Ridge filter design and optimization for the broad-beam three-dimensional irradiationsystem for heavy-ion radiotherapyBarbara Schaffner, Tatsuaki Kanai, Yasuyuki Futami, Munefumi Shimbo, and Eriko Urakabe Citation: Medical Physics 27, 716 (2000); doi: 10.1118/1.598934 View online: http://dx.doi.org/10.1118/1.598934 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/27/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Performance of the NIRS fast scanning system for heavy-ion radiotherapy Med. Phys. 37, 5672 (2010); 10.1118/1.3501313 Treatment planning for the layer-stacking irradiation system for three-dimensional conformal heavy-ionradiotherapy Med. Phys. 29, 2823 (2002); 10.1118/1.1521938 Spot scanning using radioactive 11 C beams for heavy–ion radiotherapy (in Japanese) Med. Phys. 29, 2456 (2002); 10.1118/1.1510512 Heavy-ion radiotherapy AIP Conf. Proc. 543, 25 (2000); 10.1063/1.1336267 A three-dimensional algorithm for optimizing beam weights and wedge filters Med. Phys. 25, 1858 (1998); 10.1118/1.598375

Ridge filter design and optimization for the broad-beam three-dimensionalirradiation system for heavy-ion radiotherapy

Barbara Schaffner, Tatsuaki Kanai, Yasuyuki Futami, and Munefumi ShimboTherapeutic Beam Assessment Office, Research Center of Charged Particle Therapy,National Institute of Radiological Sciences, Chiba, Japan

Eriko UrakabeNuclear Science Research Facility, Institute for Chemical Research, Kyoto University, Kyoto, Japan

~Received 18 August 1999; accepted for publication 11 January 2000!

The broad-beam three-dimensional irradiation system under development at National Institute ofRadiological Sciences~NIRS! requires a small ridge filter to spread the initially monoenergeticheavy-ion beam to a small spread-out Bragg peak~SOBP!. A large SOBP covering the targetvolume is then achieved by a superposition of differently weighted and displaced small SOBPs.Two approaches were studied for the definition of a suitable ridge filter and experimental verifica-tions were performed. Both approaches show a good agreement between the calculated and mea-sured dose and lead to a good homogeneity of the biological dose in the target. However, the ridgefilter design that produces a Gaussian-shaped spectrum of the particle ranges was found to be morerobust to small errors and uncertainties in the beam application. Furthermore, an optimizationprocedure for two fields was applied to compensate for the missing dose from the fragmentation tailfor the case of a simple-geometry target. The optimized biological dose distributions show that avery good homogeneity is achievable in the target. ©2000 American Association of Physicists inMedicine.@S0094-2405~00!00504-6#

Key words: heavy-ion radiotherapy, ridge filter, intensity modulation, multiple field optimization

I. INTRODUCTION

The main reason for the increasing interest in the use ofheavier charged particles for radiotherapy is their high po-tential for sparing healthy tissue surrounding a tumor, whichis due to their characteristic depth dose curve, the Braggpeak. In addition, particles heavier than protons show a con-siderable increase in their biological effectiveness in the peakregion.

In conventional application techniques, the heavy ionbeam is spread laterally by scattering or wobbling methods,while a uniform dose distribution in depth is achieved by anenergy modulation through a modulator wheel or a ridgefilter. However, both techniques—the modulator wheel andridge filter—produce a fixed energy spectrum and therefore afixed width of the spread-out Bragg peak~SOBP! throughoutthe irradiation field. This results in the delivery of unwanteddose in some areas proximal of the target. One solution toavoid delivering this unnecessary dose are the spot-scanningor raster-scanning techniques, which have been real-ized successfully for protons at PSI~Paul ScherrerInstitute!1 and carbon ions at GSI~Gesellschaft fu¨rSchwerionenforschung!.2 Another one, called a broad-beamthree-dimensional irradiation~BB3-DI! system, is under de-velopment at NIRS ~National Institute of RadiologicalSciences!.3–5 This system uses elements from both the broadbeam and the scanning techniques, and could also be de-scribed as a slice-scanning technique. The lateral spread ofthe beam is achieved by wobbling magnets, but in depth thebeam is broadened only slightly by a ridge filter, thus result-ing in the application of a high dose slice. A homogeneous

high dose region can be achieved by a combination of sev-eral appropriately weighted slices.

The definition of the shape of the ridge filter to be used tospread the monoenergetic beam to produce the high doseslice or small SOBP is not a trivial task. The homogeneityand sharpness of the distal falloff of the large SOBP dependon the shape of the small SOBP as well as the robustness ofthe application technique to small uncertainties in the beamapplication. In this work we will discuss methods to definethe shape of the ridge filter and its characteristics.

Once a suitable ridge filter is manufactured, homogeneousSOBPs of variable size can be produced by methods similarto the spot-scanning techniques. The position of each slice indepth can be controlled by the initial energy of the beam orabsorber material in the beam path and its fluence is con-trolled through the irradiation time. The lateral extension ofeach slice is tailored to the shape of the target by a multileafcollimator~MLC!, which results in additional sparing of nor-mal tissue distal to the tumor as compared to the conven-tional broad-beam techniques. Thus, the system allows anactive intensity modulation in one dimension. For protons,one degree of freedom would be enough for a good doseconformation and homogeneity. For heavier ions, however,the fragmentation tail of more proximal peaks adds a non-negligible dose at the positions further toward the distal endof the target. If the proximal peaks are blocked by the mul-tileaf collimator, the loss of the fragmentation tail will causea slight underdosage of the target~Fig. 1!. To correct for thiseffect, additional degrees of freedom for the intensity modu-lation are necessary. In this work we will show that the use

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of multiple field directions can produce the additional de-grees of freedom. Calculated and measured results are pre-sented for a simple-geometry target.

II. MATERIAL AND METHODS

A. Cell survival and biological dose in mixed LETbeams

Along the track of a carbon-ion beam, LET values changefrom around 10 keV/mm to a few hundred keV/mm. This hasa significant impact on the cell survival and has to be takeninto account when carbon beams of different energies arecombined.

We use the formalism originally developed by Zaider andRossi6 for mixed LET radiation, which has been found toreproduce well the experimental results.7 The formalism isbased on the linear-quadratic model~LQ model! for cell sur-vival and can be written as

Smix5exp~2amixD2bmixD2!; ~1!

amix5( i 50

N dia i

D; Abmix5

( i 50N diAb i

D; D5(

i 50

N

di .

~2!

a i , b i , anddi are thea andb coefficients and the fractionof the dose of thei th monoenergetic beam, respectively.N isthe number of representative monoenergetic beams.

In the SOBP a set of weighted monoenergetic beamsshifted in depth is added up to produce uniform biologicaleffect in depth. The weighting factors (t i) for the individualpeaks are determined by an iterative least square method toobtain uniform survival level throughout the SOBP. In theSOBP thea andb coefficients thus become

aSDBP~x!5( i 50

N tid~x1Dxi !a~x1Dxi !

DDOBP~x!, ~3!

AbSOBF~x!5( i 50

N tid~x1Dxi !Ab~x1Dxi !

DSOBP~x!, ~4!

where

DSOBP~x!5(i 50

N

tid~x1Dxi ! ~5!

is the total physical dose at the positionx in depth.Dxi is theshift of the i th peak relative to the most distal peak, i.e., itcorresponds to the water equivalent thickness of the absorbermaterial.

Using this formalism, the physical dose distribution aswell as the biological effect in terms of cell survival of amultienergetic heavy ion beam can be calculated from ameasured depth-dose curve and measureda and b coeffi-cients of a monoenergetic beam.

For this work we used thea andb coefficients obtainedfrom cell survival experiments on HSG~human salivaryglands! cells irradiated at different positions in a 290 MeV/ncarbon ion beam at NIRS.

The biological relative biological effectiveness~RBE!—as opposed to the clinical RBE8—is obtained fromthe ratio between the doses required to obtain a desired levelof cell killing of a reference radiation quality~Co-60! and ofthe heavy ion SOBP,

RBESOBPbio ~x,sl!5

DCo-60~aCo-60,bCo-60,sl!

DDOBP@aSOBP~x!,bSOBP~x!,sl#. ~6!

DCo-60 andDSOBP are calculated from Eqs.~1!, ~3!, and~4!.The RBE thus depends on the position in depth in the SOBPand on the choice of the survival level~sl!. Throughout this

FIG. 1. An example of a target and underdosage behind the multileaf colli-mator for a one-field irradiation using the broad-beam 3-D irradiation sys-tem. Profile A is taken through the thickest part of the target for which theSOBP is optimized. In profile B proximal peaks are blocked away by theMLC, and only a reduced SOBP is delivered. The dotted line shows the dosethat would be delivered by the blocked peaks and the shadowed area indi-cates the dose from the fragmentation tail that is missing in the reducedSOBP, taken along profile B.

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work we always use a survival level of 10%. The biologicaldose as a function of the depth and the survival level followsstraightforward:

DSOBPbio ~x,sl!5RBESOBP

bio ~x,sl!•DSOBPphys ~x!. ~7!

Although this value of the biological dose depends on thecell sensitivity parameters ofa and b, the formalism andresults in making SOBP described in this paper should stillbe valid for other combinations of the parameters adopted.

B. Definition of the small SOBP

For the broad-beam 3-D irradiation technique the initiallymonoenergetic beam has to be slightly modulated to becomemultienergetic, which will result in a broadening of theBragg peak deposited in the target material. The broadenedBragg peak will be called small SOBP. The summation ofappropriately weighted and shifted small SOBPs shall thenbe used to form a large homogeneous SOBP. Thus two setsof weighting factors have to be found.

The first set (r i) defines the contributions from the seriesof monoenergetic beams that are combined to form the smallSOBP. In practice, this weighting function is realized by aridge filter. The ridge filter is manufactured with small steps.The height of the step defines the shift of the monoenergeticpeak in depth compared to the peak without a ridge filter andthe width of the step is proportional to the contribution orweight (r i) of the i th shifted peak in the small SOBP. Forreasons of the manufacturing process, the height of the stepsis always kept constant and causes a shift of 0.6 mm inwater.

The second set of weights (wi) defines the contributionsfrom small SOBPs shifted in depth that are combined toform the large SOBP. The displacement of the small SOBPsin depth is performed by a range shifter~the current systemat NIRS uses a binary filter-type range shifter! and weightingis achieved through control of the irradiation time. Both theridge filter and the range shifter cause a change in the energyspectrum of the incident beam. However, for our purpose weare interested in the changes of the depth dose curve. Thedepth dose curve of the large SOBP can be calculated fromEq. ~5! from the monoenergetic depth dose curved and theweights of the shifted peakst i . Therefore it is more useful towork with a concept of displacement of peaks in depth in-stead of an energy modulation. Additionally, this conceptsimplifies the problem since a given thickness of the rangeshifter or ridge filter gives rise to the same shift in depth of apeak independent of the primary beam energy. We use theweighting functionT~wer!, which can be considered as aspectrum of displaced peaks or a spectrum of residual water-equivalent ranges~wer! of the monoenergetic beam compo-nents after the ridge filter and range shifter. In the case of theBB3-DI system, the spectrumT~wer! is a convolution be-tweenR ~the weighting function of the monoenergetic peaksin the small SOBP! and W ~the weighting of the smallSOBPs in the large SOBP!,

T~wer!5(i

W~wer2Dxi !•R~Dxi !. ~8!

The spectrum of ranges of a SOBP obtained by a conven-tional broad ridge filter can be considered to be close to theideal one~Fig. 2! and can therefore be taken as the goal to beapproximated by the resulting spectrumT~wer!. Figure 2shows that the ideal spectrum of the large SOBP is regularover a wide range and irregularities only appear close to thedistal end to improve the sharpness of the distal falloff. Theshading in the background indicates the planned thickness ofthe range shifter plates, which corresponds to the separationbetween the weightswi . It seems to be quite impossible tofind a set of identical functionsR separated by the rangeshifter plate thickness that can be added to approximate boththe regular and irregular parts of the spectrum. Therefore, wefirst evaluated functions to approximate the regular part ofthe spectrum and then optimized their exact shape andweights with respect to flatness and distal falloff of the bio-logical dose distribution obtained from Eq.~7!.

The regular part of the spectrum is almost constant over awide range. Mathematically a constant function can alwaysbe perfectly matched by a set of identical~i! rectangularfunctions, which is the trivial solution but not appropriate forour purpose since it is very sensitive to minimal uncertaintiesin the beam ranges;~ii ! Gaussian functions, which are insen-sitive to small errors in beam ranges, but are rather broadcompared to the separation between them; and~iii ! rectangu-lar functions with smoothed edges, which are a compromisebetween the first two options.

The last two options were evaluated in more detail.

1. Gaussian approach

Following a Gaussian approach, the weighting functionRhas the form

FIG. 2. Biological dose in a 50 mm wide SOBP produced by a modulation ofthe monoenergetic beam in discrete steps. The relative weights of the indi-vidual peaks~shown as vertical bars at their respective position! are sepa-rated by a range of 0.6 mm in water. This spectrum of ranges of monoen-ergetic Bragg peaks is regular over a wide range of the SOBP and irregularin the most distal 5 mm of the SOBP. The shading in the backgroundindicates a thickness of the range shifter plates of 5 mm.

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R~x!51

A2ps•expS 2

~x2x0!2

2s2 D ,

for x5~x023s,x013s!, ~9!

x0 is the position of the center of the Gaussian distribution,the positionx013s corresponds to the maximal range of theincident beam. Outside the indicated limits the functionR isdefined to be zero for practical reasons. The optimal valuefor the Gaussian widths has to be determined in relation tothe separation between the individual functionsR, i.e., thethickness of the range shifter plates.

Figure 3 shows an example of the characteristics of asmall SOBP obtained by a Gaussian approach for the weight-ing function.

2. Rectangular approach with smoothed edges

In the rectangular approach with smoothed edges, theGaussian integral has been chosen as the smoothing function,

R~x!51

A2pE

2`

~x2x010.5d!/rexpS 2

t2

2 Ddt,

x5~x02d,x0!,

51, x5x0 ,

51

A2pE

~x2x020.5d!/r

`

expS 2t2

2 Ddt,

x5~x0 ,x01d!. ~10!

r corresponds to the Gaussian width and can be used toadjust the degree of smoothing;r50 corresponds to the rect-

angular function.d is the separation between the individualfunctions R and thus corresponds to the thickness of therange shifter plates.

The thickness of the range shifter plates~d! was originallyset to 5.0 mm. However, results for range shifter plates of athickness of 2.5 mm were also evaluated for the Gaussianapproach and will be discussed.

C. Dose calculation and optimization procedures

Once the spectrum of the small SOBP has been defined,the biological dose can be calculated following Eq.~7!. In afirst approximation it is assumed that the biological doses ofthe shifted small SOBPs can be added linearly to calculatethe combined biological dose.9 However, the final calcula-tion of the biological dose in the large SOBP is done follow-ing the method discussed above.

The optimization of the weightswi of the small SOBPs toproduce the large, biologically uniform SOBP depth dose isdone using an iterative least square optimization. Theweights after the (k11)th iteration are calculated accordingto the following equation,10–12

wi ,k115wi ,k1( jg

2~xj !•di ,k~xj !•@P~xj !2Dk~xj !#

( jg2~xj !•di ,k

2 ~xj !,

~11!

where P(xj ): prescribed biological dose at positionxj ;Dk(xj ): calculated biological dose at positionxj after thekthiteration;di ,k(xj ): calculated biological dose contributed bysmall SOBPi; and g(xj ): weighting factor for the impor-tance of a good fit at positionxj .

In our caseg is set to 1 inside the large SOBP and 0outside. Thus, the large SOBP is only optimized with respectto the flatness of the dose and not the sharpness of the distalfalloff. After all weights have been calculated for the (k11)th step, the new dose distributionDk11 is calculated foruse in the next optimization step.

For the multiple-field optimization only a simple dose cal-culation algorithm was used, since this was consideredenough to show the principle of multiple-field optimizationsand check its performance. Physical dose was calculatedalong straight parallel lines by a summation of entries in amonoenergetic depth-dose lookup table. Scattering and di-vergence of the beam were neglected for the physical as wellas the biological dose calculation. The biological dose wascalculated following the method described above for eachoptimization loop. Equation~11! was expanded by a damp-ing factor12 to avoid a diverging of the iterative optimization.The weight of thei th small SOBP after (k11) iterationsteps becomes

wi ,k115wi ,k•

( j@g~xj !•di ,k~xj !#2•

P~xj !

Dk~xj !

( jg2~xj !•di ,k

2 ~xj !. ~12!

This formula can be used for the optimization of individualfields like in the spot-scanning technique~wherei is the in-

FIG. 3. An example of a small SOBP obtained from the Gaussian approach.This graph shows the physical dose deposited by a monoenergetic carbonion beam of 290 MeV/n~solid line!, the physical~dashed line!, and biologi-cal ~dotted line! dose of the small SOBP and its relative biological effec-tiveness calculated at the 10% survival level~RBE, dash–dotted line!. Therelative weights for the contributions of the monoenergetic beams are shownas vertical lines. They form a Gaussian distribution with a width for thisexample, which is chosen to be 4.3 mm. The separation between the discretemonoenergetic peaks is 0.6 mm.

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dex of the individual beam spots! or for multiple fields wherei is a continuous index running through all spots or slices andall fields.

For the first tests of the optimization a cross-shaped target~70 mm across! irradiated by two perpendicular fields waschosen~Fig. 12!. All the calculations were done in two di-mensions on a dose grid of 80380 mm and a resolution of 1mm. The optimization was performed for two ridge filtersproduced by the two approaches described above using 50iteration steps.

D. Experimental setup

HIMAC ~Heavy Ion Medical Accelerator! carbon ions of290, 350, and 400 MeV per nucleon~MeV/n! are used forradiotherapy. We used 290 MeV/n for the presented calcula-tions and measurements. At the entrance to the treatmentroom the beam is spread laterally by the wobbling method toproduce an irradiation field 80 mm across with a homogene-ity better than62% at the peak position after the ridge fil-ters.

Two types of ridge filters were chosen for the experimen-tal verification—one following the Gaussian approach withs51.8 mm to be used with 2.5 mm steps in the range shiftersetting ~G2.5! and one following the smoothed rectangularapproach withr50.6 mm andd55 mm ~R5!. The ridge fil-ters have been manufactured in aluminum with a 5 mmsepa-ration between the ridges.

Depth dose distributions of the small SOBP after the ridgefilter alone and a 40 mm SOBP after ridge filter and rangeshifter have been measured with a small parallel plate ion-ization chamber~Markus chamber PTW 23343,B 5 mm! ina water phantom. Four sets of measurements were performedfor the 40 mm SOBP and for each ridge filter. One with thenominal range shifter settings, one with a 1 mmerror in oneplate in the middle of the SOBP and one each with a 0.5 mmor 1 mm shift, respectively, in all the plates proximally of theposition in the middle of the SOBP. These measurementswere intended to test the robustness of the beam applicationwith the two ridge filters to small errors in the thickness ofthe range shifter plates.

All depth dose measurements were normalized at the re-spective most proximal data point at a water-equivalentdepth of approximately 50 mm. The effective point of mea-surement in depth for the chamber was determined by fittingthe theoretical depth dose curve of a monoenergetic Braggpeak to the corresponding measurement.

III. RESULTS

A. Ridge filters

Large SOBPs were calculated for the Gaussian approachfor different values for the widths. The homogeneity of thebiological large SOBP was evaluated as the sum of thesquared differences between the calculated and the pre-scribed flat dose. The best homogeneity was found fors54.3 mm when a range shifter thickness of 5.0 mm wasused. Figure 4 shows the resultant biological and physicaldose distributions and the cumulative spectrum of ranges

used to create the large SOBP. For comparison, a SOBPobtained from a conventional broad-beam ridge filter is over-laid. It shows clearly the loss in the steepness of the falloff~8mm from 90% to 30% of the dose!, which might be accept-able, but still leaves room for improvement.

Both a homogeneous large SOBP and a distal falloff dis-tance of 3.5 mm can be obtained by using range shifter platesof half the original thickness, i.e., equivalent to 2.5 mm ofwater in combination with a ridge filter that produces aGaussian range spectrum withs51.8 mm. Figure 5 showsthe results for this case.

FIG. 4. Biological~solid line! and physical~dashed line! dose distribution ofa 50 mm SOBP delivered by superposing small SOBPs produced by a ridgefilter design following the Gaussian approach. The Gaussian widths is 4.3mm and the thickness of the range shifter plates equivalent to 5.0 mm water.The biological SOBP produced by the conventional broad ridge filter isshown for comparison~dotted line!.

FIG. 5. Biological and physical dose distribution that can be obtained by theGaussian approach if both the Gaussian width (s51.8 mm) and the thick-ness of the range shifter plates (d52.5 mm) are smaller than the valueschosen in Fig. 4.

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The measurements on the SOBP with the Gaussian ridgefilter ~G2.5! show a very good agreement between measure-ment and calculation for the small SOBP as well as for the40 mm SOBP~Fig. 6!. The ratios between the calculated andmeasured dose are displayed in Fig. 7 for all the four sets ofmeasurements. The results for the SOBP using the nominalrange shifter settings are slightly high by about 1% but veryconstant throughout the high dose region. The influence oferrors in the thickness of the range shifter can be clearly seenin the proximal half of the SOBP, which is dominated bypeaks deposited with the erroneous range shifter thickness~0.5 and 1 mm errors, resp., in plates 8–16! or in the middleof the SOBP~1 mm error in plate 8 only!. However, the doseerrors do not exceed 2%–3%.

Dose distributions almost identical to those obtained forthe Gaussian approach with the half-thickness range shifterplates can be achieved with the original range shifter thick-ness (d55.0 mm) and the rectangular approach withsmoothed edges. The measurements on the ridge filter R5show a good agreement with the calculations~Fig. 8!, butslightly higher variations. Effects of errors in the rangeshifter thickness~Fig. 9! are more pronounced than for theG2.5 ridge filter.

B. Multiple field optimization

Results of the multiple field optimizations are evaluatedmainly by dose volume histograms~DVH! calculated for thebiological dose for the target and the surrounding area. Theeffect of the optimization in the two field case is displayed inthe dose volume histogram in Fig. 10 for the ridge filter R5.The nonoptimized dose distribution shows the underdosageof the target due to the missing dose from the fragmentation

FIG. 6. Measured depth dose distribution of a small SOBP and a 40 mmSOBP produced by the ridge filter G2.5 compared to the calculation. Thedose distributions are normalized at the most proximal point of measure-ment.

FIG. 7. Ratios between measured and calculated dose in the 40 mm SOBPfor the ridge filter G2.5. The crosses are for measurements without errors inthe thickness of the range shifter, the open symbols for measurements wherean error in the thickness of some range shifter settings was introduced to testthe robustness of the beam application. All symbols between the dotted linesrepresent measurements with deviations less than 2% from the calculation.The relatively large deviations in depths between 150 and 160 mm originatefrom the distal falloff region with its steep dose gradient.

FIG. 8. Measured depth dose distribution of a small SOBP and a 40 mmSOBP produced by the ridge filter R5 compared to the calculation. The dosedistributions are normalized at the most proximal point of measurement.

FIG. 9. Ratios between the measured and calculated dose in the 40 mmSOBP for the ridge filter R5. A comparison to Fig. 7 shows that errors in thethickness of the range shifter cause higher variations in the dose in case ofthe ridge filter R5 than for G2.5.

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tail, which has an effect on the four arms of the cross~80%of the target volume!. The optimization adjusts the weightsstep by step and leads to a better dose homogeneity.

Figure 11 shows DVHs of optimized results of one- andtwo-field irradiations for both ridge filters. Clearly, the twofield irradiation leads to a better dose distribution than theone-field irradiation. A comparison between results for thetwo ridge filters R5 and G2.5 shows almost identical resultswith respect to homogeneity inside the target and dose falloffoutside the target.

The results shown above represent always biological dosedistributions, which are the optimization criteria. Due to theincreasing biological effectiveness of carbon ion beams to-ward the Bragg peak, the physical dose distribution cannotbe homogeneous. Figure 12 shows profiles through thephysical and biological dose distributions for the cross-shaped target and the two-field irradiation.

IV. DISCUSSION

According to our calculations a biologically homogeneousSOBP can be produced by the concept of the broad-beam3-D irradiation system. However, the design of the ridge fil-ter for this application technique differs from ridge filter de-signs used for conventional broad-beam techniques. In con-ventional ridge filter designs the weighting factors for themonoenergetic Bragg peaks can be obtained directly from anoptimization procedure. For the BB3-DI system two con-nected sets of weighting factors are needed for the ridge filteritself and the contributions from the small SOBPs. The resultof the optimization procedure therefore depends on thechoice of the ridge filter.

We evaluated two approaches for the ridge filter designand manufactured two ridge filters that can be used to pro-duce almost identical large SOBPs. The measured physicaldepth dose distributions of small and large~40 mm! SOBPsproduced by both types of ridge filters~G2.5 and R5! agreed

well with the calculations. Multiple-field optimizations yieldgood, almost identical results in dose volume histograms of across-shaped target for both ridge filter types. Therefore,both are believed to be suitable for the broad-beam 3-D ir-radiation system.

Looking only at the dose distributions and the degree ofcomplexity involved in delivering them, the rectangular ap-proach with smoothed edges for the design of the ridge filterseems to be the best solution. However, different factors caninfluence the precision with which the dose can actually bedelivered. Another criteria for the choice of the optimal ridgefilter design is therefore its robustness to small errors anduncertainties in the control of the peak position in depth. Forexample, the precision of the thickness of the range shifterplates can be guaranteed by the manufacturer only to 0.25mm. We believe that this causes the small variation of theratios between measurement and calculation for the standardSOBP obtained by the R5 ridge filter~Fig. 9!.

The influence of small shifts of the individual positions of

FIG. 10. DVHs showing the effect of the optimization procedure for a cross-shaped target and the ridge filter R5. The first step increases generally thedose throughout the target to the prescribed mean value; subsequent stepsimprove the homogeneity in the target.

FIG. 11. DVHs of biological doses in the cross-shaped target optimized forone- and two-field irradiations. With two fields a better homogeneity can beachieved inside the target and the high dose component in the surroundingtissue is reduced. A comparison of DVHs for the two ridge filters R5 andG2.5 shows almost identical results.

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the small SOBPs on the biological dose distribution of thelarge SOBP have been evaluated by simulations. The peakswere displaced by 0.3 mm alternating in positive and nega-tive directions along the beam axis to simulate a maximaleffect of the uncertainty in the range shifter thickness. Theresulting biological dose distributions and survival levels areshown as dashed and dotted lines overlaid on the respectiveerror-free results in Fig. 13 for G2.5 and R5. While thesedisplacement errors have only a small impact on the resultsin the case of the G2.5 ridge filter design, they produce varia-tions in the biological dose of up to 10% in the SOBP ob-tained by the R5 ridge filter.

The higher sensibility to an error in the beam range of theridge filter R5 compared to G2.5 has been confirmed experi-mentally by deliberately introducing errors in some rangeshifter settings and measuring their effect on the depth dosedistribution ~Fig. 7 and Fig. 9!. A range shifter plate that istoo thick by 1 mm in the middle of the SOBP causes devia-tions from the calculation between about24% and13% forthe R5 ridge filter but only up to about62% for G2.5. Theother measurements show similarly a higher robustness ofG2.5 to errors.

The smoothed rectangular approach for the ridge filterdesign therefore requires a very high precision in the controlof the energy spectrum of the beam. We believe that alsouncertainties in the determination of the stopping power val-ues in the patient, patient or organ motion, and other sources

of errors might result in a higher variation of the dose in thetarget in the case of the R5 ridge filter. Therefore, a highercomplexity of the treatment~thinner range shifter plates,higher number of plates! using G2.5 should be preferred tothe use of R5 with the standard range shifter thickness.

We used an optimization procedure to optimize contribu-tions from the small SOBPs produced by the ridge filter for atwo-dimensional target. Although the described optimizationtechnique can be used, in principle, for optimizing theweights of the individual small SOBPs for single fields, nomajor improvement can be achieved with a single field only.The optimization is capable of compensating for the doseinhomogeneity across the target~perpendicular to the beamdirection! only if there is a degree of freedom in this direc-tion. This degree of freedom is provided by a second fieldperpendicular to the first. These two fields are sufficient toachieve a very good homogeneity inside the simulated targetin the two-dimensional case, as shown in Fig. 10, Fig. 11,and Fig. 12. We expect that a third non-coplanar field will be

FIG. 12. Profiles through the physical and biological dose distributions for atwo-field irradiation of the cross-shaped target. While the biological dose isnicely homogeneous, there are considerable differences between the corre-sponding profiles of a physical dose.

FIG. 13. The influence of slight displacements~60.3 mm! of the smallSOBPs on the biological dose distribution and the survival level~dashed anddotted lines! for two different ridge filter designs discussed here, G2.5~s51.8 mm, ridge filter spacing52.5 mm! and R5 (r50.6 mm,d55.0 mm).The solid line shows the expected results in the case of a perfect applicationof the dose. They are almost identical for both ridge filter designs.

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needed for an equally good homogeneity in a real three di-mensional target.

V. CONCLUSION

The broad-beam 3-D irradiation system under develop-ment at the NIRS is capable of irradiating a target volumewith a better conformation than conventional broad-beamtechniques. However, an appropriate ridge filter has to bedesigned and the problem of the missing dose from the frag-mentation tail—in the case of heavier ions—has to be over-come to achieve a comparable dose homogeneity in the tar-get.

Basically two approaches have been tested for the designof a ridge filter. The Gaussian approach results in a goodhomogeneity of the dose distributions in the large SOBP andis robust to small errors, but needs smaller steps in the rangeshifter setting to produce a similar large SOBP as thesmoothed rectangular approach. The smoothed rectangularapproach, on the other hand, is rather sensitive to small er-rors.

It is suggested, that we use the Gaussian approach be-cause of its robustness. One could also think of implement-ing different ridge filters that produce Gaussian-shaped spec-tra of different widths. Broader Gaussians will produce amore gradual distal dose falloff distance but are less sensitiveto errors, which might be a more important criterion in tar-gets where some motion is present.

It has been shown numerically, that multiple field optimi-zations are capable of compensating for the missing contri-butions from the fragmentation tail.

Therefore, the BB3-DI is expected to be capable of deliv-ering dose distributions to the target comparable in homoge-

neity to conventional broad-beam techniques, but offeringthe advantage of additional sparing of healthy tissue.

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