1 Introduction. A Monte Carlo study

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1 Current Directions in Biomedical Engineering 2017; 3(2): Sebastian Richter*, Stefan Pojtinger, David Mönnich, Oliver S. Dohm, and Daniela Thorwarth Influence of a transverse magnetic field on the dose deposited by a 6 MV linear accelerator A Monte Carlo study Abstract: An integrated system of a linear accelerator and a magnetic resonance imaging (MRI) device may provide realtime imaging during radiotherapy treatments. This work investigated changes affecting the dose deposition caused by a magnetic field (B-field) transverse to the beam direction by means of Monte Carlo simulations. Two different phantoms were used: A water phantom (Ph1) and a water-air phantom (Ph2) with a cm water-air-water cross section. Dose depositions were scored for B-field values of 0 T, 0.35 T, 0.5 T, 1.5 T, 3 T and 5 T. Beams were based on a precalculated photon spectrum taken from an earlier simulated Elekta 6 MV FFF accelerator. All lateral profiles in Ph1 showed a Lorentz force driven shift w.r.t. the B-field strength, presenting a steeper penumbra in the shift's direction. Depositions were shifted up to 0.3 cm for 5 T, showing a constant central axis plateau-dose or an increase by 2.3 % for small fields. Depth-dose curves in Ph1 showed a shift of the dose maximum towards the beam entrance direction for increasing B-field of up to 1.1 cm; the maximum dose was increased by 6.9 %. In Ph2, an asymmetric dose increase by up to 36.9 % was observed for 1.5 T at the water-air boundary, resulting from the electron return effect (ERE). In our scenario, B-field dependent dose shifts and local build-ups were observed, which consequently *Corresponding author: Sebastian Richter: University Hospital Tübingen, Department of Radiation Oncology, Section for Biomedical Physics, Hoppe-Seyler-Str. 3, Tübingen, Germany, Sebastian.Richter@med.uni-tuebingen.de Stefan Pojtinger, David Mönnich, Daniela Thorwarth: University Hospital Tübingen, Department of Radiation Oncology, Section for Biomedical Physics, Hoppe-Seyler-Str. 3, Tübingen, Germany Oliver S. Dohm: University Hospital Tübingen, Department of Radiation Oncology, Division for Medical Physics, Hoppe-Seyler- Str. 3, Tübingen, Germany affect the resulting dose distribution and need to be considered in magnetic resonance guided radiotherapy treatment planning. Keywords: radiotherapy, magnetic field, Monte Carlo simulation, dose deposition, ERE, linear accelerator, MRgRT, MR-Linac. 1 Introduction In treating cancer, radiotherapy (RT) is a well-established method among surgery or chemotherapy. Still one of the major issues in this field is positioning, in which faults can lead to unintentional radiation of healthy tissue such as organs at risk (OAR). Especially moving targets, e.g. tumours in the lung or pelvis, are clinically relevant examples to deal with during a RT treatment. A huge step in order to solve this problem could be a new technique called magnetic resonance guided radiotherapy (MRgRT). Integrating a linear accelerator and a MRI device, constructing a so called MR- Linac, might provide real-time imaging during radiotherapy treatments. Daily treatment adaptation, and consequently smaller margins, is a benefit as well as the possibility to incorporate functional MRI information, e.g. response monitoring. However, combining charged particles and a magnetic field (B-field) will lead to new challenges concerning Lorentz force driven effects: Trajectories of secondary particles will change, which results in different dose depositions than without B-field [1]. Especially a transition between materials of large density difference can lead to major changes resulting from the electron return effect (ERE) [2]. In our scenario of a perpendicular B-field, the ERE can be explained as follows:

2 282 In materials like water or tissue, the radius of the bent electron trajectories is rather large compared to the mean free path length (MFPL). This changes when the scattering electrons cross an interface to a low density medium, e.g. air or lung tissue. The MFPL will immediately increase and outperform the bending radius. Electron trajectories will be forced on a helical path and if the radius fits into the air cavity, the electrons re-enter the material of higher density and continue their scattering processes in opposite direction. This leads to a local build-up in the dose deposition right before the beam enters a cavity. This work investigated these changes affecting the dose deposition caused by a B-field transverse to the beam direction. Investigations were done by means of Monte Carlo simulations and with regard to a MR-Linac [4]. 2 Methods 2.1 Monte Carlo simulation Simulations were performed using the Monte Carlo code EGSnrc (2016) [3]. EGSnrc is an open source software toolkit that was developed from the Electron Gamma Shower (EGS) software package and is now supported by the National Research Council (nrc) Canada. Beams were based on a precalculated photon spectrum taken from an earlier simulated Elekta 6 MV FFF accelerator using the included user code BEAMnrc. Dose scoring was performed by DOSXYZnrc on the central beam axis. Two different phantom geometries were modelled and used for the investigation. The first phantom was a 20x20x20 cm³ water phantom (Ph1) with a cubic voxel size of 1 mm³. Ph1 irradiation was simulated for a 1x1 cm² (beam-s) and a 5x5 cm² (beam-l) beam, in order to estimate the Lorentz force driven shifts influencing the dose. The shift was calculated using equally distributed dose values greater than or equal to 95 % of the maximum dose and comparing the centres of these regions as well as the lateral difference for equal dose values. The second phantom was a 10x10x10 cm³ water-air phantom (Ph2) with a cm water-air-water cross section in beam entrance direction and a voxel size of mm. Ph2 irradiation was simulated for a 4x4 cm² (beam-m) beam to quantify the ERE. Phantom Ph2 is schematically displayed in Figure 1. To evoke these effects, magnetic fields of 0 T, 0.5 T, 1.5 T, 3 T, 5 T and 0.35 T (Ph2 only) were defined over the entire geometry. All beams were orientated in z-direction with their central axis at x = 10 cm for Ph1 and at x = 5 cm for Ph2, Figure 1: Schematic sketch of the water-air phantom Ph2 with beam (solid arrow) in z-direction. The total cubic dimension is given as 10x10x10 cm³, so L = 10 cm, including the cm water-air-water cross section in z-direction. aiming through the centre of the phantom. B-fields were aligned in y-direction. Dose depositions were scored for the given B-field values using a statistical accuracy below 1 %. To achieve this uncertainty, at least 10 9 histories were analysed. Differences in the lateral dose and depth-dose profiles were analysed for different B-field strengths. Plotted values were normalised to the maximum of the B = 0 T (B 0 ) data. 3 Results 3.1 Water phantom (Ph1) All lateral profiles in Ph1 were analysed in a depth of z = 5 cm. They showed a Lorentz force driven shift with respect to the B-field strength which is shown in Figure 2. A steeper penumbra in the shift's direction was noticed. The maximum shift of Beam-L was detected for 5 T and measured 0.3 cm. Beam-L s centre was maximally shifted 0.3 cm for 1.5 T. All lateral profiles of beam-l showed a constant central axis plateau-dose. For beam-s, the dose was increased by 2.3 % for 5 T with a shift of 0.3 cm (cf. Figure 3), influencing the depth-dose values scored on the central axis. All depth-dose curves in Ph1 showed a shift of the dose maximum towards the beam entrance direction for increasing B-field. Some example curves are plotted in Figure 4. A decrease of the build-up distance of up to 1.1 cm and 0.9 cm for beam-l and beam-s, respectively, for a 5 T B-field was

3 Figure 2: Lateral dose profiles of 5x5 cm² beam-l in Ph1. Values are normalised and scored in a depth of z = 5 cm. Figure 3: Lateral dose profiles of 1x1 cm² beam-s in Ph1. Values are normalised and scored in a depth of z = 5 cm. found. The maximum dose for beam-l was increased by 2.7 %, for beam-s by 6.9%. 3.2 Water-air phantom (Ph2) In Ph2, a local dose increase by up to 36.9 %, with respect to the B 0 maximum, was observed for 1.5 T at the water-air boundary in a depth of 3.9 cm. This was caused by the ERE and thus B-field dependent, as shown in Figure 5. For lower B-field strengths, the mean ionization in air was higher and we obtained local dose increases in water of 31.2 % and 17.7 % for 0.5 T and 0.35 T, respectively. Both beam entrances into water show similar behaviour like investigations in Ph1 have shown. Investigating the x-yplane of the dose increase due to ERE at its absolute maximum, in a depth of z = 3.90 cm, an asymmetric lateral dose deposition was noticed (cf. Figure 6). The asymmetry, also outside of the field, was stronger the lower the B-field was. We added an extra B-field strength value of B = 0.35 T to support this conclusion. 4 Discussion Results obtained in this simulation study of Ph1, concerning the lateral beam and depth-dose profiles, confirmed our expectations in terms of the Lorentz force and bent electron trajectories. The same applies to the steeper penumbra observed in Ph1. Those effects are well understood and described [1-3] and provided a basis to qualitatively validate our simulations. However, noticeable is the fact, that the observed difference between the shifts for B-field strengths of 1.5 T and greater is rather small compared to smaller values. As well an interesting rise of the shifted dose regarding beam-s may need further investigation. Ph2 let us observe the ERE and the local dose increase in the boundary water volume. Following the path of the beam in Ph2, the first beam entry in water is equal to the behaviour observed in Ph1. After a short interval ERE interferes. Due to different effective MFPL (fraction in beam direction) in water, dose peaks of different height can be seen and the effect is rising until electron radii become too small. For B = 5 T, fewest electrons reach the water surface and will undergo the ERE which leads to a smaller ionization in air as well as in water. A larger trajectory radius means more possibilities to ionize air as seen for 0 T < B < 1.5 T, or even 0 T where electrons just pass the air gap and start ionizing on the next entrance. At the second water entrance the build-up has to happen again but with an attenuated beam and, compared to B 0, attenuated electron fluence. Hence, B-field influenced curves appear shifted towards greater depth with respect to the B 0 curve. In the plane of the highest dose enhancement due to ERE, highly asymmetric profiles were observed, also applying to the out of field region. Main reasons for this phenomenon are, firstly, the number of electrons exiting the water surface due to a higher MFPL and, secondly, the changed Lorentz force driven trajectory radii in air. Consequently, this effect has to be considered when looking on curves representing simply the central beam axis, since, especially for small B- field values, there can be a massive difference caused by the steep in field gradient. The out of beam field dose observed for low B-fields might be clinically relevant in low field MR- Linacs.

4 284 Figure 4: Selection of depth-dose curves of beam-s and beam-l in Ph1. Values are normalised to the maximum of the B 0 curve, showing a similar trend for beam-l. Figure 5: Depth-dose curves of beam-m in Ph2 showing the ERE. Values are normalised to the maximum of the B 0 curve. In summary, our data for beam-l in Ph1 and the irradiated Ph2 data agree well and qualitatively with results of other groups that used the Monte Carlo code GEANT4 [1-3]. We intend to further investigate dose depositions under the influence of a B-field (MRgRT) using EGSnrc and compare our results to other Monte Carlo codes or even treatment planning systems. 5 Conclusion Both investigated phantom scenarios showed B-field dependent changes concerning the dose distribution. Those were qualitatively consistent to other Monte Carlo simulations. A Lorentz force driven shift and a shorter buildup distance as well as an increased maximum dose for beam- S was detected. We investigated the ERE on a water-air interface and showed a highly asymmetric lateral dose profile inside, but also outside of the radiation field. The investigated changes consequently affect the resulting dose distribution and need to be taken into account in MRgRT planning. Author s Statement Research funding: The authors acknowledge support by the state of Baden-Württemberg through bwhpc and the German Research Foundation (DFG) through grant no INST 39/963-1 FUGG. Conflict of interest: Authors state no conflict of interest. Informed consent: Informed consent is not applicable. Ethical approval: The conducted research is not related to either human or animals use. Figure 6: Lateral dose profiles of beam-m in Ph2. Values are normalised to the maximum of the B 0 curve, in a depth of z = 3.9 cm, where the maximum effect of the ERE can be seen in the central axis depth-dose profile. References [1] Raaymakers BW, Raaijmakers AJE, Kotte ANTJ, Jette D, Lagendijk JW. Integrating a MRI scanner with a 6 MV radiotherapy accelerator: dose deposition in a transverse magnetic field, Physics in Medicine and Biology 2004; 49(17):4109. [2] Raaijmakers AJE, Raaymakers BW, Lagendijk JW. Integrating a MRI scanner with a 6 MV radiotherapy accelerator: dose increase at tissue-air interfaces in a lateral magnetic field due to returning electrons, Physics in Medicine and Biology 2004; 50(7):1363 [3] O Brien DJ, Roberts DA, Ibbott GS, Sawakuchi GO. Reference dosimetry in magnetic fields: formalism and

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