Patient dosimetry for hybrid MRI-radiotherapy systemsC. Kirkbya�

Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada

T. StanescuDepartment of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada and Departments of Oncology and Physics, University of Alberta,11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada

S. Rathee, M. Carlone, and B. MurrayDepartment of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada and Department of Oncology, University of Alberta, 11560 University Avenue,Edmonton, Alberta T6G 1Z2, Canada

B. G. FalloneDepartment of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton,Alberta T6G 1Z2, Canada and Departments of Oncology and Physics, University of Alberta,11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada

�Received 27 September 2007; revised 7 January 2008; accepted for publication 8 January 2008;published 21 February 2008�

A novel geometry has been proposed for a hybrid magnetic resonance imaging �MRI�-linac systemin which a 6 MV linac is mounted on the open end of a biplanar, low field �0.2 T� MRI magnet ona single gantry that is free to rotate around the patient. This geometry creates a scenario in whichthe magnetic field vector remains fixed with respect to the incident photon beam, but moves withrespect to the patient as the gantry rotates. Other proposed geometries are characterized by aradiation source rotating about a fixed cylindrical magnet where the magnetic field vector remainsfixed with respect to the patient. In this investigation we simulate the inherent dose distributionpatterns within the two MRI-radiation source geometries using PENELOPE and EGSnrc Monte Carloradiation transport codes with algorithms implemented to account for the magnetic field deflectionof charged particles. Simulations are performed in phantoms and for clinically realistic situations.The novel geometry results in a net Lorentz force that remains fixed with respect to the patient �inthe cranial-caudal direction� and results in a cumulative influence on dose distribution for a multiplebeam treatment scenario. For a case where patient anatomy is reasonably homogeneous �brainplan�, differences in dose compared to a conventional �no magnetic field� case are minimal for thenovel geometry. In the case of a lung plan where the inhomogeneous patient anatomy allows for themagnetic field to have significant influence on charged particle transport, larger differences occur ina predictable manner. For a system using a fixed cylindrical geometry and higher magnetic field�1.5 T�, differences from the case without a magnetic field are significantly greater. © 2008 Ameri-can Association of Physicists in Medicine. �DOI: 10.1118/1.2839104�

Key words: MRI-linac, MRI-radiotherapy, patient dosimetry, magnetic field, Monte Carlo

I. INTRODUCTION

The pursuit of real time image guidance in adaptive radio-therapy has led some investigators to consider the possibilityof merging a megavoltage radiation therapy linear accelera-tor �linac� or a 60Co teletherapy unit with a magnetic reso-nance imaging �MRI� system.1–9 As a direct result of any ofthe proposed designs, megavoltage �MV� photon beamswould be delivered to a patient in the presence of a staticmagnetic field �B0�. Because the mechanisms by which ra-diation deposits energy inside of a medium are governed bythe transport and interaction of charged particles with thatmedium, the magnetic field of the MRI will modify the tra-jectories of the charged particles thus modifying the ab-sorbed dose distributions.10 It has been demonstrated that a

B0 field can alter the dose deposition characteristics of a 6

1019 Med. Phys. 35 „3…, March 2008 0094-2405/2008/35„3

MV photon beam, both in homogeneous and inhomogeneousmedia through the deflection of secondary chargedparticles.4–6,10–13 The literature has concentrated mostly onmodel problems involving slab phantoms in a specific opera-tional geometry,4–7 although one study has considered a pa-tient case.14

Four groups worldwide have proposed methods to inte-grate either a linear accelerator or a 60Co source with aMRI.1–3,8 These four proposals can be grouped into two basicgeometries. The first geometry1–3 can be summarized as asolenoidal and stationary MRI whose B0 field is along thedirection of the solenoid, which is also parallel to the cranial-caudal direction of the patient. The radiation source �linac or60Co� rotates around the MRI in a transverse plane.Lagendijk et al. have proposed a B0 field strength of

3,4,6,7

1.5 T. Other groups proposing somewhat similar ar-

1019…/1019/9/$23.00 © 2008 Am. Assoc. Phys. Med.

1020 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1020

rangements of 60Co sources in this geometry1,2 have yet tofirmly establish the B0 field strength in their systems, al-though Kron et al. have suggested a value of 0.25 T.2 Thisgeometry is henceforth referred to as a fixed cylindrical �FC�geometry. The second geometry8 instead uses a biplanar, lowfield �0.2 T� MRI and an irradiator �linac� that is coupled toone open end of the system �see Figs. 1�a� and 1�b��. Theentire system rotates around the patient, allowing beams tobe delivered from any angle. We shall refer to this as therotating biplanar �RBP� geometry.

Each of the two geometries has fundamentally differentdose deposition distributions when the gantry of the radiationsource rotates around the patient because of the differentorientations of the static magnetic field, B0 with respect toradiation beam and the patient. For the RBP geometry, dur-ing rotation of the gantry, the direction of the B0 magneticfield is always perpendicular with respect to the incidentphoton direction but changes with respect to the patient ge-ometry. For the FC geometry, during rotation of the gantry,the direction of the B0 magnetic field changes with respect tothe direction of the radiation beam, but remains fixed withrespect to the patient.

The changes of the dose deposition due to the different

FIG. 1. Schematic representations of the RBP geometry �a� and �b� and theFC geometry �c� and �d� showing the relative positioning of the linac, mag-nets, beam direction, magnetic field direction, and the net Lorentz force.Both systems �shown in �a� and �c�� have, respectively, been rotated in theclockwise direction through 90° in sketches �b� and �d�. In the RBP geom-etry the beam and B0 field rotate with respect to the patient, but remain fixedwith respect to each other. In the FC geometry the B0 field remains fixedwith respect to the patient.

geometries can be understood in the following manner. For

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simplicity, Fig. 1 shows the direction of the resultant Lorentzforce on secondary electrons moving in the direction of thephoton beam incident on the patient both in RBP and FCgeometries. Using the right hand rule, it is easily understoodthat the direction of the Lorentz force stays the same withrespect to the patient for different incident photon beam di-rections in the RBP geometry while it changes in the FCgeometry. As a result, the magnetic field influence on theresultant dose distribution patterns in the patient is differentin the two geometries.

The purpose of this investigation is to describe the inher-ent differences of dose distribution patterns of the two MRI-radiation source geometries and show the result of these dif-ferences in clinically realistic situations. In addition to thesingle and parallel opposed beams incident on an inhomoge-neous slab geometry phantom, brain and lung CT geometrieswith multiple incident beams are chosen because these rep-resent the two extreme examples of tissue homogeneity. Theeffects of a magnetic field on the dose deposition pattern maynot be significant in the brain case, which is relatively ho-mogeneous, but the effects may be significant at the tissueinhomogeneities that exist within a lung case. In this work,we specifically consider the dose distributions resulting fromthese irradiation geometries by using the MRI magneticfields that have been reported for each of the geometries: i.e.,the RPB geometry with �B0�=0.2 T and the FC geometrywith �B0�=1.5 T using a 6 MV source. Some simulations arealso performed using a 60Co source.

II. METHODS

II.A. Monte Carlo simulations in the presence of amagnetic field

We used two separate Monte Carlo codes: PENELOPE15,16

and EGSnrc.17–19 The codes have been adapted somewhatfrom their default, published forms to incorporate the influ-ence of external magnetic fields on charged particle trans-port. Two codes were used at separate stages in this work,both to provide a consistency check of results and to exploitthe advantages offered by each code system for differentaspects of this work. PENELOPE and its user-code penEasy20

offered a more exact treatment of the magnetic field influ-ence on transport and a lower cutoff energy for charged par-ticle transport, and the EGSnrc user-code DOSXYZnrc21 of-fered the ability to easily perform calculations within a CT-defined voxelized geometry.

PENELOPE has been extensively tested in the literaturewithout the presence of magnetic fields.15,22,23 A detailed de-scription of PENELOPE’s tracking algorithm for the transportof charged particles in the presence of static electromagneticfields is given in Appendix C of the PENELOPE manual.16 Thisalgorithm is implemented in the penfield.f subroutine andwas used in this work with the appropriate magnetic fieldparameters. The algorithm allows for exact tracking ofcharged particles �irrespective of step length� within a uni-form magnetic field. For each transport step, the displace-ment and velocity change of charged particles due to the

magnetic field alone are accounted for by calculating the

1021 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1021

Lorentz force’s influence on the particle’s trajectory. It isassumed that the effect of the magnetic field can be ac-counted for independently of the transport step that wouldtake place without the presence of a magnetic field. Conse-quences to a particle’s stopping power due to synchrotronradiation, which have been demonstrated to be insignificantfor most medical physics applications10 are ignored. Chenet al.24 have demonstrated that PENELOPE, when configuredwith the penfield.f subroutine, reliably reproduces dose dis-tributions to a plastic phantom in the presence of a nonuni-form magnetic field with a peak strength of 3 T. The user-code penEasy20 allows the user to write a steering file thatdefines the source and tally parameters for the PENELOPE

simulation; the transport of photons and charged particlesremains the same. The parameters used to perform the simu-lations were as follows: Wcc=60 keV and Wcr=6 keV rep-resenting the cutoff thresholds for the hard inelastic colli-sions and radiative events, respectively; C1=0.1 defining thefraction by which the mean free path for hard elastic eventscan be defined by the first transport mean free path at highenergies; and C2=0.1 defining the maximum average frac-tional energy loss between consecutive hard elastic colli-sions. The values adopted for these parameters offered rea-sonable simulation efficiency and altering them has only aweak influence on the results.16

EGSnrc is published with a macro package calledemf_macros.mortran, which is an updated but not completelyimplemented copy of the macros developed for EGS4 byBielajew.10 This macro is invoked after the completion of aconventional charged particle step. In general, the accuratesimulation of charged particle transport within electromag-netic fields requires that the step sizes within the condensedhistory algorithm be sufficiently short to ensure that: �a� thechange in the magnitude of the electromagnetic field across astep is small, �b� the relative change in the particle’s kineticenergy remains small, and �c� the relative change in the par-ticle’s direction of motion is small, where small is on theorder of 5% or less.16 Items �a� and �b� are easily achievablebecause the magnetic fields simulated are always uniform,and the magnetic field does not change the particle’s energy.Item �c�, however, remains a concern. From the EGS4 macros,step size is restricted to 0.02mec

2 / �100�B��qec� cm or less,where mec

2 is the electron’s rest mass, c is the speed of light,qe is the charge of an electron, and �B�� is the magnitude ofthe magnetic field �in tesla� perpendicular to the particle’svelocity. The value 0.02 is a user-defined parameter corre-sponding to a 2% change in direction over the transport step.For electrons traveling perpendicular to the magnetic fieldlines, this restricts the step size to approximately 0.17 and0.0023 cm for 0.2 and 1.5 T fields, respectively. No addi-tional limitation was introduced to deal with the multiplescattering treatment of charged particles applied in EGSnrc,which potentially introduces an approximation into the re-sults, i.e., large angle deflections introduced by multiple scat-tering may still occur. However, we note that for the slabphantom cases presented here, PENELOPE and EGSnrc dose

predictions were generally in agreement to within statistical

Medical Physics, Vol. 35, No. 3, March 2008

uncertainty ��1%�. Transport cutoffs for the EGSnrc simu-lations were set for electrons to AE=ECUT=0.7 MeV �restmass+kinetic energy� and for photons to AP=PCUT=0.01 MeV.

II.B. Slab phantoms

To understand the dosimetric implications of the singleand parallel opposed fields in the presence of uniform mag-netic field, we first considered the relative absorbed dose tomedium for a simple, inhomogeneous slab geometry analo-gous to �but not identical to� that of Raaijmakers et al.4 Adiagram of the slab geometry is presented in Fig. 2. Theinfluence of the magnetic field on the electron trajectories isstronger in lower density media �as density decreases weexpect the electron trajectories to approach the curved pathsseen in a vacuum scenario�. A direct consequence of this isthe “electron return effect” where dose to the tissue neartissue-air interfaces can be substantially enhanced by elec-trons returning to the tissue as a result of the magnetic fieldbending their trajectory.4 The magnitude of this effect is de-pendent on the magnetic field strength, the electrons’ veloci-ties and the patient anatomy and geometry. We created avirtual phantom consisting of semi-infinite slabs of water,ICRP lung �with mass density of 0.3 g /cm3 and chemicalcomposition as defined by NIST�,25 and water sandwiched inair. This geometry is useful in investigating the dosimetricconsequences of tissue inhomogeneities in a magnetic field.We chose ICRP lung as a central material instead of air so asto understand the consequences of the magnetic field on doseusing a realistic low density tissue. Slabs of air are explicitlydefined on either side of the phantom because PENELOPE

does not incorporate magnetic field effects into its vacuumtransport algorithm. For these simulations �performed both

FIG. 2. The slab phantom geometry. A 6 MV parallel spectrum is incident ona series of semi-infinite slabs consisting of air, ICRP lung, and water. Themagnetic field was uniform throughout the phantom, defined at 0.0, 0.2, and1.5 T. We considered both single fields and parallel, opposing fields. In theRBP geometry, B0 switches direction for the opposing beam. Air slabs of 10cm thickness are introduced on either side to force PENELOPE’s magneticfield algorithm which is not invoked in vacuum.

with PENELOPE and EGSnrc codes� we considered

1022 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1022

5�5 cm2 photon fields with parallel �nondiverging for sim-plicity� incidence comprised of a 6 MV central axis spectrumfor a Varian linac.26 Additional EGSnrc simulations wereperformed with the 6 MV spectrum replaced by the 60Cospectrum published by the EGSnrc development group.19 Weconsidered parallel opposing beams, in addition to singlebeams �as shown in Fig. 2�. For single fields the B0 fieldvector points out of the page. For parallel opposing beams,the B0 field vector changes sign �rotation through � rad� inthe RBP geometry generating net Lorentz force vectors thatpoint in the same direction for downstream-traveling elec-trons. In the FC geometry, since the direction of the magneticfield is fixed, the net Lorentz force vectors are in oppositedirections for the two beams.

For our simulations we considered magnetic B0 field mag-nitudes of: 0.0 T—as a no-field base line, 0.2 T—as proposedfor the RBP design8 and as a representative lower fieldstrength for the FC geometry, and 1.5 T—as one group hasproposed for the FC geometry.3

Dose scoring voxels were defined as 0.2�0.2�1.0 cm3

in size, the larger �1.0 cm� dimension being in the y direc-tion, parallel to the magnetic field vector, but perpendicularto the beam directions and the Lorentz force. Doses werenormalized to the depth of maximum dose for the �B0�=0.0 T case. Parallel opposing beams were assigned equalweights. An adequate number of histories were run in eachsimulation to keep the statistical uncertainty for dose to wa-ter voxels along the central axis below 1%.

II.C. Patient phantoms

While the general effects of a magnetic field on dosimetrycan be modeled using a simplified slab geometry, the ulti-mate goal in this work was to understand the consequencesof a B0 field in the particular geometries proposed on thedose distribution in a real patient. For this purpose, we con-sidered two representative scenarios. The first was a fourfield treatment plan developed for dose delivery to a brain insimulation of a glioblastoma multiform treatment, a case inwhich �aside from the bony anatomy of the skull� theanatomy is reasonably homogeneous. For this scenario weused four equally weighted orthogonal beams �anterior, pos-terior, and two lateral fields�, each shaped using blocks toconform to the target volume. The second was a lung case,representative of a highly inhomogeneous anatomy wherethe magnetic field would have strong influence on electronstraveling through low density volumes. For this scenario weapplied five equally weighted beams �incident at gantryangles of 356°, 176°, 51°, 320°, and 280°�.

For both cases, plans were developed using the Eclipsetreatment planning system �TPS� �Varian Oncology Systems,Palo Alto, CA�. Plan files, including CT data, were exportedfrom the TPS and imported into an in-house Monte Carlo�MC� treatment planning dose verification system.27,28 Thesystem simulates the head of a 6 MV linac �model param-eters were specific to the head of a Varian 21EX linac�, stor-ing BEAMnrc output as a phase space file scored at a plane

70 cm from the source for each separate beam. The system

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also generates its own model of the patient based on a CTimage set using an in-house CT number-to-mass density con-version table. The body structure contours were importedfrom the DICOM RT structure set file and used to mask thevirtual phantom such that all voxels outside the patientanatomy �including patient immobilization system andcouch� were assigned values for air. Each beam orientationwas simulated separately and the results were combined andnormalized to 100% at isocenter for the �B0�=0.0 T case�absolute dose can be obtained by multiplying all voxeldoses by the dose-to-isocenter/100%�. Voxel dimensionswere taken from the TPS at 0.25�0.25�0.30 cm3 �larger inthe cranio-caudal direction�. The dose to any voxel with amass density of less than 0.01 g /cm3 was set to 0 to avoidreporting doses to regions outside the body �i.e., air�. Statis-tical uncertainty from each beam at the isocenter was �2%,resulting in uncertainty in the combined dose at the isocenter�1%. A local mean �nearest 6 voxels in 3D� smoothing al-gorithm was applied to further reduce statistical fluctuations.

III. RESULTS

III.A. Slab phantoms

We first consider the relative dose to our lung slab phan-tom in response to a single, nondiverging 6 MV 5�5 cm2

beam along the central axis, shown in Fig. 3. All calculateddose distributions are presented relative to dose at the depthof maximum dose calculated without magnetic field. Doseresults from the EGSnrc simulations �black� are within 1%of the PENELOPE results �gray� at all magnetic field strengths.These results illustrate the potential difference in dose pro-files near water-lung interfaces due to modifications tocharged particle trajectories introduced by the magnetic field,as introduced by Raaijmakers et al.4 Our results at 1.5 Tappear to be in agreement with those of Raaijmakers et al.4

FIG. 3. Relative depth doses along the central axis of the slab phantom for asingle nondiverging 6 MV beam incident from the left-hand side. The resultsfrom the EGSnrc simulations are shown in black, which are superimposedon PENELOPE results in gray. The magnetic field points out of the page. At 1.5T there is a clear, substantial increase ��40%� in dose at the water-to-lungboundary and a decrease ��25%� in the lung-to-water boundary. At 0.2 T,slight differences of only �2% are seen. Dose to air is not shown.

given that our phantom incorporated 10 cm of ICRP lung

1023 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1023

instead of 2 cm of air between water slabs. We note that theresults of Raaijmakers et al. were experimentally verified.5

Along the central axis for a single beam, there will be essen-tially no difference between the FC and RBP geometries, asthe Lorentz force is perpendicular to the beam in both cases.For the 1.5 T field strength, at the water-to-lung interface thesimulations indicate a relative dose increase of up to 28% towater and up to 40% to lung and at the lung-to-water inter-face a relative dose decrease of up to 26% to lung and up to24% to water. There are also notable differences in thebuildup region and at the exit region �last centimeters ofwater in the second water slab�. For a field strength of 0.2 T,dose differences relative to the 0.0 T field are generallywithin �2.5% along this axis, with exit dose increased by5% in the last voxel of water.

Extending the picture we looked at dose along a planeperpendicular to the magnetic field through the beam’s cen-tral axis in the slab phantom for single fields using both 6MV and 60Co spectra. The results of the EGSnrc simulationsusing magnetic field magnitudes of 0.0 and 0.2 T are shownin Fig. 4. Doses have been normalized independently foreach spectrum to the central axis dose maximum for the�B0�=0.0 T case. In general, dose distribution differences arecharacterized by a slight shift in the direction of the Lorentzforce �upwards in Fig. 4.� in the lung tissue, along with an

FIG. 4. Relative dose to the central plane for single beams using a 6 MVspectrum �a�–�c� and a 60Co spectrum �d�–�f�. �a� and �d� show the conven-tional result where �B0�=0.0 T. �b� and �e� show the results for �B0�=0.2 T. �c� and �f� show the difference maps D0.2 T−D0.0 T. Exit dose en-hancement due to electrons returning is similar at +20% for both sources. Inlung tissue, the 60Co difference regions are narrower.

electron return effect dose enhancement at the exit surface of

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approximately 20% for both spectra. Because the 6 MV in-cident photon spectrum gives rise to an electron spectrumwith higher energies compared to the 60Co source, the dosedifferences for the 6 MV case are spread out over a largerarea and are slightly larger in magnitude.

The EGSnrc dose results along the beam central axisplane resulting from a parallel opposing pair on the sameslab phantom are shown in Fig. 5. We determined thatPENELOPE results for the 6 MV cases �not shown� are ingeneral agreement with the EGSnrc results �within ��1%,with maximum differences up to 3% in regions most stronglyinfluenced by the magnetic field in the 1.5 T cases�. Thedoses have been normalized to the central axis depth ofmaximum dose for the �B0�=0.0 T case. This was performedindependently for the 6 MV source and the 60Co source.Figures 5�a�–5�c� show the dose to the central plane for �a�the 6 MV RBP case at �B0�=0.2 T, �b� the 60Co FC case at�B0�=0.2 T, and �c� the 6 MV FC case at �B0�=1.5 T. Dif-ference maps �D�B0�−D0.0 T� are shown in Figs. 5�d�–5�f� tocompare these distributions to their corresponding cases with�B0�=0.0 T. Note that this simulation is constructed with themagnetic field direction being out of the page for left sidebeam and into the page for right side beam incase of RBPgeometry as shown in Fig. 2. The magnetic field direction

FIG. 5. Relative dose to the central plane resulting from parallel opposingbeams. Shown, are �a� the RBP geometry using a 6 MV source with �B0�=0.2 T with B0 direction reversing between opposing beams, �b� the FCgeometry using a 60Co source with �B0�=0.2 T and B0 direction remainingfixed between opposing beams, �c� the FC geometry using a 6 MV sourcewith �B0�=1.5 T, again with B0 direction remaining fixed, and �d�–�f� dif-ference maps of D�B0�−D0.0 T for each of the above conditions, respectively.Dose values are normalized to the central axis value at depth of maximumdose for the conventional ��B0�=0.0 T� case, independently for each source.

was pointing out of the page for both beams in case of FC

1024 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1024

geometry. The simulation was done in this manner to bettercompare the two situations on the plane containing the Lor-entz force which represents a coronal plane for the RBP ge-ometry and transverse plane for the FC geometry for thepatient orientation depicted in Fig. 1. Therefore, in the actualpatient geometry, the top of the figure would represent thepatient inferior for the RBP geometry �Figs. 5�b� and 5�d��and the patient posterior for the FC geometry �Figs. 5�c� and5�e��.

It is immediately apparent that for the RBP geometry thissituation of opposing beams results in a scenario where thedose modifications due to the magnetic field are adding con-structively. This is not surprising if one considers that the netLorentz force on a forward-peaked electron velocity distri-bution �pointing downstream� is in the same direction forboth beams since the relative orientation of the photon beamwith respect to the magnetic field remains fixed. In this casethe Lorentz force is pointing toward the top of the figure forboth beams, and thus we see a slight shift in the dose distri-bution toward the top of the figure. The shift is more pro-nounced in the lung material, as the electrons have a longermean free path in the lower density material. As a result, inthe lung tissue we see a dose increase at one field edge and adecrease at the other of up to 12%. As observed in the singlebeam there are small differences in dose at the water-lunginterface for the 0.2 T case, therefore, in the opposed casethese small hot and cold spots come very close to cancelingeach other completely, leaving very minimal differences atthe interfaces.

In the FC geometry the net Lorentz force ends up being inopposite directions for the two beams. The difference maps�somewhat in Fig. 5�e� and more strongly in Fig. 5�f�� showhot and cold spots due to asymmetry in the dose deposition.For the higher field strength ��B0�=1.5 T�, the hot spot at thewater to lung interface as seen in the single beam geometryis not fully compensated by the cold spot at the lung to waterinterface of the opposing beam. Therefore, along the centralaxis we still see significant hot spots as the beams enter thelung material. Similarly, the hot and cold spots that occur inthe buildup/exit regions do not cancel thus leaving hot spotsnear the surface of up to +22% over several millimeters�mm�. Along the beam edges, since the Lorentz force is inopposite directions for the two beams, the net effects willtend to cancel each other to a certain extent. However, due tothe lower and lower fluence of electrons available as thebeam travels through the phantom, this cancellation cannotbe exact. For example, at 14 cm depth in Fig. 5�c�, moreelectrons are available to be pushed upward in the beamentering from the left hand side than the electrons availableto be pushed downward in the beam entering from the righthand side. Of course, this lack of cancellation is accentuatedat the higher field strength and one observes narrow regionsof both hot and cold doses near the field edge in the lungmaterial. These observations are still somewhat apparent forthe low field 60Co case, but result in differences below 2%.The increase in dose at the exit surfaces is still apparent for

both magnetic field strengths.

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III.B. Patient phantoms

In general, the results from the patient models reinforcethose observed in the slab phantoms. The results of EGSnrcsimulations for the four field brain plan are illustrated in Fig.6. Figures 6�a� and 6�b� show the combined, relative dose�normalized to the dose at the isocenter� from all four beamsin the absence of an external magnetic field in the transverseand sagittal planes through central axis. Figures 6�c� and 6�d�consider the difference in dose �D0.2 T−D0.0 T� between irra-diation in the RBP geometry with �B0�=0.2 T and in theconventional geometry with �B0�=0.0 T in the transverseand sagittal planes, respectively. Similarly, Figs. 6�e� and 6�f�consider the difference in dose �D1.5 T−D0.0 T� between irra-diation in the FC geometry with �B0�=1.5 T and the conven-tional geometry with �B0�=0.0 T. Because of the homoge-neous nature of the brain tissue, dose differences in bothconfigurations are small �compared to those seen for the lungplan�. For the RBP geometry with �B0�=0.2 T we see hotspots of +4% �maximum� and cold spots that are no worsethan −2%. We note that there is some increase in the surfacedose to skin inferior to the beam entry regions. This is theresult of electrons following large arcs �a few centimeters inradius� after exiting the patient anatomy. In the FC geometrywith �B0�=1.5 T the exiting electron trajectories travelthrough tighter arcs and result in surface hot spots of +10%�maximum� that extend several mm into the patient. Coldspots down to −5% are seen along the geometric edges of thebeams. Rerunning the FC geometry with the magnetic fieldstrength reduced to �B0�=0.2 T, the maximum and minimumrelative dose differences were similar in magnitude to thoseseen for the RBP geometry �results not shown�.

In Fig. 7 we consider the results of our five field lungplan. Figures 7�a� and 7�b� show the relative dose �normal-ized to isocenter� when the simulation is performed withoutany external magnetic field. The difference maps in Figs.7�c� and 7�d� show the D0.2 T−D0.0 T differences in thetransverse and sagittal planes, respectively, for irradiation inthe RBP geometry with �B0�=0.2 T compared to the no mag-netic field case. Likewise, the difference maps in Figs. 7�e�and 7�f� show the D1.5 T−D0.0 T differences in the transverseand sagittal planes, respectively, for irradiation in the FCgeometry with �B0�=1.5 T compared to the no magneticfield case. In the RBP �B0�=0.2 T geometry the most signifi-cant hot and cold spots ��12%� are seen in the sagittal viewat the edges of the field. Unlike the anatomy within the brain,the low density tissue and air within the lungs allows for themagnetic field to more strongly influence the electron trajec-tories, even at this low field strength. Dose increases towardthe patient’s inferior. In comparison, the D1.5 T−D0.0 T dif-ferences reveal hot spots as high as +30% and cold spots aslow as −15% near tissue-lung boundaries and along beamedges. In comparison the differences at the tissue lungboundaries are quite minimal in the RBP geometry at 0.2 T.When the simulation using the FC geometry was rerun with�B0�=0.2 T, hot and cold spots of similar magnitude

��12%� to those seen for the RBP geometry were seen,

1025 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1025

again with the general pattern being a shift of dose distribu-tion in the direction of the Lorentz force �results not shown�.

IV. DISCUSSION

The work presented here has been cross validated usingtwo different MC codes, but the results have not been di-rectly measured at this time. As mentioned, PENELOPE hasdemonstrated reliable results compared to measurement inthe presence of a magnetic field.24 If we modify our slabphantom and source model to approximate the experimentperformed by Raaijmakers et al.,5 on a poly�methyl-methacrylate � PMMA-air-PMMA phantom, we find that theEGSnrc code is able to reproduce their central axis depthprofiles �which they measured using GafChromatic film� formagnetic field strengths of 0.6 and 1.3 T to within reasonableresolution ��2% /2 mm of curves published by Raaijmakerset al.5� Thus, we can be confident that the results presented inthis work are reasonably valid. At this time, the hybrid MRI-radiotherapy systems discussed in this work are under vari-ous stages of construction, and as prototype models comeonline we can expect more rigorous experimental investiga-tions of dosimetry in the presence of magnetic fields.

As can be seen from all of the comparisons presented, thenet influence of the magnetic field in either geometry is tocause a shift of the dose distribution in the direction of theLorentz force. If the magnetic field is large there can besignificant return effects when the beam enters a low density

material. From the perspective of clinical implementation of

Medical Physics, Vol. 35, No. 3, March 2008

any of these products, it would be desirable to account forthese dose changes in the treatment planning algorithms. Itwould be difficult to account for the dose return effects seenat the beam entrance, exit, and tissue interfaces caused by thehigh magnetic field without using a Monte Carlo planningsystem. Since the lower magnetic field strengths do not ex-hibit significant dose perturbation at the entrance and tissueinterfaces, it is surmised that a simple correction could beimplemented which shifts the dose by a small amount in thedirection of the Lorentz force. For the RBP 0.2 T system thiscorrection could be implemented in such a way that the shiftis scaled according to the density of the material such that itcould account for the larger perturbation seen in the lungphantoms. This correction could be applied after the dosehad been calculated to water in much the same way that earlyinhomogeneity algorithms were implemented. The issue ofsimple magnetic field correction to dose requires furtherevaluation.

Additionally, in the RBP geometry the electrons in thepenumbra are pushed toward the inferior side of the patientirrespective of the beam orientation in the transverse plane.This results in dose enhancement at the inferior side of thepatient and dose reduction at the superior side of the patient.These changes occur over a few cm. The impact of thesehot/cold spots can be easily reduced by using a few junctionmovements during the course of fractionated radiotherapy.

FIG. 6. The relative dose for a four field brain plansuperimposed on CT data slices for the conventionalgeometry, �B0�=0.0 T, case shown in �a� transverse,and �b� sagittal planes through the isocenter. Dose isnormalized at isocenter for the �B0�=0.0 T case for allsimulations. Also shown are differences of D0.2 T

−D0.0 T in the �c� transverse and �d� sagittal planeswhere D0.2 T was calculated in the RBP geometry with�B0�=0.2 T. Hot spots �maximum+4%� occur on thesurface anatomy and drift significantly outside the beamgeometry. Cold spots are minimal. Differences ofD1.5 T−D0.0 T are shown in the �e� transverse and �f�sagittal planes where D1.5 T was calculated in the FCgeometry with �B0�=1.5 T. Hot spots up to +10% ex-tend several mm down from the surface. Cold spots arealso present down to −5% inside the field edges.

Such simplicity is easily afforded in this geometry since the

1026 Kirkby et al.: Patient dosimetry for hybrid MRI-radiotherapy systems 1026

superior-inferior boarders of the coplanar treatment fieldstend to be similar irrespective of the orientation in the trans-verse plane.

V. CONCLUSIONS

This work has, through specific examples, quantified theexpected influence a uniform magnetic field will have ondose distribution in the context of two different hybrid MRI-linac geometries: �1� the RBP geometry where a linacmounted on the open end of a biplanar MRI system results ina B0 vector that rotates along with the radiation beam withrespect to the patient as the gantry angle is varied and �2� theFC geometry where a stationary solenoidal magnet generatesa B0 vector that remains fixed with respect to the patient asthe gantry angle is varied. We have considered both modelcases �in phantom� and in patient brain and lung cases. Thesimulations using the RBP geometry at a low magnetic fieldstrength �0.2 T� have demonstrated hot spots limited to amaximum/minimum of �12% �of normalization point dosefor a 0.0 T field case� in regions where the anatomy allowsfor the maximal influence of the magnetic field on the elec-tron trajectories �lung plan�. In the case of a four field brainplan, the influence of the magnetic field on dose distributionfor the RBP geometry is minimal �although not necessarilynegligible� for low magnetic field strength. In comparison,

dose distributions generated in the FC geometry using a

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magnetic field strength of 1.5 T indicate differences in doseof up to +10% and −5% for the brain plan and +30% and−15% for the lung plan.

ACKNOWLEDGMENTS

The authors would like to thank J. Sempau, A. Bielajew,and I. Kawrakow for assistance and discussion on variousaspects of the MC simulations. Funding for this work wasprovided by the Alberta Cancer Foundation and the AlbertaCancer Board.

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FIG. 7. The relative dose for a five field lung plan su-perimposed on CT data slices for the conventional�B0�=0.0 T case shown in �a� transverse and �b� sagittalplanes through the isocenter. The dose is normalized atthe isocenter for the �B0�=0.0 T case for all simula-tions. Also shown are differences of D0.2 T−D0.0 T inthe �c� transverse and �d� sagittal planes where D0.2 T

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