Dose enhancement from electron beam simulations in a linac-MRI with a longitudinal magnetic field N Berg1, A Bielajew1, T Zhang2 and N Tyagi3 of Michigan, Ann Arbor, 2William Beaumont Hospital, 3Memorial Sloan-Kettering Cancer Center
Purpose and Objective
The above equation, using a a collimator to surface distance of 50 cm, resulted in required magnetic fields of 0.13, 0.2, and 0.26 T for half rotations and 0.4, 0.59, and 0.79 T for 3/2 rotations for 6, 9 and 12 MeV electron beams respectively.
Rela%ve'Dose'
= 0 rotations
= 1/2 rotations
8"
8"
7"
7"
5x5 cm 6 MeV
6" 5" 4" 3" 2" 0" 1"
2"
3"
TEMPLATE DESIGN © 2008
www.PosterPresentations.com
4" 2"
0"
1"
2"
7"
7"
5"
Rela%ve'Dose'
5x5 cm 9 MeV
6" 4" 3" 2"
1.6" 1.4"
5x5 cm 6 MeV
1.2" 1" 0.8" 0.6" 0.4" 0.2" 1"
2"
3"
2"
5"
0"
6"
1"
2"
5" 4"
Rela%ve'Dose'
Rela%ve'Dose'
3"
4"
5"
10x10 cm 6 MeV
3" 2"
10x10 cm 12 MeV
6" 5" 4" 3" 2" 0"
4"
6"
8"
0"
2"
4"
6"
1"
1"
2"
3"
The beam narrowing effects (figure 6) of the magnetic fields reduced the surface widths, for a 12 MeV beam, by 44% and 52%, the half electron range (0.5r) widths by 49% and 56%, and the 0.75r widths by 48% and 56% for one half and 3/2 rotations, respectively.
0.6" 0.4"
10x10 cm 9 MeV
1.2" 1"
1/2 rotations
0.8" 0.6" 0.4" 0"
0" 0"
1"
2"
3"
4"
5"
0"
6"
1"
2"
1.6"
1.4"
1.4"
1"
Rela%ve'Dose'
5x5 cm 12 MeV
1.2"
3"
4"
5"
6"
Depth'(cm)'
Depth'(cm)' 1.6"
0.8" 0.6" 0.4"
1"
3/2 rotations
0.8" 0.6" 0.4" 0"
0" 0"
2"
4"
Depth'(cm)'
6"
8"
0"
2"
4"
6"
8"
Depth'(cm)'
Figure 4. Peak dose enhancement is seen for 6, 9, and 12 MeV when beams are subjected to induced rotations.
2M. A.
Earl and L. Ma, “Depth dose enhancement of electron beams subject to external uniform longitudinal magnetic fields: A Monte Carlo study,” Med. Phys. 29, 484-491 (2002) Contact
10x10 cm 12 MeV
1.2"
0.2"
0.2"
References
Kirkby, B. Murray, S. Rathee, and B. G. Fallone, “Lung dosimetry in a linac-MRI radiotherapy unit with a longitudinal magnetic field,” Med. Phys. 37, 4732-4722 (2010)
4"
0.2"
0.2"
-Beaumont Hospital for the financial support during the summer of 2012 -Josep Sempau for the penEasy package and the assistance in implementing magnetic field routines into PENELOPE
0 rotations
Depth'(cm)' 1.4"
0.8"
Acknowledgements
1C. 0"
Rela%ve'Dose'
1.2"
8"
Depth'(cm)'
0.4"
1.6"
5x5 cm 9 MeV
The calculated B fields result in the redirecting of diverging electrons towards the central axis, while also shifting the electrons closer to the central axis when they strike the front face of the phantom. The proposed RBP design of the linac-MRI using an electron beam provides both the benefits of the localized dose of a pseudo-Bragg peak and the reduced width and penumbra of the electron beam without the use of an applicator. Moreover, future investigation of higher energy electron beams and even stronger magnetic fields, which produce 5/2 rotations, may result increased dose enhancement factors and width and penumbra narrowing.
1" 2"
0.6"
Depth'(cm)' 1.4"
6"
Depth'(cm)' 7"
5x5 cm 12 MeV
6"
Figure 5. Surface dose increases varied from factors of 3 to 5.
0.8"
4"
1.6"
Rela%ve'Dose'
4"
Depth'(cm)'
= 3/2 rotations
1"
3"
0" 0"
Rela%ve'Dose'
3"
0"
1.2"
4"
0.2"
0"
e ω cycl Bd = 2πγc
2"
1"
= 1/2 rotations Rela%ve'Dose'
Rela%ve'Dose'
= 0 rotations
1"
7"
Dose enhancement factors, with respect to surface dose, of 39% and 48% for 6 MeV, 34% and 48% for 9 MeV, and 34% and 45% for 12 MeV beams were seen under one half and 3/2 induced rotations, as seen in figure 4.
1.4"
5"
Depth'(cm)'
0"
1.6"
10x10 cm 9 MeV
6"
0" 0"
Results
4"
1"
0"
Figure 3. Illustration of the spiraling effect of the magnetic fields when 0, 1/2, and 3/2 rotations are induced.
3"
Depth'(cm)' 8"
8"
Figure 2. Simulated geometry which has the magnetic field extending through the water phantom.
Conclusions
3"
Depth'(cm)'
Methods and Materials
where wecycl is 1.758 82x1011 rad s-1T-1, B is the magnetic field in T, d is the collimator to surface distance in cm, γ = 1+T/(mc2),€and c is the speed of light. Figure 3 illustrates electron tracts for 0, 1/2, and 3/2 induced rotations. Specific combinations of these variables were shown to achieve as much as 70% enhancement in the peak dose relative to the surface dose2.
5"
4"
The spiraling of the electron beam due to the Lorentz force also dramatically reduces the penumbra of the beam by 31%-50%. The corresponding penumbra reduction for a 12 MeV beam for one half and 3/2 rotations were 1.6 cm and 2.2 cm respectively at half the electron range depth.
10x10 cm 6 MeV
6"
0" 0"
Figure 1. RBP geometry has the magnetic field parallel to the central axis of the electron beam. Figure reproduced from Kirkby et. al1.
N rot
= 3/2 rotations
1"
1"
1"
Monte Carlo simulations in the presence of magnetic fields were performed using PENELOPE code implemented with tracking algorithms specifying for the transport of charged particles in magnetic fields. In a simplified model, a point electron source was position at 100 cm from water surface. The longitudinal B-field was turned on outside the linac window (which was simulated as a void space with zero particle importance) located at a distance of 50 cm from the phantom. A 5x5 cm2 and 10x10 cm2 collimated electron beam was incident on a rectangular homogeneous water phantom of 50x50x50 cm3. Figure 2 illustrates the simulated geometry. Central axis PDDs and 2-D dose maps were calculated in 3x3x2 mm3 voxels, using 6, 9 and 12 MeV. B-fields resulting in half and 3/2 rotations (Nrot ) were determined using the following equation, as prescribed by Earl et. al2:
Results (continued)
The surface doses increased by factors of up to 3 and 5 for one half and 3/2 rotations, as seen in figure 5. The dose enhancement factors and surface dose increases were nearly identical for both collimation sizes.
Rela%ve'Dose'
Rotating Biplanar design (RBP) has been proposed for a linac-MRI where the radiation source has its central axis parallel to the main MR magnetic field, shown in figure 1.1 Contrast to orthogonal magnetic fields, which deflect electrons according to the Lorentz force, this approach allows electron treatments. Furthermore, longitudinal magnetic fields present a potentially enhanced electron therapy, including beam penumbra narrowing and peak dose enhancement. We performed Monte Carlo simulations using this design for an electron beam directed at a water phantom. We believe that such geometry and specific magnetic field strengths would result in an increased dose to central axis and magnetically collimated electrons, rendering the use of an applicator non-essential.
Results (continued)
Methods and Materials (continued)
Rela%ve'Dose'
1University
Figure 6. Narrowing effects are seen for a 10x10 cm beam undergoing 0, 1/2, and 3/2 rotations..
Nathaniel Berg: University of Michigan College of Engineering Department of Nuclear Engineering and Radiological Sciences • nateberg@umich.edu • 619-952-9709