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I. INTRODUCTIONHistorically, radiation oncologists have disregarded the ef-fects of different densities in the human body.14 SinceCompton interactions, which dominate in therapeutic energybeams, are dependent on electron density and not physicaldensity, this approximation has been generally correct. Algo-rithms attempting to correct for density differences ~Equiva-lent Pathlength, TAR ratio, Power Law! have been based onscaling beam data measured in a water phantom according tophysical densities. These corrections ignore electron trans-port.

Currently there is a great interest in combining multiplesmall beamlets to create a predefined dose distribution.Intensity-modulated radiation therapy ~IMRT! uses a seriesof beamlets varying in intensity to paint a dose picture orintensity map. Beamlets of greater intensity create darkerpixels ~higher dose! than those of lower intensity. By de-creasing the size of the beamlets, a higher resolution inten-sity map can be created, resulting in a finer ability to tailorthe dose distribution. Multileaf collimators ~MLCs! creatingbeams of 0.5 cm and less, including the Millenium 120 fromVarian Oncology Systems, Palo Alto, CA, the Beak slit col-limator from NOMOS Corp, Sewickley, PA, and the m3micro-MLC from Brainlab AG Heimstetten, Germany, arenow commercially available.

Although some studies have been conducted on the do-simetry of small photon beams,510 the effect of density dif-

ferences on such small beams has not been extensively stud-ied. Previous reports focused mainly on radiosurgical beamsgreater than 1.25 cm in diameter.24 The effects of air cavi-ties on radiosurgical beams, showing a dose drop across thecavity, subsequent buildup, and dose enhancement on thedistal side of the cavity, have been reported.3,4 Algorithmcomparisons in the presence of lung and air cavities havealso been studied down to 434 cm2 field sizes.1 Small beams~,1 cm! passing through different densities of lung or bone,however, have not been well studied.

Small radiation beams are inherently difficult tomeasure.511 Standard ion chambers are large in comparisonto the beam and do not have the spatial resolution needed toresolve the narrow central region of uniform dose and thesteep dose gradients of the penumbra;8 they may have a doserate dependence.12 Film, particularly Gaf chromic film, pre-pared and read carefully, may be the best availabledosimeter.1,2,47 It is widely available and does not requirespecialized development or reading equipment.

Ideally, one would like to study multiple densities, com-positions, energies, and field sizes without disturbing thebeam. This is best done using Monte Carlo computersimulation.4,5,8,11

II. MATERIALS AND METHODSThis research utilized the EGSnrc13 ~Electron Gamma

Shower, National Research Council! Monte Carlo code madeA Monte Carlo study of IMRT beamletAndrew O. Jonesb)Radiation Sciences, Drexel University College of MedicineIndra J. DasDepartment of Radiation Oncology, University of PennsylvFrederick L. Jones, Jr.Department of Thoracic Medicine, Geisinger Medical Cen~Received 19 March 2002; accepted for publication 16

Intensity Modulated Radiation Therapy ~IMRT! has trthereby increasing the resolution of the intensity maptors with beam apertures of 0.5 cm and less. The beanot been adequately assessed, especially in the presevices have significant limitations due to finite size, dthe effect of inhomogeneities on small beamlets. Thethe EGSnrc Monte Carlo code. Point source beams of cwere simulated in a water phantom at 100 SSD. A 3porated between 3 and 6 cm in the phantom. The depbeam size and density of the inhomogeneity. The Mfields a marked dose decrease in the presence of lelectronic equilibrium is observed. As the density andpronounced and for the 10 cm field there is an increasThis data suggests that current TPS may dramaticallygeneous media for small field sizes that are used foPhysicists in Medicine. @DOI: 10.1118/1.1539040#296 Med. Phys. 30 3, March 2003 0094-2405200330in inhomogeneous mediaa

hiladelphia, Pennsylvania 19102

ia, Philadelphia, Pennsylvania 19104

, Danville, Pennsylvania 17821

ovember 2002; published 5 February 2003!

ded toward smaller multiple radiation fieldsVendors have introduced multileaf collima-characteristics of these smaller fields havee of inhomogeneities. Most dosimetric de-e rate, and energy dependence. We studied15, and 24 MV beams were modeled using

cular field sizes 0.5, 1.0, 3.0, 5.0, and 10 cmm inhomogeneity of lung tissue was incor-dose curves and profiles were compared bynte Carlo simulations show that for small-density media due to the lack of lateraleld size increase, the dose reduction is lessdose as expected due to lack of attenuation.

over- or underestimate the dose in inhomo-IMRT. 2003 American Association of29632965$20.00 2003 Am. Assoc. Phys. Med.

297 Jones, Das, and Jones: A Monte Carlo study of IMRT beamlets 297available from the National Research Council of Canada.This is the latest version of the EGS series that simulateradiation interactions in any media. The user code DOSRZ14was used to define the problem. DOSRZ creates the input filesfor EGSnrc as defined in the cylindrical coordinate system.Photon spectra can be defined, as can geometry. Many mediaare provided with EGSnrc, or arbitrary media can be createdusing the PEGS4 ~preprocessor for EGS! software.

Predefined water, lung ~density 0.26 gram per cubic cen-timeter!, and bone ~density 1.85 grams per cubic centimeter!media were used. For lung tissue of different density PEGS4was used to define the lung using the elemental composition.Photon spectra for 6, 15, and 24 MV beams from Varianlinear accelerators from Mohan et al.15 provided with theEGSnrc package, were used. The parameters set for EGSnrcwere ECUT50.521 MeV, PCUT50.001 MeV, using thePRESTA algorithm. The only variance reduction used wasphoton forced interaction in the media.

Point source, circular beams were simulated at 100 cmsourcesurface distance ~SSD! from a semi-infinite phantom.The inhomogeneous media was placed between 3 and 6 cmin the phantom. The dose was calculated for 0.2 cm thick

FIG. 1. Depth dose curves for Monte Carlo simulated and measured 6 MVphoton beams in water. The curves show good agreement at all depths.

FIG. 2. Depth-dose curves for 6 ~dark solid!, 15 ~dashed!, and 24 ~lightsolid! MV beams using a 0.5 cm field size through lung and in a homoge-neous phantom. The large drop in dose across the lung density is evident asis the dose enhancement beyond the lung.Medical Physics, Vol. 30, No. 3, March 2003slabs from 0 to 12 cm. The radii of the dose volumes weredifferent for different field sizes. Simulations were run untilthe statistical errors were below 1%.

The verification of the Monte Carlo code was done bycomparing 0.5 cm depth dose curves generated for the 6 MVphoton beams to data measured on a clinical 6 MV photonbeam ~Varian Oncology Systems, Palo Alto, CA!. Figure 1shows good agreement between the Monte Carlo simulationand the measured beam data are very close at all depths.

Percentage depth dose curves were created for lung den-sities of 0.15, 0.20, 0.26, 0.30, 0.35, and 0.40 g/cm3, forbone of density of 1.85 g/cm3 and for water. Circular diam-eter field sizes of 0.5, 1.0, 3.0, 5.0, and 10.0 cm and beamenergies of 6, 15, and 24 MV were simulated. These curveswere compared with the homogeneous phantom data using a

FIG. 3. Depth dose curves for 24 MV photon beam showing the effects offield size. Increasing the field size decreases the dose drop across the inho-mogeneity, but the dose drop is still present at the relatively large field sizeof 5 cm.

FIG. 4. 6 MV photon depth dose curves for field sizes 0.5, 1, 3, and 5 cmgenerated using Monte Carlo calculations in a phantom with tissue density0.26 g/cm3 between 3 and 6 cm depth. By the 5 cm field size the dosedecrease in lung has nearly disappeared.

298 Jones, Das, and Jones: A Monte Carlo study of IMRT beamlets 298Dose Perturbation Factor ~DPF!, defined as the ratio of thedose at a point in the medium to the dose at that point inwater.

III. RESULTSIncreased photon transmission and the loss of lateral elec-

tronic equilibrium in small fields leads to a significant dosedrop in the lung tissue. Figure 2 shows a large dose drop inthe lung with a 0.5 cm field size for 6, 15, and 24 MV photonbeams. The decrease begins proximal to the tissuelung in-terface as the contribution from backscattered photons andelectrons decreases. Across the lung tissue the depth dosedecreases only slightly before rising abruptly at the distallungtissue interface. Beyond the interface the dose is en-hanced, mainly due to the increased photon fluence throughthe lung.

For the 24 MV photon beam the dose decrease effect isevident with field sizes as large as 5 cm, as seen in Fig. 3.

FIG. 5. Graph of average DPF versus Field size for 6, 15, 24 MV beamenergies showing decreased DPF with increased energy for all field sizes.

FIG. 6. Average Dose Perturbation Factors ~DPFs! for 6 MV photons as afunction of density for 0.5, 1.3, and 5 cm field sizes with lung tissue locatedbetween 3 and 6 cm depth showing the dependence of the DPF on field sizeand density. The humps at 0.2 g/cm3 density may be the result of statisticalnoise in the Monte Carlo calculation.Medical Physics, Vol. 30, No. 3, March 2003The higher-energy electrons have greater range, leading tolateral electronic disequilibrium persisting through largerfield sizes. Increased photon transmission also leads to adose enhancement distal to the second lung tissue interface,even for the large 10 cm field. Although the region beyondthe lung benefits from an increased dose, the region nearestthe interface is underdosed as the dose builds up due to in-creased photon attenuation and decreased electron range.Similarly, Fig. 4 shows a drop in the depth dose across thelung for the 6 MV photon beam. The buildup beyond thesecond interface is similar as well, however, the effects of thefield size are not as great for the low-energy beam. By thetime the field size reaches 5 cm, the dose deficit in the lunghas been erased and a slight increase is seen.

The effect of the lung tissue on the dose as a comparisonto the homogeneous case can be determined by looking atthe DPF. A gauge of the generalized effects is a plot of theaverage DPF through the center of the lung volume, as seenin Fig. 5. As expected, the average DPF across the lungincreases with decreasing energy due to the increased photontransmission and electron range of the high-energy beams.The curves converge at the extremes of field size. For thelarger fields, lateral electronic equilibrium is eventually es-tablished even for the high energy beams and the effects ofthe low-density lung become more consistent with the lower-energy beams, which established equilibrium at smaller fieldsizes. For the small fields the DPF converges as the fieldsbecome so small that even the low-energy electrons thatdominate in the 6 MV photon beam escape the field. Thisconvergence is to be expected since extrapolating the fieldsto a zero field size where all of the secondary electrons es-cape the field would create a convergence, even for thelowest-energy photon field.

Figures 6 and 7 show the effects of density on the dose tothe lung. The average DPF taken across the central region ofthe lung is plotted against the density of the lung for 6 MV~Fig. 6! and 15 MV ~Fig. 7! photon beams. As expected,decreased photon transmission and electron range combine

FIG. 7. DPF curves for a 15 MV photon beam showing the effects of densityand field size. For smaller field sizes the change in DPF with density israpid. Once lateral electronic equilibrium is reached, the density effect ismuch less.

299 Jones, Das, and Jones: A Monte Carlo study of IMRT beamlets 299to increase the DPF as the media becomes denser. With morephotons liberating secondary electrons and the pathlengths ofthe electrons becoming shorter, more of the KERMA is ulti-mately captured within the field as dose. The increase in DPFwith density is not, however, linear. The DPF increases morerapidly than the density for all field sizes at both energies.The bumps in the 10 cm field size curves are likely due tostatistical noise in the Monte Carlo data for that particularfield size. These curves suggest a more complex relationshipin low-density dosimetry than simple radiological scaling ofthe physical density.

IV. DISCUSSIONSignificant dose perturbations are observed proximally,

distally, and within different density media. For lower-density media like lung, all beam energies show a significantdose decrease in the inhomogeneity, as seen in Fig. 2. This isat odds with the traditional dose algorithms, such as theequivalent pathlength algorithm, which scale the dose ac-cording to the inverse of the density. Although the dose de-crease is most prominent at small field sizes, for higher en-ergies such as the 24 MV beam shown in Fig. 3, it persists upto more traditional clinical field sizes of 10 cm.

The study also shows the dose changing proximal to thetissuemedia interface, either dropping at the lung interfaceor increasing for the bone. The changes, the result of differ-ences in the electron backscatter at the interface, are notmodeled even in modern dose algorithms like convolutionsuperposition.

The dose decrease in the lung is nonlinearly related tofield size, as evidenced in the DPF curves in Fig. 5. Thepoint at which the DPF reaches 1.0, i.e., no dose changefrom water, occurs when the field radius is about 2 cm for a6 MV beam. At this point lateral electronic equilibrium isreached and electrons that are created within the field willdeposit their energy within the field. The higher-energy 15and 24 MV beams show a dose decrease through correspond-ingly larger field sizes, finally reaching a DPF of 1.0 at closeto a 10 cm field size. This observation points out that thedensity scaling flaw of traditional algorithms is present for ahigh-energy beam even at more traditional clinical fieldsizes.

The DPF increases with increasing density of the lung,but again nonlinearly, as seen in Figs. 6 and 7. Larger fieldsizes show less variation due to density. The 15 MV 0.5 cmfield shows a greater than 40% increase in DPF from a den-sity of 0.15 g/cm3 to 0.40 g/cm3, whereas the 5 cm fieldincreases only about 15%. The increases are not linear withdensity reflecting a need to use a different scaling factor thanphysical density.

Dose beyond the lung is increased regardless of field sizeor energy. Even in cases where the lung dose is enhanced,the dose beyond the lung is also enhanced. This is due todecreased photon attenuation and increased transmission offorward scattered electrons through the lung depositing theirdose distal to the interface. A secondary buildup region isseen at the lungtissue interface that corresponds to this hy-Medical Physics, Vol. 30, No. 3, March 2003pothesis. Traditional experience with density-scaled algo-rithms also supports dose enhancement beyond the low-density media.

For small fields of diameter less than the range of theelectrons set into motion, electrons and scattered photon gen-erated anywhere within the field can potentially escape. Forfields that are approximately the width of the range, the ef-fects are small since the photon interactions are dominatedby Compton interactions and the scatter is forward-peaked.As the field size decreases, photons and electrons scattered atsmaller angles will leave the field and not be replaced. Thetotal KleinNishina cross section per electron is independentof the atomic number because the electron binding energy isassumed to be 0, since the photon energy is much greaterthan the electron binding energy.15 Hence, the Compton massattenuation coefficient is linearly dependent on the electrondensity. Electron density is approximately independent ofatomic number ~except for hydrogen; Z/A is about constantexcept at high Z! so the total Compton mass attenuation forall elements and mixtures found naturally in the body isabout equal. Thus, the largest effect on the cross sections willbe the electron density, which is proportional, generally, tothe density of the material.

The KleinNishina interaction cross section and the scat-tering angle cross section decrease with increasing energy.Thus, fewer photons are interacting and the recoil angle ofthe electron is decreasing.16 At the same time the range of theCompton electrons is increased. The stopping power of themedium for electrons is also dependent upon the electrondensity and inversely dependent on their velocity. Therefore,lower-density media and higher-energy electrons combine toincrease the range.

Taking all these issues into consideration shows that smallfields in low-density media will experience decreased photonattenuation and increased electron range. Increasing thebeam energy in this situation would decrease the photon at-tenuation, increase the electron range, and decrease the elec-tron recoil angle. For the energies commonly used in radio-therapy ~425 MV! the change in the angular distribution ofthe recoil electrons is slight. The result is fewer photonsinteracting, electrons depositing their dose farther down-stream, and more electrons leaving the radiation field; lateralelectronic disequilibrium. Within the low-density regionthere is a dose deficit.

The magnitude of the change in dose is not linearly re-lated to the physical density despite the relationship of theattenuation coefficients and the mass stopping power tophysical density. Although the stopping power for the elec-trons and the attenuation coefficients for the photons are re-lated to the density they are interdependent and the combi-nation is nonlinear. This observation may be due to changesin the electron and photon spectra or changes in the scatter-ing characteristics of the photons and electrons. Electronstopping power varies as the natural logarithm of the meanexcitation potential of the media, however, converting thedose in lung to dose in water changes the results by less than2%,17 ruling out the effect of different elemental composition

of the lung. The net effect is a function of beam energy,physical density, and field size.

Although this study looked only at the effects of the cen-tral axis dose, the low-density regions will affect the beamprofile as well. Several studies looked at the influence of aircavities on radiosurgical beams.3,4,9 These studies haveshown that the penumbra of small beams is flattened out,becoming wider on the low dose area and narrower towardthe center of the beam with the change in full-width at tenthmaximum increasing up to a factor of 1.23 with decreasingfield size.4 The total penumbra width measured from the90%10% lines has been shown to increase with increasingfield size and air gap depth.3 The full-width at half-maximumwas nearly the same in both the heterogeneous and homoge-neous phantoms for all the studies. This result correlates withthe lateral loss of electrons from the center of the field to the

2 S. N. Rustgi, A. K. Rustgi, S. B. Jiang, and K. M. Ayyangar, Doseperturbation caused by high-density inhomogeneities in small beams instereotactic radiosurgery, Phys. Med. Biol. 43, 35003518 ~1998!.

3 A. K. Rustgi, M. A. Samuels, and S. N. Rustgi, Influence of air inho-mogeneities in radiosurgical beams, Med. Dosim 22, 95100 ~1997!.

4 T. D. Solberg, F. E. Holly, A. A. F. DeSalles, R. E. Wallace, and J. B.Smathers, Implications of tissue heterogeneity for radiosurgery in headand neck tumors, Int. J. Radiat. Oncol., Biol., Phys. 32, 235239~1995!.

5 B. E. Bjamgard, J.-S. Tsai, and R. K. Rice, Doses on the central axes ofnarrow 6-MV x-ray beams, Med. Phys. 17, 794799 ~1990!.

6 R. K. Rice, J. L. Hansen, G. K. Svensson, and R. L. Siddon, Measure-ments of dose distributions in small beams of 6 MV x-rays, Phys. Med.Biol. 32, 10871099 ~1987!.

7 S. N. Rustgi and D. M. D. Frye, Dosimetric characterization of radio-surgical beams with a diamond detector, Med. Phys. 22, 21172121~1995!.

8 M. Westermark, J. Arndt, B. Nilsson, and A. Brahme, Comparative do-simetry in narrow high-energy beams, Phys. Med. Biol. 45, 685702

300 Jones, Das, and Jones: A Monte Carlo study of IMRT beamlets 300edges and the corresponding drop on the central axis doseseen in this study. How penumbral widening changes relativeto density was not studied, but it can be surmised that theeffect would mimic the central axis depth loses and becomeless pronounced with increasing density as the electron rangedecreases. Further study in this area is warranted.

V. CONCLUSIONSSignificant changes occur in and near tissue inhomogene-

ities. These changes are not easily modeled using only physi-cal density. They are dependent upon multiple interconnectedfactors including density, field size, and beam energy. Dosealgorithms that attempt to scale dose only by physical den-sity do not accurately predict dose within or near inhomoge-neities. This is especially true with the smaller field sizesbeing used for IMRT. More study is being conducted toevaluate the magnitude of the differences between the MonteCarlo results and current IMRT algorithms.

a!Presented in part at the 2001 AAPM meeting in Salt Lake City, Utah.b!Please address correspondence to Andrew Jones, MS, Department of Ra-

diation Oncology, Bryn Mawr Hospital, 130 South Bryn Mawr Avenue,Bryn Mawr, Pennsylvania 19010. Telephone: ~610! 526-3372; electronicmail: JonesAO@netscape.net

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