59.8

    60.6

    60.5

    60.5

    60.7

    99.5

    99.5

    99.4

    99.4

    0.0

    0.0

    0.0

    0.0

    Liver

    (RL)

    0.0

    0.5

    1.0

    1.5

    43.8

    43.9

    44.0

    44.1

    45.0

    45.0

    45.0

    45.0

    47.4

    47.4

    47.2

    46.9

    99.4

    99.5

    99.6

    99.8

    0.6

    0.5

    0.3

    0.3

    Liver

    (RPO-RAO)

    0.0

    0.5

    1.0

    1.5

    44.5

    44.5

    44.5

    44.5

    45.0

    45.0

    45.0

    45.0

    45.9

    45.9

    45.9

    45.8

    100.0

    100.0

    100.0

    100.0

    0.0

    0.0

    0.0

    0.0

    Prostate

    (RL-LR)

    0.0 0

    5 1.0

    1.5

    65.6

    65.6

    65.6

    65.6

    68.0

    68.0

    68.0

    68.0

    69.0

    69.0

    69.0

    69.0

    99.6

    99.5

    99.5

    99.6

    0.0

    0.0

    0.0

    0.0

    TABLE A.2. Plan quality indicators including mean dose Dmean, D50%, D10%, and maximum dose, Dmax, of selected OARs for the liver tumor and prostate cancer in the cases of reference IMPT plans and for the perpendicular-B-field-optimized IMPT plans using gantry angle and beam spot delivery correction of pencil beams prior to plan optimization. The results for the reference IMPT plans are indicated by the plans with magnetic field of 0T. The statistical errors of the plan quality indicators are smaller than the last significant digit
    Tumor site (treatment fields) OAR B-field [T] Dmean [Gy] D50% [Gy] D10% [Gy] Dmax [Gy]

    Liver

    (RL)

    Heart

    0.0

    0.5

    1.0

    1.5

    1.1

    1.1

    1.1

    1.0

    0.0

    0.0

    0.0

    0.0

    1.3

    1.2

    1.0

    0.8

    46.9

    47.0

    46.3

    46.2

    Liver

    0.0

    0.5

    1.0

    1.5

    5.5

    5.5

    5.5

    5.4

    0.0

    0.0

    0.0

    0.0

    33.2

    33.1

    33.1

    32.6

    49.3

    49.3

    49.5

    49.2

    Liver

    (RPO-RAO)

    Heart

    0.0

    0.5

    1.0

    1.5

    1.2

    1.1

    1.1

    1.0

    0.0

    0.0

    0.0

    0.0

    1.1

    1.0

    0.9

    0.8

    45.0

    45.2

    45.0

    45.0

    Liver

    0.0

    0.5

    1.0

    1.5

    5.8

    5.8

    5.7

    5.7

    0.0

    0.0

    0.0

    0.0

    25.7

    25.8

    25.5

    25.6

    46.9

    46.9

    47.0

    46.8

    Prostate

    (RL-LR)

    Bladder

    0.0

    0.5

    1.0

    1.5

    24.6

    24.6

    24.8

    24.7

    15.3

    15.8

    16.7

    17.3

    67.8

    67.8

    67.8

    67.8

    69.7

    69.7

    69.7

    69.7

    Rectum

    0.0

    0.5

    1.0

    1.5

    28.6

    28.7

    28.9

    29.1

    32.7

    32.9

    33.2

    33.2

    53.4

    53.2

    53.4

    53.4

    69.8

    69.8

    69.8

    69.8

    Details are in the caption following the image
    Dose-volume histograms for irradiation in the absence of magnetic field (reference plan) and in the presence of perpendicular 1.5 T B-field for (a) liver irradiated with RL field and (b) prostate cancer

    APPENDIX B: DOSE OBJECTIVES

    B.1 Squared deviation objective

    The squared deviation objective is used in the optimization of the dose d i $d_i$ to a prescribed dose d ̂ $\hat{d}$ in every voxel i $i$ of a target structure S $S$ by minimizing the following objective:
    f sq deviation = 1 N S i S d i d ̂ 2 , \begin{equation*} f_{\rm sq\nobreakspace deviation} = \frac{1}{N_S}\sum _{i \in S} {\left(d_i - \hat{d} \right)}^2 {\rm ,} \end{equation*}
    where N S $N_S$ corresponds to the number of voxels in the target structure S $S$ .

    B.2 Squared overdose objective

    The squared overdose objective is used to penalize any dose d i $d_i$ above a predefined reference dose d ̂ $\hat{d}$ in every voxel i $i$ of an OAR structure S $S$ by minimizing the following objective:
    f sq overdose = 1 N S i S Θ ( d i d ̂ ) d i d ̂ 2 , \begin{equation*} f_{\rm sq\nobreakspace overdose} = \frac{1}{N_S}\sum _{i \in S} \Theta (d_i - \hat{d}) {\left(d_i - \hat{d} \right)}^2 {\rm ,} \end{equation*}
    where N S $N_S$ corresponds to the number of voxels in the OAR structure S $S$ and Θ $\Theta$ is the Heaviside step function.

    DATA AVAILABILITY STATEMENT

    The data that support the findings of this study are available from the corresponding author upon reasonable request.