Dose response of alanine detectors irradiated with carbon ion beamsRochus Herrmanna�

Department of Physics and Astronomy, Aarhus University, 8000 Aarhus, Denmark; Division of MedicalPhysics in Radiation Oncology, German Cancer Research Center (DKFZ) Heidelberg, 69120 Heidelberg,Germany; and Department of Experimental Clinical Oncology, Århus University Hospital,8000 Aarhus, Denmark

Oliver JäkelDivision of Medical Physics in Radiation Oncology, German Cancer Research Center (DKFZ) Heidelberg,69120 Heidelberg, Germany and Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg UniversityHospital, 69120 Heidelberg, Germany

Hugo Palmans and Peter SharpeNational Physical Laboratory, Teddington, Middlesex, TW 11 OLW United Kingdom

Niels BasslerDepartment of Physics and Astronomy, Aarhus University, 8000 Aarhus, Denmark; Division of MedicalPhysics in Radiation Oncology, German Cancer Research Center (DKFZ) Heidelberg, 69120 Heidelberg,Germany; and Department of Experimental Clinical Oncology, Århus University Hospital,8000 Aarhus, Denmark

�Received 3 September 2010; revised 8 February 2011; accepted for publication 9 February 2011;published 10 March 2011�

Purpose: The dose response of the alanine detector shows a dependence on particle energy andtype when irradiated with ion beams. The purpose of this study is to investigate the responsebehavior of the alanine detector in clinical carbon ion beams and compare the results to modelpredictions.Methods: Alanine detectors have been irradiated with carbon ions with an energy range of 89–400MeV/u. The relative effectiveness of alanine has been measured in this regime. Pristine and spreadout Bragg peak depth-dose curves have been measured with alanine dosimeters. The track structurebased alanine response model developed by Hansen and Olsen has been implemented in the MonteCarlo code FLUKA and calculations were compared to experimental results.Results: Calculations of the relative effectiveness deviate less than 5% from the measured valuesfor monoenergetic beams. Measured depth-dose curves deviate from predictions in the peak region,most pronounced at the distal edge of the peak.Conclusions: The used model and its implementation show a good overall agreement for quasi-monoenergetic measurements. Deviations in depth-dose measurements are mainly attributed touncertainties of the detector geometry implemented in the Monte Carlo simulations. © 2011American Association of Physicists in Medicine. �DOI: 10.1118/1.3560459�

Key words: alanine, dosimetry, carbon ions, Monte Carlo

I. INTRODUCTION

Dosimetry of mixed particle radiation using solid state detec-tors is complicated by the nonlinear dose response of mostdetectors as a function of the particle charge Z and particleenergy E. The relative effectiveness � of a detector for agiven particle energy combination is usually expressed rela-tive to a reference radiation such as 60Co. Thus, the relativeeffectiveness ��E ,Z� is here defined as the relation betweenthe applied dose and the isoeffective dose of 60Co

� = � D�

Dion�

isoresponse, �1�

where D� is the dose deposited with 60Co, which causes thesame detector response as the dose deposited by the ionbeam �Dion�. The term “relative effectiveness” is not uni-formly used in literature; some authors1–3 use the definition

of a dose ratio at isoresponse, which is similar to the defini-

1859 Med. Phys. 38 „4…, April 2011 0094-2405/2011/38„4…

tion of the relative biological effectiveness �RBE�. Other au-thors prefer the ratio of detector responses at isodose.4–6 Ifthe detector response is a linear function of dose for thereference and the ion radiation and the dose-response curvegoes through the origin, both definitions give the same result.The benefit of using definition �1� will be further dealt within Sec. V B. Since � is a function of Z and E, knowledge ofthe mixed radiation field is necessary in order to determine �of a given field.

The alanine detector as described by Bradshaw et al.7 isan interesting detector in the context of mixed particle fielddosimetry, given its late onset of saturation effects at highdoses when irradiated with 60Co photons. It transforms into

the stable radical CH3u CHuCOOH when irradiated withionizing radiation. Using an electron paramagnetic resonance�EPR� spectrometer, the signal caused by the unpaired elec-tron can be read out. As shown by Hansen and Olsen,8 the

detector response as function of dose follows Eq. �2�

1859/1859/8/$30.00 © 2011 Am. Assoc. Phys. Med.

1860 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1860

S�D� � 1 − e−D/D0. �2�

Here, S denotes the detector response, D denotes the dose,and D0 denotes the characteristic �-ray dose. Since D0 is inthe order of 1�105 Gy,8 the response can be approximatedto be linear in terms of dose for therapeutic doses. In thisdose regime, the dose-response curves for different radiationtypes are parallel and we can therefore use Eq. �1� withoutlosing the possibility to compare our data to those from otherauthors who used the isodose definition.

The EPR signal is remarkably stable if irradiated withphotons at moderate doses. Signal fading gets significant forphoton doses over 10 kGy;9 for lower doses it is in the orderof 1% p.a.10 However, following Ref. 11, it may becomesignificant for high-LET particles due to the high dose in thecenter of the ion track and has been observed following high-LET irradiation.12 Signal fading occurs through recombina-tion of the radical molecules or transformation into nonpara-magnetic products.9 Depending on the local concentration ofradicals, signal fading increases with increasing dose.

The storage conditions of alanine detectors have an influ-ence on fading, which can be reduced by storage under con-trolled humidity before irradiation.10,13

According to Refs. 14 and 15, the average � for a mixedradiation field can be calculated by a direct superposition ofthe individual components of the mixed particle spectra, i.e.,

� =�i� j�i�Ej�Di

Dtotal, �3�

where �i�Ej� is the relative effectiveness of the particle i withthe energy Ej, Di is the dose deposited by particle i, and Dtotal

is the total dose deposited in the volume of interest.In this work, we want to test this assumption further by

using the alanine response model from Hansen and Olsen8 inthe regime of heavy ion therapy. This model is based on theoriginal idea from Butts and Katz,16 but neglects the ion-killformalism, which in the original model is accounting fortrack-interaction effects.

Palmans4 summarized several quoted relative effective-nesses for alanine detectors irradiated with protons in an en-ergy range from 1.2 to 60.0 MeV/u in a literature study.Furthermore, alanine has been irradiated with alphas, 7Li,16O, 19F, 20Ne, 32S, 40Ar, and 40Ca ions stopping in the de-tector in the energy range from 2.5 to 18.5 MeV/u and alphascrossing the detector with energies of 58.6 and 162.5MeV/u.11,12,17

Our research is motivated by finding new detectors suit-able for dosimetry of mixed particle fields as found in par-ticle therapy. Therefore, we felt it necessary to enhance thedata set with response measurements for carbon ions. Wehave measured the alanine response in monoenergetic carbonion beams and compared the measured � to that predicted bythe Hansen and Olsen model. In addition, we have also ex-posed alanine detectors to the mixed radiation field found ina spread out Bragg peak �SOBP� used for carbon ion radio-therapy.

Finally, we investigated signal fading effects after irradia-

tion of the alanine pellets.

Medical Physics, Vol. 38, No. 4, April 2011

II. EXPERIMENTAL METHODS

Alanine pellets provided by the National Physical Labo-ratory �NPL� were used as detector for our experiments.They consist of 90.9% by weight L-�-alanine and 9.1% highmelting point paraffin wax. The average density is1.23 g cm−3. There are two kinds of pellets with differentthickness, both with a diameter of 5.05 mm. The thick pelletshave a thickness of 2.27 mm and are normally used in a doserange of �5–70 kGy; the thin ones have a thickness of 0.44mm and are used in a dose range of �40 Gy–70 kGy. Do-simeters are conditioned at 55% relative humidity for 10weeks prior to use in order to reduce postirradiation fading.They have been read out at the NPL following the standardprocedure as described in detail by Sharpe et al.18 This pro-cedure has a precision of better than 0.05 Gy. For singleenergy measurements, the radiations have been planned toyield doses of 20 Gy; for the measurement of depth-dosecurves, a dose of 20 Gy was also intended in the entranceregion. Therefore, the thin pellets were, according to theirdose-range specification, only used in the peak area of apristine peak.

The samples were irradiated in the medical treatmentroom �Cave M� of the Gesellschaft für Schwerionenfors-chung �GSI�, Darmstadt, Germany, offering an energy rangefrom 89 to 430 MeV/u. At GSI, the raster scan method isused, which can deliver homogeneous fields by superposingsingle Gaussian shaped beam profiles. The beam has anangle of 2.2° relative to the horizontal axis and the experi-mental setup was accordingly aligned. The isocenter of thebeam is indicated by a laser system.

The delivered beams are monitored by large area multi-wire proportional chambers and by ionization chambers tocontrol the beam position relative to central position and theintensity of the beam. They are placed directly behind thebeam line exit window.

For single energy measurements, the pellets were irradi-ated with beams at seven energy steps in an energy rangefrom 89 to 400 MeV/u. The homogeneous field was sizedbetween 1.1�1.1 and 1.5�1.5 cm2 and the overall fieldsize was 2.5�2.5 cm2. Two thick pellets have been ar-ranged in a polymethyl methacrylate �PMMA� holder, with1.1 mm of PMMA in front of them. The first pellet in thebeam direction was placed in the isocenter. Behind the sec-ond pellet, a self-developing radiochromic film was placedfor immediate verification of the beam delivery and fieldsize. For these experiments, we used a PTW �Freiburg, Ger-many� Markus chamber �type 23343� to measure absolutedelivered dose to water. We choose the Markus chamber be-cause the diameter of its sensitive volume is 5.3 mm andhence closely matches the size of a pellet. A sketch of thesetup is shown in Fig. 1. The pellets irradiated in this setuphave been used for measurements of signal fading, as well asfor determination of �.

The Markus chamber was placed directly behind the ra-

diochromic film �see Fig. 1�. The absorbed dose to water Dw

1861 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1861

was calculated according to the ion dosimetry protocol de-scribed in IAEA TRS-398 �Ref. 19� using the followingequation:

Dw,Q = MQ · ND,w · kQ. �4�

Here, MQ is the corrected ion chamber reading and ND,w isthe calibration factor for 60Co provided by the manufacturer.The correction for recombination was calculated using thetwo-voltage method by Boag.20 The correction factor kQ asrecommended by IAEA �Ref. 19� was used. The calibrationfactor of the Markus chamber is traceable to the Phys-ikalische Technische Bundesanstalt �PTB�, but the calibra-tion of the alanine pellets is traceable to the NPL and thus todifferent primary standards. This factor of uncertainty is in-cluded in the calculations.

Depth-dose curves have been measured using alaninestacked in PMMA tubes. We measured depth-dose curves ata beam energy of 270.55 MeV/u. The irradiation was donetwice, once with a pristine beam and once with a ripplefilter21 installed in order to slightly widen the pristine Braggpeak to have a 3 mm FWHM longitudinal width. We placedten thin pellets in the stack irradiated without the ripple filterin the area where we expected the peak in order to achievebetter spatial resolution.

Two SOBPs with 3 cm modulation depth and with maxi-mal depth of 6 cm have also been measured at different doselevels. The SOBP consisted of 16 single peaks of energiesbetween 120 and 169 MeV/u. The field size of the individualenergies ranged between 1.9�1.9 and 2.1�2.1 cm2, whichproduced homogeneous areas between 1.0�1.0 and 1.2�1.2 cm2.

The minimum time between irradiation at GSI and read-out at NPL has been 6 h.

In order to benchmark the Monte Carlo simulations andour implementation of a ripple filter, a depth-dose curve of a270.55 MeV/u beam with installed ripple filter has beenmeasured in water. A Markus chamber installed in a MP3water phantom �PTW, Freiburg, Germany� for horizontal ra-

alanine detector

Markus chamber

radiochromic film

PMMA

beam

FIG. 1. Illustration of the setup for single energy measurements.

diation therapy beams has been used.

Medical Physics, Vol. 38, No. 4, April 2011

III. MODEL CALCULATIONS

For model calculations, we used the Monte Carlo codeFLUKA

22,23 version 2008.3b, including the Boltzmann masterequation �BME� model24 for nuclear interaction below 100MeV/u. The detailed experimental geometry was carefullyimplemented. The delivered field was built up in an identicalway as in the physical delivery, i.e., spot by spot using theplanned particle numbers and beam positions from the accel-erator control files. The actually applied particle numbers areassumed to be identical to the control file. The FLUKA defaultsettings for hadron therapy “HADROTHE” was used, alongwith the “DPMJET” �Ref. 25� event generator. The totalphysical dose Dtot was scored in every pellet using the“USRBIN” scoring routine in FLUKA. Since the Markuschamber measurements of dose in air are transformed to doseto water �see Eq. �4��, we calculated the dose in the Markuschamber in FLUKA by scoring dose in a volume filled withwater.

The FLUKA user routine “COMSCW” was modified suchthat any energy deposition from a particle i is multiplied witha weight �i derived from Hansen and Olsen as done byBassler et al. in Ref. 15. Thus, FLUKA calculates the nomi-nator and the denominator of Eq. �3�, which ultimately pro-duces � for the given radiation field. This is possible due tothe definition of � as a ratio of doses, as done in Eq. �1�.

The 3 mm ripple filter as used by GSI was integrated inFLUKA. The shape of one ripple, taken from the publicationfrom Weber and Kraft,21 was parametrized and a script waswritten to approximate the shape with rectangular parallel-epipeds. The shape of a 2 mm thick ripple filter as presentedin the before mentioned paper has been scaled to 3 mm,since this is the width of the ripple filter used in the experi-ments. For one 0.15 cm wide ripple, we used 225 parallel-epipeds. Since our maximum field size used with a ripplefilter has been 2.1�2.1 cm2, we created a filter with 4�4 cm2 instead of the real size of 26�26 cm2 in order toreduce calculation time. For the calculations in water, weused an I-value of 78 eV as recommended by the Interna-tional Commission on Radiation Units and Measurements�ICRU�.26

IV. RESULTS

The pellets irradiated with monoenergetic beams havebeen read out 6 h after irradiation and several times again ina time period of 666 h. The variation in the measured signalis showing a distribution with a deviation less than 1%.Variation is here expressed as deviation in percent from thefirst measured value. Figure 2�a� shows the deviation fordifferent beam energies and Fig. 2�b� for two different doses.

The values measured at the NPL are giving the dose D60Co

to water, which would be needed to be deposited by a 60Cosource to get the same EPR signal. We used the dose mea-sured with the Markus chamber as reference for calculatingthe physical dose Dtot for every pellet using FLUKA. Wesimulated the dose ratios between pellets and Markus cham-

ber and used these to calculate the dose in the pellets.

1862 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1862

Independent from this we used the accelerator controlfiles to calculate the dose to water deposited in the sensitivevolume of the Markus chamber. The calculated dose valuesfor the Markus chamber deviate less than 4% from the mea-sured ones. Here, the dose per primary particle calculatedwith FLUKA has been multiplied by the number of particlesdelivered by the accelerator.

The ratio between the measured photon-dose equivalentdetector response D60Co and the total physical dose Dtot

yields the relative effectiveness �exp following Eq. �1�.Based on the Hansen and Olsen model, �mod has been

calculated using the FLUKA user routines as described in Sec.III. The results are shown in Fig. 3 in comparison with themeasured efficiencies �exp. The error bars in the energy di-rection represent the width �1�� of the particle energy distri-bution of carbon ions in the pellet calculated with FLUKA,

6 1 0 5 0 1 0 0 5 0 0 1 0 0 0− 1 . 5

− 1 . 0

− 0 . 5

0 . 0

0 . 5

1 . 0

1 . 5deviation[%

]a ) 2 0 G y c a r b o n i o n s

6 1 0 5 0 1 0 0 5 0 0 1 0 0 0t i m e s i n c e i r r a d i a t i o n [ h ]

− 1 . 5

− 1 . 0

− 0 . 5

0 . 0

0 . 5

1 . 0

1 . 5

deviation[%

]

b ) 2 9 9 . 9 4 M e V / u c a r b o n i o n s

7 0 1 0 0 2 0 0 3 0 0 4 0 0m e a n p a r t i c l e e n e r g y [ M e V / u ]

0 . 7 5

0 . 8 0

0 . 8 5

0 . 9 0

0 . 9 5

1 . 0 0

η

s i m u l a t e d e f f e c t i v e n e s s

m e a s u r e d e f f e c t i v e n e s s

FIG. 3. Comparison of the model calculated and measured relative effective-ness as a function of energy. The error bars in energy direction represent thewidth �1�� of the energy distribution in a pellet. A line for calculated rela-

tive effectiveness is drawn to guide the eyes.

Medical Physics, Vol. 38, No. 4, April 2011

respectively. This distribution can be well described asGaussian shaped. The standard uncertainty of the measuredvalues of �exp is estimated to be 3.4%.

The depth-dose curve measured with the Markus chamberin water was simulated with our implementation of the ripplefilter. The results are shown in Fig. 4 and plotted as functionof the depth in water behind the phantom entrance window.The line shows the simulated curve; the points representmeasurements with the Markus chamber. The dose values areabsolute, but were shifted 1.3 mm along the x-axis for peakmatching.

The standard uncertainty of the Markus chamber mea-surements is estimated to be 3.4%. The determination of thisvalue followed the recommendations in IAEA TRS-398.19

The geometry of the depth-dose curve measurements hasalso been setup in FLUKA simulations. The shape of the pel-

M e V / u

0 M e V / u

5 M e V / u

0 M e V / u

0 M e V / u

0 M e V / u

0 M e V / u

G y

G y

FIG. 2. Diagram �a� shows the distribution of the mea-sured signal at different energies at 20 Gy in a timeperiod of 666 h. Diagram �b� shows the deviation at299.94 MeV/u with 20 and 40 Gy.

0 5 0 1 0 0 1 5 0 2 0 0d e p t h i n w a t e r p h a n t o m [ m m ]

0

5

1 0

1 5

2 0

2 5

absolute

dose[G

y]

2 7 0 . 5 5 M e V / u c a r b o n i o n s

M a r k u s c h a m b e r

F L U K A

1 3 4 1 3 6 1 3 8 1 4 0 1 4 2 1 4 40

5

1 0

1 5

2 0

FIG. 4. Comparison between depth-dose curves for a 270.55 MeV/u carbonion beam using the ripple filter, simulated with own FLUKA implementation

8 8

1 0

1 2

1 6

2 1

3 0

4 0

2 0

4 0

and measurements with a Markus chamber. Dose values are absolute.

1863 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1863

lets is not perfectly cylindrical; the corners are slanted. Fig-ure 5 shows the depth-dose curve for a carbon ion beam withan energy of 270.55 MeV/u without a ripple filter. Four thinalanine pellets located in the Bragg peak fractured and aretherefore not included as data points in the figure. Figure 6shows a curve with the same energy but the ripple filter wasinserted. Figure 7 shows the depth-dose curve for a SOBPwith a planned peak dose of 20 Gy.

The calculated values deviate from the measured ones upto 8.35 Gy in the steep dose fall off behind the peak of thecurve with included ripple filter; this corresponds to a devia-tion of 21% in terms of peak response. Deviations in the tailregion of the pristine beam measurement go up to 4.2 Gy,which corresponds to 8.9%. The solid lines show the simu-lated dose and the dashed lines the calculated alanine re-sponse. The data points represent measurements.

7 8 9 1 0 1 1 1 2 1 3 1 4p o s i t i o n i n p h a n t o m [ c m ]

0

2 0

4 0

6 0

8 0

1 0 0

absolute

dose[G

y]

2 7 0 . 5 5 M e V / u c a r b o n i o n s

s i m u l a t e d d o s e

s i m u l a t e d r e s p o n s e

a l a n i n e r e s p o n s e

FIG. 5. Depth-dose curve of a 270.55 MeV/u carbon ion beam. Simulationand measured data, both absolute in dose. The x-axis was not peak matched.

7 8 9 1 0 1 1 1 2 1 3 1 4p o s i t i o n i n p h a n t o m [ c m ]

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

absolute

dose[G

y]

2 7 0 . 5 5 M e V / u c a r b o n i o n s w i t h R i f i

s i m u l a t e d d o s e

s i m u l a t e d r e s p o n s e

a l a n i n e r e s p o n s e

FIG. 6. Same initial energy as in the experiment presented in Fig. 5, but with

ripple filter inserted and different detector placement.

Medical Physics, Vol. 38, No. 4, April 2011

V. DISCUSSION

V.A. Signal fading

Since we have not seen any trend in the signal measure-ments, but just statistical noise, we neglect signal fading forparticle energies between 89 and 400 MeV/u in a time periodmore than 6 h after irradiation in the dose range we used. Wecannot make any statement about the first 6 h after irradia-tion.

V.B. Relative effectiveness

Figure 3 presents the values we calculated for the relativeeffectiveness �mod, which show a deviation from our mea-sured values �exp by less then 4.6%. The deviations are largerthan the uncertainties for the two measurements with thelowest particle energies. The same figure indicates that thenature of the underestimation of the relative effectiveness forparticle energies below 200 MeV/u may be systematic.

The width of the particle energy distribution in one pellet�as indicated in Fig. 3� for the lower two energies indicatesthat here the lower end of the so-called track segment ap-proximation is reached, thus implying that the thickness ofthe detector is not longer negligible. Furthermore, the as-sumption of a monoenergetic measurement is not justified forlower energies with the used detector thickness. Still, thiscannot explain the systematic underestimation observed.Therefore, the nature of the underestimation is suspected tooriginate from the applied RE model, i.e., an indication thatthe model may not be fully valid for carbon ions at lowerenergies.

The definition of � �see Sec. I� as used here is motivatedby several reasons. First of all, it represents what we measurein the experiment, since we relate the dose deposited in analanine pellet directly to a dose measured with the Markuschamber. The pellets are read out at the NPL, where themeasured EPR signal is related to a 60Co dose. In order to

0 1 2 3 4 5 6 7p o s i t i o n i n p h a n t o m [ c m ]

0

5

1 0

1 5

2 0

2 5

absolute

dose[G

y]

2 0 G y p l a t e a u d o s e

s i m u l a t e d d o s e

s i m u l a t e d r e s p o n s e

a l a n i n e r e s p o n s e e q . d o s e

FIG. 7. Spread out Bragg peak with 20 Gy plateau dose. Simulation andmeasured data, both absolute.

get the averaged relative effectiveness for one pellet, we cal-

1864 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1864

culated the ratio of the physical dose to the 60Co equivalentdose. Second, the way we calculate the expected responsewith FLUKA by dose-weighting the relative effectiveness ofevery single dose-depositing event also relies on the defini-tion used. Furthermore, the definition is equal to the defini-tion of the RBE, which makes detector response modelscomparable to models predicting biological effectiveness ofion radiation. Also, for most cases in dosimetry, the radiationfield is well known and one is interested in the delivereddose. Thus, � can be calculated and be applied to the re-sponse equivalent 60Co dose to obtain the delivered physicaldose. This is not possible with the isodose definition of therelative effectiveness, since this would require knowledge ofthe applied dose beforehand. Nevertheless, it has to bepointed out that it is possible to interchange the definitions ofthe relative effectiveness, as done here, due to the detectorcharacteristics of alanine. For dose ranges close to saturationor other detectors with nonlinear response, this may not befeasible.

V.C. Ripple filter

As shown in Fig. 4, the shape of the simulated curve fitsthe measured data quite well in the entrance region as well asin the fragmentation tail at the distal end. The position of thepeak has been shifted by 1.3 mm for peak matching.

The accuracy of the position of the measurement points ismainly determined by the uncertainty of the absolute posi-tion of the chamber in relation to the water phantom wall.We can only estimate the position with a precision of notbetter than 1 mm, since the mounting device used for theMarkus chamber was customized by us. The distance be-tween two measurement points is known to an accuracy of0.1 mm as specified by the manufacturer.

The peak position in the Monte Carlo calculation dependshighly on the stopping power used and thus the I-value. Weused a value of 78 eV as recommended in Ref. 26, but otherauthors suggested different values.27 As shown by Andreo,28

the particle range for different I-values may differ in theorder of a millimeter. Thus we assume our implementation ofthe ripple filter as valid, which is further supported by thegood agreement of the shape of the depth-dose curve, even inthe transition form peak to tail.

V.D. Depth-dose curves

In the entrance region of the curves measured with thealanine pellets, there is a good agreement between simula-tions and measurements. Since the simulation provides abso-lute values, this confirms that the Hansen and Olsen model isvalid for the used particle energy range. In the peak region,there are deviations between simulation and measurementsfor all setups.

For the pristine peak measurement and the measurementwith ripple filter inserted, an energy of 270.55 MeV/u wasused. For this energy, Sommerer et al.29 have shown thatFLUKA can predict dose measurements, but has deviations inthe fragmentation spectra. The effect of fragmentation spec-

tra remains to be investigated. At the current state, our im-

Medical Physics, Vol. 38, No. 4, April 2011

pression is that this is a minor issue. Even turning on and offthe BME model for fragmentation below 100 MeV/u particleenergy causes effects which where smaller than the observedgeometry defects.

The measured tail region behind the peak is unusuallyhigh compared to the simulated depth-dose curve of carbonions in water �Fig. 4�. We trace this observation back to twogeometrical factors. One of them is that the edges of thepellets have been found to be slanted, as pellets are �0.5 mmthinner at their border than at the center. As illustrated in Fig.8, part of the particles crosses less matter per pellet. An adap-tion of the pellet shape in the simulations improved theiroutcome.

Another issue is that the tubes’ diameter is 0.1 mm widerthan the pellets diameter and hence there might have beensmall misalignments. These would lead to some particlestransversing less matter and thus having a range beyond theexpected position of the Bragg peak, as indicated in Fig. 8.Since the pellets in the tube were aligned randomly, the mis-alignment could not be reproduced and was therefore notincluded in the calculations. As a consequence, the calcu-lated signal and dose partly underestimate the measured sig-nal for pellets behind the peak. The same effect has been alsoobserved for protons.4

The geometry issue is also believed to be the main reasonfor underestimations of the detector response in the peakarea, where a range shift has the highest impact on responsedue to the presence of a high dose gradient. They outrank thepossible response underestimations by the model, as ob-served in the monoenergetic measurements in Sec. V B.

The simulation of the spread out Bragg peak �Fig. 7�shows some deviations between simulated and measured re-sponse at the distal edge of the peak and in the tail region.The response is in these regions underestimated by our cal-culations, which we trace back to the same reasons as for thesingle energy depth-dose measurements.

An advantage of alanine is the possibility of neglectingtrack-interaction effects in the response calculations at medi-cal dose ranges due do its high saturation dose, as discussedby Bassler.15 Track interactions add an extra layer of com-plexity in the detector response models and exact calculationof these effects may be nontrivial.30,31 The Hansen and Olsenmodel is based on the track structure theory conceived byButts and Katz,16 which describes the detector response aris-ing from activation of an element. The activation process

slanted & disordered

cylindric

FIG. 8. Illustration of the alanine pellet stack. The sizes are not true to scale,here emphasizing the slant edge at the rim of the pellets and themisalignment.

could be a single-strand break in a cell for biological systems

1865 Herrmann et al.: Alanine detectors irradiated with carbon ion beams 1865

or formation of a radical in an alanine molecule. Butts andKatz discriminate between an ion-kill and �-kill process,where the former is associated with a delta-electron from anion track activating the element. The �-kill process is asso-ciated with two or more delta rays from different ion tracksactivating an element, though this part is not included in theHansen and Olsen model. However, the Hansen and Olsenmodel predicts the experimental results well. Following de-rivatives of the track structure theory such as the local effectmodel,30,32,33 the amorphous dose distribution around an iontrack will overlap with those of other ion tracks. The accu-mulated dose from all overlapping ion tracks will translate toa local response using the �-response curve and as long asthe dose level is well below the saturation level of the detec-tor, the dose contributions from each individual ion can betreated separately, i.e., a total negation of track-overlap ef-fects. When exposed to 60Co radiation, alanine starts to satu-rate above 10 kGy, which is a very high saturation level fora detector. This is the main reason we trust that the underly-ing assumption in Eq. �3� is valid at our dose levels. Trackoverlap may become significant at higher ion dose levelsbeyond those normally applied in a clinical setting. Currentlywe plan to investigate this closer by extending the Hansenand Olsen model with a track-interaction formalism by usingthose provided by the libamtrack library.31 Testing these cal-culations against experiments, for which pellets are irradi-ated with high-fluence ion beams, will help to investigate thevalidity of the track-overlap concept in amorphous trackmodels.

For dosimetry and quality assurance �QA� in radiotherapywith charged particles, several solid state detectors have beenproposed; most of them suffer from a LET dependency of thesignal, as do films,34,35 thermoluminescent detectors,36,37

COTS silicon diodes,38 diamond detectors,39 and alanine, asshown here. However, for the latter, we have shown that it ispossible to calculate the response with a reasonable accuracyin the given particle field and hence it is possible to use thesedetectors for absolute dosimetry.

The nondestructive readout eases documentation and thedose range, down to 1 Gy,40 makes alanine a good candidatefor QA of particle beams, which may be useful during com-missioning, dose verification, or even in vivo dosimetry.

VI. CONCLUSION

We irradiated alanine dosimeters with single energeticcarbon ion beams between 89 and 400 MeV/u and measuredthe relative effectiveness of the detector at these energies. Animplementation of a detector response model by Hansen andOlsen was found to be in agreement within 4.6% of the mea-sured effectiveness. Signal fading was not found in the in-vestigated energy range and time interval.

Measured depth-dose curves for single energy beams andfor superpositions of several energies show good agreementwith calculated detector response values in the entrance re-gion. In the low energy mixed particle field behind the peakposition, differences were found up to 21%, which we trace

back to uncertainties in the geometry.

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The Hansen and Olsen model neglects the overlapping oftracks. As mentioned by Bassler,15 saturation effects due tooverlapping tracks can be neglected for alanine in the doseregime investigated. To fully validate the model, further in-vestigations for lower energies, as found in the peak, and forhigher fluences, where track-interaction effects may becomesignificant, are necessary.

However, alanine proves to be a robust and promisingdosimeter in clinical heavy ion beams. Fine tuning of thedetector response model and the pellet geometry may still beneeded for QA level dosimetry in particle beams.

ACKNOWLEDGMENTS

Rochus Herrmann and Niels Bassler acknowledge theDanish Cancer Society for their financial support. RochusHerrmann is also supported by CIRRO, The Lundbeck Foun-dation Center for Interventional Research in Radiation On-cology and The Danish Council for Strategic Research. NielsBassler also thanks the German Research Society �DFG� forGrant No. JA1687/1-1. The authors want to thank BenjaminAckermann and Peter Heeg for their assistance during thebeam times at GSI and Franceso Cerutti for letting the au-thors use the FLUKA BME model.

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