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Electron paramagnetic resonance (EPR) dosimetry using lithium formate in radiotherapy:

comparison with thermoluminescence (TL) dosimetry using lithium fluoride rods

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2004 Phys. Med. Biol. 49 4701

(http://iopscience.iop.org/0031-9155/49/20/003)

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INSTITUTE OF PHYSICS PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 49 (2004) 4701–4715 PII: S0031-9155(04)83122-1

Electron paramagnetic resonance (EPR) dosimetryusing lithium formate in radiotherapy: comparisonwith thermoluminescence (TL) dosimetry usinglithium fluoride rods

Tor Arne Vestad1, Eirik Malinen1,2, Dag Rune Olsen2, Eli Olaug Hole1

and Einar Sagstuen1

1 Department of Physics, University of Oslo, PO Box 1048, Blindern, N-0316 Oslo, Norway2 Department of Biophysics, Institute for Cancer Research, The Norwegian Radium Hospital,N-0310 Oslo, Norway

E-mail: eirik.malinen@fys.uio.no

Received 4 July 2004Published 24 September 2004Online at stacks.iop.org/PMB/49/4701doi:10.1088/0031-9155/49/20/003

AbstractSolid-state radiation dosimetry by electron paramagnetic resonance (EPR)spectroscopy and thermoluminescence (TL) was utilized for the determinationof absorbed doses in the range of 0.5–2.5 Gy. The dosimeter materials usedwere lithium formate and lithium fluoride (TLD-100 rods) for EPR dosimetryand TL dosimetry, respectively. 60Co γ -rays and 4, 6, 10 and 15 MV x-rayswere employed. The main objectives were to compare the variation in dosimeterreading of the respective dosimetry systems and to determine the photon energydependence of the two dosimeter materials. The EPR dosimeter sensitivity wasconstant over the dose range in question, while the TL sensitivity increasedby more than 5% from 0.5 to 2.5 Gy, thus displaying a supralinear doseresponse. The average relative standard deviation in the dosimeter readingper dose was 3.0% and 1.2% for the EPR and TL procedures, respectively.For EPR dosimeters, the relative standard deviation declined significantly from4.3% to 1.1% over the dose range in question. The dose-to-water energyresponse for the megavoltage x-ray beams relative to 60Co γ -rays was inthe range of 0.990–0.979 and 0.984–0.962 for lithium formate and lithiumfluoride, respectively. The results show that EPR dosimetry with lithiumformate provides dose estimates with a precision comparable to that of TLdosimetry (using lithium fluoride) for doses above 2 Gy, and that lithiumformate is slightly less dependent on megavoltage photon beam energy thanlithium fluoride.

0031-9155/04/204701+15$30.00 © 2004 IOP Publishing Ltd Printed in the UK 4701

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1. Introduction

Dosimetry provides pivotal quality assurance of equipment, techniques and treatmentsemployed in radiotherapy. Thermoluminescence dosimetry (TLD) is the most widelyused solid-state method for in vivo dose determinations during external beam radiotherapy(Essers and Mijnheer 1999). The main advantages of the TLD technique are its highsensitivity and the extensive selection of reusable dosimeters of various materials, sizesand shapes (Kron 1994). Lithium fluoride, doped with magnesium and titanium (TLD-100; LiF:Mg,Ti), is the most common TLD material and has been employed in patientdosimetry for nearly 50 years (Kron 1995). Reported fading rates of lithium fluoridedosimeters vary considerably, but a pre-heat in the reading cycle, intended to excluderapidly fading glow peaks in the TL signal, is associated with reduced signal fading(Horowitz 1990). TLD-100 rods used for dosimetry in the radiotherapy dose range showa reproducibility of about 2% (1 SD) in the dosimeter reading if careful calibration hasbeen performed (Essers and Mijnheer 1999). Lithium fluoride dosimeters are apparently notparticularly dependent on megavoltage photon beam energy (Mobit et al 1996). Althoughbeing a very versatile technique, TLD has some disadvantages. These include a destructivereadout process (with respect to the dose record) and a supralinear dose response(Kron 1994).

Solid-state dosimetry by electron paramagnetic resonance (EPR) spectroscopy, usuallywith the amino acid L-α-alanine as dosimeter material (Regulla and Deffner 1982), hasbeen proven useful for a variety of applications, especially for high doses (kGy region)(Mehta and Girzikowsky 2000). In EPR dosimetry, the peak-to-peak amplitude of the first-derivative EPR spectrum of radiation-induced radicals in the dosimeter is used to monitorthe absorbed dose. Alanine dosimeters display a very low signal fading (Sleptchonok et al2000) and are nearly water equivalent at megavoltage photon energies (Bergstrand et al2003). EPR dosimeter readout is generally non-destructive, and may provide cumulative doseestimates during, e.g., fractionated radiotherapy. However, EPR dosimeters are not reusable.Alanine has been used for in vivo dose estimates in radiotherapy (Schaeken and Scalliet 1996,Ciesielski et al 2003), but its relatively low sensitivity results in reduced precision (standarddeviation not within ±5%) for doses below 1 Gy unless very elaborate signal processingmethods are employed (Hayes et al 2000, Nagy et al 2002).

Recently, EPR studies have shown that lithium formate monohydrate (lithium formatein the following) is more sensitive than alanine by a factor of about 6, and is suitable formeasuring doses down to at least 0.1 Gy using practical dosimeter reading times (Vestad et al2003). Also, very little signal fading has been observed at normal atmospheric conditions(Vestad et al 2003). The effective atomic number of lithium formate (about 7.3) is close to thatof water (7.5), while alanine and lithium fluoride have, in contrast, effective atomic numbers ofapproximately 6.8 and 8.3, respectively (Nowotny 1998). Thus, the interaction probabilitiesof ionizing radiation in lithium formate are expected to be more similar to water in comparisonwith alanine or lithium fluoride.

Although TL dosimetry is suitable for in vivo dose estimates in radiotherapy, it is stillimportant to investigate whether other methods provide similar precision using a comparableworkload. EPR dosimetry is a rather simple measurement technique, and has some advantagesin comparison with TL dosimetry. With the advent of lithium formate as a promising materialfor EPR dosimetry in the radiotherapy dose range, comparing this method with the ‘goldstandard’ of patient dosimetry, that is, TL dosimetry with lithium fluoride rods, is essential.Various aspects of such a comparison, relevant for radiotherapy applications, are addressed inthe present work: the variation in dosimeter reading over a relevant dose range (0.5–2.5 Gy),

Comparison study of EPR and TL dosimetry in radiotherapy 4703

the photon energy response of lithium formate and lithium fluoride, and the cost and workloadassociated with the respective techniques.

2. Materials and methods

2.1. EPR dosimeters and measurements

EPR dosimeters were made in the form of cylindrical pellets of polycrystalline lithium formatemonohydrate (HCO2Li·H2O, Sigma–Aldrich) using a 5.0 mm diameter manual Weber pelletpress with a force of 10 kN for 1 min. The average dosimeter height and mass was 3.5 ±0.2 mm and 89 ± 4 mg, respectively. Ninety-six EPR dosimeters were made for thestudy. The density of single crystals of lithium formate monohydrate is reported to be about1.48 g cm−3 (Thomas et al 1975). The temperature and relative humidity in the laboratoryduring preparation, storing and EPR measurements were 22 ± 2 ◦C and 33 ± 5%, respectively.The EPR dosimeters were stored in darkness, and exposed to luminescent light only duringshort intervals upon transfer from storage conditions to irradiation and EPR measurements.

EPR measurements were performed at room temperature using a Bruker ESP300Espectrometer equipped with a standard x-band bridge and a dual rectangular cavity (TE104).The EPR dosimeter was placed in a quartz tube with an inner diameter of 5.25 mm, and a samplesupport system was used to ensure identical and reproducible positions of dosimeters in thecavity. EPR spectra were recorded using a microwave power of 50.3 mW, a modulationamplitude of 1.5 mT, a magnetic field sweep width of 4.0 mT and a time constant of1.3 s. One thousand and twenty-four sampling points and five magnetic field scans gavea total acquisition time of 3.5 min per dosimeter. The microwave frequency was about9.773 GHz. Typical EPR spectra of irradiated lithium formate may be found elsewhere(Vestad et al 2003). A Mn2+/MgO reference sample (JEOL Co) was placed in the secondcavity, and the EPR spectrum of Mn2+ was recorded immediately after each EPR dosimeterrecording to check for spectrometer instabilities. Cavity tuning was performed for eachdosimeter. The EPR signal from the reference sample was obtained using a microwave powerof 8.0 mW and a modulation amplitude of 0.16 mT.

The nomenclature ‘EPR dosimeter reading’ corresponds to the peak-to-peak intensityof the first-derivative EPR spectrum, corrected for dosimeter mass, background signals (seebelow) and EPR spectrometer sensitivity variations (using the relative intensity of the Mn2+

reference signal). The Mn2+ reference sample measurements showed a relative standarddeviation of about 0.4% (largest correction was 0.9%), thus indicating that the sensitivity ofthe EPR spectrometer remained virtually constant during the measurement period (11 days).

EPR dosimeters were irradiated using five different radiotherapy beams (see below) in thedose range 0.5–2.5 Gy, with five different doses and three (occasionally six) dosimeters foreach dose. EPR measurements of dosimeters were performed two times, as the non-destructivereadout allows for repeated EPR recordings of the same dosimeter. Spectra of 15 unirradiateddosimeters were also recorded.

An EPR dosimeter analysis program was developed in Visual Basic/Excel (Microsoft),allowing for a computerized readout of dosimeter signals. In the program, 15 backgroundspectra (obtained from EPR recordings of unirradiated dosimeters) were used to constructan average background spectrum that was subtracted from the EPR dosimeter spectra beforeany peak-to-peak readout was done. Thus, only the radiation-induced component of the EPRspectra is employed in the dosimeter analysis, and the average dosimeter reading at zero dosebecomes zero after the subtraction. This procedure also allows for a direct comparison with theTL dosimeter readings. Finally, smoothing of EPR spectra by a convolution with a Gaussian

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function (σ = 20 sampling points) was performed in order to reduce noise contributions (theEPR line width was about 380 sampling points).

2.2. TL dosimeters and measurements

LiF:Mg,Ti rods (TLD-100 dosimeters) with square cross sections (1 × 1 × 6 mm3) and a densityof 2.64 g cm−3 were obtained from Bicron RMP (USA). The rods were carefully handled withtweezers, and stored on a custom made numbered plate in order to keep track of the individualdosimeters. Fifty TL dosimeters were employed, which were re-used one time. A Harshaw5500 Automatic TLD reader (Bicron RMP, USA) was used for all TL measurements. Briefly,the dosimeters were heated under a hot, steady flow of nitrogen (about 5 l min−1), wherethe temperature was increased from 80 to 300 ◦C in 33.3 s during TL recording. The totalacquisition time per dosimeter was about 1 min. The TL dosimeter reading corresponds to theintegrated thermoluminescence over the temperature range in question. An average zero-dosesignal was subtracted from the thermoluminescence signal of irradiated dosimeters. Typicalglow curves of lithium fluoride may be found elsewhere (Horowitz 2001). In the TL equipmentmanual (Bicron RMP, USA), the stated short-term variation in the sensitivity of the TL reader(the ‘test light stability’) was reported to be less than 0.5%, which was not attempted to beexperimentally verified. Annealing of TL dosimeters was performed in a PTW-TLD oven.Pre-read annealing at 100 ◦C for 10 min was performed, while after TL readout, the dosimeterswere heated to 400 ◦C for 1 h followed by 100 ◦C for 2 h.

For individual calibration, which was performed prior to the current investigations, all TLdosimeters were irradiated to a dose of 1 Gy and the thermoluminescence from each dosimeterwas recorded. From the resulting distribution of TL dosimeter readings, the mean reading wascalculated. The ratio of the individual and mean reading was taken to represent the relativesensitivity for a given dosimeter. Subsequent readings of a given dosimeter were correctedby its relative sensitivity. Finally, the TL dosimeters were irradiated using five differentradiotherapy beams (see below) in the dose range 0.5–2.5 Gy, with five different doses andthree dosimeters for each dose.

2.3. Dosimeter holder

During irradiation, the dosimeters (three at a time) were positioned in a water phantom (seebelow) by means of a homemade polymethylmethacrylate (PMMA) holder (figure 1(a)) withan outer shape similar to the ionization chamber used in this study. The EPR dosimeterswere stacked inside the holder (inner diameter 5.5 mm) and kept in place with a PMMA rod(figure 1(b)). The TL dosimeters were kept in suitable wells of a PMMA cylinder. Thecylinder was joined to a PMMA rod by a thin cap (figure 1(c)), and placed in the holder. Thebeam direction was perpendicular to the symmetry axis of the holder.

2.4. Irradiation

The dosimetry protocol used was the IAEA TRS-398 (IAEA 2000). All dosimeters wereirradiated in a 30 × 30 × 15 cm3 water phantom at a depth of 10 cm, placed on additionalslabs (10 cm) of solid water (Gammex RMI). The phantom has a PMMA sleeve with athickness of 0.6 mm, suitable for insertion of thimble chambers. The total PMMA thicknessof the phantom sleeve and dosimeter holder (i.e. the dosimeter wall) is about 1.6 and 2.1 mmfor EPR and TL dosimeters, respectively. A Mobaltron 80 therapy unit (TEM instruments)was employed for 60Co γ -irradiation, while linear accelerators (Clinac 2100 CD and Clinac

Comparison study of EPR and TL dosimetry in radiotherapy 4705

Figure 1. Dosimeter holder of polymethylmethacrylate (PMMA) used to position the EPR andTL dosimeters in the water phantom: (a) complete design without dosimeters, (b) outlined partwith three EPR dosimeters and (c) outlined part with three TL dosimeters. Cross sections of thedosimeter-holding part (dashed line) are shown to the right of (b) and (c).

600 C, Varian Medical Systems) were utilized for generating 4, 6, 10 and 15 MV x-rays.The TPR20,10 values ranged from 0.572 (for 60Co γ -rays) to 0.765 (for 15 MV x-rays). Seetable 1 for an overview of the beams employed. The field size at the position of the dosimeterswas 10 × 10 cm2, while the distance between the source and dosimeter was 80 or 100 cmduring γ - or x-irradiation, respectively. The average temperature and pressure duringirradiation was 22 ± 1 ◦C and 998 ± 10 Pa, respectively. For absolute water-based dosimetry,a Wellhofer FC65-G ionization chamber, traceable to a secondary standard at the NRPA1,and a Standard Imaging MAX-4000 electrometer was employed. Using this equipment, thestandard deviation of the measured output from the linear accelerators was found to be lessthan 0.1%.

2.5. Data analyses

The dosimeter reading R is the principal quantity of interest in the current work, and is alwaysgiven as a function of the absorbed dose in water, Dw. The dose response R(Dw) is thusdefined as the dependence of the dosimeter reading on the absorbed dose, and is, in the idealcase, a first-order linear function intercepting with the origin.

The individual dosimeter reading per dose to water for a given photon beam quality E,(Ri/Dw)E, is used in the analysis of reading variations. However, as the dosimeter readingis not directly related to the absorbed dose in the dosimeter (which gives rise to the energyresponse defined below), the relative reading ri is defined as

ri = (Ri/Dw)E

(R/Dw)E(1)

where (R/Dw)E is the average reading per dose for the given beam quality. In this way, theindividual readings for different beam qualities can be pooled into one group of observations.

The energy response, or quality dependence factor, of a dosimeter may be defined as(Mobit et al 1996, Bergstrand et al 2003):

FE = (R/Dw)E

(R/Dw)60Co. (2)

In this notation, R is the expectation value of the dosimeter reading. In order to check forlinearity with dose, many doses were employed for each of the photon beam qualities and

1 The Norwegian Radiation Protection Authority, PO Box 55, N-1332 Østerås, Norway (http://www.nrpa.no/).

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FE could thus be calculated for five different dose levels. An average energy response overthe given dose region was then calculated by a weighted average of the FE values obtainedat each dose level. The normalized weights used were inversely proportional to the observedvariance σ (FE)2 at the given doses and beam qualities. Thus, the contribution from outliersis minimized in the energy response calculations. Also, such an approach is not dependenton parametrized dose response models (Bergstrand et al 2003), which would complicate theanalysis of the (supralinear) TL dose response.

Following the IAEA TRS-398 protocol (IAEA 2000), the dose to water Dw, as determinedby ionometry (ionization chambers), is principally composed of three factors: a chambercalibration factor, a chamber reading and a beam quality correction. The uncertainty analysesof the response function FE should include the contributions from various error sources fromthese three factors (IAEA 2000) together with the uncertainty in (EPR or TL) dosimeterreading. However, if the same chamber has been used for all measurements, as in the currentstudy, the energy response estimates are not dependent on the chamber calibration factor(and accompanying uncertainties). This is because the calibration factor is eliminated inequation (2). In effect, this leaves the beam quality correction factor kQ as the major contributorto the standard uncertainty in the energy response function FE, in addition to the variation inthe EPR or TL dosimeter reading. The standard uncertainty of kQ is estimated to be about 1%(IAEA 2000). Thus, the energy response of the dosimeter materials cannot be estimated withmore than about 1% accuracy. The total standard uncertainty of FE, where both the solid-statedosimeter and the ion chamber uncertainty were taken into account, was calculated by regularpropagation of error methods (ISO 1995).

3. Results

3.1. Dosimeter reading

In figure 2, the dependence of the dosimeter reading on the absorbed dose in water followingexposure to 60Co γ -radiation and 6 MV x-rays is given for EPR (upper panel) and TL (lowerpanel) dosimeters. Both types of dosimeters (deceivingly) display linear characteristics overthe dose range in question, as was the case for all radiation beam qualities (data not shown).The small difference in the slope of the regression line between 60Co γ -rays and 6 MV x-rays(figure 2) is due to the photon energy dependence of the dosimeter reading, which is to beanalysed in section 3.2.

In figure 3, the relative dosimeter reading per dose for all photon beam qualities are plottedagainst the absorbed dose in water. For EPR dosimeters (figure 3, upper panel), the standarddeviation decreases from 4.3% at an average dose of 0.47 Gy to about 1.1% at a dose of 2.4 Gy.Furthermore, the average reading per dose (i.e., the sensitivity) is practically constant with theabsorbed dose, as indicated by a linear regression (data not shown). The standard deviation inthe relative reading of all irradiated EPR dosimeters was 3.0%. For TL dosimeters (figure 3,lower panel), the sensitivity is increasing by about 5% from 0.5 Gy to 2.0 Gy before a quasi-plateau is reached. There is virtually no dose dependency in the standard deviation of TLdosimeters. Corrected for supralinearity (by evaluating each dose level separately), the relativestandard deviation for TL dosimeters became 1.2%.

All relative dosimeter readings per dose are presented for both dosimetry methods infigure 4. From the calculated standard deviations of the observed EPR and TL distributions,corresponding normal distributions have been plotted in the same panel. It is apparent that thesum of the squared deviations between the observed and expected distribution is largest forEPR dosimeters. A χ2-test of the data indicates that it is unlikely that the EPR observations

Comparison study of EPR and TL dosimetry in radiotherapy 4707

Figure 2. Dose response of EPR (upper panel) and TL (lower panel) dosimeters for 60Co γ -rays(circles) and 6 MV x-rays (triangles). Individual dosimeter readings (three at each dose point) areshown. Corresponding linear regressions are given with the solid and dashed lines, respectively.The regressions are for illustrational purposes only.

follow the normal distribution (p � 0.01), while the TL readings very probably follows anormal distribution (p ≈ 1). If all EPR readings outside the 1 ± 2σ interval were excludedfrom the analysis (about 5% of all observations), the standard deviation was reduced from 3%to 2%. Furthermore, a following χ2-test showed a p-value close to 1, thus indicating that theEPR readings of the reduced sample space probably follows a normal distribution. Therefore,it is likely that a few outliers in the EPR readings contribute significantly to the relatively largevariance and the deviation from the normal distribution.

3.2. Photon energy dependence

The increase in sensitivity of TL dosimeters depicted in figure 3 (lower panel) shows thatparametrized dose response modelling by first-order linear regression is not suitable forthis dosimetry system in the present work. Therefore, instead of using the slope ratio offirst-order dose response regression lines (Bergstrand et al 2003), the energy response wascalculated at each of the five dose levels (figure 5). The average energy response for each ofmegavoltage x-ray beams was found by taking the weighted mean. It was chosen to treat theEPR dosimeter readings per dose similarly. As the dosimeters irradiated with megavoltagex-rays or 60Co γ -rays were not given exactly the same doses (the largest difference was 6.6%for TL dosimeters), the dose depicted in figure 5 is the mean dose level for the two respective

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Figure 3. The dependence of the relative reading per dose of EPR (upper panel) and TL (lowerpanel) dosimeters on the absorbed dose to water.

Table 1. The energy response (including standard uncertainties) of EPR and TL dosimeters for thevarious radiotherapy photon beams employed. See the text for further details.

Energy response, Energy response,Beam TPR20,10 lithium formate lithium fluoride

60Co γ -rays 0.572 1.000 1.0004 MV 0.635 0.990 ± 0.013 0.984 ± 0.0126 MV 0.675 0.983 ± 0.013 0.978 ± 0.01410 MV 0.745 0.988 ± 0.014 0.962 ± 0.01215 MV 0.765 0.979 ± 0.014 0.969 ± 0.014

photon beam qualities in question. In figure 5, it is apparent that the photon energy responsesshow little or no dependence on the absorbed dose.

In figure 6, the average photon energy response of lithium formate and lithium fluoridedosimeters depending on the megavoltage beam quality, as given by the TPR20,10 value, isshown. For convenience, the response factors, with accompanying uncertainties, are alsogiven in table 1. It is apparent from figure 6 and table 1 that lithium fluoride displays anenergy response significantly smaller than 1 (within one standard uncertainty) for all fourx-ray beams. In addition, a weak decline with increasing TPR20,10 is observed. For lithiumformate, the energy response appears similar to that of lithium fluoride, but is always closerto 1 (although no significant differences are present).

Comparison study of EPR and TL dosimetry in radiotherapy 4709

Figure 4. The distribution of relative EPR (upper panel) and TL (lower panel) dosimeterreadings per dose over the dose range in question. The TL dosimeter readings were correctedfor supralinearity. In both panels, the normal distribution based on the observed standard deviationfor the respective dosimetry method has been plotted.

4. Discussion

4.1. General

The current investigations show that EPR dosimetry with lithium formate is useful for dosedeterminations in the dose range of 0.5–2.5 Gy, i.e., that lithium formate is suitable for in vivodosimetry in radiotherapy. This was also indicated in a previous study (Vestad et al 2003). Thesame conclusion can obviously be made for the well established method of TL dosimetry withlithium fluoride. The dose response of both types of dosimeters was fairly linear, but the TLsensitivity increased with about 5% over the dose range in question, displaying a supralineardose response. Furthermore, the relative standard deviation in the TL dosimeter reading was1.2%, against 3.0% for EPR dosimeters. Incidentally, if correction for supralinearity andindividual calibration was not performed, the TL standard deviation increased to 4.0% (datanot shown).

The supralinear dose response of TL dosimeters implies that the accuracy of this methodis significantly reduced for doses above about 0.5 Gy if the effect is not properly corrected for.Our findings (figure 3, lower panel) are quite similar to what was observed by Feist (1988).In that work, the sensitivity increased by about 15% over a dose range from 0.5 to 6 Gy usingan automatic Harshaw TL reader. A similar feature was also observed by Tawil et al (1994).As in the present work, these studies (Feist 1988, Tawil et al 1994) display a saturation of the

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Figure 5. The photon energy response relative to 60Co γ -rays of lithium formate (upper panel)and lithium fluoride (lower panel) for 4, 6, 10 and 15 MV x-rays, as evaluated at different doselevels. The error bars in the absorbed dose are the absolute difference between the 60Co γ -rayand megavoltage x-ray doses employed. The error bars in the energy response are combinedstandard uncertainties from both uncertainties in the determination of absorbed dose to water anduncertainties in the EPR or TL dosimeter readings.

Figure 6. The dependence of the photon energy response relative to 60Co γ -rays for EPR (opensquares) and TL (filled circles) dosimeters on the photon beam quality (as given by the TPR20,10).The findings are weighted averages of the data presented in figure 5. The error bars represent thestandard uncertainty.

Comparison study of EPR and TL dosimetry in radiotherapy 4711

Figure 7. First-derivative x-band EPR spectra of 18 lithium formate dosimeters given a dose ofapproximately 0.5 Gy, compared with EPR spectra of 15 unirradiated dosimeters. The solid linesare average spectra, while the dotted lines are spectra from individual dosimeters.

supralinearity at roughly 3 Gy. EPR dosimeters of lithium formate do not display any suchfeatures (figure 3, upper panel), which obviously is an advantage.

The observed standard deviation in dosimeter reading for lithium formate dosimeters wasrather high (3.0%). However, if the observations outside the (1 ± 2σ ) limit were discardedfrom the investigations of variations in dosimeter reading (this may be a reasonable hypothesisfor testing the lower limit of uncertainty), the standard deviation over the hence reduced samplespace was 2.0%. The calculated correlation between corresponding dosimeter readings for thefirst and second measurement sessions was 0.25 (data not shown), indicating that the observedvariance in the EPR dosimeter reading is mostly due to random errors in the EPR measurementprocess. If variations in the intrinsic EPR dosimeter sensitivity were present, a much strongercorrelation is expected between the first and second measurements of the very same dosimeters.Thus, random factors, like non-identical positioning in the EPR cavity and sample anisotropycould contribute to the observed outliers (Nagy et al 2002). Sample anisotropy may arise froma non-random directional distribution of microcrystals in the polycrystalline EPR dosimeter.

In figure 7, the raw EPR spectra of 15 unirradiated dosimeters and of all dosimeters givena dose of about 0.5 Gy, only corrected for dosimeter mass, are shown. No subtraction of theaverage background spectrum was performed in this case. It is apparent that the variation inthe reading of unirradiated dosimeters (the ‘background signal’) is comparable to the variationin the peak-to-peak reading of irradiated dosimeters (in absolute terms). ‘Peak-to-peak’amplitudes of unirradiated dosimeters were taken at the magnetic field values corresponding tomaximum and minimum intensity of the radiation-induced resonance. The standard deviationin the ‘peak-to-peak’ reading of unirradiated dosimeters, relative to the average peak-to-peakreading at 0.5 Gy, was about 5%. This is comparable to the standard deviation obtained abovefor irradiated EPR dosimeters at 0.5 Gy (4.3%). Therefore, it is not likely that properties of thelithium formate dosimeters (such as sample anisotropy) contribute significantly to the observedvariation, and the background signal is in this case not a dosimeter-related quantity. Althougha positioning system was employed in order to ensure identical EPR cavity conditions foreach dosimeter, it could still be that the dosimeter recordings were performed with smallvariations in sample position. Furthermore, as a high signal-to-noise ratio was desired, ratherhigh microwave power and modulation amplitude were used. Thus, small variations in thesample positioning may possibly have given rise to signal offsets in the acquisition channeland the EPR cavity resonance pattern, resulting in a varying background signal. From ourdata, it is difficult to judge whether rotation of the dosimeters in the EPR cavity and subsequent

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Figure 8. The dependence of the mass collision stopping power (Sc/ρ) and mass energyabsorption coefficient (µen/ρ) of lithium formate and lithium fluoride relative to that of wateron the kinetic energy of electrons or photons. Stopping powers are obtained using the ESTARcode by (Berger et al 2000), while energy absorption coefficients are calculated by the programXMuDat (Nowotny 1998).

spectrum averaging (Nagy et al 2002) could correct for the outliers observed in the currentstudy. In general, rotation of samples obviously complicates and prolongs the EPR recordingprocess, although automatic rotation devices have been developed (Haskell et al 1997).

4.2. Photon energy dependence

The dose deposition of photons (under charged particle equilibrium) and electrons in a smallvolume of a substance is proportional to the mass energy absorption coefficient (µen/ρ) andthe mass stopping power (Sc/ρ), respectively (Attix 1986). In figure 8, the energy dependenceof (µen/ρ) and (Sc/ρ) for lithium formate and lithium fluoride, relative to water, is given. It isapparent that the (µen/ρ) ratio for lithium fluoride varies considerably more with the energythan lithium formate. In particular, it is therefore expected that the orthovoltage x-ray energyresponse of lithium formate is much closer to unity. Also, the difference between the (µen/ρ)and (Sc/ρ) ratios is smaller for lithium formate. Estimates of the megavoltage photon energyresponse may be obtained from a weighted sum of the (µen/ρ) and (Sc/ρ) ratios following thetheory of Burlin (1966), but experimental methods or Monte Carlo techniques are the currentstandards for estimating the energy response.

This is, to our knowledge, the first study to investigate the megavoltage photon energyresponse of lithium formate. There are small differences between lithium fluoride and lithiumformate for the current photon beam quality range (figure 6 and table 1), although lithiumformate always gave a FE value closer to unity. The energy response of lithium formatedecreases to about 0.98 at TPR20,10 values above 0.7, but the uncertainties in these estimates(about 1.4%) prevent any firm conclusions to be made. As apparent from figure 6 and table 1,the average photon energy response is 0.985 ± 0.005 (1σ ). Thus, on the basis of the findingsin the current work, the recommended megavoltage photon energy response factor for lithiumformate is 0.985, due to the small variation over the range of TPR20,10 values. For lithiumfluoride, recommended energy response factors are 0.984 for TPR20,10 ∈ |0.6, 0.65| and 0.965for TPR20,10 ∈ |0.7,→〉, based on the current findings. It is important to emphasize that theenergy response estimates for both EPR and TL dosimeters include wall effects due to thePMMA dosimeter holder used.

Comparison study of EPR and TL dosimetry in radiotherapy 4713

Table 2. Estimated workload and costs for the dosimetry techniques employed in the current study.All prices are given on a relative scale.

Feature EPR dosimetry TL dosimetry

Pre-readout anneal a 30 minReadout per dosimeter 3.5 min 1 minPost-readout anneal a 3 hCalibration (10 dosimeters)b 1 h 1 hCost per dosimeter 0.02c 0.1d

Dosimetry lab, total cost 1000e 1000f

a No annealing of EPR dosimeters are needed.b Calibration includes irradiation, pre-read anneal (for TL dosimeters only), reading of dosimetersand update of instrument (and/or dosimeter batch) sensitivity.c The price of lithium formate dosimeters is estimated from that of alanine pellets (polycrystallinesamples have similar prices) obtained from Bruker Biospin GmbH.d Price of TLD-100 dosimeters obtained from Norwegian distributor of TLD equipment (Laborel).e Price for an e-scan A spectrometer (including necessary equipment for automated readout)obtained from Bruker Biospin GmbH.f Price for an automatic Harshaw model 5500 TL reader (including an oven for annealing) obtainedfrom the Norwegian distributor of TLD equipment (Laborel).

Regarding the photon energy response of lithium fluoride dosimeters, the current findingsare quite similar to those found in the very thorough work by Mobit et al (1996), wherephoton energy responses in the range of 0.99–0.98 of lithium fluoride rods at comparableTPR20,10 values were found. Our findings are on an average about 1.2% lower than what wasestablished in that work, but this difference is not significant. The IPSM dosimetry protocol(Lillicrap et al 1990) was used in the study by Mobit et al (1996), while the TRS-398 code ofpractice (IAEA 2000) was used in the present work. The two protocols differ with regards to,e.g., depth of irradiation, and photon and electron spectra at the position of the dosimeter arethus not the same. In addition, a dosimeter holder of solid water with an unspecified thicknesswas employed by Mobit et al (1996). These differences may give rise to the 1.2% deviationobserved between the two studies.

4.3. Costs and workload

An estimate of the total costs and workload associated with the different dosimetry techniqueshas been made (table 2). A dosimetry laboratory with all the essential components costapproximately the same for the EPR and TL methods. Also, the workload is quite similar—in EPR dosimetry, longer acquisition times are needed, but no annealing of dosimeters isnecessary. If a procedure of pre-read annealing is preferred in TL dosimetry (having a totalduration of about 30 min in the current work), EPR readout may be performed faster.

Individual calibration and keeping track of the respective TL dosimeters is time consumingand certainly not ideal for daily clinical practice. Also, the individual TL sensitivity maychange with increasing differences in accumulated doses in a TL dosimeter batch, as indicatedby Pedersen et al (1995). Therefore, quite elaborate methods are needed in TL dosimetry inorder to obtain a good precision level. A sort of individual calibration is also performed in theEPR measurement process, as each dosimeter is weighed and the peak-to-peak amplitude isdivided by the dosimeter mass. However, a homogeneous batch of dosimeters with respect tomass may make this procedure redundant.

TL dosimeters are reusable, which weighs up for the relatively high price. Polycrystallinelithium formate is, on the other hand, very inexpensive. The destructive readout process of TLdosimetry makes this method more vulnerable to measurement failures than EPR dosimetry.

4714 T A Vestad et al

In the TL dosimeter reader currently used (table 2), nitrogen gas flow is an integral part of themeasurement process. The EPR spectrometer employed (Bruker ESP300E) is dependent onwater cooling, but smaller EPR units like the Bruker e-scan A (table 2) are not. Although theESP300E spectrometer is a more flexible all-purpose unit, it is expected that the sensitivity ofthe e-scan A model (dedicated to dosimetry) is comparable.

4.4. Lithium formate versus alanine

Although not a major topic in the current work, it is tempting to include a few remarks onthe properties of lithium formate as compared to alanine for EPR dosimetry purposes. In afeasibility study on alanine/EPR dosimetry in daily clinical practice (Ciesielski et al 2003),the reported standard deviation at 0.5 Gy was 6.7%, as opposed to 4.3% for lithium formatein the current work. In that study (Ciesielski et al 2003), polyethylene sachets filled withpolycrystalline L-alanine were exposed to 60Co γ -rays and radiotherapy electron beams. Thecross section of the sachets was more than 10 times larger than the cross sections of the EPRdosimeters used in the current study (about 260 versus 20 mm2). The active sample volume ofthe alanine powder in the EPR cavity was about twice the size of the EPR dosimeters used inthe current study (about 140 versus 70 mm3). Furthermore, the acquisition time was more thanfour times longer than in the current study (16 versus 3.5 min). For lithium formate, in contrastto alanine, strong pellets can be made without any binder material. In addition, it is expectedthat anisotropic effects (if present) are smaller for lithium formate than alanine, becauselithium formate has much smaller anisotropy in hyperfine couplings (however, slightly higherg-anisotropy (Vestad et al 2004)). Alanine/EPR dosimetry has furthermore been reported toprovide acceptable accuracy in the dose range 1.5–5 Gy using commercial dosimeters andwithout unreasonable time and labour expenses (Nagy et al 2002). Over the dose range 0.5–2.0 Gy, the uncertainty decreased from 12.1% to 3.8%, suggesting that operating with dosesabove 2 Gy should be preferred. That study (Nagy et al 2002) is comparable to our studyregarding experimental setup. These comparisons display the superior sensitivity of lithiumformate in comparison with alanine for EPR dosimetry in radiotherapy.

4.5. Conclusions

Both the EPR and TL dosimetry methods employed in the current work displayed reasonablecharacteristics in order to be used for in vivo dosimetry in radiotherapy, but each of the methodshas its clear advantages and disadvantages. TL dosimeters of lithium fluoride are more sensitiveat low doses, and the precision is thus higher. However, the photon energy dependence issmaller for EPR dosimeters of lithium formate (although this was not significant). In TLdosimetry, the readout process destroys the dosimeter signal (as opposed to EPR dosimetry),but TL dosimeters are reusable. It is expected that TL dosimetry is even better in comparisonwith EPR dosimetry at doses below 0.5 Gy, due to the contributions from background signalsand noise for the latter method. However, for doses above 2 Gy, EPR dosimetry usinglithium formate is preferred since no supralinear dose response is present and the precision isquite high.

Acknowledgments

Discussions with Eva Stabell Bergstrand at the Norwegian Radium Hospital and HansBjerke and Elin A Hult at the Norwegian Radiation Protection Authority are greatlyacknowledged. This work was in part supported by the Norwegian Research Council (grant no.129079/720).

Comparison study of EPR and TL dosimetry in radiotherapy 4715

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