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Pressure and frequency effects on the damping of a cantilever beam in a magnetic field
Dow, Jerome Paul.
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James C.H. Chu Ph.D.1,&D,*, Leonard Reiffel Ph.D.2, Wen C. Hsi Ph.D.1 andV.A. Saxena M.D.1DOI:&10.1002/ijc.10352
International Journal of Cancer pages 131&137, Author Information1Departments of Radiation Oncology and Medical Physics, Rush Medical Center, Chicago, Illinois2Exelar Corporation, Chicago, IllinoisEmail: James C.H. Chu Ph.D. (jchu@rush.edu)*Departments of Radiation Oncology and Medical Physics, Rush Medical Center, 1653 W. Congress Parkway, Chicago, IL 60612Publication HistoryIssue online: 26 APR 2002Version of Record online: 26 APR 2002Manuscript Accepted: 24 JAN 2002Manuscript Revised: 23 JAN 2002Manuscript Received: 30 JUL 2001
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treatment planningThe purpose of this study was to explore the potential advantages of using strong magnetic fields to increase tumor dose and to decrease normal tissue dose in radiation therapy. Strong magnetic fields are capable of altering the trajectories of charged particles. A magnetic field applied perpendicularly to the X-ray beam forces the secondary electrons and positrons to spiral and produces a dose peak. The same magnetic field also prevents the electrons and positrons from traveling downstream and produces a lower dose region distal to the dose peak. The locations of these high- and low-dose regions are potentially adjustable to enhance the dose to the target volume and decrease the dose to normal tissues. We studied this effect using the Monte Carlo simulation technique. The EGS4 code was used to simulate the effect produced by a coil magnet currently under construction. The coil magnet is designed to support up to 350 A operating current and 15 T peak field on windings. Dose calculations in a water phantom show that the transverse magnetic field produces significant dose effects along the beam direction of radiation therapy X-rays. Depending on the beam orientation, the radiation dose at different depths along the beam can be increased or reduced. This dose effect varies with photon energy, field size, magnetic field strength, and relative magnet/beam geometry. The off-axis beam profiles also show considerable skewness under the influence of the magnetic field. The magnetic field-induced dose shift may result in high dose regions outside the geometrical boundary of the initial radiation beam. We have demonstrated that current or near-term magnet technology is capable of producing significant dose enhancement and reduction in radiation therapy photon beams. This technology should be further developed to improve our ability to deliver higher doses to the tumor and lower doses to normal tissues in radiation therapy. & 2002 Wiley-Liss, Inc.The effect of an external magnetic field on electron beam dose distributions was first reported more than 50 years ago []. However, the magnetic field effect on photon beams was not reported until some 40 years later, when Bielajew [] showed reduction of the penumbral width using strong longitudinal magnetic fields. A modest longitudinal magnetic field was also shown to minimize potential target underdosing for tumors located in or near low-density regions such as the lung or trachea [,].Reiffel et al. [] recently proposed that a transverse magnetic field can be used to increase the dose to the tumor and reduce the dose to adjacent normal tissues for patients treated with high-energy photon beams. The dose enhancement is a result of trapping the electrons and positrons by the transverse component of the magnetic field. The dose reduction is due to the loss of transient charged particle equilibrium downstream from the magnetic field. Jette [,] confirmed this effect by using electron multiple-scattering theory and Monte Carlo calculations. Li et al. [] also demonstrated the effect along the central axis of the radiation beam using idealized step, ramp, and dipole fields. While the results from Li et al. are insightful, it is necessary to conduct further studies using physically realistic magnetic fields. In addition, due to the three-dimensional nature of the magnetic field, dose distribution effects should be studied over a region larger than the central axis of the radiation beam.Whitmire et al. [,] and Paliwal et al. [,] demonstrated magnetic field-induced electron dose distribution changes using water-cooled electromagnets. The magnets used were very heavy (up to 1.2 tons) with narrow pole separations. Litzenberg et al. [] recently reported electron and photon dose effects produced by a 3.5 T superconducting solenoid with a 20-cm diameter bore. All the above magnets produced appr however, they were not practical for clinical applications. The objective of this article is to present the magnetic field effects on dose distributions using practical magnetic fields and to explore their potential use in radiation therapy for cancer.As in previous reports, the EGS4 Monte Carlo code with PRESTA electron transport algorithm was used for this study [,]. The macros for inclusion of magnetic field effects in the electron transport were developed by Bielajew initially []. Additional macros developed by Ma et al. [,] were used to adapt the general user code DOSXYZ to accept a general magnetic field distribution file. The macros input the magnetic field file and convert the magnetic field coordinates to the patient coordinates. The user code BEAM was used to specify the beam irradiation geometry []. Data calculated by Mohan et al. [] were used for the X-ray beam input spectra. The plane radiation sources of the expected field sizes were used. The transport parameters AE, the energy threshold for creating a secondary electron, and ECUT, the cutoff energy for electron transport, were set at 700 keV. This implied that electrons and positrons with a kinetic energy of 189 keV (range less than 0.5 mm in water) deposited their energy locally. The corresponding parameters for photons, AP and PCUT, were set at 10 keV. Parameters for PRESTA were set at default values. The batch method from DOSXYZ divided each simulation into 10 batches and calculated the standard deviations. The dose distributions were sampled over a voxel size of 0.25 & 0.5 & 0.5 cm The standard deviations were generally well under 2% in the high-dose region since 10&100 million histories were run for each simulation.Two magnetic fields were used in this study. For illustrative purposes, a nonphysical 1&10 T ramp transverse magnetic field was used to show its effect on particle tracks graphically. The magnetic field used for dosimetry studies was produced by a superconducting magnet currently in the final phase of construction. The FEMM code was used for the design of the magnet []. The code was based on the well-established finite element method of approximating the solutions to Maxwell's equations []. The magnet was designed as a nested set of four concentric subcoils assembled into a disk-like structure with an overall diameter of 10 cm and approximately 3 cm thick. Pertinent properties for this externally applied topical superconducting magnet are listed in Table . The magnet is mounted on the end of an approximately 0.5 meter long cryogen-free cryostat. The cryostat carries current leads and cooling from a remote cryogen-free refrigerator and power supply with standard safety features and controls. The entire assembly is mounted on a mobile gantry and may be rotated and positioned at any angle from vertical to horizontal. The stray magnetic field is expected to be less than 5 & 10-4 T at 1 meter axially and 0.8 meter radially. It is less than 5 & 10-5 T (about the same as the earth's magnetic field) at 2.1 m away. Consultation with the manufacturer indicates that these fields are not likely to affect the operation of the linear accelerator. However, this will have to be verified when the magnet is available for experiment.Table&1.&&Properties of Superconducting Coil MagnetCoil i.d.3 cmCoil o.d.10 cmCoil thickness3 cmCoil materialNb3SnDistance from coil face to warm wall of cryostat0.5 cmPeak field on winding&15 TMaximum current& 350 AAs shown in Figure , the magnet was assumed to be embedded in a water phantom with the center of the coil magnet placed at 10 cm depth during simulation. The X-ray beam was directed along the x-axis and the coil surface was initially set to be parallel to the xy-plane. The distance between the beam axis and the center of the magnet varied from 2.5&4.5 cm for horizontal beam simulations. The magnet was rotated counterclockwise about the indicated center of rotation (depth = 13.5, z = &3.5) to study beam/magnet orientation effects. The dose distributions in the presence of the magnetic field are presented in both xy- and xz-planes. All isodose distributions are normalized to the dose at dmax when no magnetic field was applied.Figure&1. Schematic showing the beam arrangement relative to the magnet. The radiation beam is directed along the x-axis. The surface of magnet is parallel to the xy-plane. The beam axis is parallel to the magnet surface for most simulations. The magnet is rotated counterclockwise about the indicated center of rotation (at depth = 13.5 z = &3.5) for 10&30& during angled beam studies.The principle of the magnetic field induced dose effects of interest here is illustrated in Figure . The figure shows the charged particle tracks produced by 24 MV X-rays. The particles are predominantly traveling in the forward direction before encountering a hypothetical and nonphysical 1&10 T ramp purely transverse magnetic field applied between 7.5 and 12.5 cm depths. The magnetic field forces the particles (electrons and positrons) into a spiral motion, resulting in local energy deposition. This is indicated as a region of higher track density around a depth of 8&10 cm. The spiraling secondary charged particles also reduces the number of particles traveling downstream, thus producing a region of charged particle disequilibrium at the distal end of the magnetic field. The transverse magnetic field is, therefore, capable of producing high-dose and low-dose regions along the X-ray beams. The location of these high- and low-dose regions is potentially adjustable by the positioning of the magnetic field.Figure&2. Charged particle tracks generated by 24 MV photons in the presence of a ramp magnetic field. The radiation beam is incident from the left and a ramp magnetic field of 1&10 T is applied over depths of 7.5&12.5 cm. The regions of high- and low-track density are corresponding to regions of dose enhancement and reduction, respectively.The magnitude of the magnetic field induced dose effects depends on the energy of the X-ray beam. Figure A shows the dose distributions for 4 & 4 cm2 12, 24, and 50 MV X-rays with the center of the proposed magnet positioned at 10 cm depth and 4.5 cm below the central axis of the beams. The bottom panel shows the z-component of the magnetic field calculated along the central axis of the radiation beam. It is clear that the dose effect increases with the energy of the beam due to the longer secondary particle track length associated with higher energy photons. The penumbral width may also be widened with energy. For example, the 50 MV 20% isodose line in the positive and negative Y directions is shifted 0.2 and 0.7 cm, respectively, more laterally than the corresponding 12 MV isodose line at 9 cm depth. It is also interesting to note that the location of maximum dose enhancement corresponds to the region of high magnetic field gradient, not the region of maximum magnetic field strength. Figure B shows the ratios of central axis doses with the magnetic field divided by those without the magnetic field. Approximately 10% to 40% dose enhancement or reduction is obtained along the central axis. The shape of the magnetic field-induced dose enhancement region depends on the direction and magnitude of the magnetic field strength and gradient. In addition, the rate of secondary charged particle build-up affects the shape of the dose reduction region. These combined effects result in a more sharply defined region of dose enhancement than that for dose reduction.Figure&3. Variation of magnetic field-induced dose effect for 12, 24, and 50 MV photons. The center of the magnet coil is positioned at z = &4.5 cm. A: Isodose distributions on the xy-plane. The bottom panel shows the z-component of the magnetic field calculated along the central axis of the beam. B: Ratio of central axis dose without magnetic field divided by that with magnetic field.The variation of the magnetic field effect with field size is illustrated for the 24 MV X-rays. The same relative beam and magnet geometry used for Figure
is used here. The field sizes studied are 4 & 2, 4 & 4, and 4 & 8 cm2. As shown in Figure , similar effects are observed for 4 & 4 and 4 & 8 cm2 fields in regions close to the central axis. There is less dose enhancement along the central axis for the 4 & 2 cm2 beam due to the slight lateral shift of the high-dose region.Figure&4. Effect of field size on the magnetic field-induced dose effect. Beam energy and field sizes are indicated. A: Isodose distributions on the xy-plane. B: Ratio of central axis dose without magnetic field divided by that with magnetic field.The dose effect as a function of distance from the magnet is presented in Figure . The center of the magnet is positioned from 2.5, 3.5, and 4.5 cm from the central axis of the 24 MV X-ray beam. The field size is 4 & 4 cm2. The dose enhancement ranges from 30% to 90% and dose reduction ranges from 20% to 40% along the beam axis (Fig. c). Larger dose effects are produced by the stronger magnetic field and field gradient at shorter distances from the magnet. The dose distributions on the xz-plane also show that the high-dose regions are now shifted away from the central region of the beam. This is due to the fact that charged particle tracks are now following the highly concentrated magnetic field lines.Figure&5. Variation of magnetic field-induced dose effect over a distance from 2.5&4.5 cm from the magnet for 4 & 4 cm2 24 MV photons. A: Isodose distributions on the xy-plane. B: Isodose distributions on the xz-plane. C: Ratio of central axis dose without magnetic field divided by that with magnetic field.The magnetic field-induced dose effect also changes with the orientation of the magnet relative to the radiation beam. Figure
shows the magnetic field-modulated dose distributions when the magnet is rotated counterclockwise from its position in Figure . The data show that the dose enhancement effect decreases from more than 30% to less than 5% when the angle of rotation is changed from 0 to 30&. This is due to the reduced magnetic field gradient at larger angles. However, the magnitude of the magnetic field remains consequently, the dose reduction effect is nearly the same for all orientations studied.Figure&6. Change of dose distributions for various beam incidence angle relative to the magnet. A: Isodose distributions on the xy-plane. B: Ratio of central axis dose without magnetic field divided by that with magnetic field.One of the main objectives of radiation therapy treatment planning for cancer patients is to deliver high doses to the target volume while sparing the adjacent normal tissues. Our ability to achieve this goal has improved significantly in recent years due to many technological advances in radiation treatment planning and delivery. For example, geometrically conformal and/or intensity-modulated radiation treatment fields can now be delivered from many commercial radiation treatment machines [,]. However, X-rays cannot yet be modulated in the beam direction, whereas proton radiotherapy beams are routinely modulated with depth. As demonstrated here, magnetic fields can vary the radiation intensity at specific locations along the beam by adjusting the position of the magnet. This magnetic field-induced effect can, in principle, be employed alone or in conjunction with existing geometrically conformal and intensity modulated beams. This added beam intensity control capability may, therefore, further enhance our ability to increase the tumor to normal tissue dose ratio during radiation therapy.Although the magnetic field-induced dose effects presented here are obtained with the magnet embedded in the phantom, we expect similar effects for relatively shallow lesions (located no more than 4&5 cm from the magnet) when the magnet is applied topically. The degree of dose enhancement achievable depends on the proximity of tumor relative to the magnet. For deep-seated tumors, other magnet designs, such as an insertable one, may be necessary. However, as with most new technologies there are many considerations that need to be addressed before magnetic field-modulated radiation beams are used clinically. For example, the shift of high dose regions shown in Figure B may be of concern as some of the normal tissues outside the initial treatment field may receive a higher dose. However, it is possible to reduce this effect by reversing the coil magnet for half the treatment when clinically feasible. Some other important issues are, among others, the ability to deliver high magnetic fields and gradients to deeper target locations, development of special-purpose magnets for various clinical situations, the reproducibility of magnet positioning, the potential biological effects produced by intense magnetic fields, techniques to minimize beam optics effects from a linear accelerator, development of treatment planning tools taking into account the magnetic field effects, and general safety issues related to high magnetic field environments. It is to be noted that the small size of our magnet coil produces a slightly modified dipole field that drops off very nearly as 1/r3 with distance along the axis. The field strength a few cm into the body (although not the gradients) are not far from those currently used in MRI procedures and not likely to produce significant biological effects.Our Monte Carlo simulations show that significant dose enhancement and reduction can be achieved by using a practical magnet. These dose effects, limited by the flexibility of magnet placement, potentially can be used to control the dose delivered to the tumors and adjacent normal tissues during radiation therapy. With recent significant advances in magnet technology, the application of this mode of radiation beam control should be further explored.1
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