A method for determining multileaf collimator transmission and scatter for dynamicintensity modulated radiotherapyMark R. Arnfield, Jeffrey V. Siebers, Jong O. Kim, Qiuwen Wu, Paul J. Keall, and Radhe Mohan

Citation: Medical Physics 27, 2231 (2000); doi: 10.1118/1.1312190 View online: http://dx.doi.org/10.1118/1.1312190 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/27/10?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in On empirical methods to determine scatter factors for irregular MLC shaped beams Med. Phys. 31, 2222 (2004); 10.1118/1.1767695 Dosimetric evaluation of partially overlapping intensity modulated beams using dynamic mini-multileaf collimation Med. Phys. 30, 846 (2003); 10.1118/1.1562170 Head scatter off-axis for megavoltage x rays Med. Phys. 30, 533 (2003); 10.1118/1.1556609 Intensity modulated arc deliveries approximated by a large number of fixed gantry position sliding windowdynamic multileaf collimator fields Med. Phys. 29, 2359 (2002); 10.1118/1.1508110 Characterization of a commercial multileaf collimator used for intensity modulated radiation therapy Med. Phys. 28, 752 (2001); 10.1118/1.1367863

A method for determining multileaf collimator transmissionand scatter for dynamic intensity modulated radiotherapy a…

Mark R. Arnfield,b) Jeffrey V. Siebers, Jong O. Kim, Qiuwen Wu, Paul J. Keall,and Radhe MohanDepartment of Radiation Oncology, Medical College of Virginia at Virginia Commonwealth Universityand McGuire VA Hospital, Richmond, Virginia 23298

~Received 16 September 1999; accepted for publication 12 July 2000!

The main purpose of this work is to demonstrate a practical means of determining the leaf trans-mission and scatter characteristics of a multileaf collimator~MLC! pertinent to the commissioningof dynamic intensity modulated radiotherapy, especially for the sweeping window technique. Thedata are necessary for the conversion of intensity distributions produced by intensity-modulatedradiotherapy optimization systems into trajectories of MLC leaves for dynamic delivery. Measure-ments are described for two, tungsten alloy MLCs: a Mark II 80-leaf MLC on a Varian 2100Caccelerator and a Millenium 120-leaf MLC on a Varian 2100EX accelerator. MLC leakage wasmeasured by film for a series of field sizes. Measured MLC leakage was 1.68% for a 10310 cm2

field for both 6 and 18 MV for the 80-leaf MLC. For the 6 MV field, the 1.68% leakage consistedof 1.48% direct transmission and 0.20% leaf scatter. Direct transmission through the 80-leaf MLC,including the rounded leaf tip, was calculated analytically taking into account the detailed leafgeometry and a Monte Carlo-generated energy spectrum of the accelerator. The integrated fluenceunder the leaf tip was equivalent to an inward shift of 0.06 cm of a hypothetical leaf with a flat,focused tip. Monte Carlo calculations of the dose to phantom beyond a closed 80-leaf MLC showedexcellent agreement with the analytic results. The transmission depends on the density of the MLCalloy, which may differ among individual MLCs. Thus, it is important to measure the transmissionof any particular MLC. Calculated doses for a series of uniform fields produced by dynamicsweeping windows of various widths agree with measurements within 2%. ©2000 AmericanAssociation of Physicists in Medicine.@S0094-2405~00!01810-1#

Key words: multileaf collimator, intensity modulated radiotherapy, dosimetry, Monte Carlomethod

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I. INTRODUCTION

The purpose of this paper is to provide an accurate, pracmethod for determining several of the most important dometric parameters of a multileaf collimator~MLC! that areneeded for the clinical implementation of intensity modlated radiotherapy~IMRT!.

The delivery of intensity-modulated radiotherapy beamay be accomplished using several different techniquescluding physical compensators, tomotherapy,1–4 step-and-shoot technique5 and dynamic MLC.6–10 The MLCs are usedfor both dynamic and step-and-shoot modes. In the formthe beam is on while the leaves are in motion, whereas inlatter the beam is off while the leaves move. In either cathe accuracy of the dose delivered and the agreementtween calculated and measured dose depend upon adeaccounting of the various effects associated with Mcharacteristics.11 These include, for example, the roundleaf tips, tongue-and-groove leaf design, leaf transmissleaf scatter, and collimator scatter upstream from the ML

In IMRT, when intensity patterns are characterizedrelatively large and closely spaced fluctuations, the averwindow width ~the distance between leading and followinMLC leaves! is small. Since the window width is smaller, fothe same dose received by the tumor the treatment tim

2231 Med. Phys. 27 „10…, October 2000 0094-2405 Õ2000Õ27„

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longer than for ‘‘smoother’’ intensity distributions. The increased treatment time results in an increase in leaf transsion, rounded leaf tip transmission, and leaf scatter contrtions~‘‘indirect contributions’’! as a fraction of the total dosdelivered. Knowledge of the magnitude of these effectsnecessary for the conversion of intensity distributions pduced by IMRT optimization systems into trajectoriesMLC leaves. Leaf trajectories are also used in the final dcalculation. Since the corrections applied for these effectsapproximate, the uncertainty in dose delivered increasethe average window width decreases.

This study is mainly directed at the dynamic sweepiwindow implementation of IMRT. The average windowidth for dynamic sweeping window delivery is smaller thain other techniques such as the step-and-shoot techniqueto a finer intensity grid. Since the window width is smalleaccurate accounting of the dosimetric properties of Mleaves will have a greater effect for the sweeping windmethod. However, the dosimetric parameters establishedour method are valid for other techniques, when needed

Previous studies have examined some of the issuesscribed by this paper, including leaf bank leakage, equivaleaf shift, and the leaf tip transmission function for the 8leaf Varian MLC.11 The present work differs from previou

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2232 Arnfield et al. : Dynamic intensity modulated radiotherapy 2232

work in several respects, in addition to presenting data onnewer Varian 120-leaf MLC. This paper determines the toamount and the spatial distribution of the MLC leaf scatportion of the leakage dose. The leakage consists ofcomponents. The term direct radiation denotes the comnent that is transmitted through the MLC without interactinthe term leaf scatter denotes radiation exiting the MLC ainteracting within it. Since both primary photons from thtarget and head scatter photons may or may not interacthe MLC, both will have leaf scatter and direct componenWe have investigated the magnitude of MLC leaf scattermeasuring the MLC leakage as a function of field size. Texperimentally determined values of leaf scatter were cfirmed by analytic and Monte Carlo calculations. We hachosen to neglect the depth dependence of leakage, whas been studied previously.11 The depth dependence oleakage essentially demonstrates the effect on the accelebeam quality ~or, depth dose! of interposing a beammodifying device~the MLC! in the beam.12,13

Sections II and III together comprise the technical aspeof the paper most directly applicable to commissioningMLC for dynamic IMRT. In Sec. III, we illustrate ourmethod with two examples: an 80-leaf MLC and a 120-leMLC.

Our method for determining the MLC characteristicsquires two series of measurements. The first series conof MLC leakage measurements as a function of field susing film. This determines the direct transmission throuthe leaves and the MLC scatter as a function of field sThe second series of measurements, also using film, idynamic, uniform intensity fields. The purpose of these msurements is to determine the equivalent shift due torounded leaf tips of the Varian MLC design. This quanthas been previously measured by a static field techniquewas called the leaf gap offset.11 A convenient means of approximately accounting for the rounded tip design in calclations is to regard the additional fluence through the tipsbeing equivalent to an effective increase in the windwidth between opposing leaves over the geometrical distabetween leaf tips. This effective increase in the windwidth is equal to twice the equivalent shift of a single leThe equivalent shift~or leaf gap offset! in the boundary ofthe radiation field for the 80-leaf Varian MLC is about 0cm or less per leaf.10,11 This effective widening has a neglgible effect on treatments involving static fields shaped wMLCs. It must, however, be accounted for in intensitmodulated treatments delivered with a dynamic MLC, whit can be a significant fraction of the variable distancetween the leaves.

Section IV presents an analytic method for calculatdirect transmission of primary radiation through the MLAlthough such calculations are not always necessary forimplementation of IMRT, they are useful for determining tleaf tip fluence transmission function. Comparing the callation with measurements shows that the measured leafconsists of two components: an intrinsic shift due torounded tip and an additional component related to mech

Medical Physics, Vol. 27, No. 10, October 2000

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cal tolerances. This has implications for quality assuraand output constancy.

Also presented in Sec. IV are Monte Carlo calculationsphoton transport through the MLC. This Monte Carlo daillustrates the separation of the MLC-transmitted radiatdose into the direct and MLC scatter components and shtheir spatial distribution. A conclusion from the analytic anMonte Carlo studies is that calculations cannot predictMLC leakage without accurate knowledge of the MLC desity. Significant differences in leakage among MLCs of tsame design may arise from variations in the average denof the material composing the leaves.

II. METHODS

A. Measurements of MLC leakage versus field size

An 80-leaf multileaf collimator~Mark II MLC, VarianMedical Systems, Palo Alto, CA! mounted on a Varian Cli-nac 2100C linear accelerator and a 120-leaf Millenium MLmounted on a Clinac 2100EX accelerator were used instudy. The MLCs were of tungsten-alloy composition. MLleakage was measured with Kodak XV-2 film, at 100 csource to axis distance and a depth of 5 cm in a waequivalent epoxy/plastic phantom~‘‘plastic water,’’ NuclearAssociates, Carle Place, NY!. All films in a given experi-ment were from the same batch and a standard film calition was performed.

The measured leakage through the leaves varies withcollimator-defined field size, since some portion is duescatter from the leaves. The surface area of the MLCposed to the beam increases with field size, hence the Mscatter contribution increases with field size as well. In prciple, the amount of scatter for a given field size canobtained by subtracting the zero field size transmission frthe measured transmission~leakage! for the field of interest.In an attempt to estimate the leaf scatter contribution,measured the leakage for various field sizes.

The field size dependence of the leakage was determby adjusting the jaw positions to various field sizes, and hing the MLC set to block the entire open area. For fiewidths up to 10 cm, the field width~field dimension parallelto the direction of leaf travel! was varied, while the fieldlength was kept at a constant 5 cm. The fixed field length5 cm ensured that the same four inner leaves were useintegrate the leakage. This avoids uncertainties introducevariations in the interleaf gap and associated transmissThese measurements were carried out for both the 80-and 120-leaf MLCs. For the larger fields, the width was hconstant at 10 cm, while the field length was increased ua maximum of 40 cm. In this case the width was limitedorder to avoid overlap between the jaw-defined field andline of abutment between the leaf banks. The large-fimeasurements, with variable length, were carried out ofor the 120-leaf MLC.

The MLC-blocked field may be created by displacing tline of abutment between opposing leaf banks either toright or to the left of central axis, or by displacing alternatinleaves to the right and left. In any case the Varian ML

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2233 Arnfield et al. : Dynamic intensity modulated radiotherapy 2233

design limits the maximum displacement between leaf bato 14.5 cm. When shifting an entire bank to one side itimportant that a single leaf~e.g., the one nearest the fieedge! be displaced in the opposite direction from the othleaves. This prevents the leaf carriage from inadvertentlying interposed in the field during leakage measuremeHaving the carriage in the field causes the attenuationincrease by approximately 20%.

The leakage was determined by exposing a film to 9monitor units~MU!, with the MLC blocking the beam. Without changing the field size as defined by the collimator jaa second film was exposed to 25 MU, with the MLC rtracted. This gave approximately the same optical densitboth films. The film with MLC retracted was repeatedorder to account for uncertainties due to film batch and pcessing variability. The central axis of the films was regtered by marking the cross-hair locations or lasers on theprior to their exposure. Using a scanning densitometer,each film a profile along the field length, intersecting tbeam central axis, was scanned. For the smaller field sthe average leakage of the MLC was taken as the mean vof the ratio of the two curves, over the central 4.0 cm ofcurve. For larger fields, the central 80% of the field was uto determine the leakage.

For the 120-leaf MLC, ion chamber measurements wtaken simultaneously with the film exposures. A 0.6 c3

Farmer-type ion chamber was placed on central axis, at 6depth, with the chamber axis perpendicular to leaf travThe purpose of these measurements was as a check ouncertainties associated with film-to-film variability, whicare typically about 2%.

B. Equivalent leaf shift

1. Measurements on uniform intensity fieldscreated by dynamic sweeping windows

The equivalent leaf shift has been previously measureda least-squares fit to the integrated dose of differentstatic fields.11 Another possible technique for measuring tshift is by exposing film in phantom to adjacent half-fielwith an overlap equal to the shift. We have chosen a metbased on simple, dynamic uniform fields. This methodthe advantage of high sensitivity. A disadvantage is thecessity of creating several dynamic MLC files, which adescribed next.

Dynamic MLC ~DML ! files are files that contain leaf positions as a function of monitor units, and are used byMLC controller to position the MLC leaves dynamically duing beam delivery. DML files were designed with the intetion of creating a series of 10310 cm2 uniform fields. Eachfield was created by a sweeping window formed by the ctral ten pairs of opposing leaves, with fixed separationstween the leaf banks ranging from 0.5 to 10 cm. This repsents a typical range of window sizes for clinical fields. Fa given window width, all ten leaves moved with the samconstant velocity across the treatment field. Similar fiehave been described by Stein.14 Such files are readily create

Medical Physics, Vol. 27, No. 10, October 2000

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using a text editor. Each of these fields was designeddeliver the equivalent of 25 MU to a 10310 cm2 area, as-suming idealized doubly focused leaves~i.e., no leaf tip cur-vature! with zero leaf transmission. To determine MU setings for a given window width, it was assumed that tleaves start with the window closed on the left edge ofsquare field. The leading~L! leaf begins to travel at a constant velocity until the window opening is equal to the dsired width. Then both L and the following~F! leaves beginto move at the same velocity until the L leaf followed by thF leaf reach the right boundary of the field. Figure 1 illutrates graphically the trajectory in terms of leaf position vsus MU for the 0.3 and 10 cm window fields.

Under these conditions, dose greater than 25 MU receiat the isocenter plane is due to transmission and scatterthe leaves. Further details of leaf velocity, etc., are givenMohan et al.15 The analysis of dose measurements of~nominally! uniform fields must take into consideration‘‘ripple’’ effect superimposed on the beam profile that resufrom intra- and interleaf variation in transmission.15 This ef-fect increases with decreasing window width due to the exbeam-on time. Due to this effect, measuring the dose usan ion chamber is problematic unless an integral numbeleaf cycles is subtended on the chamber. With film measuments, this problem can be easily dealt with by averagiFilm measurements for each field were taken at the isoceplane, at 5 cm depth in water-equivalent plastic phantom.both 80-leaf and 120-leaf MLCs, the dose to the film wtaken as the average of a linear scan through the centralperpendicular to leaf motion, encompassing eight leavThis avoided the penumbra region of the 10310 cm2 field.For calibration purposes, the dose was measured at the sdepth for an open, static 10310 cm2 field. A standard filmcalibration was performed to convert optical density to do

FIG. 1. Diagram of leaf position vs MU for two of the uniform fields produced by constant velocity sweeping windows. All 40 leaf pairs move wthe same trajectory. The open field MU at each point is equal to the verdistance between the lines representing the leading~L! and following ~F!leaf in each pair.

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2234 Arnfield et al. : Dynamic intensity modulated radiotherapy 2234

2. Best fit analysis of equivalent shift

We use the term ‘‘opening density,’’Mopen at a point inthe field as the portion of total ‘‘beam on time’’ for whicthe point is exposed to the source of primary radiation,obstructed by dynamic leaves.15 The units of opening densityare MU. During beam on, the point will also receive indireradiation due to direct transmission through and scatter fthe MLC leaves. The total of primary radiation and indireradiation is denoted as ‘‘effective opening density,’’Meff .

For uniform fields created in the above given manner,central axis fluence is considered to be equivalent to dWe also assume for simplicity that an opening density ofMU gives a fluence/dose of 25 at the measurement poin5.0 cm depth. For the fields described previously, withleaves moving in tandem at constant velocity, the averdose over the central portion of the field is given by

Meff5S Mopen12dR

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whereMopen is the nominal opening density,M is the totalbeam on-time in units of MU,T is the average measureleakage for the field of interest,d is the~apparent! equivalentleaf shift in cm,R is the accelerator dose rate in MU/miandV is the leaf velocity in cm/s.Mopen is constant for the10310 cm2 fields considered here. For each field represenin Fig. 1 it is equal to the vertical distance between the gralines that correspond to each pair of leaves. It shouldmentioned thatMopenis termed the ‘‘nominal’’ opening density because it is not corrected for that portion of the leshift that is due to systematic errors in leaf position~i.e., theleaf gap error, see Sec. IV!. This portion of the leaf shiftcontributes some open field dose.

In Eq. ~1!, the factor of 2 in the second term accountsthe additional dose due to the outward shift of both leavesshould be noted that a more accurate way of accountingthe fluence transmission though the leaf tip is to modeltransmission as a function of position, rather than as a simshift. The transmission function for the 80-leaf MLC is dicussed in Sec. IV. The fluence at a point is then calculatedintegrating the transmission function as the tip passespoint of interest. However, for the case of leaves movingconstant velocity, as considered here, if the integral of tramission through the tip region is known, the total calculafluence on central axis will be the same whether it is callated by an equivalent shift or using a tip transmission fution.

The simple formula, Eq.~1!, can be used to determine thequivalent shift in the tip position from the measurementsdynamic, uniform fields produced by constant velocleaves, as follows. The average dose to the central portiothe field, as measured by film, is represented byMeff in Eq.~1!. The measured values ofMeff are substituted into Eq.~1!,which is solved for the equivalent shift,d, using forT in theformula the measured leakage for a 10310 cm2 field. This iscarried out for each uniform field. For each uniform field, tcalculated width of the sweeping window is equal to the~nominal! window width, plus twice the equivalent shift,d.

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III. RESULTS

A. Measurements of MLC leakage versus field size

1. 80-leaf MLC

Figure 2 shows measured MLC cross-leaf leakage profithrough the closed MLC, for a series of collimator jawdefined fields with a common length of 5 cm and four dferent widths ranging from 0.5 to 10 cm, for 6 and 18 MVInspection of the graphs shows that the line average of leage increases with increasing field size. This increase infective transmission reflects the increased scatter fromMLC leaves when a greater surface area of the leaveexposed to the beam, for the larger openings as definethe collimator jaws. Figure 3 shows the line-averaged croleaf leakage as a function of field width. Two sets of mesurements taken 18 months apart show excellent reproibility. The 18 MV leakage data are similar to the 6 Mresults.

The difference in transmission between a finite field sand a ‘‘zero area’’ field~representing the primary beam! isthe component of dose due to scatter from the MLC leafor that field size. It was not feasible to extend the expement to field widths narrower than 0.5 cm, due to measument uncertainties and the mechanical limitations of thecelerator jaws. Linear extrapolation to zero field width gav

FIG. 2. Measured leakage dose at 5 cm depth in water-equivalent phanthrough a closed, 80-leaf MLC for~a! 6 MV and ~b! 18 MV. Displayedcurves correspond to a common length of 5 cm and widths of 0.5, 1, 3,10 cm. Although fluence calculations show a factor of 153 difference be-tween inter- and intraleaf fluence transmission, the measured dose cshow only a factor of about 1.53 difference, owing to lateral electron transport in the phantom.

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2235 Arnfield et al. : Dynamic intensity modulated radiotherapy 2235

direct transmission of 1.4860.01 %. The leaf scatter cathen be found from the graph, by subtracting the direct tramission from the apparent transmission~leakage! for thefield of interest. For example, the leaf scatter of a310 cm2 field is 0.2060.01 %. These and other MLC dosmetric parameters are summarized in Table I. The spadistribution of the leaf scatter will be discussed in Sec. IV

2. 120-leaf MLC

Figure 4 shows the leakage profile for a 10340 cm2 field,for the 120-leaf MLC in the direction perpendicular to lemotion. The variability of the intraleaf transmission is leregular than for the 80-leaf MLC, because of substantialferences in the leaf cross-sectional design of the two MLSince Fig. 4 represents the ratio of transmitted to open bprofiles, the shape of the open beam cannot account forpronounced rounded shape. The shape is partly duegreater leakage through the 40 central leaves with isoce

FIG. 3. Measured leakage vs field size, through the closed, 80-leaf MLC6 MV and 18 MV. Each point represents the line-averaged transmisover the central 4 cm of the fields shown in Fig. 2. The two sets of dat6 MV represent the same measurements, repeated after 18 months. Exlating to zero field width gives the approximate direct component of ration transmission through the MLC.

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widths of 0.5 cm than through the outer leaves with widtof 1.0 cm. Also, some of the differential attenuation acrothe profile is from the spatial distribution of scatter, whichas its largest contribution in the center.

Figure 5 encompasses the line-averaged, cross-leaf trmission versus field size data for 6 MV, for the 120-leMLC. Figure 5~a! shows the large field data, where the fiewidth was held constant at 10 cm, and the length varied fr10 to 40 cm. Figure 5~b! shows the data for small fieldwhere, similar to the 80-leaf MLC, the field length was heconstant at 5 cm and the width was varied from 0.5 to 10 cIndependent measurements of the right and left leaf bagave similar results. Extrapolation to zero field size gavdirect transmission of 1.3460.03 % for the 120-leaf MLC.The estimated value of leaf scatter, averaged over rightleft leaf banks, was 0.2160.03 % for a 10310 cm2 field and0.4060.03 % for a 10340 cm2 field ~Table I!. It is notable

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TABLE I. Measured and calculated multileaf collimator characteristics for 6 MV. The MLC direct transmiswas found by extrapolating the measured leakage to zero field width. MLC scatter for a specific field sizfound by subtracting the direct transmission from the measured leakage for that field size. The equivaled, consists of the sum of the intrinsic tip shift and the leaf gap error~see the text!. The equivalent shift wasdetermined by a least-squares analysis of uniform, dynamic fields~Fig. 6!. The leaf gap error was measuredirectly using a mechanical gauge.

80 leaf MLCMeasurement

80 leaf MLCAnalytic

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120 leaf MLCMeasurement

MLC direct transmission~% of open field dose!

1.4860.01 1.48 1.49560.005 1.3460.03

MLC scatter, 10310 cm2 field~% of open field dose!

0.2060.01 ¯ 0.18560.002 0.2160.03

MLC scatter, 10340 cm2 field~% of open field dose!

¯ ¯ ¯ 0.4060.03

Intrinsic tip shift ~cm! ¯ 0.06 ¯ ¯

Leaf gap error~cm! 0.04160.004 ¯ ¯ ¯

Equivalent shift,d ~cm! 0.11460.004 ¯ ¯ 0.08860.003

aIn this calculation the assumed MLC density needed to reproduce the measured direct transmission wg/cm3.

bIn this calculation the assumed MLC density needed to reproduce the measured leakage of 1.68% wg/cm3.

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2236 Arnfield et al. : Dynamic intensity modulated radiotherapy 2236

that the amount of leaf scatter for a 10310 cm2 field deter-mined by this method was the same for both 80-leaf a120-leaf MLCs. This is consistent with the fact that the buproperties of the two MLC designs affecting leaf scatteressentially the same.

B. Equivalent leaf shift

1. 80-leaf MLC

Values of equivalent leaf tip shift were determined expementally for the 80-leaf MLC for each dynamic uniformfield, as described in Sec. II. Figure 6~a! shows a regressionanalysis of these values. Extrapolation to zero window wiyielded a value of 0.11460.004 cm for the equivalent shiftOthers have measured a leaf shift of 0.08 cm for the 80-Varian MLC, using a static field technique.10,11 In one ofthese studies the leaf shift was also measured by a dynuniform field method, with a resulting value of 0.12 cm.10,11

This value agrees with our result.As a check, the value of the equivalent shift as determi

by linear regression was used to calculate for each unif

FIG. 5. Measured leakage vs field size, through the closed, 120-leaf MLC6 MV. Each point represents the average transmission of the central 80a line through the central axis, perpendicular to the direction of leaf motof the respective field.~a! Fields with a common width of 10 cm and lengthof 5, 10, 20, 30, and 40 cm.~b! Fields with a common length of 5 cm anwidths of 0.5, 1, 3, 5, and 10 cm. Separate sets of measurementsperformed for left and right leaf banks. Extrapolating to zero field widgives the approximate value of direct transmission through the MLC.

Medical Physics, Vol. 27, No. 10, October 2000

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field the effective monitor units~or dose!, Meff , by Eq. ~1!.These values ofMeff agreed within 1% with the average dosvalues as measured by film.

2. 120-leaf MLC

Figure 6~b! shows a regression analysis of the equivalleaf shift for the 120-leaf MLC. In this case the equivaleshift was determined to be 0.08860.003 cm. For the 120-leaf MLC, the values ofMeff calculated by substituting thisresult in Eq.~1! agreed within 2% with the average dosvalues as measured by film.

Considering the 2% agreement with all measurementsboth MLCs, we conclude that the accuracy of Eq.~1! foruniform fields is excellent even for narrow sweeping widows, where transmission and scatter is a relatively largeof the total dose. It should be noted that the apparent difence between the values of equivalent shift for the 80-land 120-leaf MLCs is not determined by the shape oftips, which is identical for the two leaf designs~although thecross-section differs, the tip curvature does not!. As is dis-cussed in Sec. IV C, this difference can be explained byferences in mechanical tolerances between the two MLC

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FIG. 6. Linear regression analysis of average dose data from uniform ficreated by moving windows for~a! 80-leaf MLC and~b! 120-leaf MLC. Theset width for each moving window is the programmed, nominal distabetween the leaf tips of opposing leaf banks. The measured width iseffective distance between the opposing leaf banks, as derived formoving window from the average measured dose for that field by Eq.~1!.The intercept with the vertical axis gives the equivalent leaf shift.

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2237 Arnfield et al. : Dynamic intensity modulated radiotherapy 2237

IV. CALCULATIONS

A. Analytic calculation of leaf transmission for the 80leaf MLC

One of the complications in calculating the overall tranmission of the leaf bank is in accurately accounting forcomplex leaf shape. The individual tungsten alloy leavhave a projected nominal width of 1 cm at isocenter~100cm! and a physical thickness of 6.13 cm at their thickpoint. The leaves of the MLC are single focused, i.e.,sides are shaped to converge at the source but eachrounded in the vertical direction in order to present anproximately constant penumbra at the isocenter plane.radius of curvature at the center of the leaf profile is 8 cThe remainder of the tip profile is defined by two lines, eabeing tangent to the circular arc and at an 11.3° angle tovertical. The detailed physical shape of the tungsten leawas obtained from drawings provided by the vendor.16 Asimplified rendition of the leaf tip shape and cross sectcan be found in LoSasso, Chui, and Ling.11

A relatively simple analytic model was used to calculathe transmission as a function of position, through a givleaf of the 80-leaf MLC. In the following, we discuss thtransmission through the leaf in directions parallel to, aperpendicular to the direction of leaf travel. An equivaleanalysis was not performed for the 120-leaf MLC; suchanalysis would be more difficult to carry out since therethree different leaf designs incorporated in that MLC.

In principle, the leaf transmission function can be coputed analytically with the knowledge of the shape of tleaf and the energy spectrum. We used the Monte Cagenerated energy spectrum for our treatment mach~Varian Clinac 2100C! for such computations.17 The photonenergy fluence fractional transmission below a single leT(x,y), in a plane 100 cm from the target, at displacemenxin the direction of leaf motion, was calculated by

T~x,y!5( i 51

n N~Ei !Ei exp~2mWl ~x,y!!

( i 51n N~Ei !Ei

, ~2!

whereEi is the photon energy,mW is the linear attenuationcoefficient of tungsten,18 l (x,y) is the path length throughthe leaf of a ray originating at the target and passing throposition~x,y!, andN(Ei) is the energy spectrum~in terms ofnumber of photons in the energy binEi andEi1dE). Theycoordinate designates the direction perpendicular to leaftion, accounting for the leaf cross-sectional design. Weonly the primary portion of the energy spectrum generaby Monte Carlo simulations,17 averaged over 10 cm diametein a plane through the isocenter. The reason for choosin10-cm-diam field is that on average the IMRT beam isproximately 10310 cm wide. The widest IMRT beam possible with Varian MLC is 14.5 cm. The scattered portionthe incident beam was omitted because it has a significalower energy and a large angular spread. This portion ofbeam is attenuated more strongly in the MLC leaves.also neglect beam hardening effects, which would affectcalculation by introducing the energy absorption coefficiof water at the depth of measurement into the calculatio

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The 80-leaf cross-section incorporates a tongue-in-grodesign, to prevent unimpeded radiation transmission throthe interleaf gap. The design of the leaf bank provides fonarrow interleaf gap between adjacent leaf surfaces. Thechine drawing shows that the leaf cross section can beresented by four distinct sections, denotedj 51,2,...,4, withdifferent thicknesses in the vertical direction and fractionwidthswj . The breakdown into four sections is somewhata simplification, but is sufficiently accurate for these puposes. By definition, the sum of the fractional widthswj isunity. Since the projected width of a single leaf plus tinterleaf gap at isocenter is 1.0 cm, the partial width of easection iswj31.0 cm. In Eq.~2! the x dependence of thepath lengthl (x,y) is along the leaf length and they depen-dence is across the leaf width. Thusl (x,y) can be replacedby l j (x), wherej refers to thej th leaf section.

The rounded leaf tip was dealt with by computing ttransmission curve from the open field region to several ctimeters under the leaves according to

Tav~x!5(j 51

4

Tj~x!wj , ~3!

whereTj (x) is given by Eq.~2!, with the subscriptj replac-ing they coordinate in bothT(x,y) and l (x,y).

At distances greater than 1 cm from the tip the path lenthrough the leaf of a ray originating at the source is equathe full effective thickness of the respective section andconstant in thex direction, neglecting divergence. The effetive thicknesses varied from 2.55 cm for the section incluing the overlap of the tongue of a leaf with the groove of tadjoining leaf, to 6.13 cm, which is the thickness throughcentral part of the leaf.

The nominal interleaf gap at isocenter is 0.014 cm, butactual partial width,wj , of the interleaf gap is larger thathis due to details of the tongue-in-groove geometry. Tprimary transmissions through the interleaf gap and thecenter regions were calculated to be 12.6% and 0.83%spectively, a difference of a factor of 15. However, theterleaf gap component of transmission does not dominateoverall transmission due to its narrow partial width.

The effects of the intra- and interleaf sections on transmted dose can be seen in Fig. 2. Because of the smearinfluence caused by lateral transport of radiation in the phtom, the measured value at each point does not represenpure transmission. For instance, the measured value wbe higher than the calculated transmission in the middle oleaf and lower than the calculated value between leaves.interleaf transmitted fluence is 15 times greater than thetraleaf transmitted fluence, but because of the small intergap and effects of lateral electron transport in phantom,transmitted dose at the peak is only about a factor ofgreater than the dose in the valley.

B. MLC density

The average transmission is sensitive to the physical dsity of the MLC. Since in order to make it machinable th

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2238 Arnfield et al. : Dynamic intensity modulated radiotherapy 2238

MLC composition is a tungsten alloy, assuming the MLCbe pure tungsten with density of 19.3 g/cm3 will give erro-neous results for the calculated transmission. Tungstenterial, per Mil spec T-21014D, is 90%–95% tungsten palloying elements and may vary in density within the ran17–18 g/cm3. The simplest way to modify Eq.~2! to accountfor the lower density is to retain the attenuation coefficieand multiply the path lengthsl (x,y) by a density scalingfactor less than unity. In practice, short of dismantling tMLC the alloy density can be determined for a particuMLC by matching the calculated direct transmission tomeasured direct transmission~i.e., for a hypothetical zeroarea field!. Thus, the density becomes the only free paraeter in the calculation. To match the measured direct tramission of 1.48% required an assumed MLC physidensity of 17.7 g/cm3. This is in excellent agreement witMonte Carlo calculations described in the following, whirequired the assumption of a density of 17.6 g/cm3 to repro-duce the measured leakage dose for a 10310 cm2 field of1.68%.

It is interesting to apply Eq.~3! to the results of LoSassoChui, and Ling11 for the Varian 80-leaf MLC. For a 6 MV,10310 cm2 beam at 5 cm depth, a leakage dose of 1.8was reported in that study. Considering our results it is rsonable to assume a value of leaf scatter of 0.2%, whgives a direct transmission for their MLC of 1.65%. Tmatch this value by applying the forgoing analysis requireMLC physical density of 17.1 g/cm3. Comparing this resultwith the density and transmission values for our own MLsuggests that variations in the average material density,consequently the transmission, could be significant amindividual MLCs. This finding suggests it is necessary ththe transmission properties of every MLC be individuameasured.

C. Tip transmission and equivalent shift

If the leaf tip were flat and focused, the fluence transmsion would be unity on the open side of the leaf and equathe full-thickness transmission on the side under the leHowever, due to rounding, there is a distance of about 1in the isocenter plane over which the transmission decreprecipitously from unity to the full thickness value of 0.014At present, some IMRT planning systems take the effectleaf tip curvature into account by assuming an equivalshift in the position of the field edge. A more accurate meof accounting for the leaf tip shape is by modeling it withtransmission function. The use of a transmission functrather than a simple equivalent shift may in some circustances improve the accuracy of fluence calculations indynamic sweeping window technique. It will have less snificance in the step-and-shoot technique.

The curve for the 80-leaf MLC calculated by Eq.~3! ispictured in Fig. 7~a!. The leaf tip is assumed to align with thcentral axis. Equivalent curves to that in Fig. 7~a! were com-puted for displacements of 3 and 10 cm from isocenter. Crently, the curve which represents a displacement of 3from isocenter is used in our clinical software to incorpor

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leaf transmission and rounded leaf tip effects in the comtation of leaf trajectories for the 80-leaf MLC.

If the full thickness 0.0148 transmission is subtractfrom the leaf transmission curve and the remaining transmsion integrated, the integrated amount constitutes the ational transmission that is solely due to leaf tip curvatuThis integrated amount may then be equated to a fractiotransmission of unity, multiplied by a distance that represethe inward displacement~intrinsic shift! of a hypothetical flatleaf tip. The calculated intrinsic shift was found to b0.060 cm.

The intrinsic shift of 0.06 cm is significantly less than thequivalent shift of 0.114 cm derived empirically from thsweeping window data for the 80-leaf MLC. This is becaufor Varian MLCs the empirical or measured shift is comprised of two components: the intrinsic shift due to trounded tip and an additional component related to mechcal tolerances. The latter component is termed by Varian‘‘leaf gap error,’’ and represents a small offset that is addto the nominal window width~leaf gap! in order to preventcollisions. The leaf gap error depends on software settiand thus may change, which is significant for quality assance since the output constancy of dynamic fields depeon the constancy of leaf position settings. We have measu

FIG. 7. ~a! 6 MV energy fluence transmission through the rounded leaf tipdistance from central axis, in the isocenter plane, calculated by Eq.~2!. ~b!6 MV energy fluence transmission through the leaf tip in the isocenter plfor a leaf displaced 5 cm off central axis. Circles: Monte Carlo calculatiLine: analytic calculation. Both calculations are for primary only, assuma leaf thickness of 6.13 cm and the leaf edge located 5 cm from centralIn the region past 7 cm, the analytic calculation differs by 3% fromaverage Monte Carlo value.

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2239 Arnfield et al. : Dynamic intensity modulated radiotherapy 2239

the leaf gap error by terminating dynamic treatments us0.5 and 1.0 cm moving windows. The cover was removfrom the accelerator head and a precise measurement oseparation of the leaf banks was made. The average leaerror from two measurements was found to be 0.060.004 cm. The combined displacement of the calculaintrinsic leaf shift plus this measured offset gave an equilent shift per leaf of 0.10 cm. Considering mechanical tolances and the small distances involved, this is in good agment with the shift of 0.114 cm determined by sweepiwindow measurements. These values are summarizeTable I. The leaf gap error of the 120-leaf MLC was nmeasured, but it is smaller than that of the 80-leaf MLbecause of closer mechanical tolerances. This is consiswith the 0.088 cm equivalent shift of the 120-leaf MLC bing smaller than the 0.114 cm shift of the 80-leaf MLC.

D. Monte Carlo calculations for the 80-leaf MLC

Monte Carlo calculations usingMCNP Version 4b219 wereperformed to evaluate the MLC leaf transmission and scafor 6 MV x rays from a Varian 2100C accelerator, incideupon the MLC. ThisMCNP4B code has been shown to givsimilar results to those of theEGS4 Monte Carlo code fordose computations in phantom.20 The problem was brokenup into four stages: modeling of the accelerator head, jaMLC, and phantom. The MLC geometry was reproducusing the manufacturer’s drawings. Further details ofMonte Carlo modeling of the MLC have been published21

Data from Sieberset al.21 that is pertinent for interpretingand comparing to our other results is reproduced in thelowing.

1. Transmission through the leaf tip

In this calculation the details of the leaf cross section wneglected. For simplicity each leaf bank was modeled asingle leaf, semi-infinite in the direction perpendicular to lemotion, of thickness equal to the central part of the leaf~6.13cm!. Therefore interleaf leakage was not accounted forthis calculation, resulting in decreased transmission.MLC was modeled to produce a 10-cm-wide openingtween the opposing leaf banks and the jaws were set toduce a 40340 cm2 field size at isocenter. The rounded leprofile near the end of the leaf was modeled using the drings referred to previously. In this simulation the transmsion of primary fluence through the leaf tip was tallied at tisocenter plane, in order to compare with the analytic callation. Scattered and nonscattered events were separatelocation of last interaction.

In Fig. 7~b! the data points represent the Monte Caresults for 6 MV, averaged over the two penumbrae regiproduced by the leaf tips. Also shown in Fig. 7~b! is ananalytic calculation of the leaf tip transmission curve throuthe thickest section of the leaf. In both Monte Carlo aanalytic calculations the projection of the leaf tip was 5.0lateral to the central axis. The analytic calculation usedenergy spectrum corresponding to primary radiation onwithin the central 5 cm radius of the beam, with this spe

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trum averaged into energy bins. The Monte Carlo calculatused the same energy spectrum, but each particle was traseparately. Even with these approximations, the analyticculation shows excellent agreement with the Monte Caresults, the value of integral transmission under the leaffering only 3% from the average Monte Carlo value in thregion. The analytic calculation was performed with no frparameters or other modifications to published attenuacoefficients. This agreement to the physically reliable MoCarlo calculations is strong evidence of the validity of tanalytic method.

It should be noted that in both analytic and Monte Cacalculations the same erroneous density value of 19.3 g/3

was assumed in these early calculations. This meansalthough the two methods agree, in both cases the calcultransmission is lower than the actual transmission throthe center of the leaf. The correct density to be used inculations can only be determined by comparison with tramission measurements, as discussed previously.

2. Transmission and scatter of a 10 Ã 10 cm2 fieldthrough the closed MLC

The above-mentioned calculation of fluence transmissthrough the leaf tips considered an open MLC field andsimple model of the MLC itself. For the calculation of tranmission through the closed MLC leaf bank, a more sophicated model was developed that incorporated the full geetry of the MLC leaves, including tongue-in-groove. Also,this case dose in phantom rather than energy fluencetallied, making possible a direct comparison with measuments. Sufficient particles were run to keep statistical unctainties below 1%. The MLC composition by weight waassumed to be 90% tungsten, 6% nickel, 2% iron, andcopper. The calculation was iterated using different valuealloy density until the calculated leakage dose at isocematched that of measurements. The required density toproduce the measurements was 17.6 g/cm3.

Figure 8 shows a histogram of the dose at 5.0 cm deptphantom due to different portions of the 10310 cm2, 6 MVbeam, after penetrating the closed MLC. Each portion isported as a fraction of the open field dose. The three cur

FIG. 8. Monte Carlo calculation of~a! total leakage,~b! MLC leaf scatter,and ~c! head scatter dose as a fraction of open field dose, at 5 cm depwater, after penetration of a 10310 cm2, 6 MV field through a closed 80-leaf MLC.

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2240 Arnfield et al. : Dynamic intensity modulated radiotherapy 2240

represent~1! the total of all photons that penetrated tMLC, ~2! photons originating from the target that interactin the MLC ~‘‘MLC scatter’’ !, and~3! head scatter photonthat are transmitted through the MLC. The Monte Carlo cculation gave a leakage of 1.6860.006% for a 10310 cm2

field of which 0.18560.002% was leaf scatter, in excelleagreement with experiment~see Sec. III and Table I!. TheMLC scatter contributes 11% of the MLC leakage dose,0.185% of the open field dose. Figure 8 shows that the stial distribution of MLC scatter is relatively constant over th10 cm field.

This level of MLC leaf scatter is insignificant for statfields, but it becomes significant in dynamic IMRT treaments with large field sizes and low efficiencies. Leaf scaincreases with field size due to the increased MLC surfarea exposed to the beam. For dynamic IMRT, efficienrefers to the ratio of the monitor units for a static field to ttotal monitor units for a dynamic field that delivers the sadose. Low efficiency denotes fields with a long beam-time relative to dose delivered, which occurs for fields wstrongly fluctuating intensity patterns.15 The contribution ofMLC transmission and scatter increases as efficiencycreases. For example, for the uniform field created by acm-wide sweeping window, leakage radiation contribu36% of the dose at isocenter. This was calculated using~1!. In Eq. ~1! the leaf gap error component of the equivaleshift contributes to the open field dose, since the actual wdow width is increased over the set window width byamount equal to the leaf gap error. The remainder ofequivalent shift, the intrinsic part, contributes to the leakadose.

V. SUMMARY AND CONCLUSIONS

In this paper we have presented detailed measuremenleakage radiation through Varian multileaf collimators. Eperimentally derived values of direct transmission and Mscatter were confirmed by analytic and Monte Carlo calcutions. Leaf scatter photons are diffusely distributed, thmagnitude varying slowly as a function of position in thfield. The measured MLC scatter is small: only 0.20% fo10310 cm2 field, or approximately 12% of the total leakagfor that field size. The amount of MLC scatter probably donot vary much among individual Varian MLCs. The smamagnitude and relatively weak spatial variation of the lescatter in the Monte Carlo results, suggests that leaf sccorrections in IMRT calculations may be simply implmented as an offset.

Scatter from leaves contributes dose even when a poiwithin the open window, whereas radiation directly transmted through leaves without interaction contributes only whthe point is in the shadow of the MLC. Analytic calculationshowed that interleaf transmission of energy fluence wgreater than intraleaf transmission by a factor of 15. Hoever, because of the lateral transport of radiation the msured dose under the MLC varied by only up to a factor1.5. The direct transmission is sensitive to the average dsity of the MLC. The alloy density may vary among ind

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vidual MLCs, thus it is important to measure the transmsion of any particular MLC.

We have demonstrated a sensitive and accurate meameasuring the equivalent shift due to rounded leaf tips, baon dynamic uniform fields. When leaves move at constvelocity, a simple formula can predict the dose from thefields within 2% accuracy. Since part of the equivalent shmay vary based on software setting, regular measuremendynamic window width constancy are a necessary partquality assurance. In this study we have not addressedissue of the relative accuracy for clinical IMRT of using aequivalent shift versus a full transmission function for trounded leaf tip. The capability of using such data maymay not be available in a particular IMRT system.

ACKNOWLEDGMENTS

The authors would like to thank Bruce Libby for providing the spectral particle fluence data for the Varian 210accelerator and Chris Bartee for his help with measuremeThis research was supported by Grant Nos. CA74043CA74158 from the National Cancer Institute.

a!This paper was presented in part at the 41st Annual Meeting of the Amcan Society for Therapeutic Radiology and Oncology, 31 October–4vember 1999, San Antonio, Texas.

b!Electronic mail: marnfield@hsc.vcu.edu1M. P. Carol, ‘‘Integrated 3-D conformal multivane intensity modulatiodelivery system for radiotherapy,’’ inThe Use of Computers in RadiatioTherapy, edited by A. R. Hounsell, J. M. Wilkinson, and P. C. William~Medical Physics Publishing, Madison, WI, 1994!, pp. 172–173.

2M. P. Carol, ‘‘Peacock™: A system for planning and rotational deliveof intensity-modulated fields,’’ Int. J. Imaging Syst. Technol.6, 56–61~1995!.

3T. R. Mackie, T. W. Holmes, S. Swerdloff, P. J. Reckwerdt, J. O. DeaJ. Yang, B. R. Paliwal, and T. J. Kinsella, ‘‘Tomotherapy: A new concefor the delivery of conformal radiotherapy,’’ Med. Phys.20, 1709–1719~1993!.

4T. R. Mackie et al., ‘‘Tomotherapy: A proposal for a dedicatecomputer-controlled delivery and verification system for conformaldiotherapy,’’ in Ref. 1, pp. 176–177.

5P. Xia and L. J. Verhey, ‘‘Multileaf collimator leaf sequencing algorithfor intensity modulated beams with multiple static segments,’’ MePhys.26, 1424–1434~1998!.

6D. J. Convery and M. E. Rosenbloom, ‘‘The generation of intensimodulated fields for conformal radiotherapy by dynamic collimationPhys. Med. Biol.37, 1359–1374~1992!.

7S. V. Spirou and C. S. Chui, ‘‘Generation of arbitrary intensity profilby dynamic jaws or multileaf collimators,’’ Med. Phys.21, 1031–1041~1994!.

8S. V. Spirou, J. Stein, T. LoSasso, Q. Wu, R. Mohan, and C. S. C‘‘Incorporation of the source distribution function and rounded leaf edeffects in dynamic multileaf collimation~abstract!,’’ Med. Phys. 23,1074–1074~1996!.

9J. Stein, T. Bortfeld, B. Doerschel, and W. Schlegel, ‘‘Dynamic X-rcompensation for conformal radiotherapy by means of multi-leaf comation,’’ Radiother. Oncol.32, 163–173~1994!.

10X. Wang, S. Spirou, T. LoSasso, J. Stein, C. S. Chui, and R. Moh‘‘Dosimetric verification of intensity modulated fields,’’ Med. Phys.23,317–327~1996!.

11T. LoSasso, C.-S. Chui, and C. C. Ling, ‘‘Physical and dosimetric aspof a multileaf collimation system used in the dynamic mode for impmenting intensity modulated radiotherapy,’’ Med. Phys.25, 1919–1927~1998!.

12M. B. Podgorsak, S. S. Kubsad, and B. R. Paliwal, ‘‘Dosimetry of larwedged high-energy photon beams,’’ Med. Phys.20, 369–373~1993!.

i-e

s

othys

ge

er-h

-

forst

-

ace

n,

.

2241 Arnfield et al. : Dynamic intensity modulated radiotherapy 2241

13R. C. Tailor, D. S. Followill, and W. F. Hanson, ‘‘A first order approxmation of field-size and depth dependence of wedge transmission,’’ MPhys.25, 241–244~1998!.

14J. Stein, ‘‘Investigations on intensity-modulated treatment techniqueconformal radiotherapy,’’ Ph.D. thesis, Heidelberg, DDR, 1997.

15R. Mohan, M. Arnfield, S. Tong, Q. Wu, and J. Siebers, ‘‘The impactfluctuations in intensity patterns on the number of monitor units andquality and accuracy of intensity modulated radiotherapy,’’ Med. Ph27, 1226–1237~2000!.

16Varian Oncology Systems Monte Carlo Modeling Information PackaPalo Alto, CA: Varian Oncology Systems, 1996.

17B. Libby, J. Siebers, and R. Mohan, ‘‘Validation of Monte Carlo genated phase-space descriptions of medical linear accelerators’’ Med. P26, 1476–1483~1999!.

18J. H. Hubbell and S. M. Seltzer,Tables of X-ray Mass Attenuation Co

Medical Physics, Vol. 27, No. 10, October 2000

d.

in

fe.

.

ys.

efficients and Mass Energy-Absorption Coefficients 1 keV to 20 MeVElements Z51 to 92 and 48 Additional Substances of Dosimetric Intere~NIST, Gaithersburg, MD, 1995!.

19J. F. Briesmeister, ‘‘MCNP-A general Monte Carlon-particle transportcode, version 4B,’’ Los Alamos National Laboratory Report No. LA13181, 1997.

20J. V. Siebers, P. J. Keall, B. Libby, and R. Mohan, ‘‘Comparison ofEGS4

and MCNP4B Monte Carlo codes for generation of photon phase spdistributions for a Varian 2100C,’’ Phys. Med. Biol.44, 3009–3026~1999!.

21J. V. Siebers, P. Keall, M. Arnfield, J. O. Kim, and R. Moha‘‘Dynamic-MLC modeling for Monte Carlo dose calculations,’’ inTheUse of Computers in Radiation Therapy, edited by W. Schlegel and TBortfeld ~Springer-Verlag, New York, 2000!, pp. 455–457.