- Email: [email protected]
Theory, simulation and experiments for precise deflection control of radiotherapy electron beams
Author’s Accepted Manuscript Theory, simulation and experiments for precise deflection control of radiotherapy electron beams R. Figueroa, J. Leiva, R. Moncada, L. Rojas, M. Santibáñez, M. Valente, J. Velásquez, H. Young, G. Zelada, R. Yáñez, Y. Guillen www.elsevier.com/locate/apradiso
PII: DOI: Reference:
S0969-8043(17)31410-0 https://doi.org/10.1016/j.apradiso.2018.03.004 ARI8287
To appear in: Applied Radiation and Isotopes Received date: 12 December 2017 Revised date: 28 February 2018 Accepted date: 6 March 2018 Cite this article as: R. Figueroa, J. Leiva, R. Moncada, L. Rojas, M. Santibáñez, M. Valente, J. Velásquez, H. Young, G. Zelada, R. Yáñez and Y. Guillen, Theory, simulation and experiments for precise deflection control of radiotherapy electron beams, Applied Radiation and Isotopes, https://doi.org/10.1016/j.apradiso.2018.03.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Theory, simulation and experiments for precise deflection control of radiotherapy electron beams R. Figueroa1.2*, J. Leiva1, R. Moncada1,3, L. Rojas1,2, M. Santibáñez1,2, M. Valente1,2,4, J. Velásquez5, H. Young1,3, G. Zelada6, R. Yáñez7, Y. Guillen7 *[email protected] 1
Centro de Física e Ingeniería en Medicina - CFIM, Universidad de La Frontera. (Av. Francisco Salazar 1145, Casilla 54-D, Temuco, Chile) 2 3 4
Departamento de Ciencias. Físicas, Universidad de la Frontera, Temuco, Chile.
Departamento de Ingeniería Eléctrica, Universidad de La Frontera, Temuco, Chile.
Instituto de Física Enrique Gaviola – CONICET & LIIFAMIRX, Universidad Nacional de Córdoba. (Av. M. Allende s/n, 5000, Córdoba, Argentina). 5 6
Instituto Oncológico del Sur- ICOS- Inmunomédica, Lago Puyehue 01745, Temuco, Chile.
Clínica Alemana de Santiago, Santiago de Chile, Av. Vitacura 5951, Vitacura, Santiago de Chile. 7
Hospital Base de Valdivia, Calle Simpson 850, Valdivia Chile.
Abstract Conventional radiotherapy is mainly applied by linear accelerators. Although linear accelerators provide dual (electron/photon) radiation beam modalities, both of them are intrinsically produced by a megavoltage electron current. Modern radiotherapy treatment techniques are based on suitable devices inserted or attached to conventional linear accelerators. Thus, precise control of delivered beam becomes a main key issue. This work presents an integral description of electron beam deflection control as required for novel radiotherapy technique based on convergent photon beam production. Theoretical and Monte Carlo approaches were initially used for designing and optimizing device´s components. Then, dedicated instrumentation was developed for experimental verification of electron beam deflection due to the designed magnets. Both Monte Carlo simulations and experimental results support the reliability of electrodynamics models used to predict megavoltage electron beam control.
1
Keywords: Electron beam deflection; Convergent photon beam; Monte Carlo simulation
1.- INTRODUCTION
As known, radiotherapy employs typically X-rays for the treatment of different diseases, like cancer. There exist both external and internal irradiation modalities. Teletherapy or external radiotherapy aims high-energy photons or electrons at the affected region (target volume) by means of dedicated machines, whereas internal radiotherapy involves infusing radioactive material inside the body. Regardless the irradiation modality, radiotherapy works by destroying cancer cells within the target volume. Nowadays, linear accelerator (linac) is the machine most commonly used for teletherapy. All linacs produce high energy electrons and photons (X-rays), which are then carefully aimed at the target volume according to oncologist’s specifications. From its origin in the ’50 decade medical linacs maintain their status as one of the most advanced radiation technologies available capable of delivering radiation with milimetric precision. The linac operates accelerating electrons (potentials around 6-25MV) through a linear tube to high speeds. Then, electrons smash into a metal target where they are stopped producing high energy X-rays. Typically, the acceleration cavity is mounted on a gantry which allows the linac to point at a specific point in space (isocenter) enabling a full circle rotation to reach lesions anywhere in or on the patient's body. All linacs are designed to generate inherently divergent radiation fields. Therefore, achieving high dose concentration in the tumor requires overlapping divergent fields arriving from different angles. Some modern computer-aided technological advances like tomotherapy (Mackie et al., 1993) and Cyber Knife (Bassalow and Rodebaugh, 2006) have shown high performance and promising capability for improving radiation therapy quality, specifically high dose concentration within the target volume However, these technologies are, comparatively, very expensive and they are still based on superposition of intrinsic divergent beams. In this context, it might be suitable to consider 2
alternatives for inherent convergent beams for treatment purposes (Figueroa and Valente, 2015). To this aim, precise control of the megavoltage electron beam becomes mandatory. The present work reports some of the more relevant issues regarding theoretical, Monte Carlo, and experimental approaches about high energy electron beam control for its potential use for modern radiotherapy applications, like convergent radiotherapy. A VARIAN 2100 linac was used for the experimental tests of the present work.
2.- MATERIALS AND METHODS As mentioned, theoretical, simulations, instrumentation and experiments were performed aimed at investigating and characterizing mechanisms for megavoltage electron beam deflection.
2.1.- Electron beam deflection According to relativistic formulation of Maxwell equations, the effect of interaction between charged particle in motion with external electromagnetic fields can be accurately described. Specifically, curvature radius R of a filiform electron beam interacting with an external magnetic field B with components perpendicular to electron velocity v can be assess by: (1) where γ is the relativistic term for Lorentz transformation (v= γc), me and qe are electron mass and charge, respectively; and c is speed of light in vacuum. Velocity module is directly obtained from kinetic energy, thus converting equation (1) in a direct relationship for evaluating curvature ratio in terms of electron beam energy.
2.2.- Bending magnet design and characterization Both electric and magnetic fields have been previously investigated as suitable options to control the deflection of the electron beams aimed at producing convergent photon beams 3
(Figueroa and Valente, 2015) establishing that required voltage and current are technically achievable. The present work focused on magnetic fields, produced by permanent magnets, as potential option to control megavoltage electron beams from a typical medical linac. The bending magnet where designed according to the magnetic circuit approach to obtain the desired flux density in the air-gap. Grade 52 Neodymium-iron-boron (NdFeB) magnets with different sizes where used to build de bending magnets. Iron core saturation and flux density distribution in the air-gap was verified by numerical simulation carried out with finite element analysis through FEMM 4.2 free software. After design and construction, bending magnets were carefully characterized in terms of spatial intensity distribution. Magnetic field strength measurements were performed with the AlphaLab GM2 Gaussmeter, whose dynamic range varies 0.0 to 1999.9.9 G in steps of 0.1 G and from 20000 to 29999 kG in steps of 1 G, also indicating corresponding polarity. The rigid transverse standard probe has the sensor to measure the field component parallel to the thin dimension of the probe (dimensions are 75×3.25×0.65 mm3), served to perform a scanning within the active area of the magnet, obtaining 49 points operating the device in DC mode and repeating several times each measurement aimed at accounting for statistical fluctuations.
2.3.- Instrumentation design for experimental measurements A dedicated device was designed and constructed aimed at experimentally testing the performance of the designed magnets for deflection of electron beam produced by a typical medical linac. The device consisted, mainly, on a hermetic transparent box containing the mending magnets and EBT3 radiochromic films as radiation detectors aimed at recording beam impact position at different positions. Air is extracted by external pump in order to avoid spurious interactions. According to specific film location, irradiations were performed delivering 400 to 1000 MU. The methodology used for designing the device for measurements of medical linac electron beam deflection by permanent magnets accounted for dimensions predicted by theoretical models and actual dimensions of manufactured bending magnets suggesting dimensions around 320×120×100mm3 15mm thick 4
transparent acrylic box. All the designs of the parts and components for the deflection device were designed by CATIA CAD software V5, which in turn allows the production plans of these components to be generated for later manufacture through the CNC machining center. Figure 1 reports different views extracted from the CAD technical design along with corresponding photograph.
Figure 1.- Constructed device for experimental performance testing.
The instrumentation in Figure 1 was designed with the aim of satisfying specific requirements, including: Resisting low internal pressure (less than 10-3 atm.), allowing bending magnet motion accurately along pre-defined axes and, of course, the insertion of EBT3 GafChromic® films at different locations in order to get independent measurements of electron beam, impact position aimed at assessing effective angular deflections. Electron beam enters the deflection device crossing the corresponding 3mm diameter collimator, thus ensuring a filiform beam inside.
2.4.- Monte Carlo simulations Monte Carlo techniques have become one of the more used and accurate techniques to model different physical processes, including radiation-matter interaction in the medical physics framework. (Rogers, 2006). Nowadays, there exists a broad range of available Monte Carlo codes capable of simulation coupled radiation transport within complex media. However, not necessary all of those available codes are capable of accurate handle of radiation transport with external user-defined electromagnetic fields. In this context, the FLUKA code (Battistoni et al., 2006) has largely demonstrated to provide reliable and precise description of radiation transport within complex media accounting also for external user-defined electromagnetic fields. For comparisons purposes, the PENELOPE (Salvat et al., 2014) Monte Carlo code was also used to model electron beam degradation inside VARIAN 2100 head. 5
Dedicated adaptations were carried out for the purposes of the present work aimed at defining the corresponding magnetic field distribution in specific magfld FLUKA module, which was further linked by compilation with the corresponding input. Information about VARIAN 2100 linac was used in order to define the corresponding simulation geometry in FLUKA, as reported in Figure 2. The deflection device is adapted to linac head using the rails for portable electron applicators.
Figure 2.- Geometry for FLUKA Monte Carlo simulation showing relevant parts of VARIAN 2100 head and the deflection device adapted to linac head. Central portion of accelerator´s parts (from right to left): tungsten target (gray disk), air gap (gray background), first tantalum flattening filter (yellow disk), air gap (gray background), second tantalum flattening filter (yellow disk), air gap (gray background), Kapton walls of ionization chamber (cyan disks) and air gap (gray background). Central portion of convergent beam prototype (from right to left): shielding (brown), air gap where magnet B1 is located (gray background), acrylic walls (white disks), air gap (gray background) and EBT radiochromic films (green disks).
Due to the specific requirements for the present work, only the central region of the linac head needs to be simulated. Thus, primary/secondary collimation systems and other devices could be neglected. The relevant issue regards the proper modeling of the central (axial) portion of the electron beam, which reaches the deflection device after emerging the linac head. As mentioned, magnetic fields were defined in the corresponding module introduced as arrays of different intensities, according to experimental characterization of the bending magnets. Materials and dimensions used for the Monte Carlo simulations were exactly the same as experimental configurations. Dedicated tallies were defined in the FLUKA input aimed at evaluating spatial distributions of photon and electron fluence and energy deposited in the films.
6
3.- RESULTS As first step, bending magnets were constructed according to technical specifications obtained from simulations of magnetic field distributions corresponding to two different design models: the C-arm and the 8-shaped, as shown in Figure 3.
Figure 3.- C-arm (left) and 8-shaped (right) designs for the bending magnets as obtained from design software showing corresponding fields.
Monte Carlo simulations for the electron spectrum entering the deflection device located immediately after linac head are reported in Figure 4.
Figure 4.- Electron spectrum entering linac head coming from waveguide (black squares) and emerging linac head calculated by FLUKA (red triangles) and PENELOPE (blue circles) for the 6 MeV mode. Uncertainties correspond to 1 standard deviation.
Aimed to use realistic data for the input spectrum, which stands for the waveguide emission, a Gaussian distribution centered at nominal energy (‹E›=6.0 MeV) with FWHM=0.1 MeV was incorporated. Emerging spectra present
central
energy
‹E› and corresponding FWHM of:
(‹E›=(5.80±0.05) MeV, FWHM=0.15 MeV) and (‹E›=(5.75±0.05) MeV, FWHM=0.10 MeV) for FLUKA and PENELOPE, respectively.
Figure 5.- Characterization of bending magnets: C-arm (left) and 8-shaped (right).
7
Characterization of magnetic field intensity for the different bending magnets confirmed very good uniformity across active magnetic zone (32×32mm2 for the C-arc and 35×35mm2 for the 8-shaped magnet), as reported in Figure 5. Finally, irradiations were performed and radiochromic films registered the corresponding opacity level, which was further readout using dedicated home-made visible light transmission imaging device (Valente, 2007).
Figure 6.- Experimental setup: views (top), positioning (bottom left) and images of irradiated film (bottom right).
As shown in Figure 7, Monte Carlo simulations provided electron fluence distributions for the incident (+z direction) electron beam interacting with magnetic fields B1 and B2 that are used for the first and second deflection stage, respectively.
Figure 7.- Electron fluence obtained from FLUKA simulations highlighting the effect of different magnetic fields: 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6T, from top left to bottom right, respectively. Statistical uncertainties are less than 2%. Showed region of interest corresponds to a 100cm×100cm area in YZ plane. Electron beam enters at (x,y,z)=(50cm,50cm,0cm) and encounters W target located at (x,y,z)=(50cm,50cm,10cm), where fluence starts to be clearly sparser.
Figure 8 reports the energy distribution in radiochromic films obtained by FLUKA Monte Carlo simulations from which effective deflection angles were assessed.
Figure 8.- Energy distribution in film 1(left) and film 2 (right) obtained from FLUKA Monte Carlo simulations for the set composed by C-arc and 8-shaped bending magnets.
8
Looking for a wide description, FLUKA Monte Carlo simulations were performed for different parameters combinations, modifying magnetic field intensity and dimensions of active are, obtaining results as those reported in Figure 9.
Figure 9.- Effective deflection angle for different magnetic field intensities for a 30×30mm2 active area obtained by image processing of film 1 (blue) and film 2 (red).
Table 1 summarizes the corresponding estimations for effective deflection angle obtained by theoretical, Monte Carlo and experimental approaches.
Table 1.- Effective deflection angle for the bending magnets. Bending Magnet Theory (peak) Theory (spectrum) Monte Carlo Experiment C-arc
(25±2)°
(29±3)°
(31±3)°
(33±4)°
8-shaped
(30±2)°
(34±3)°
(34±3)°
(34±4)°
4.- DISCUSSION The design options considered for the bending magnets (C-arm and 8-shaped) were proposed aimed at simplifying the process. The obtained results from technical design, construction, characterization and operating performance support this proposal as reliable options. Electron fluence entering the experimental device (acrylic box) stands as an essential requirement for this work. However, direct measurements are not possible, so accurate Monte Carlo simulations performed by means of two independent validated codes were used as input data for theoretical approaches and device design. Actually, the
9
excellent agreement between FLUKA and PENELOPE for the electron spectrum emerging the VARIAN 2100 linac head supports the reliability of this quantity to be further used. Characterization of bending magnet magnetic fields by direct measurements was successfully performed confirming that constructed magnet present, in fact, the expected uniformity within active area. However, magnetic field intensity was somewhat lower than nominal intensity reported by Neodymium-iron-boron manufacturer. Monte Carlo simulations demonstrated to be a practical and reliable tool to characterize spatial distribution of electron fluence according to different combinations of magnetic fields. In fact, final configuration was optimized in terms of Monte Carlo predictions before definitive experimental tests. Although requiring a week, in average, FLUKA Monte Carlo simulations coupling radiation-matter interactions and external field effects offered a suitable and accurate description of the whole process. Some tests, not here reported, pointed out that simulating actual magnetic field distribution or averaging magnetic field along electron path produced comparable effects in terms of effective deflection angles within the energy range here investigated.
5.- CONCLUSIONS An original task for characterizing theoretically, experimentally and by means of simulations, the deflection of megavoltage electron beams from medical linac was presented. Two alternatives for bending magnet (C-arc and 8-shaped designs) were designed, constructed and completely characterized regarding their performance for controlling 6MeV nominal electron beam from a typical medical linac. Theoretical model based on relativistic formulation of Maxwell equations provided reliable description for the studied systems, while Monte Carlo simulations demonstrated to be a high appreciated tool for a complete description of the whole physical process including electron beam transport in linac head and further interactions with external magnetic fields. 10
Finally, experimental measurements confirmed also the suitability of the proposed method showing quite non-distinguishable results among theory, Monte Carlo and experiments. These results may be used for further developments in the novel field of convergent beam radiotherapy (Figueroa and Valente, 2017).
Acknowledgments This study was financed by FONDEF (Chile) project ID15i10337. Authors are grateful to radiotherapy unit Icos-Inmunomedica of Temuco, radiotherapy center Clínica Alemana de Santiago of Chile and radiotherapy department Hospital Base de Valdivia.
REFERENCES Bassalow, R., and Rodebaugh. R., 2006. Medical Physics. 33, 2100. Battistoni, G., Muraro, S., Sala, P.R., Cerutti, F., Ferrari, A., Roesler, S., Fassò, A., Ranft, J., Albrow, M., 2006. AIP. Conf. Proc. 896, 3-49. Figueroa, R. and Valente, M., 2015. Physics in Medicine and Biology. 60, 7191-7206. Figueroa, R., and Valente. M., 2017. Convergent photon and electron beam generator device. US Patent US 9583302 B2. Mackie, T.R., Holmes, T., Swerdloff, S., Reckwerdt, P., Deasy, J.O., Yang, J., Paliwal, B., Kinsella, T., 1993. Medical Physics. 20, 1709-1719. Rogers, D.W., 2006. Physics in Medicine and Biology, 51, R287-301. Salvat, F., Fernández-Varea, J.M., Sempau, J., PENELOPE-2014: A Code System for Monte Carlo Simulation of Electron and Photon Transport. France, NEA Valente, M., 2007. Fricke gel dosimetry for 3D imaging of absorbed dose in radiotherapy. PhD Dissertation University of Milan. Italy.
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FIGURES
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Figure 3.-
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Figure 4.-
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Figure 5.-
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Figure 6.-
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Figure 7.-
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Figure 8.-
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Figure 9.-
Highlights 1. Novel method for high energy electron beam control is presented and investigated. 2. Deflection systems based on permanent magnets demonstrated promising capability. 3. Experiments, theory and Monte Carlo characterized radiotherapy beam deflection. 4. Electron beam from clinical linear accelerators can be suitably controlled. 5. Very good agreement was found between theory, simulation and experiments.
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PII: DOI: Reference:
S0969-8043(17)31410-0 https://doi.org/10.1016/j.apradiso.2018.03.004 ARI8287
To appear in: Applied Radiation and Isotopes Received date: 12 December 2017 Revised date: 28 February 2018 Accepted date: 6 March 2018 Cite this article as: R. Figueroa, J. Leiva, R. Moncada, L. Rojas, M. Santibáñez, M. Valente, J. Velásquez, H. Young, G. Zelada, R. Yáñez and Y. Guillen, Theory, simulation and experiments for precise deflection control of radiotherapy electron beams, Applied Radiation and Isotopes, https://doi.org/10.1016/j.apradiso.2018.03.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Theory, simulation and experiments for precise deflection control of radiotherapy electron beams R. Figueroa1.2*, J. Leiva1, R. Moncada1,3, L. Rojas1,2, M. Santibáñez1,2, M. Valente1,2,4, J. Velásquez5, H. Young1,3, G. Zelada6, R. Yáñez7, Y. Guillen7 *[email protected] 1
Centro de Física e Ingeniería en Medicina - CFIM, Universidad de La Frontera. (Av. Francisco Salazar 1145, Casilla 54-D, Temuco, Chile) 2 3 4
Departamento de Ciencias. Físicas, Universidad de la Frontera, Temuco, Chile.
Departamento de Ingeniería Eléctrica, Universidad de La Frontera, Temuco, Chile.
Instituto de Física Enrique Gaviola – CONICET & LIIFAMIRX, Universidad Nacional de Córdoba. (Av. M. Allende s/n, 5000, Córdoba, Argentina). 5 6
Instituto Oncológico del Sur- ICOS- Inmunomédica, Lago Puyehue 01745, Temuco, Chile.
Clínica Alemana de Santiago, Santiago de Chile, Av. Vitacura 5951, Vitacura, Santiago de Chile. 7
Hospital Base de Valdivia, Calle Simpson 850, Valdivia Chile.
Abstract Conventional radiotherapy is mainly applied by linear accelerators. Although linear accelerators provide dual (electron/photon) radiation beam modalities, both of them are intrinsically produced by a megavoltage electron current. Modern radiotherapy treatment techniques are based on suitable devices inserted or attached to conventional linear accelerators. Thus, precise control of delivered beam becomes a main key issue. This work presents an integral description of electron beam deflection control as required for novel radiotherapy technique based on convergent photon beam production. Theoretical and Monte Carlo approaches were initially used for designing and optimizing device´s components. Then, dedicated instrumentation was developed for experimental verification of electron beam deflection due to the designed magnets. Both Monte Carlo simulations and experimental results support the reliability of electrodynamics models used to predict megavoltage electron beam control.
1
Keywords: Electron beam deflection; Convergent photon beam; Monte Carlo simulation
1.- INTRODUCTION
As known, radiotherapy employs typically X-rays for the treatment of different diseases, like cancer. There exist both external and internal irradiation modalities. Teletherapy or external radiotherapy aims high-energy photons or electrons at the affected region (target volume) by means of dedicated machines, whereas internal radiotherapy involves infusing radioactive material inside the body. Regardless the irradiation modality, radiotherapy works by destroying cancer cells within the target volume. Nowadays, linear accelerator (linac) is the machine most commonly used for teletherapy. All linacs produce high energy electrons and photons (X-rays), which are then carefully aimed at the target volume according to oncologist’s specifications. From its origin in the ’50 decade medical linacs maintain their status as one of the most advanced radiation technologies available capable of delivering radiation with milimetric precision. The linac operates accelerating electrons (potentials around 6-25MV) through a linear tube to high speeds. Then, electrons smash into a metal target where they are stopped producing high energy X-rays. Typically, the acceleration cavity is mounted on a gantry which allows the linac to point at a specific point in space (isocenter) enabling a full circle rotation to reach lesions anywhere in or on the patient's body. All linacs are designed to generate inherently divergent radiation fields. Therefore, achieving high dose concentration in the tumor requires overlapping divergent fields arriving from different angles. Some modern computer-aided technological advances like tomotherapy (Mackie et al., 1993) and Cyber Knife (Bassalow and Rodebaugh, 2006) have shown high performance and promising capability for improving radiation therapy quality, specifically high dose concentration within the target volume However, these technologies are, comparatively, very expensive and they are still based on superposition of intrinsic divergent beams. In this context, it might be suitable to consider 2
alternatives for inherent convergent beams for treatment purposes (Figueroa and Valente, 2015). To this aim, precise control of the megavoltage electron beam becomes mandatory. The present work reports some of the more relevant issues regarding theoretical, Monte Carlo, and experimental approaches about high energy electron beam control for its potential use for modern radiotherapy applications, like convergent radiotherapy. A VARIAN 2100 linac was used for the experimental tests of the present work.
2.- MATERIALS AND METHODS As mentioned, theoretical, simulations, instrumentation and experiments were performed aimed at investigating and characterizing mechanisms for megavoltage electron beam deflection.
2.1.- Electron beam deflection According to relativistic formulation of Maxwell equations, the effect of interaction between charged particle in motion with external electromagnetic fields can be accurately described. Specifically, curvature radius R of a filiform electron beam interacting with an external magnetic field B with components perpendicular to electron velocity v can be assess by: (1) where γ is the relativistic term for Lorentz transformation (v= γc), me and qe are electron mass and charge, respectively; and c is speed of light in vacuum. Velocity module is directly obtained from kinetic energy, thus converting equation (1) in a direct relationship for evaluating curvature ratio in terms of electron beam energy.
2.2.- Bending magnet design and characterization Both electric and magnetic fields have been previously investigated as suitable options to control the deflection of the electron beams aimed at producing convergent photon beams 3
(Figueroa and Valente, 2015) establishing that required voltage and current are technically achievable. The present work focused on magnetic fields, produced by permanent magnets, as potential option to control megavoltage electron beams from a typical medical linac. The bending magnet where designed according to the magnetic circuit approach to obtain the desired flux density in the air-gap. Grade 52 Neodymium-iron-boron (NdFeB) magnets with different sizes where used to build de bending magnets. Iron core saturation and flux density distribution in the air-gap was verified by numerical simulation carried out with finite element analysis through FEMM 4.2 free software. After design and construction, bending magnets were carefully characterized in terms of spatial intensity distribution. Magnetic field strength measurements were performed with the AlphaLab GM2 Gaussmeter, whose dynamic range varies 0.0 to 1999.9.9 G in steps of 0.1 G and from 20000 to 29999 kG in steps of 1 G, also indicating corresponding polarity. The rigid transverse standard probe has the sensor to measure the field component parallel to the thin dimension of the probe (dimensions are 75×3.25×0.65 mm3), served to perform a scanning within the active area of the magnet, obtaining 49 points operating the device in DC mode and repeating several times each measurement aimed at accounting for statistical fluctuations.
2.3.- Instrumentation design for experimental measurements A dedicated device was designed and constructed aimed at experimentally testing the performance of the designed magnets for deflection of electron beam produced by a typical medical linac. The device consisted, mainly, on a hermetic transparent box containing the mending magnets and EBT3 radiochromic films as radiation detectors aimed at recording beam impact position at different positions. Air is extracted by external pump in order to avoid spurious interactions. According to specific film location, irradiations were performed delivering 400 to 1000 MU. The methodology used for designing the device for measurements of medical linac electron beam deflection by permanent magnets accounted for dimensions predicted by theoretical models and actual dimensions of manufactured bending magnets suggesting dimensions around 320×120×100mm3 15mm thick 4
transparent acrylic box. All the designs of the parts and components for the deflection device were designed by CATIA CAD software V5, which in turn allows the production plans of these components to be generated for later manufacture through the CNC machining center. Figure 1 reports different views extracted from the CAD technical design along with corresponding photograph.
Figure 1.- Constructed device for experimental performance testing.
The instrumentation in Figure 1 was designed with the aim of satisfying specific requirements, including: Resisting low internal pressure (less than 10-3 atm.), allowing bending magnet motion accurately along pre-defined axes and, of course, the insertion of EBT3 GafChromic® films at different locations in order to get independent measurements of electron beam, impact position aimed at assessing effective angular deflections. Electron beam enters the deflection device crossing the corresponding 3mm diameter collimator, thus ensuring a filiform beam inside.
2.4.- Monte Carlo simulations Monte Carlo techniques have become one of the more used and accurate techniques to model different physical processes, including radiation-matter interaction in the medical physics framework. (Rogers, 2006). Nowadays, there exists a broad range of available Monte Carlo codes capable of simulation coupled radiation transport within complex media. However, not necessary all of those available codes are capable of accurate handle of radiation transport with external user-defined electromagnetic fields. In this context, the FLUKA code (Battistoni et al., 2006) has largely demonstrated to provide reliable and precise description of radiation transport within complex media accounting also for external user-defined electromagnetic fields. For comparisons purposes, the PENELOPE (Salvat et al., 2014) Monte Carlo code was also used to model electron beam degradation inside VARIAN 2100 head. 5
Dedicated adaptations were carried out for the purposes of the present work aimed at defining the corresponding magnetic field distribution in specific magfld FLUKA module, which was further linked by compilation with the corresponding input. Information about VARIAN 2100 linac was used in order to define the corresponding simulation geometry in FLUKA, as reported in Figure 2. The deflection device is adapted to linac head using the rails for portable electron applicators.
Figure 2.- Geometry for FLUKA Monte Carlo simulation showing relevant parts of VARIAN 2100 head and the deflection device adapted to linac head. Central portion of accelerator´s parts (from right to left): tungsten target (gray disk), air gap (gray background), first tantalum flattening filter (yellow disk), air gap (gray background), second tantalum flattening filter (yellow disk), air gap (gray background), Kapton walls of ionization chamber (cyan disks) and air gap (gray background). Central portion of convergent beam prototype (from right to left): shielding (brown), air gap where magnet B1 is located (gray background), acrylic walls (white disks), air gap (gray background) and EBT radiochromic films (green disks).
Due to the specific requirements for the present work, only the central region of the linac head needs to be simulated. Thus, primary/secondary collimation systems and other devices could be neglected. The relevant issue regards the proper modeling of the central (axial) portion of the electron beam, which reaches the deflection device after emerging the linac head. As mentioned, magnetic fields were defined in the corresponding module introduced as arrays of different intensities, according to experimental characterization of the bending magnets. Materials and dimensions used for the Monte Carlo simulations were exactly the same as experimental configurations. Dedicated tallies were defined in the FLUKA input aimed at evaluating spatial distributions of photon and electron fluence and energy deposited in the films.
6
3.- RESULTS As first step, bending magnets were constructed according to technical specifications obtained from simulations of magnetic field distributions corresponding to two different design models: the C-arm and the 8-shaped, as shown in Figure 3.
Figure 3.- C-arm (left) and 8-shaped (right) designs for the bending magnets as obtained from design software showing corresponding fields.
Monte Carlo simulations for the electron spectrum entering the deflection device located immediately after linac head are reported in Figure 4.
Figure 4.- Electron spectrum entering linac head coming from waveguide (black squares) and emerging linac head calculated by FLUKA (red triangles) and PENELOPE (blue circles) for the 6 MeV mode. Uncertainties correspond to 1 standard deviation.
Aimed to use realistic data for the input spectrum, which stands for the waveguide emission, a Gaussian distribution centered at nominal energy (‹E›=6.0 MeV) with FWHM=0.1 MeV was incorporated. Emerging spectra present
central
energy
‹E› and corresponding FWHM of:
(‹E›=(5.80±0.05) MeV, FWHM=0.15 MeV) and (‹E›=(5.75±0.05) MeV, FWHM=0.10 MeV) for FLUKA and PENELOPE, respectively.
Figure 5.- Characterization of bending magnets: C-arm (left) and 8-shaped (right).
7
Characterization of magnetic field intensity for the different bending magnets confirmed very good uniformity across active magnetic zone (32×32mm2 for the C-arc and 35×35mm2 for the 8-shaped magnet), as reported in Figure 5. Finally, irradiations were performed and radiochromic films registered the corresponding opacity level, which was further readout using dedicated home-made visible light transmission imaging device (Valente, 2007).
Figure 6.- Experimental setup: views (top), positioning (bottom left) and images of irradiated film (bottom right).
As shown in Figure 7, Monte Carlo simulations provided electron fluence distributions for the incident (+z direction) electron beam interacting with magnetic fields B1 and B2 that are used for the first and second deflection stage, respectively.
Figure 7.- Electron fluence obtained from FLUKA simulations highlighting the effect of different magnetic fields: 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6T, from top left to bottom right, respectively. Statistical uncertainties are less than 2%. Showed region of interest corresponds to a 100cm×100cm area in YZ plane. Electron beam enters at (x,y,z)=(50cm,50cm,0cm) and encounters W target located at (x,y,z)=(50cm,50cm,10cm), where fluence starts to be clearly sparser.
Figure 8 reports the energy distribution in radiochromic films obtained by FLUKA Monte Carlo simulations from which effective deflection angles were assessed.
Figure 8.- Energy distribution in film 1(left) and film 2 (right) obtained from FLUKA Monte Carlo simulations for the set composed by C-arc and 8-shaped bending magnets.
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Looking for a wide description, FLUKA Monte Carlo simulations were performed for different parameters combinations, modifying magnetic field intensity and dimensions of active are, obtaining results as those reported in Figure 9.
Figure 9.- Effective deflection angle for different magnetic field intensities for a 30×30mm2 active area obtained by image processing of film 1 (blue) and film 2 (red).
Table 1 summarizes the corresponding estimations for effective deflection angle obtained by theoretical, Monte Carlo and experimental approaches.
Table 1.- Effective deflection angle for the bending magnets. Bending Magnet Theory (peak) Theory (spectrum) Monte Carlo Experiment C-arc
(25±2)°
(29±3)°
(31±3)°
(33±4)°
8-shaped
(30±2)°
(34±3)°
(34±3)°
(34±4)°
4.- DISCUSSION The design options considered for the bending magnets (C-arm and 8-shaped) were proposed aimed at simplifying the process. The obtained results from technical design, construction, characterization and operating performance support this proposal as reliable options. Electron fluence entering the experimental device (acrylic box) stands as an essential requirement for this work. However, direct measurements are not possible, so accurate Monte Carlo simulations performed by means of two independent validated codes were used as input data for theoretical approaches and device design. Actually, the
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excellent agreement between FLUKA and PENELOPE for the electron spectrum emerging the VARIAN 2100 linac head supports the reliability of this quantity to be further used. Characterization of bending magnet magnetic fields by direct measurements was successfully performed confirming that constructed magnet present, in fact, the expected uniformity within active area. However, magnetic field intensity was somewhat lower than nominal intensity reported by Neodymium-iron-boron manufacturer. Monte Carlo simulations demonstrated to be a practical and reliable tool to characterize spatial distribution of electron fluence according to different combinations of magnetic fields. In fact, final configuration was optimized in terms of Monte Carlo predictions before definitive experimental tests. Although requiring a week, in average, FLUKA Monte Carlo simulations coupling radiation-matter interactions and external field effects offered a suitable and accurate description of the whole process. Some tests, not here reported, pointed out that simulating actual magnetic field distribution or averaging magnetic field along electron path produced comparable effects in terms of effective deflection angles within the energy range here investigated.
5.- CONCLUSIONS An original task for characterizing theoretically, experimentally and by means of simulations, the deflection of megavoltage electron beams from medical linac was presented. Two alternatives for bending magnet (C-arc and 8-shaped designs) were designed, constructed and completely characterized regarding their performance for controlling 6MeV nominal electron beam from a typical medical linac. Theoretical model based on relativistic formulation of Maxwell equations provided reliable description for the studied systems, while Monte Carlo simulations demonstrated to be a high appreciated tool for a complete description of the whole physical process including electron beam transport in linac head and further interactions with external magnetic fields. 10
Finally, experimental measurements confirmed also the suitability of the proposed method showing quite non-distinguishable results among theory, Monte Carlo and experiments. These results may be used for further developments in the novel field of convergent beam radiotherapy (Figueroa and Valente, 2017).
Acknowledgments This study was financed by FONDEF (Chile) project ID15i10337. Authors are grateful to radiotherapy unit Icos-Inmunomedica of Temuco, radiotherapy center Clínica Alemana de Santiago of Chile and radiotherapy department Hospital Base de Valdivia.
REFERENCES Bassalow, R., and Rodebaugh. R., 2006. Medical Physics. 33, 2100. Battistoni, G., Muraro, S., Sala, P.R., Cerutti, F., Ferrari, A., Roesler, S., Fassò, A., Ranft, J., Albrow, M., 2006. AIP. Conf. Proc. 896, 3-49. Figueroa, R. and Valente, M., 2015. Physics in Medicine and Biology. 60, 7191-7206. Figueroa, R., and Valente. M., 2017. Convergent photon and electron beam generator device. US Patent US 9583302 B2. Mackie, T.R., Holmes, T., Swerdloff, S., Reckwerdt, P., Deasy, J.O., Yang, J., Paliwal, B., Kinsella, T., 1993. Medical Physics. 20, 1709-1719. Rogers, D.W., 2006. Physics in Medicine and Biology, 51, R287-301. Salvat, F., Fernández-Varea, J.M., Sempau, J., PENELOPE-2014: A Code System for Monte Carlo Simulation of Electron and Photon Transport. France, NEA Valente, M., 2007. Fricke gel dosimetry for 3D imaging of absorbed dose in radiotherapy. PhD Dissertation University of Milan. Italy.
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Figure 9.-
Highlights 1. Novel method for high energy electron beam control is presented and investigated. 2. Deflection systems based on permanent magnets demonstrated promising capability. 3. Experiments, theory and Monte Carlo characterized radiotherapy beam deflection. 4. Electron beam from clinical linear accelerators can be suitably controlled. 5. Very good agreement was found between theory, simulation and experiments.
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