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Int. J. Radiation Oncology Biol. Phys., Vol. 66, No. 5, pp. 1576–1583, 2006Copyright © 2006 Elsevier Inc.

Printed in the USA. All rights reserved0360-3016/06/$–see front matter

doi:10.1016/j.ijrobp.2006.08.059

HYSICS CONTRIBUTION

DOSIMETRIC VALIDATION OF THE MCNPX MONTE CARLOSIMULATION FOR RADIOBIOLOGIC STUDIES OF

MEGAVOLTAGE GRID RADIOTHERAPY

HUALIN ZHANG, PH.D.,*† ELLIS L. JOHNSON, PH.D.,† AND ROBERT D. ZWICKER, PH.D.†

*Department of Radiation Medicine, The Ohio State University, Columbus, OH; †Department of Radiation Medicine,University of Kentucky Chandler Medical Center, Lexington, KY

Purpose: To validate the MCNPX Monte Carlo simulation for radiobiologic studies of megavoltage gridradiotherapy.Methods and Materials: EDR2 films, a scanning water phantom with microionization chamber and MCNPXMonte Carlo code, were used to study the dosimetric characteristics of a commercially available megavoltage gridtherapy collimator. The measured dose profiles, ratios between maximum and minimum doses at 1.5 cm depth,and percentage depth dose curve were compared with those obtained in the simulations. The simulatedtwo-dimensional dose profile and the linear-quadratic formalism of cell survival were used to calculate survivalstatistics of tumor and normal cells for the treatment of melanoma with a list of doses of the fractionated gridtherapy.Results: A good agreement between the simulated and measured dose data was found. The therapeutic ratiobased on normal cell survival has been defined and calculated for treating both the acute and late respondingmelanoma tumors. The grid therapy in this study was found to be advantageous for treating the acutelyresponding tumors, but not for late responding tumors.Conclusions: Monte Carlo technique was demonstrated to be able to provide the dosimetric characteristics forgrid therapy. The therapeutic ratio was dependent not only on the single �/� value, but also on the individual� and � values. Acutely responding tumors and radiosensitive normal tissues are more suitable for using the gridtherapy. © 2006 Elsevier Inc.

Grid, Therapeutic ratio, Monte Carlo simulation, MCNPX, Melanoma.

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INTRODUCTION

he concept of intensity modulation in radiation therapy hasndergone major development in the past few years. Recentdvances in understanding radiobiologic effects as wells technological improvements in treatment delivery havereatly expanded the use of intensity-modulated beams (1–7).ost efforts have been directed at approaches that use

everal highly modulated beams that overlap so as to pro-uce a relatively uniform dose in target areas while keepingoses to critical structures as low as possible. However,ohiuddin et al. (8) have suggested a novel use for intensityodulation of megavoltage therapy beams, commonly re-

erred to as spatially fractionated or grid therapy, that pur-osefully maintains a high degree of dose variation acrosshe treated volume. Grid therapy has shown promise as aethodology for improved treatment for advanced, bulky

umors (9). Whereas multileaf collimator or compensator-

Reprint requests to: Hualin Zhang, Ph.D., Department of Radi-tion Medicine, Ohio State University, 300 W. 10th Ave, Colum-us, OH 43210-1228. Tel: (614) 293-7497; Fax: (614) 293-4044;-mail: zhang.568@osu.educknowledgments—We authors thank Dr. R. F. Barth and Dr. J.

ang of the Ohio State University for helpful discussions and A

1576

ased intensity-modulated radiation therapy uses conven-ional fractionation schemes (typically 1.8 to 2.0 Gy perraction), grid therapy relies on a single, large dose fraction,enerally 15 Gy, followed by additional conventional treat-ents. The grid fraction has been shown to improve the

esponse to the conventionally administered radiotherapy9) and may possibly have cell-killing effects outside theirectly irradiated area (6). The radiobiologic response tohe grid fraction is not well understood and is currentlyeing investigated by several researchers. The single gridraction is well tolerated, and it is generally believed thatow-dose regions in normal tissues act as regenerative cen-ers for these tissues (9, 10).

Dosimetric properties of megavoltage grid fields haveeen previously investigated. Reiff et al. (11) measuredepth dose curves and peak-to-valley ratios in a waterhantom for various field sizes of a square pattern grid.

r. M. Mohiuddin of the University of Kentucky for support of theork. We also thank Dr. Cyril Smith, Chief Physicist of Velindreospital of Cardiff, United Kingdom, for providing the 6X energy

pectrum of the Varian linac machine.Received Feb 16, 2006, and in revised form Aug 21, 2006.

ccepted for publication Aug 23, 2006.

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1577Dosimetric validation of megavoltage grid radiotherapy ● H. ZHANG et al.

rapp et al. (12) have measured three-dimensional doseistributions of grid collimated photon fields using gels.lectron grid fields have also been investigated (13).wicker et al. (14) have calculated cell survival statisticsnd therapeutic ratios based on an assumed axially symmet-ic dose profile for a single aperture circular unit area of arid field. This work expands upon these previous efforts bysing methods with EDR2 film, a scanning water phantomith microionization chamber, and MCNPX Monte Carloethods. We have used film and water phantom measure-ents to obtain estimates of percent depth dose and various

ose profiles. The results validated the Monte Carlo simu-ation. In addition, radiobiologic studies of grid fields haveeen generated using the actual two-dimensional (2D) sim-lated dose distributions, thereby obviating the need for thexially asymmetric dose profile assumption. Cell survivaltatistics and therapeutic ratios have been calculated usinghe linear-quadratic model for treating the acutely and lateesponding melanoma at a list of fractionated doses rangingrom 10 to 30 Gy.

METHODS AND MATERIALS

rid collimatorThe grid collimator used for obtaining measured data in this

tudy (High Dose Radiation Grid; Radiation Products Design,lbertville, MN) consists of a series of cylindrical apertures withivergent axes arranged in a hexagonal close-packed form withinCerrobend block 7.5 cm thick. The Cerrobend block is mountedn a support plate with dimensions of a standard block tray, andhe assembly fits into the custom block accessory mount in theead of the linear accelerator. The aperture diameter of the gridollimator is 0.60 cm on the upper surface and 0.85 cm on theower surface. The center-to-center spacing of holes on the colli-ator is 1.15 cm. The aperture diameter and center-to-center

pacing are 1.3 cm and 1.8 cm, respectively, as projected in thelane of isocenter. The plane of the grid field can be considered toonsist of a tiled array of equilateral triangles with sides 1.8 cmong whose vertices correspond to the centers of circular apertures.his arrangement of aperture size and spacing results in a ratio ofpen area to blocked area of approximately 2:3. A diagram of therid collimator is shown in Fig. 1, illustrating the arrangement ofpertures and the triangular shaped repeating area unit.

DR2 film dosimetryEDR2 film (Eastman Kodak, Rochester, NY) has been widely

sed in radiotherapy applications, including intensity-modulatedadiation therapy quality assurance, and has been shown to have aetter dose–response range and improved linearity (15). In thisork, EDR2 film was irradiated in Solid Water (Gammex RMI,iddleton, WI) slab phantoms to obtain cross-beam profiles. Filmsere irradiated at a depth of 1.5 cm using 6-MV photons from alinac 2100 EX linear accelerator (Varian Oncology Systems,ilpitas, CA). Calibration curves were obtained for each batch

f film. The film was processed at least 3 h after irradiation toinimize known time-dependent film sensitivity (16). All filmsere scanned using an Epson Expression 1680 flat bed scanner

Epson America, Inc., Long Beach, CA) and analyzed with Procheck

. 2.7 (NMPE, Lynnwood, WA). Beam profiles of the grid field S

ere obtained in both the radial and transverse directions, as wells in a full 2D representation.

ater phantom measurementsAll water phantom measurements were performed using a Well-

oeffer scanning system (Scanditronix-Wellhoeffer North Amer-ca, Bartlett, TN). The system consisted of a 48 � 48 � 48 cmater tank, a CU 500E electrometer, and WP700 v. 3.4 data

cquisition/processing software. A Wellhoeffer CC01 microion-zation chamber was used for all in-field measurements. The gridas placed in the blocking tray slot of the Clinac 2100 EX linear

ccelerator. Data were acquired for 6-MV photon beams at 100ource to surface distance (SSD).

Depth ionization scans were obtained along the beam centralxis under the central aperture of the grid for 5 � 5, 10 � 10, 15 �5, and 20 � 20 cm collimator jaw settings. The scanning systemas carefully aligned to maintain the ion chamber at the center of

he beam profile at all depths. Depth doses were assumed to beirectly obtainable from the normalized depth ionization profilesithout any further consideration for loss of electronic equilibriumr energy spectrum changes.Cross-beam ionization profiles were obtained in both the trans-

erse and radial planes at a depth of 1.5 cm. Because the gridpertures were arranged in a hexagonal close-packed form, theransverse profiles cut the grid along a line joining opposite ver-ices (apertures) of the central hexagon, whereas the radial profilesut the grid along a line bisecting opposite sides of the centralexagon. Therefore, the spacing between the peaks and the heightsf the peaks and valleys in the profiles are different for the tworthogonal scan directions. The transverse and radial dose profilesere obtained directly from the normalized ionization profilesithout any further consideration for loss of electronic equilibriumr energy spectrum changes.

onte Carlo simulationA Monte Carlo N-particle Transport Code (MCNPX, V. 2.5)

17) was used to calculate the doses in water at a depth of 1.5 cm.he code is the extension for particle types and energy ranges ofCNP (18). The photon interaction cross-section file used in this

tudy was the DLC-200 library distributed by the Radiation

Fig. 1. Schematic diagram of grid collimator.

hielding Information Computing Center (RSICC). The MCNPX

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1578 I. J. Radiation Oncology ● Biology ● Physics Volume 66, Number 5, 2006

ode considers photoelectric, coherent, Compton, and pair produc-ion interactions. There are several tally types available in the

CNPX code for dose calculation. The *f8 tally calculates theifference between the energy carried into and out of the tally celly particles. In this project, the *f8 tally type was used to deter-ine the dose rate distribution in the flat water phantom at the

epth of interest, 1.5 cm, as well as the central axis percent depthose.A simplified source model, first described by DeMarco et al.

19) and Lewis et al. (20), was used in this study and is illustratedn Fig. 2b. Although this design ignores the true photon phasepace distribution, as pointed out by Siebers et al. (21), its effec-iveness and accuracy have been demonstrated for flat phantomshen fine beam structure is not emphasized. However, this sim-lified model ignores the existence of electron contamination inhoton beam. The cone-beam angle was chosen to allow a maxi-um field size of 40 � 40 cm on the phantom surface at 100 cmSD by collimators located 53 cm from the source. A spectrumepresentative of photon energies that exit the monitor ionizationhamber was used. This spectrum was previously determined for aarian 21 EX 6-MV photon beam by Spezi et al. (22) andalidated by comparison to that obtained from EGS4 code (23).The grid collimator was simulated as a 2D array of 19 cylindri-

al apertures having an 0.8-cm diameter and a 7.5-cm lengthrranged within a Cerrobend block in the hexagonal pattern shownn Fig. 1. The long cylinder axis was aligned parallel to the beamentral axis. This arrangement represented the central area (4 �cm) well, but not the holes far away from the beam axis, because

hese holes were divergent in both shape and direction to makehe dose output of each the same as that of the central ones. Theeasurements have shown that this design produced the same out-

ut from all of the holes. To avoid the complex work of modelingistant holes, the simulations in this work focused on the centralrea, and the data were then extended to the other areas. The SSDor the phantom was set at 100 cm. An array of spherical voxelsaving a 1-mm diameter and 4-mm center-to-center spacing wasefined at a depth of 1.5 cm for dose profile simulation. The depthose was obtained using 1-mm voxels with a 2-mm spacing

ig. 2. Schematic diagram of linac photon source showing (a)etailed head design and (b) the simplified model used in thisimulation.

rranged along the beam central axis. For each simulation, the low

nergy cutoff was set at 10 keV and used a minimum of 5 � 108

istories.

adiobiological propertiesThe linear-quadratic model was used to obtain cell survival

tatistics for both tumor and normal cells. The fraction of cellsurviving a uniform dose, D, is given by (24, 25):

SF � e (��D���G · D2) (1)

here SF is the fraction of surviving cells; � and � are the linearnd quadratic coefficients, respectively; and D is uniform irradia-ion dose. G is the LeaCatheside function. When the actual treat-ent time is shorter than the estimated characteristic repair time,

he G function could be used as:

G � 1 ⁄ N (2)

here N is the number of fractions (26).We used the �/� values ranging from 1.2 to 8.7 Gy for theelanoma cell lines reported by Brenner and Hall (25). The �/�

alue for muscle is 3.1 Gy, which was taken from Rodney et al.27). Considering that Thames et al. reported an �/� value for lateffects in the normal tissue of 2–4 Gy (28) and Bodey et al.eported 3 Gy (29), the value of 3.1 Gy can be considered typicalor late responding normal tissues. For the melanoma cell linessed in this study, the � and � values were also taken from anrticle by Brenner and Hall (25). Because experimental data forndividual � and � values for the normal muscle tissue were

Table 1. Radiation linear-quadratic parameters of tumors andnormal tissues

Tissue type Cell lines�

(Gy�1)�

(Gy�2)�/�(Gy)

elanoma Sk-me128 0.13 0.0113 1.2elanoma EE 0.21 0.1 2.1elanoma MF 0.28 0.0879 3.2elanoma EF 0.35 0.0701 5.0elanoma RPMI7951 0.27 0.0468 5.8elanoma G.E 0.61 0.101 6.0elanoma HX-34 0.27 0.0421 6.4elanoma V.N 0.53 0.0783 6.8elanoma HX-118 0.33 0.038 8.7ormal tissue 1 SFNT(2 Gy) � 0.3 0.366 0.118 3.1ormal tissue 2 SFNT(2 Gy) � 0.5 0.211 0.068 3.1ormal tissue 3 SFNT(2 Gy) � 0.7 0.108 0.035 3.1

Tumor cell linear-quadratic parameters were taken from theiterature [25]. Normal tissue 1, 2, and 3 represent the normaluscle tissue (NT) surviving fraction (SF) of 0.3, 0.5, and 0.7 atGy open field irradiation, respectively.

Table 2. Maximum/minimum dose ratio for 1-cm-diameter gridholes in a 6-MV photon beam at 1.5 cm depth

Technique Max/Min ratio

EDR2 film 5.3:1 (�10%)Ion chamber 5.4:1 (�5%)

Monte Carlo 5.9:1 (�7%)

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1579Dosimetric validation of megavoltage grid radiotherapy ● H. ZHANG et al.

acking, we assumed that 2 Gy open field irradiation would kill0%, 50%, and 70% of the cells, then calculated the individualalues of � and � by deriving Eq. 1, which produced 0.366 Gy�1

nd 0.118 Gy�2, 0.211 Gy�1 and 0.068 Gy�2, 0.108 Gy�1 and.035 Gy�2, respectively, for those percentages. The �/� value foruscle was set at 3.1 Gy. Using these radiobiology parameters

Table 1), we were able to evaluate the therapeutic advantage ofrid therapy.We now assumed that the overall behavior for cell survival in

he highly nonuniform dose field of the grid could be approximateds a simple average of Eq. 1. We also assumed that the dose extreman the 2D grid distribution would not vary significantly in magni-ude over the entire grid field and that the field would be coveredy a whole number of repeating unit areas. These assumptionserve to limit the required integration space of Eq. 1 to that of aingle repeating unit area, as shown in Fig. 1. Using these assump-ions, the average surviving fraction over the grid field is given by:

SF �

�A

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�A

dxdy(3)

here SF is the average cell survival fraction, SF[D(x, y)] is theurvival fraction at the point (x, y), D(x, y) is the simulated 2D gridose distribution over the x, y plane, and A is the repeating unitrea.

Average cell survival fractions were determined for both normal

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ig. 3. Percent depth dose (PDD) along the central axis aper-ure.

Radial dose profile

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20

40

60

80

100

120

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Monte Carlo EDR2 film Wellhoeffer

Fig. 4. Radial dose profiles obtained from a 10 � 10 grid field. E

nd tumor cells in open beams as well as grid collimated fields. Forhe grid collimated fields, 10-, 14-, 20-, 26-, and 30-Gy maximumoses were assumed to be delivered at a depth of 1.5 cm in water.he dose for the open field at 1.5 cm depth, Dopen, was adjusted toive the same surviving fraction for tumor cells as that determinedrom the grid field. Therefore, the endpoint for comparison of therid and open fields was equivalent surviving fractions of tumorells. We now defined a therapeutic ratio based upon survivingractions of normal cells as:

TRnormal �SFnormal (Grid)

SFnormal (Open)(4)

here TRnormal was the therapeutic ratio for survival of normalells, SFnormal (Grid) was the fraction of surviving normal cells

Transverse dose profile

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40

60

80

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120

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ig. 5. Transverse dose profiles obtained from a 10 � 10 grideld.

ig. 6. Two-dimensional dose distribution at 1.5 cm depth from

DR2 film measurement.

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1580 I. J. Radiation Oncology ● Biology ● Physics Volume 66, Number 5, 2006

fter a grid irradiation, and SFnormal (Open) was the fraction ofurviving normal cells after an equivalent open field irradiationhat killed the same fraction of investigated tumor cells. A value ofRnormal greater than 1 would infer a survival advantage forormal tissue cells in a grid irradiation.

RESULTS

aximum/minimum dose ratioThe maximum/minimum dose ratio is an important char-

cteristic for a megavoltage grid field, because it gives anndication of how the grid treatment will be tolerated byormal tissues. Maximum/minimum dose ratios were mea-ured by EDR2 film, water phantom scanning, and Montearlo simulation. These ratios are summarized in Table 2.

ercent depth doseMeasurements of percent depth dose were made along the

entral axis aperture for a 10 � 10 cm grid field using theellhoeffer scanning system and compared with data ob-

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ig. 7. Two-dimensional dose distribution at 1.5 cm depth fromonte Carlo simulation.

Table 3. Therapeutic ratios as a function of melanoma �/� value w

Cell lines �/�10 Gy

(2 Gy � 5 fx)14 Gy

(2 Gy � 7 fx

k-me128 1.2 0.898 0.845.E. 2.1 0.918 0.883.F. 3.2 0.931 0.913

.F. 5.0 0.954 0.96PMI7951 5.8 1.060 1.107.E. 6.0 0.941 0.958X-34 6.4 1.082 1.143.N. 6.8 0.892 0.896X-118 8.7 1.068 1.138

verage — 0.972 0.983

ained from the Monte Carlo simulation. These results showood agreement and are summarized in Fig. 3.

ose profilesCross-beam profiles at a depth of 1.5 cm were obtained

or the 10 � 10 cm grid collimated field using EDR2 film,he Wellhoeffer scanning system, and Monte Carlo simula-ion. Results are summarized below for both radial andransverse directions, as illustrated in Figs. 4 and 5, respec-ively. Although agreement was excellent for the centralxis aperture, some differences could be seen for noncentralpertures.

D dose distributionThe 2D dose distribution at a depth of 1.5 cm was

btained from EDR2 film scanning and Monte Carlo sim-lation. The film and Monte Carlo results are shown in Figs.and 7, respectively.

adiobiological studiesSurvival statistics were determined for 10-, 14-, 20-, 26-,

nd 30-Gy doses delivered by a grid collimated field at aepth of 1.5 cm in a list of melanoma tumor cell lines andssumed normal muscle (Table 1). The corresponding dosesor same tumor cell killing of a uniform open field wereerived, and the normal tissue survival ratios at those openelds were further calculated. The therapeutic ratios ofelanoma for the normal tissue 2-Gy surviving fraction at

.5 are summarized in Table 3. Table 3 shows that gridherapy has an advantage, i.e., produces therapeutic ratios

1.0, when treating acutely responding tumors (�/� �5.0y) except for the V.N. cell lines. The results indicated

mproved normal tissue tolerance for the grid-modulatedelds over that obtained by uniform open beams. Table 3lso shows that there is no advantage in treating late re-ponding melanoma tumors (�/� �5.0 Gy) with grid ther-py, i.e., the therapeutic ratios were less than or equal to 1.0.

Table 4 presents the data analysis used in this work forach cell line by singling out the melanoma HX-34 cell line.able 4 indicates that the therapeutic ratio increases with the

normal tissue 2-Gy surviving fraction at 0.5 [SFNT(2 Gy) � 0.5]

Therapeutic ratio (TR)

20 Gy(2 Gy � 10 fx)

26 Gy(2 Gy � 13 fx)

30 Gy(2 Gy � 15 fx)

0.776 0.715 0.6780.841 0.805 0.7820.898 0.889 0.8850.984 1.019 1.0461.186 1.273 1.3361.013 1.086 1.1431.245 1.358 1.4410.929 0.979 1.0191.267 1.424 1.546

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ose for radiosensitive normal tissues [SFNT(2 Gy) � 0.3,.5]. The radioresistant normal tissue [SFNT(2 Gy) � 0.7]as an almost constant therapeutic ratio value, showing nodvantage from the grid therapy.

Table 5 summarizes the mean therapeutic ratio values ofll melanoma cell lines for different normal tissue types asfunction of doses. The therapeutic ratio increases with theose for the radiosensitive normal tissues [SFNT(2 Gy) �.3, 0.5], but the radioresistant normal tissue [SFNT(2 Gy) �.7] does not favor the grid therapy. Table 6 gives theormal tissue cell survival fractions at different doses. Theverall normal tissue survival fraction decreases with in-reasing dose and therapeutic ratio.

DISCUSSION

The general dosimetric properties of the grid collimatedeld, such as percent depth dose and dose profiles near theentral axis, were reproduced quite well by the simulation.hese results demonstrate the adequacy of the simplifiedhoton source model used in this simulation. However,ome differences can be seen for apertures located awayrom the central axis. In addition, the disagreement worsenss the off-axis distance of the aperture increases. We believehe reason for this discrepancy lies in the manner in whichhe aperture array was defined in the Monte Carlo simula-ion. The apertures were defined as an array of cylindricaloles whose axes were all aligned parallel to the beamentral axis. This lack of divergence for apertures locatedway from the central axis led to reduced photon emittanceor these apertures. The result was an artificial narrowing of

Table 4. Surviving fractions in open and gri

Dose ingrid therapy

(Gy)

Tumorsurvivingfraction

Equivalentopen fielddose (Gy)

Tumor SF atequivalentopen field

Nor[SFNT

SF(grid)

10 0.436 3.27 0.436 0.34914 0.357 2.69 0.357 0.27420 0.275 3.19 0.275 0.19826 0.217 3.62 0.217 0.14530 0.186 3.88 0.186 0.119

Abbreviations: SF � surviving fraction; NT � normal tissues;

Table 5. Therapeutic ratios as a function of no

Normal tissue10 Gy 14 Gy

(2 Gy � 5 fx) (2 Gy � 7 fx)

FNT(2 Gy) � 0.3 1.227 1.337FNT(2 Gy) � 0.5 0.972 0.983FNT(2 Gy) � 0.7 0.900 0.869verage 1.033 1.063

Abbreviations: NT � normal tissues; SF � surviving fraction.

he beam profile and reduced amplitude of the peak inten-ity.

Compared with a real photon beam generated by a mod-rn linac machine, our simplified model ignored the exis-ence of electron contamination. Therefore, it is to be ex-ected that the simulated dose ratio of maximum/minimumill be slightly higher than the measured one. Because the

lectrons in the contaminated photon beam would increasehe valley dose of the profiles, the measured maximum/inimum ratio would be lower than the simulated one.Although the dosimetric differences in the profiles are

eadily understood in relation to the nondivergent apertureeometry, the effects of the simulated 2D dose profile on theell survival calculations are less clear. However, a com-arison of 1D cell survival/therapeutic ratio calculationssing both the measured and simulated data shows similaresults. In addition, limitation of the calculation area for cellurvival to a central repeating unit where the dosimetricifferences are minimal would reduce the impact of theeficiencies in the current simulation on the radiobiologicalesults. While these results are in general agreement withhe values of Zwicker et al. (14), the use of more accurateose profiles and experimental radiobiology parameters� and �) in this work has provided more reliable data as theeferences for clinical trials. Our results in Tables 3, 4, and

show that the acutely responding melanoma tumors�/� �5) and radiosensitive normal tissues [SFNT(2 Gy) �.3, 0.5] may benefit from grid therapy. The therapeuticatios depend not only on the single �/� value of tumor cellines, but also on the individual values of � and � as well ashe responses of normal tissues. This result is in agreement

mated fields to melanoma HX-34 cell lines

sue 1) � 0.3]

Normal tissue 2[SFNT(2 Gy) � 0.5]

Normal tissue 3[SFNT(2 Gy) � 0.7]

) TRSF

(grid)SF

(open) TRSF

(grid)SF

(open) TR

1.474 0.472 0.436 1.082 0.621 0.652 0.9521.726 0.397 0.347 1.143 0.546 0.580 0.9412.118 0.318 0.255 1.245 0.465 0.495 0.9392.563 0.260 0.191 1.358 0.407 0.427 0.9532.902 0.229 0.159 1.441 0.375 0.388 0.967

therapeutic ratio.

ssue sensitivity at different fractionated doses

20 Gy 26 Gy 30 Gy(2 Gy � 10 fx) (2 Gy � 13 fx) (2 Gy � 15 fx)

1.513 1.720 1.8831.015 1.061 1.0970.843 0.834 0.8331.124 1.208 1.271

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1582 I. J. Radiation Oncology ● Biology ● Physics Volume 66, Number 5, 2006

ith the study by Brenner and Hall (25), in which theyoncluded that using a single value for parameter �/� forvaluating treatments may not be justified. After averaginghree types of normal tissue cells, an observable therapeuticatio 1.271 at the dose 30 Gy is estimated. Table 6 suggestshat large dose may have killed too many normal tissue cellshen the treatment is taking advantage of larger therapeutic

atio. So the excessive pursuit of large therapeutic ratio mayesult in adverse outcomes.

Most studies involving grid therapy have used a gridollimator with aperture diameters of approximately 1 cm,rojected in the plane of isocenter, and aperture spacing

Table 6. Normal tissue survival fractiofractionat

GyNumber offractions SFNT(2 Gy) � 0.3

10 5 0.34914 7 0.27420 10 0.19826 13 0.14530 15 0.119

Abbreviation: SF � surviving fraction; NT

esulting in an open area of 40–50%. Although this aperture h

REFEREN

1999;45:721–727.

1

1

1

1

1

1

1

1

1

1

2

ize and fraction of open beam may have had some basis inarlier orthovoltage grid applications (10), there has beenittle evidence provided thus far that this design representsptimal grid collimation for megavoltage applications. Theesults of Zwicker et al. (14) did suggest weak dependencef therapeutic ratios on aperture spacing when using theame aperture diameter. However, model assumptions abouthe dose distribution and the inability to evaluate otherperture diameters limit the usefulness of these results. Welan to use the techniques validated in this study as a basisor more detailed studies of other grid designs and theiradiobiology effects, such as the effects of grid spacing,

ifferent doses after irradiation by thetherapy

SF

SFNT(2 Gy) � 0.5 SFNT(2 Gy) � 0.7

0.472 0.6210.397 0.5460.318 0.4650.260 0.4070.229 0.375

mal tissues.

ole dimension, other tumor, and normal tissue types.

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