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Low-energy photons in high-energy photon fields – Monte Carlo generated spectra and a new descriptive parameter
ORIGINALARBEIT
Low-energy photons in high-energy photon fields – Monte Carlo generated spectra and a new descriptive parameter Ndimofor Chofor a,b,∗ , Dietrich Harder c , Kay Willborn b , Antje Rühmann a,b , Björn Poppe a,b a
Working Group Medical Radiation Physics, Carl von Ossietzky University Oldenburg, Germany Pius-Hospital, Clinic of Radiotherapy and Oncology, Oldenburg, Germany c Prof. em., Medical Physics and Biophysics, Georg-August University Göttingen, Germany b
Received 20 December 2010; accepted 19 February 2011
Abstract The varying low-energy contribution to the photon spectra at points within and around radiotherapy photon fields is associated with variations in the responses of non-water equivalent dosimeters and in the water-to-material dose conversion factors for tissues such as the red bone marrow. In addition, the presence of low-energy photons in the photon spectrum enhances the RBE in general and in particular for the induction of second malignancies. The present study discusses the general rules valid for the low-energy spectral component of radiotherapeutic photon beams at points within and in the periphery of the treatment field, taking as an example the Siemens Primus linear accelerator at 6 MV and 15 MV. The photon spectra at these points and their typical variations due to the target system, attenuation, single and multiple Compton scattering, are described by the Monte Carlo method, using the code BEAMnrc/EGSnrc. A survey of the role of low energy photons in the spectra within and around radiotherapy fields is presented. In addition to the spectra, some data compression has proven useful to support the overview of the behaviour of the low-energy component. A characteristic indicator of the presence of low-energy photons is the dose fraction attributable to photons with energies not exceeding 200 keV, termed PD 200keV . Its values are calculated for different depths and lateral positions within a water phantom. For a pencil beam of 6 or 15 MV primary photons in water, the radial distribution of PD 200keV is bellshaped, with a wide-ranging exponential tail of half value 6 to 7 cm. The PD 200keV value obtained on the central axis of a photon
∗ Corresponding
Niederenergetische Photonen in hochenergetischen Photonenfeldern – Monte-Carlo-berechnete Spektren und ein neuer charakteristischer Parameter Zusammenfassung Der unterschiedliche niederenergetische Anteil der Photonenspektren an Aufpunkten innerhalb und außerhalb von Bestrahlungsfeldern beeinflusst die Ansprechvermögen von nicht wasseräquivalenten Dosimetern sowie die Dosisumrechnungsfaktoren zwischen Wasser und Geweben wie dem roten Knochenmark. Auch eine Erhöhung der RBW, besonders für die Induktion von Zweitkarzinomen, ist auf niederenergetische Photonen zurückzuführen. Diese Arbeit beschäftigt sich mit den Gesetzmäßigkeiten der niederenergetischen Komponente der Spektren von Photonenstrahlungen an Punkten innerhalb und außerhalb des Bestrahlungsfeldes am Beispiel eines Siemens-Primus-Linearbeschleunigers bei 6 MV und 15 MV. Mithilfe des BEAMnrc/EGSnrc Monte-CarloProgramms werden die Photonenspektren und deren Änderungen durch das Target-System, durch Schwächung sowie durch einfache und mehrfache Comptonstreuung studiert. Die Rolle der niederenergetischen Photonen in Spektren innerhalb oder außerhalb des Feldes wird untersucht. Zusätzlich zu den Spektren erweist sich eine Datenkompression als nützlich, um die Gesetzmäßigkeiten der niederenergetischen Komponente zu beschreiben. Ein typischer Indikator für niederenergetische Photonen ist der
author. Ndimofor Chofor, Pius-Hospital Oldenburg, Georgstr. 12, 26121 Oldenburg. E-mail: [email protected] (N. Chofor).
Z. Med. Phys. 21 (2011) 183–197 doi:10.1016/j.zemedi.2011.02.002 http://www.elsevier.de/zemedi
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field shows an approximately proportional increase with field size. Out-of-field PD 200keV values are up to an order of magnitude higher than on the central axis for the same irradiation depth. The 2D pattern of PD 200keV for a radiotherapy field visualizes the regions, e.g. at the field margin, where changes of detector responses and dose conversion factors, as well as increases of the RBE have to be anticipated. Parameter PD 200keV can also be used as a guidance supporting the selection of a calibration geometry suitable for radiation dosimeters to be used in small radiation fields.
Keywords: Photon spectra, Monte Carlo, low-energy photons, detector responses, RBE
1 Introduction Under the aspects of radiotherapy physics, experimental determinations of beam quality parameter Q [1,14] and of incident photon beam spectra [30,38] have been complemented by Monte-Carlo calculated photon spectra for points within the phantom or patient at varying depths and off-axis distances [6,10,15,16,32,33]. Shifts of the photon spectra towards lower energies are resulting from Compton interaction processes within the treatment head and within absorbers in the beam path. The corresponding changes of the energy-dependent responses of non-waterequivalent dosimetric detectors such as ionization chambers [6,10,15], radiographic films [31–33,40,44] and silicon diodes [7,9,11,37] are likely to occur at points within and around the field borders. Edwards and Mountford [9] have shown that diode detectors may overestimate the out-of-field dose by as much as two thirds, whereas thermoluminescence dosimeters (TLD) provide a more invariant response. Even for the in-field-region, Palm et al [32,33] observed depth-dependent variations of the film response up to 30% in water phantoms, and Eklund and Ahnesjö [11] demonstrated the influence of the field size upon the depth dependent response of silicon diodes. Detector responses at low photon energies have been systematically studied with synchrotron radiation [27]. The second reason for the interest in the low-energy spectral region is the energy dependence of the water-to-tissue dose conversion factors, e.g. for the red bone marrow, well known from dose calculations for voxel phantoms [26,52].
Parameter PD 200keV , der prozentuale Dosisbeitrag von Photonen mit Energien unter 200 keV. Dieser Parameter wurde für unterschiedliche Tiefen und laterale Positionen in einem Wasserphantom berechnet. Für einen Nadelstrahl bei 6 oder 15 MV ist das radiale Profil von PD 200keV glockenförmig, mit einem weiten Ausläufer mit Halbwertsradius 6 bis 7 cm. Auf der Achse eines Photonenfeldes nimmt PD 200keV annähernd linear mit dem Feldradius zu. Die Werte von PD 200keV außerhalb des Feldes sind um eine Größenordnung höher als innerhalb des Feldes. In zweidimensionalen Darstellungen von PD 200keV erkennt man Bereiche, z.B. am Feldrand, wo Änderungen der Ansprechvermögen von Detektoren und der Dosisumrechnungsfaktoren sowie erhöhte RBW-Werte zu erwarten sind. PD 200keV ist auch ein nützliches Kriterium für die Auswahl der Kalibrierbedingungen für die Dosimetrie von schmalen Photonenfeldern. Schlüsselwörter: Photonenspektren, Monte Carlo, niederenergetische Photonen, Detektor Ansprechvermögen, RBW
Thirdly, there are variations of the relative biological effectiveness (RBE) of photon radiations dependent upon the dose contribution by low-energy photons [13,16–18,21,35,39,43]. This phenomenon results from the enhanced linear density of the physical interactions along the tracks of low-energy secondary electrons and Auger electrons [13,16,17]. The lowenergy components of the photon spectra inside absorbers such as the human body have gained increasing interest since, in the development of intensity modulated radiotherapy and radiosurgery, it has become necessary to pay attention to the peripheral dose levels around radiotherapy fields [4,28,42,48–51]. A large fraction of the second malignancies attributable to radiotherapeutic treatment [47] occurred near the field border or in the periphery of the treatment field [5,8]. Recently, Kirkby et al [25] used Monte Carlo calculated secondary electron spectra to show that the radiation quality in the periphery of a typical radiotherapy field is differing greatly from that within the field limits, due to the spectral shifts towards lower energies via the Compton effect. This may lead to an increase of the potential radiobiological damage in outof-field regions. In a radiobiological study, Syme et al [45] showed that the shift in Monte Carlo computed secondary electron spectra towards low energies in the penumbra region is accompanied by a significant increase in radiobiological damage per unit dose when compared to the region within the open beam. In consideration of the impact which the shifts in the photon spectrum of a radiation field towards lower energies may have on dosimetry and on relative biological effectiveness, we have undertaken a study focusing upon the general regularities of
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Fig. 1. Water phantom arrangements used in the Monte Carlo calculations of photon spectra and peripheral doses (a) with and (b) without scatter from the directly irradiated phantom region. The scoring regions for the spectra were rings concentric with the beam axis, at water depth 10 cm. The small squares indicate the section areas of these rings with the drawing plane. Coordinate x is the variable ring radius. The source-surface distance was taken as SSD = 90 cm for the bench-marking shown in Figs. 2 and 3, and SSD = 100 cm for the bench-marking shown in Figs. 4 and 5. Drawing not to scale.
this spectral shift in and around radiotherapy photon fields in dependence upon depth, field size, and off-axis distance. Monte Carlo calculations of photon spectra, using a validated model of the beam head and of in-phantom photon scattering, have been performed for the example of a Siemens Primus linear accelerator operating at 6 MV and 15 MV for regions of a water absorber within and around the radiotherapy field. The large amount of geometry-dependent spectral data however makes it difficult to keep track of the general geometrical regularities holding for the low-energy component of the spectrum. A useful data compression by a single parameter descriptive of the low-energy component has been proposed in previous papers [2,3,16]. This characteristic figure is PD 200keV , the dose fraction due to low-energy photons with energies not exceeding 200 keV. The value of PD 200keV , regarded as a function of the spatial coordinates, can serve to outline the regions of an absorber where variations of the low-energy spectral component and therefore of the responses of non-water equivalent radiation detectors, of the water-totissue conversion factors and of the RBE have to be expected. Parameter PD 200keV can also be applied as a guidance to optimize the calibration geometry for dosimeters intended for use in small field dosimetry. These applications of parameter PD 200keV as a simple indicator of spectral changes will however not comprise the computation of dosimetric conversion factors and RBW values in and around photon fields; for these purposes the uncompressed spectral information is needed.
2 Materials and Methods 2.1 The Monte-Carlo beam head model and its dosimetric validation The Siemens Primus linear accelerator was modeled for 6 MV and 15 MV nominal energy photon beams using BEAMnrc/EGSnrc [22,36]. The model was built to represent
a clinical linear electron accelerator continuously serving in the radiotherapy department at our clinic. The initial electron beam energy and the Gaussian profile of the electron beam hitting the bremsstrahlung target were based initially on manufacturer data and work from other researchers [34]. For the 6 MV beam, a 5.75 MeV monoenergetic electron source with a Gaussian full width at half-maximum spread of 2 mm was chosen and was observed to give the best fit between simulated and measured dose profiles. For the 15 MV beam, the initial electron energy was 12.25 MeV, with a 1 mm Gaussian spread, selected in the same way [20]. The modeled components of the accelerator head were target [12], flattening filter (with compensator for the 15 MV configuration), primary collimator, monitor chamber, mirror, secondary collimator jaws (Y blocks), multileaf collimator system (leaves moving in the X direction) and the reticle. The cutoff energies used in all simulations were 700 keV for electron and 10 keV for photon histories. Following the method described by Kawrakow et al [23], the directional bremsstrahlung splitting (DBS) variance reduction technique was implemented in order to increase the calculation efficiency. Bremsstrahlung photon splitting was performed with a splitting number of 1000. The Russian Roulette plane for photons was placed at z = 9.565 cm (6 MV) and z = 8.860 cm (15 MV), in both cases slightly upstream the bottom plane of the flattening filter. A splitting radius of 25 cm was chosen for all field sizes. Electron splitting was performed exactly in the bottom plane of the flattening filter, i.e. at z = 9.971 cm (6 MV) and z = 9.782 cm (15 MV). Before the onset of the simulations, the accelerator head defined in BEAMnrc was compiled as an “internal shared library”, for use as the input during the computation of in-water depth-dose curves as well as transversal dose profiles. This was preferred to the use of phase space files which are intermediately saved, thereby requiring much disk space. The treatment head model was validated by comparing the simulated and measured values of transversal dose profiles
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Fig. 2. Monte-Carlo calculated and measured lateral dose profiles at a, b) 6 MV and c, d) 15 MV at depth 10 cm for square field sizes from 5 × 5 cm2 to 40 × 40 cm2 , focus-surface distance 90 cm. (Measured data were taken from our TPS database).
and percent depth-dose curves within the primary photon field, as well as of out-of-field dose profiles due to all causes and especially to phantom-scattered radiation. For the calculation of the in-field doses, a (50 × 50 × 50) cm3 water tank phantom and 90 or 100 cm source-to-surface (SSD) distance were assumed (Fig. 1). Square fields with side lengths 5, 10, 20 and 40 cm were generated at 10 cm depth, and the lateral dose profiles (inplane direction) were scored at 10 cm depth within the water phantom. The DOSXYZnrc/EGSnrc package [24] was used for computing the dose profiles within the water phantom. Water phantoms were modeled individually for each simulated field size, with voxel sizes of 1 cm3 for regions outside the field and (0.5 × 0.5 × 1) cm3 for the in-field regions, except for the voxels along the central axis which were 1 cm3 in volume. The experimental arrangement set up to validate the Monte-Carlo model by measurements of dose distributions in absorbers was congruent with the geometry used for the calculations shown in Figure 1. The values of the absorbed dose to water were obtained with the flexible 0.125 cm3 chamber PTW 31010, and the results of the lateral dose distributions as well as the depth-dose curves were normalized to their maximum values. In Figures 2 and 3 the comparison between the Monte-Carlo calculated and the measured dose distributions is performed for the in-field region. With the exception of a part of the lateral dose distribution for the largest field at 15 MV, good agreement is achieved, with no detectable deviation unless caused by the statistical variations of the Monte Carlo data. Obviously, the simplified treatment of secondary electron transport at ener-
gies below 700 keV does not result in detectable differences in the build-up region of the depth-dose curves. For Monte-Carlo dose calculations of the peripheral doses outside the field limits, the calculation geometry was the same as in Figure 1 using DOSRZnrc/EGSnrc, but the photon splitting radius was taken as 30 cm in order to obtain good photon statistics even in the peripheral region. In these calculations, the phantom surface was at SSD 100 cm, and the field size was measured at the phantom surface. The experimental setup used for the validation was congruent with Figure 1, but we used the water-equivalent solid phantom material RW3 (white polystyrene) (PTW Freiburg, Germany), because the phantom had to consist of two parts, whose in-field part could be removed to permit peripheral dose measurements free from scatter originating in the directly irradiated part of the phantom. The RW3 to water ratio of the electron densities is 1.012, therefore RW3 appeared as sufficient for the purpose of validating the Monte-Carlo calculated peripheral dose values. At depth 10 cm, the reference dose values on the beam axis and the dose profiles outside the geometrical field limits were recorded with a Farmer 0.6 cm3 chamber type M 30001 (PTW Freiburg, Germany). The small (< 2%) kQ changes expressing the photon-energy dependent changes of the wall correction factor and of the stopping-power ratio when photon chambers of this type are used either within the useful beam on or off axis [6] or under out-of-field conditions [10], were neglected since the interest of this validation of the Monte Carlo code was on comparably large effects. All measured peripheral dose profile values were presented as percentages of the dose value
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Fig. 3. Monte-Carlo calculated and measured relative depth dose profiles at a, b) 6 MV and c, d) 15 MV for square field sizes from 5 × 5 cm2 to 40 × 40 cm2 , focus-surface distance 90 cm. (Measured data were taken from our TPS database).
obtained on the beam axis at 10 cm depth. The differences between calculated and measured values in Figures 4 and 5 are small, even for the largest field, and are likely to reflect imperfections in the modeling of the beam head shielding. Overall, the achieved degree of accuracy of the simulation of doses was deemed as a sufficient dosimetric validation of the Monte Carlo model for the purposes of the present
study, whose main subject of investigation were the typical regularities of the photon spectra within and outside the field limits. 2.2 Monte-Carlo simulations of photon spectra Using FLURZnrc/EGSnrc [22], photon spectra were scored within a large water tank of 40 cm radius and 38 cm deep for
Fig. 4. Monte-Carlo calculated and measured lateral profiles of the total dose in the out-of field region at a) 6 MV and b) 15 MV at depth 10 cm for square field sizes from 2 × 2 cm2 to 30 × 30 cm2 , focus-surface distance 100 cm. Calculations were done for water; measurements were performed in the water-equivalent solid RW3 (white polystyrene).
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Fig. 5. Monte-Carlo calculated and measured lateral dose profiles due to photons scattered from the directly irradiated part of the phantom, in the out-of field region at a) 6 MV and b) 15 MV at depth 10 cm for square field sizes from 2 × 2 cm2 to 20 × 20 cm2 , focus-surface distance 100 cm. Calculations were done for water; measurements were performed in the water-equivalent solid RW3 (white polystyrene).
100 cm SSD. In order to reduce the statistical fluctuations in the spectra, the scoring regions had rotational symmetry with respect to the central beam axis. Accordingly, a modification of the accelerator head model to obtain circular beams was performed. This was done by taking the already tuned head model and defining circular apertures of the jaw collimator and the multi-leaf collimator using the CONS3R component module, so that the projected fields at the isocenter plane were circular. The radii of the circular beams were so defined that they corresponded to side lengths of 5, 10, 20 and 30 cm of the equivalent square fields. This was achieved by taking radii √ equal to the quotient of the square-field side length and π [29]. In plots of the spectral results, the side lengths of the equivalent square fields are used to characterize the field size. The accelerator head model with circular shaped collimators was then compiled as a shared library for use as input for the FLURZnrc simulations (ISOURCE 23). The fluence was scored either in a small cylindrical volume of 0.5 cm radius and 0.3 cm thickness, centered on the beam axis, or in concentric rings of 1 cm width and 0.3 cm thickness whose inner radius was x - 0.5 cm, in a water phantom of 30 cm radius and 30 cm deep, as shown in Figure 1a. Directional bremsstrahlung splitting with a splitting number of 1000, Russian Roulette for photons in a plane slightly upstream the bottom plane of the flattening filter, and a selection radius of 30 cm for all field sizes were used. This large splitting radius was used in order to improve the calculation statistics for regions outside the field borders of smaller fields. Electron splitting was implemented as described in section 2.1. In all cases, the spectra will be represented as the “normalized spectral energy fluence”, i.e. the product of the spectral
fluence and the photon energy, with the numbers shown in all channels adding to unity. 2.3 The new spectral parameter: the dose fraction due to low-energy photons A simple, summarizing parameter comprising in one number the space-dependent spectral changes of dosimetric or radiobiological concern should have its focus on the lowenergy part of the photon spectrum below cut-off energy Ecut . The spatial pattern of such summarizing parameter could be used to visualize regions of a phantom (and similarly of a patient’s body) where such concern would be warranted. A cut-off energy Ecut = 200 keV is likely to be chosen because the largest changes of the responses of non-water equivalent dosimeters and of some water-to tissue dose conversion factors occur at energies below 200 keV. For illustration, Figure 6 shows the photon energy dependence of the quotient of the mass energy absorption coefficient of either AgBr film emulsion, Si, LiF or compact bone and the mass energy absorption coefficient of water. In the same low-energy region, the main changes of the energy-dependent RBE values for photon radiations are occurring [13,16–18,21,35,39,43]. Using the computed fluence spectra as described above, the relative contribution of energy-degraded Compton scattered photons to the dose D at a point in the medium, PD Ecut , for photons with energies not exceeding the value Ecut is defined as [3]: Ecut PD =
D(E ≤ Ecut ) Dtotal
(1)
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3.1 Field size dependence of the low-energy spectral component at on- and off-axis points
Fig. 6. Photon energy dependence of the quotient of the mass-energy absorption coefficients of AgBr film emulsion, Si, compact bone or LiF and the mass-energy absorption coefficient of water. From NIST X-ray data [19].
For the computation of parameter PD Ecut , Eq. (1) can be written as m Ecut PD
=
i=1 n i=1
m μ
Di
en
= Di
i=1 n i=1
ρ
μen ρ
i
Ei φ i (2)
i
E i φi
where 1 ≤ i ≤ n sums over all spectral components at the scoring point, and i = m corresponds to energy Ecut . Factor μen /ρ is the mass energy absorption coefficient of water, and φi the spectral photon fluence at energy Ei . The precise meaning of the product (μen /ρ)i Ei Φι is the bremsstrahlung-corrected value of water kerma, equal to the local absorbed dose to water under secondary electron equilibrium, produced by the photons in energy bin i. (In order to keep the PD 200keV concept simple, the so-called “kerma approximation” is applied in equation 2 in spite of the fact that secondary electron equilibrium is not exactly achieved in some situations such as the build-up region or the penumbra region). Using Ecut = 200 keV, PD 200keV has been calculated for different depths and lateral positions within a water phantom, for different field sizes. The values of PD 200keV are always given in percent of the local dose at the point of interest.
3 Results Photon spectra and values of the dose fraction due to lowenergy photons, determined by Monte Carlo calculations, will now be presented together with short physical interpretations.
The field size is a prominent parameter which modulates the relative magnitude of the low-energy component of the photon spectrum with increasing depth. The calculated spectra of a 6 MV photon beam at points on the central beam axis in 2 cm and 20 cm depth within water are shown in Figure 7a - 7d for various field sizes and SSD 90 cm. For the smaller fields, 5 × 5 cm2 and 10 × 10 cm2 , the dominant effect is a reduction of the low-energy components of the spectrum (“beam hardening”) with increasing depth, caused by spectral filtration in the low-Z absorber water via the Compton effect. However, this filtering effect recedes as the field size is increased. Now the competing effect, the build-up of a field of Compton-scattered photons with degraded energies, enhances the low-energy spectral components with increasing depth. The same influences can be observed in the spectra of the 15 MV beam (Fig. 7e- 7h). For off-axis points within the field limits, there exists a “beam softening” effect, attributable to the angular dependence of the bremsstrahlung spectrum, to Compton scatter from the flattening filter and to the reduced thickness and therefore to the reduced filtering effect of the flattening filter with increasing off-axis distance (Fig. 8 a,b). With increasing depth, this “softening” effect however becomes less apparent due to the superposition with the phantom scatter (Fig. 8 c,d). A comparison with the off-axis spectra obtained without the flattening filter showed that the main reasons for this “softening effect” are (a) the reduced filtering by the thinner outer regions of the flattening filter and (b) the preferentially outward directed Compton scatter from the thick central region of the filter.
3.2 Photon spectra at points on the field margin and outside the field The total photon spectra at off-axis distances x = 7 cm, 11 cm and 15 cm, including the components attributable to head leakage and collimator transmission, extra-focal radiation and phantom scatter, were calculated for the phantom arrangement described in Figure 1(a). Total off-axis spectra for SSD = 90 cm are shown in Figure 9 by bold lines and are compared with the spectrum at the beam axis (x = 0 cm). Already the spectra at x = 7 cm and 11 cm, just outside the useful beam, show a strong low-energy contribution. The spectra at x = 15 cm consist of a predominating low-energy component and a high-energy tail. In order to separate the spectra into their components, the calculation was performed for the arrangement without scatter from the directly irradiated part of the phantom, Figure 1(b). The spectra obtained under this condition are indicated by letter L, being due to beam head leakage, collimator transmission and extra-focal radiation. The spectrum obtained by subtracting spectrum L from the
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Fig. 7. Monte-Carlo calculated photon spectra at points of interest on the beam axis at depths 2 cm and 20 cm, for field sizes from 5 × 5 cm2 to 30 × 30 cm2 . a) - d) 6 MV, e) - h) 15 MV.
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Fig. 8. Monte-Carlo calculated photon spectra for 30 × 30 cm2 field size, at points of interest 12 cm from the beam axis, for 2 cm and 20 cm depth. a, c) 6 MV, b, d) 15 MV.
total spectrum, denoted by S, is due to photons scattered from the irradiated part of the phantom. The high-energy portions of the spectra at x = 7 cm and x = 15 cm, compared with the spectrum on the beam axis (x = 0), show a very strong attenuation, attributable to the effect of pair production in the high-Z shielding materials of the primary collimator and the adjustable collimators on the leakage radiation. The other prominent effect is the increase of the low-energy portion of the spectra with increasing offaxis distance, attributable to scatter from the irradiated part of the phantom. The shift of the scattered portion towards lower energies with increasing distance from the field border may be interpreted by the increasing contribution of multiple Compton scattering. Both effects contribute to an overall shift of the spectra towards lower energies with increasing off-axis distance, and this can be observed for both field sizes and both photon beam energies. 3.3 The lateral transport of low-energy photons The understanding of the wide-ranging lateral transport of scattered, energy degraded photons, recognizable in the
spectra at off-axis distance 15 cm (Fig. 9), shall be further underpinned by an analysis of the geometric spread of the lowenergy dose component. As a first example, the geometrical arrangement of Figure 1a has been applied in the simulation of a narrow photon beam (radius 1.4 cm) of given total number of primary photons. The ring-shaped scoring regions of Figure 1a were used to record the relative values of the spectral energy fluence of photons with energies below 200 keV. The relative values of the associated absorbed doses to water at secondary electron equilibrium, D200keV , were calculated by multiplication of the spectral energy fluence with the energy-dependent mass energy absorption coefficients of water. The resulting radial distribution of the normalized values of D200keV is shown in Figure 10 for 6 and 15 MV and for various depths in water from 5 to 28 cm at SSD = 90 cm. Each of the radial profiles of D200keV has a central region, radially extending up to about 2 cm, which contains not only scattered, but also primary photons with energies below 200 keV. In this region, the somewhat stronger attenuation of the 6 MV beam with increasing depth can be recognized. At larger off-axis distances, there is an approximately exponential decrease of D200keV with increasing radius, appearing in the semi-log plot
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Fig. 9. Monte Carlo-calculated photon spectra for points of interest on the central axis (x = 0 cm), immediately outside the field border (x = 7 cm, x = 11 cm) and at x = 15 cm from the central axis. a) - d) 6 MV and e) - h) 15 MV, field sizes 5 cm x 5 cm and 10 cm x 10 cm, depth 10 cm. The spectra at 7, 11 and 15 cm from the central axis are analyzed in terms of their beam-head leakage (L) and phantom scatter (S) components.
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Fig. 10. Radial distributions of the dose to water due to photons with energies below 200 keV, for a) 6 MV and b) 15 MV photon beams of radius 1.4 cm at various scoring depths d within the water phantom. The ordinate values have been normalized to the maximum value for d = 5 cm. The curves for depths 10, 20 and 28 cm have been shifted down by scaling factors 0.3, 0.1 and 0.03 respectively for better distinction between the curves which belong to different depths.
as a straight line. The half-value radius of this exponential function, ranging from 6 to 7 cm, is almost depth- and energy independent, and the radial attenuation factor is approximately ␣ ≈ 0.11 cm-1 . This means that in high-energy photon beams there is a wide-ranging lateral transport of the low-energy component of the scattered radiation. As an application example of the wide-ranging lateral transport of the low-energy component of the photon spectrum, Figure 11 shows the Monte-Carlo-calculated depth-dependent values of the dose fraction PD 200keV , attributable to photons with energies not exceeding 200 keV, for points of interest on the central axis of circular photon beams of various radii R of which the equivalent square field side lengths are indicated. The slightly S-shaped, almost linear increase of PD 200keV at points on the beam axis with the side length can be under-
stood by considering the lateral transport of energy-degraded scattered photons (Fig. 10): For a narrow field, the dominating effect is the outward-directed transport of the scattered low-energy photons into the space external to the beam; but with increasing field size more scattered photons are accumulated inside the geometrical region of the beam, and this effect is even enhanced with increasing depth, as shown in Figure 11. In order to complete the picture, Figure 12 shows the MonteCarlo calculated dose contribution by Compton-scattered photons with energies degraded below 200 keV at a point about 2 cm from the field border. The field border was taken as the lateral position at which the dose, normalized to the dose at the beam axis, is reaching 50%. Again at this position and for 6 and 15 MV, the low-energy dose contribution increases
Fig. 11. Dependence of PD 200keV on field size and depth for points of interest on the beam central axis at various depths for 6 MV and 1 cm from the central axis for 15 MV.
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Fig. 12. Dependence of PD 200keV on field size for points at 10 cm depth and 2 cm from the field border, the latter defined by the lateral position of the 50% dose value.
with increasing field size. For 15 MV the effect is smaller than for 6 MV, due to the more forward directed emission of the scattered photon in a Compton process. 3.4 2D profiles of PD 200keV within a water phantom As mentioned in the introduction and in section 2.3, the geometric pattern of parameter PD 200keV is suited to specify absorber regions where detector responses, dose conversion factors and RBE values are likely to vary. Figure 13 illustrates the radial and depth-dependence of PD 200keV for the 5 × 5 cm2 and 30 × 30 cm2 fields with the 6 MV beam (a and b) and the 15 MV beam (c and d) respectively. Within the field borders, the dose fraction due to low-energy components is relatively invariant. In the out-of-field regions PD 200keV is increasing by up to one order of magnitude as compared to the values on the central beam axis, due to the wide spread, already observed in the previous results, of the scattered low-energy photons originating from the irradiated phantom material. For the large field size, the “transition zone” from the field border to the region of the maximum PD 200keV values is much narrower than for the small field size, because for the larger field, the phantomscattered photons are more dominating in comparison with the head leakage radiation.
4 Discussion The aim of the present study has been to investigate the changes of the photon spectrum, especially of its low-energy component, within water phantoms, which may occur in a very similar way in the patient’s body at points in and around radiotherapy treatment fields. This investigation is an extension of the work of several authors who studied the changes of the photon spectrum in body-like phantoms, especially with
regard to the associated changes of detector sensitivities compared with the absorbed dose to water [6,7,9–11,15,32,33,37], or to the associated changes of the RBE for various biological effects, among them cancer induction [16,25,28,45]. The applied Monte-Carlo code BEAMnrc/EGSnrc [22,36] and the accelerator head model representative of the Siemens Primus linac were validated by a comparison of calculated and measured dose distributions, resulting in good agreement inand outside the field limits (see Figs. 2-5). On this basis, the Monte Carlo method was applied to calculate the photon spectra and their typical changes within a large water phantom for 6 MV and 15 MV photon beams. The low-energy portion of the depth-dependent spectra within the beam, Figure 7, reflects the counteracting depth-dependent phenomena of beam hardening, preponderant at small field size, and accumulation of Compton-scattered photons of low energy, which dominates at large field size. Figure 8 illustrates the well-known effect of “beam softening” with increasing off-axis distance, which is most expressed at shallow depths but superposed by phantom scatter at the larger depths. The variation of the photon spectra at the field border or at points in the periphery undergo much larger changes, as shown in Figure 9. Here, we have separated the spectral components into (a) the low-energy contribution from scatter out of the water phantom, S, and (b) the remaining high-energy contribution due to leakage and extra-focal radiation, L. Near the field border, Compton-scattered photons are the main component, superposed with a high-energy component mainly due to extra-focal radiation. In the periphery, the spectrum is furthermore shifted towards lower energies, now consisting of multiply scattered photons and the leakage radiation, filtered by the high-Z shielding materials of the beam head, similar to the results of Edwards and Mountford [9] and Kry et al. [28]. Means for reducing collimator transmission and leakage doses have been investigated recently [4]. The new parameter PD 200keV , i.e. the fraction of the absorbed dose to water under conditions of secondary electron equilibrium, produced by photons with energies below 200 keV (eq. 1 and 2), is then proposed as a simple instrument of characterizing the spatial regions in- and outside the irradiated field where detector responses, dose conversion factors and RBE values are likely to change [2,4,16]. The value 200 keV of the cut-off energy was chosen with regard to the large changes of typical dose conversion factors below 200 keV (Fig. 6). A similar bipartition approach has been applied by Palm et al. [32] and by Eklund and Ahnesjö [11], who have chosen cut-off energies at 100 keV and 5 MeV. Clearly, any choice of a single cut-off energy will be somewhat arbitrary, and other similar values might be more significant in special cases of dosimetrical or radiobiological relevance. Keeping these precautions in mind, we have chosen the cut-off energy of 200 keV in order to demonstrate the general trends of the dose contributions by low-energy photons. Parameter PD 200keV was then applied to characterize the field of low-energy scattered photons associated with narrow
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Table 1 Examples of the response enhancement of dosimetric detectors and biological objects due to exposure to photons of reduced energy. Detector or biol. object
Test radiation quality
Reference radiation quality
Response enhancement factor
Reference
X-Omat film TLD LiF:Mg, Ti Unshielded p-type Si diode Swater,air
112 keV, spectrum 112 keV, spectrum 6 MV X-rays, A = 20x20cm2 d = 25cm 6 MV X-rays* , 3 cm out of field border,d = 5cm 100 keV, spectrum (interpolated value) 6 MV X-rays, only backscattered radiation
6 MV X-rays 6 MV X-rays 6 MV X-rays, A = 10x10cm2 , d = 10 cm 6 MV X-rays* , on axis, d = 5cm Co-60 gamma rays
4.37 1.10 1.05
27 27 11
1.017
10
3.02
13
6 MV X-rays
1.48
45
Human lymphocytes** Human fibroblasts*** * ** ***
A = 10 x 10 cm2 . Yield of dicentric chromosomes, low-dose limit. Yield of DNA dsb at 4 Gy.
Fig. 13. 2D profiles of PD 200keV within water for the Primus 6 MV and 15 MV linear accelerator at field sizes 5 cm x 5 cm and 30 cm x 30 cm. The PD 200keV values are shown in percent of the total dose at the same point.
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primary photon beams. A characteristic exponential lateral distribution of PD 200keV with radial attenuation factor ␣ ≈ 0.11 cm-1 was obtained (Fig. 10). This description is the analytical analogue to the graphic display of the scattered photons published by Eklund and Ahnesjö [10]. The exponential shape of the scattering kernel is similar to the scattering kernel applied by Spies et al. [41] in their analysis of image blurring in portal imaging devices. The wide-ranging radial spread of the scattering kernel was then applied to understand that the low-energy dose fraction at a point on the axis of a circular field increases approximately in proportion with the field radius respectively the corresponding equivalent square field side length (Fig. 11). A dosimetric conclusion to be drawn from the small values of PD 200keV for small field sizes is that in narrow-field dosimetry the dose fraction due to low-energy photons is small, which should be accounted for by special narrow-field calibration conditions for dosimeters with over-response to low-energy photons like Si diodes. Some published examples of measured or calculated detector overresponse to low-energy photons are shown in Table 1. Note that the test radiation in the first two examples was X-rays of 112 keV, whereas in the third example only the field size was varied. The PD 200keV values at the field margin were also shown to increase with field size (Fig. 12), corresponding to the experimental result that the relative peripheral dose at a point 5 cm outside the field border increases with field size due to increases in the scatter contribution [4]. Parameter PD 200keV is also a simple indicator of body regions in which enhanced RBE values for radiobiological effects are to be expected, especially the peripheral region (Fig. 13). Since peripheral doses may reach the order of 5% of the on-axis dose (see Figs. 4 and 5) peripheral doses to be weighted, e.g., by an RBE of two would amount to 10% of the RBE weighted dose on the beam axis. Two examples of the increase of the RBE due to exposure with low-energy photons are given in Table 1. This has a bearing on the discussion of carcinogenic side effects of radiotherapy due to the peripheral doses, because increased organ-specific RBE values for carcinogenesis have to be expected in the peripheral region. The present investigation has been confined to conventional beam-head constructions of electron accelerators for use in photon-beam radiotherapy. The modifications of photon spectra known to occur in the case of flattening-filter free constructions [46] will be studied in further work of this group. The characteristic wide-ranging radial spread of the scattered low-energy photons from each pencil beam of primary photons will however remain unchanged.
5 Conclusions In this paper the typical changes of the photon spectra within and around therapeutic photon beams have been assessed by Monte Carlo calculations. The increase, due to Comptonscattered photons, of the low-energy component within the
field borders with increasing field size and increasing depth, and the build-up of the low-energy component in the periphery of the therapeutic photon beam have been quantified. We propose a method of comprehensively mapping the relative weight of the low-energy component within the total radiation field by using the parameter PD 200keV , the dose fraction due to photons with energies not exceeding 200 keV. Profiles and maps of PD 200keV can be used to identify the regions of a phantom (and similarly of a patient’s body) where the responses of non-water equivalent radiation detectors, the water to tissue dose conversion factors and the RBE values for the induction of radiobiological effects are likely to be influenced by the presence of low-energy photons. Low values of PD 200keV are a characteristic of small-field dosimetry and therefore of the conditions desirable for the calibration of dosimeters for use in small therapeutic photon fields.
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Low-energy photons in high-energy photon fields – Monte Carlo generated spectra and a new descriptive parameter Ndimofor Chofor a,b,∗ , Dietrich Harder c , Kay Willborn b , Antje Rühmann a,b , Björn Poppe a,b a
Working Group Medical Radiation Physics, Carl von Ossietzky University Oldenburg, Germany Pius-Hospital, Clinic of Radiotherapy and Oncology, Oldenburg, Germany c Prof. em., Medical Physics and Biophysics, Georg-August University Göttingen, Germany b
Received 20 December 2010; accepted 19 February 2011
Abstract The varying low-energy contribution to the photon spectra at points within and around radiotherapy photon fields is associated with variations in the responses of non-water equivalent dosimeters and in the water-to-material dose conversion factors for tissues such as the red bone marrow. In addition, the presence of low-energy photons in the photon spectrum enhances the RBE in general and in particular for the induction of second malignancies. The present study discusses the general rules valid for the low-energy spectral component of radiotherapeutic photon beams at points within and in the periphery of the treatment field, taking as an example the Siemens Primus linear accelerator at 6 MV and 15 MV. The photon spectra at these points and their typical variations due to the target system, attenuation, single and multiple Compton scattering, are described by the Monte Carlo method, using the code BEAMnrc/EGSnrc. A survey of the role of low energy photons in the spectra within and around radiotherapy fields is presented. In addition to the spectra, some data compression has proven useful to support the overview of the behaviour of the low-energy component. A characteristic indicator of the presence of low-energy photons is the dose fraction attributable to photons with energies not exceeding 200 keV, termed PD 200keV . Its values are calculated for different depths and lateral positions within a water phantom. For a pencil beam of 6 or 15 MV primary photons in water, the radial distribution of PD 200keV is bellshaped, with a wide-ranging exponential tail of half value 6 to 7 cm. The PD 200keV value obtained on the central axis of a photon
∗ Corresponding
Niederenergetische Photonen in hochenergetischen Photonenfeldern – Monte-Carlo-berechnete Spektren und ein neuer charakteristischer Parameter Zusammenfassung Der unterschiedliche niederenergetische Anteil der Photonenspektren an Aufpunkten innerhalb und außerhalb von Bestrahlungsfeldern beeinflusst die Ansprechvermögen von nicht wasseräquivalenten Dosimetern sowie die Dosisumrechnungsfaktoren zwischen Wasser und Geweben wie dem roten Knochenmark. Auch eine Erhöhung der RBW, besonders für die Induktion von Zweitkarzinomen, ist auf niederenergetische Photonen zurückzuführen. Diese Arbeit beschäftigt sich mit den Gesetzmäßigkeiten der niederenergetischen Komponente der Spektren von Photonenstrahlungen an Punkten innerhalb und außerhalb des Bestrahlungsfeldes am Beispiel eines Siemens-Primus-Linearbeschleunigers bei 6 MV und 15 MV. Mithilfe des BEAMnrc/EGSnrc Monte-CarloProgramms werden die Photonenspektren und deren Änderungen durch das Target-System, durch Schwächung sowie durch einfache und mehrfache Comptonstreuung studiert. Die Rolle der niederenergetischen Photonen in Spektren innerhalb oder außerhalb des Feldes wird untersucht. Zusätzlich zu den Spektren erweist sich eine Datenkompression als nützlich, um die Gesetzmäßigkeiten der niederenergetischen Komponente zu beschreiben. Ein typischer Indikator für niederenergetische Photonen ist der
author. Ndimofor Chofor, Pius-Hospital Oldenburg, Georgstr. 12, 26121 Oldenburg. E-mail: [email protected] (N. Chofor).
Z. Med. Phys. 21 (2011) 183–197 doi:10.1016/j.zemedi.2011.02.002 http://www.elsevier.de/zemedi
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field shows an approximately proportional increase with field size. Out-of-field PD 200keV values are up to an order of magnitude higher than on the central axis for the same irradiation depth. The 2D pattern of PD 200keV for a radiotherapy field visualizes the regions, e.g. at the field margin, where changes of detector responses and dose conversion factors, as well as increases of the RBE have to be anticipated. Parameter PD 200keV can also be used as a guidance supporting the selection of a calibration geometry suitable for radiation dosimeters to be used in small radiation fields.
Keywords: Photon spectra, Monte Carlo, low-energy photons, detector responses, RBE
1 Introduction Under the aspects of radiotherapy physics, experimental determinations of beam quality parameter Q [1,14] and of incident photon beam spectra [30,38] have been complemented by Monte-Carlo calculated photon spectra for points within the phantom or patient at varying depths and off-axis distances [6,10,15,16,32,33]. Shifts of the photon spectra towards lower energies are resulting from Compton interaction processes within the treatment head and within absorbers in the beam path. The corresponding changes of the energy-dependent responses of non-waterequivalent dosimetric detectors such as ionization chambers [6,10,15], radiographic films [31–33,40,44] and silicon diodes [7,9,11,37] are likely to occur at points within and around the field borders. Edwards and Mountford [9] have shown that diode detectors may overestimate the out-of-field dose by as much as two thirds, whereas thermoluminescence dosimeters (TLD) provide a more invariant response. Even for the in-field-region, Palm et al [32,33] observed depth-dependent variations of the film response up to 30% in water phantoms, and Eklund and Ahnesjö [11] demonstrated the influence of the field size upon the depth dependent response of silicon diodes. Detector responses at low photon energies have been systematically studied with synchrotron radiation [27]. The second reason for the interest in the low-energy spectral region is the energy dependence of the water-to-tissue dose conversion factors, e.g. for the red bone marrow, well known from dose calculations for voxel phantoms [26,52].
Parameter PD 200keV , der prozentuale Dosisbeitrag von Photonen mit Energien unter 200 keV. Dieser Parameter wurde für unterschiedliche Tiefen und laterale Positionen in einem Wasserphantom berechnet. Für einen Nadelstrahl bei 6 oder 15 MV ist das radiale Profil von PD 200keV glockenförmig, mit einem weiten Ausläufer mit Halbwertsradius 6 bis 7 cm. Auf der Achse eines Photonenfeldes nimmt PD 200keV annähernd linear mit dem Feldradius zu. Die Werte von PD 200keV außerhalb des Feldes sind um eine Größenordnung höher als innerhalb des Feldes. In zweidimensionalen Darstellungen von PD 200keV erkennt man Bereiche, z.B. am Feldrand, wo Änderungen der Ansprechvermögen von Detektoren und der Dosisumrechnungsfaktoren sowie erhöhte RBW-Werte zu erwarten sind. PD 200keV ist auch ein nützliches Kriterium für die Auswahl der Kalibrierbedingungen für die Dosimetrie von schmalen Photonenfeldern. Schlüsselwörter: Photonenspektren, Monte Carlo, niederenergetische Photonen, Detektor Ansprechvermögen, RBW
Thirdly, there are variations of the relative biological effectiveness (RBE) of photon radiations dependent upon the dose contribution by low-energy photons [13,16–18,21,35,39,43]. This phenomenon results from the enhanced linear density of the physical interactions along the tracks of low-energy secondary electrons and Auger electrons [13,16,17]. The lowenergy components of the photon spectra inside absorbers such as the human body have gained increasing interest since, in the development of intensity modulated radiotherapy and radiosurgery, it has become necessary to pay attention to the peripheral dose levels around radiotherapy fields [4,28,42,48–51]. A large fraction of the second malignancies attributable to radiotherapeutic treatment [47] occurred near the field border or in the periphery of the treatment field [5,8]. Recently, Kirkby et al [25] used Monte Carlo calculated secondary electron spectra to show that the radiation quality in the periphery of a typical radiotherapy field is differing greatly from that within the field limits, due to the spectral shifts towards lower energies via the Compton effect. This may lead to an increase of the potential radiobiological damage in outof-field regions. In a radiobiological study, Syme et al [45] showed that the shift in Monte Carlo computed secondary electron spectra towards low energies in the penumbra region is accompanied by a significant increase in radiobiological damage per unit dose when compared to the region within the open beam. In consideration of the impact which the shifts in the photon spectrum of a radiation field towards lower energies may have on dosimetry and on relative biological effectiveness, we have undertaken a study focusing upon the general regularities of
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Fig. 1. Water phantom arrangements used in the Monte Carlo calculations of photon spectra and peripheral doses (a) with and (b) without scatter from the directly irradiated phantom region. The scoring regions for the spectra were rings concentric with the beam axis, at water depth 10 cm. The small squares indicate the section areas of these rings with the drawing plane. Coordinate x is the variable ring radius. The source-surface distance was taken as SSD = 90 cm for the bench-marking shown in Figs. 2 and 3, and SSD = 100 cm for the bench-marking shown in Figs. 4 and 5. Drawing not to scale.
this spectral shift in and around radiotherapy photon fields in dependence upon depth, field size, and off-axis distance. Monte Carlo calculations of photon spectra, using a validated model of the beam head and of in-phantom photon scattering, have been performed for the example of a Siemens Primus linear accelerator operating at 6 MV and 15 MV for regions of a water absorber within and around the radiotherapy field. The large amount of geometry-dependent spectral data however makes it difficult to keep track of the general geometrical regularities holding for the low-energy component of the spectrum. A useful data compression by a single parameter descriptive of the low-energy component has been proposed in previous papers [2,3,16]. This characteristic figure is PD 200keV , the dose fraction due to low-energy photons with energies not exceeding 200 keV. The value of PD 200keV , regarded as a function of the spatial coordinates, can serve to outline the regions of an absorber where variations of the low-energy spectral component and therefore of the responses of non-water equivalent radiation detectors, of the water-totissue conversion factors and of the RBE have to be expected. Parameter PD 200keV can also be applied as a guidance to optimize the calibration geometry for dosimeters intended for use in small field dosimetry. These applications of parameter PD 200keV as a simple indicator of spectral changes will however not comprise the computation of dosimetric conversion factors and RBW values in and around photon fields; for these purposes the uncompressed spectral information is needed.
2 Materials and Methods 2.1 The Monte-Carlo beam head model and its dosimetric validation The Siemens Primus linear accelerator was modeled for 6 MV and 15 MV nominal energy photon beams using BEAMnrc/EGSnrc [22,36]. The model was built to represent
a clinical linear electron accelerator continuously serving in the radiotherapy department at our clinic. The initial electron beam energy and the Gaussian profile of the electron beam hitting the bremsstrahlung target were based initially on manufacturer data and work from other researchers [34]. For the 6 MV beam, a 5.75 MeV monoenergetic electron source with a Gaussian full width at half-maximum spread of 2 mm was chosen and was observed to give the best fit between simulated and measured dose profiles. For the 15 MV beam, the initial electron energy was 12.25 MeV, with a 1 mm Gaussian spread, selected in the same way [20]. The modeled components of the accelerator head were target [12], flattening filter (with compensator for the 15 MV configuration), primary collimator, monitor chamber, mirror, secondary collimator jaws (Y blocks), multileaf collimator system (leaves moving in the X direction) and the reticle. The cutoff energies used in all simulations were 700 keV for electron and 10 keV for photon histories. Following the method described by Kawrakow et al [23], the directional bremsstrahlung splitting (DBS) variance reduction technique was implemented in order to increase the calculation efficiency. Bremsstrahlung photon splitting was performed with a splitting number of 1000. The Russian Roulette plane for photons was placed at z = 9.565 cm (6 MV) and z = 8.860 cm (15 MV), in both cases slightly upstream the bottom plane of the flattening filter. A splitting radius of 25 cm was chosen for all field sizes. Electron splitting was performed exactly in the bottom plane of the flattening filter, i.e. at z = 9.971 cm (6 MV) and z = 9.782 cm (15 MV). Before the onset of the simulations, the accelerator head defined in BEAMnrc was compiled as an “internal shared library”, for use as the input during the computation of in-water depth-dose curves as well as transversal dose profiles. This was preferred to the use of phase space files which are intermediately saved, thereby requiring much disk space. The treatment head model was validated by comparing the simulated and measured values of transversal dose profiles
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Fig. 2. Monte-Carlo calculated and measured lateral dose profiles at a, b) 6 MV and c, d) 15 MV at depth 10 cm for square field sizes from 5 × 5 cm2 to 40 × 40 cm2 , focus-surface distance 90 cm. (Measured data were taken from our TPS database).
and percent depth-dose curves within the primary photon field, as well as of out-of-field dose profiles due to all causes and especially to phantom-scattered radiation. For the calculation of the in-field doses, a (50 × 50 × 50) cm3 water tank phantom and 90 or 100 cm source-to-surface (SSD) distance were assumed (Fig. 1). Square fields with side lengths 5, 10, 20 and 40 cm were generated at 10 cm depth, and the lateral dose profiles (inplane direction) were scored at 10 cm depth within the water phantom. The DOSXYZnrc/EGSnrc package [24] was used for computing the dose profiles within the water phantom. Water phantoms were modeled individually for each simulated field size, with voxel sizes of 1 cm3 for regions outside the field and (0.5 × 0.5 × 1) cm3 for the in-field regions, except for the voxels along the central axis which were 1 cm3 in volume. The experimental arrangement set up to validate the Monte-Carlo model by measurements of dose distributions in absorbers was congruent with the geometry used for the calculations shown in Figure 1. The values of the absorbed dose to water were obtained with the flexible 0.125 cm3 chamber PTW 31010, and the results of the lateral dose distributions as well as the depth-dose curves were normalized to their maximum values. In Figures 2 and 3 the comparison between the Monte-Carlo calculated and the measured dose distributions is performed for the in-field region. With the exception of a part of the lateral dose distribution for the largest field at 15 MV, good agreement is achieved, with no detectable deviation unless caused by the statistical variations of the Monte Carlo data. Obviously, the simplified treatment of secondary electron transport at ener-
gies below 700 keV does not result in detectable differences in the build-up region of the depth-dose curves. For Monte-Carlo dose calculations of the peripheral doses outside the field limits, the calculation geometry was the same as in Figure 1 using DOSRZnrc/EGSnrc, but the photon splitting radius was taken as 30 cm in order to obtain good photon statistics even in the peripheral region. In these calculations, the phantom surface was at SSD 100 cm, and the field size was measured at the phantom surface. The experimental setup used for the validation was congruent with Figure 1, but we used the water-equivalent solid phantom material RW3 (white polystyrene) (PTW Freiburg, Germany), because the phantom had to consist of two parts, whose in-field part could be removed to permit peripheral dose measurements free from scatter originating in the directly irradiated part of the phantom. The RW3 to water ratio of the electron densities is 1.012, therefore RW3 appeared as sufficient for the purpose of validating the Monte-Carlo calculated peripheral dose values. At depth 10 cm, the reference dose values on the beam axis and the dose profiles outside the geometrical field limits were recorded with a Farmer 0.6 cm3 chamber type M 30001 (PTW Freiburg, Germany). The small (< 2%) kQ changes expressing the photon-energy dependent changes of the wall correction factor and of the stopping-power ratio when photon chambers of this type are used either within the useful beam on or off axis [6] or under out-of-field conditions [10], were neglected since the interest of this validation of the Monte Carlo code was on comparably large effects. All measured peripheral dose profile values were presented as percentages of the dose value
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Fig. 3. Monte-Carlo calculated and measured relative depth dose profiles at a, b) 6 MV and c, d) 15 MV for square field sizes from 5 × 5 cm2 to 40 × 40 cm2 , focus-surface distance 90 cm. (Measured data were taken from our TPS database).
obtained on the beam axis at 10 cm depth. The differences between calculated and measured values in Figures 4 and 5 are small, even for the largest field, and are likely to reflect imperfections in the modeling of the beam head shielding. Overall, the achieved degree of accuracy of the simulation of doses was deemed as a sufficient dosimetric validation of the Monte Carlo model for the purposes of the present
study, whose main subject of investigation were the typical regularities of the photon spectra within and outside the field limits. 2.2 Monte-Carlo simulations of photon spectra Using FLURZnrc/EGSnrc [22], photon spectra were scored within a large water tank of 40 cm radius and 38 cm deep for
Fig. 4. Monte-Carlo calculated and measured lateral profiles of the total dose in the out-of field region at a) 6 MV and b) 15 MV at depth 10 cm for square field sizes from 2 × 2 cm2 to 30 × 30 cm2 , focus-surface distance 100 cm. Calculations were done for water; measurements were performed in the water-equivalent solid RW3 (white polystyrene).
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Fig. 5. Monte-Carlo calculated and measured lateral dose profiles due to photons scattered from the directly irradiated part of the phantom, in the out-of field region at a) 6 MV and b) 15 MV at depth 10 cm for square field sizes from 2 × 2 cm2 to 20 × 20 cm2 , focus-surface distance 100 cm. Calculations were done for water; measurements were performed in the water-equivalent solid RW3 (white polystyrene).
100 cm SSD. In order to reduce the statistical fluctuations in the spectra, the scoring regions had rotational symmetry with respect to the central beam axis. Accordingly, a modification of the accelerator head model to obtain circular beams was performed. This was done by taking the already tuned head model and defining circular apertures of the jaw collimator and the multi-leaf collimator using the CONS3R component module, so that the projected fields at the isocenter plane were circular. The radii of the circular beams were so defined that they corresponded to side lengths of 5, 10, 20 and 30 cm of the equivalent square fields. This was achieved by taking radii √ equal to the quotient of the square-field side length and π [29]. In plots of the spectral results, the side lengths of the equivalent square fields are used to characterize the field size. The accelerator head model with circular shaped collimators was then compiled as a shared library for use as input for the FLURZnrc simulations (ISOURCE 23). The fluence was scored either in a small cylindrical volume of 0.5 cm radius and 0.3 cm thickness, centered on the beam axis, or in concentric rings of 1 cm width and 0.3 cm thickness whose inner radius was x - 0.5 cm, in a water phantom of 30 cm radius and 30 cm deep, as shown in Figure 1a. Directional bremsstrahlung splitting with a splitting number of 1000, Russian Roulette for photons in a plane slightly upstream the bottom plane of the flattening filter, and a selection radius of 30 cm for all field sizes were used. This large splitting radius was used in order to improve the calculation statistics for regions outside the field borders of smaller fields. Electron splitting was implemented as described in section 2.1. In all cases, the spectra will be represented as the “normalized spectral energy fluence”, i.e. the product of the spectral
fluence and the photon energy, with the numbers shown in all channels adding to unity. 2.3 The new spectral parameter: the dose fraction due to low-energy photons A simple, summarizing parameter comprising in one number the space-dependent spectral changes of dosimetric or radiobiological concern should have its focus on the lowenergy part of the photon spectrum below cut-off energy Ecut . The spatial pattern of such summarizing parameter could be used to visualize regions of a phantom (and similarly of a patient’s body) where such concern would be warranted. A cut-off energy Ecut = 200 keV is likely to be chosen because the largest changes of the responses of non-water equivalent dosimeters and of some water-to tissue dose conversion factors occur at energies below 200 keV. For illustration, Figure 6 shows the photon energy dependence of the quotient of the mass energy absorption coefficient of either AgBr film emulsion, Si, LiF or compact bone and the mass energy absorption coefficient of water. In the same low-energy region, the main changes of the energy-dependent RBE values for photon radiations are occurring [13,16–18,21,35,39,43]. Using the computed fluence spectra as described above, the relative contribution of energy-degraded Compton scattered photons to the dose D at a point in the medium, PD Ecut , for photons with energies not exceeding the value Ecut is defined as [3]: Ecut PD =
D(E ≤ Ecut ) Dtotal
(1)
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3.1 Field size dependence of the low-energy spectral component at on- and off-axis points
Fig. 6. Photon energy dependence of the quotient of the mass-energy absorption coefficients of AgBr film emulsion, Si, compact bone or LiF and the mass-energy absorption coefficient of water. From NIST X-ray data [19].
For the computation of parameter PD Ecut , Eq. (1) can be written as m Ecut PD
=
i=1 n i=1
m μ
Di
en
= Di
i=1 n i=1
ρ
μen ρ
i
Ei φ i (2)
i
E i φi
where 1 ≤ i ≤ n sums over all spectral components at the scoring point, and i = m corresponds to energy Ecut . Factor μen /ρ is the mass energy absorption coefficient of water, and φi the spectral photon fluence at energy Ei . The precise meaning of the product (μen /ρ)i Ei Φι is the bremsstrahlung-corrected value of water kerma, equal to the local absorbed dose to water under secondary electron equilibrium, produced by the photons in energy bin i. (In order to keep the PD 200keV concept simple, the so-called “kerma approximation” is applied in equation 2 in spite of the fact that secondary electron equilibrium is not exactly achieved in some situations such as the build-up region or the penumbra region). Using Ecut = 200 keV, PD 200keV has been calculated for different depths and lateral positions within a water phantom, for different field sizes. The values of PD 200keV are always given in percent of the local dose at the point of interest.
3 Results Photon spectra and values of the dose fraction due to lowenergy photons, determined by Monte Carlo calculations, will now be presented together with short physical interpretations.
The field size is a prominent parameter which modulates the relative magnitude of the low-energy component of the photon spectrum with increasing depth. The calculated spectra of a 6 MV photon beam at points on the central beam axis in 2 cm and 20 cm depth within water are shown in Figure 7a - 7d for various field sizes and SSD 90 cm. For the smaller fields, 5 × 5 cm2 and 10 × 10 cm2 , the dominant effect is a reduction of the low-energy components of the spectrum (“beam hardening”) with increasing depth, caused by spectral filtration in the low-Z absorber water via the Compton effect. However, this filtering effect recedes as the field size is increased. Now the competing effect, the build-up of a field of Compton-scattered photons with degraded energies, enhances the low-energy spectral components with increasing depth. The same influences can be observed in the spectra of the 15 MV beam (Fig. 7e- 7h). For off-axis points within the field limits, there exists a “beam softening” effect, attributable to the angular dependence of the bremsstrahlung spectrum, to Compton scatter from the flattening filter and to the reduced thickness and therefore to the reduced filtering effect of the flattening filter with increasing off-axis distance (Fig. 8 a,b). With increasing depth, this “softening” effect however becomes less apparent due to the superposition with the phantom scatter (Fig. 8 c,d). A comparison with the off-axis spectra obtained without the flattening filter showed that the main reasons for this “softening effect” are (a) the reduced filtering by the thinner outer regions of the flattening filter and (b) the preferentially outward directed Compton scatter from the thick central region of the filter.
3.2 Photon spectra at points on the field margin and outside the field The total photon spectra at off-axis distances x = 7 cm, 11 cm and 15 cm, including the components attributable to head leakage and collimator transmission, extra-focal radiation and phantom scatter, were calculated for the phantom arrangement described in Figure 1(a). Total off-axis spectra for SSD = 90 cm are shown in Figure 9 by bold lines and are compared with the spectrum at the beam axis (x = 0 cm). Already the spectra at x = 7 cm and 11 cm, just outside the useful beam, show a strong low-energy contribution. The spectra at x = 15 cm consist of a predominating low-energy component and a high-energy tail. In order to separate the spectra into their components, the calculation was performed for the arrangement without scatter from the directly irradiated part of the phantom, Figure 1(b). The spectra obtained under this condition are indicated by letter L, being due to beam head leakage, collimator transmission and extra-focal radiation. The spectrum obtained by subtracting spectrum L from the
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Fig. 7. Monte-Carlo calculated photon spectra at points of interest on the beam axis at depths 2 cm and 20 cm, for field sizes from 5 × 5 cm2 to 30 × 30 cm2 . a) - d) 6 MV, e) - h) 15 MV.
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Fig. 8. Monte-Carlo calculated photon spectra for 30 × 30 cm2 field size, at points of interest 12 cm from the beam axis, for 2 cm and 20 cm depth. a, c) 6 MV, b, d) 15 MV.
total spectrum, denoted by S, is due to photons scattered from the irradiated part of the phantom. The high-energy portions of the spectra at x = 7 cm and x = 15 cm, compared with the spectrum on the beam axis (x = 0), show a very strong attenuation, attributable to the effect of pair production in the high-Z shielding materials of the primary collimator and the adjustable collimators on the leakage radiation. The other prominent effect is the increase of the low-energy portion of the spectra with increasing offaxis distance, attributable to scatter from the irradiated part of the phantom. The shift of the scattered portion towards lower energies with increasing distance from the field border may be interpreted by the increasing contribution of multiple Compton scattering. Both effects contribute to an overall shift of the spectra towards lower energies with increasing off-axis distance, and this can be observed for both field sizes and both photon beam energies. 3.3 The lateral transport of low-energy photons The understanding of the wide-ranging lateral transport of scattered, energy degraded photons, recognizable in the
spectra at off-axis distance 15 cm (Fig. 9), shall be further underpinned by an analysis of the geometric spread of the lowenergy dose component. As a first example, the geometrical arrangement of Figure 1a has been applied in the simulation of a narrow photon beam (radius 1.4 cm) of given total number of primary photons. The ring-shaped scoring regions of Figure 1a were used to record the relative values of the spectral energy fluence of photons with energies below 200 keV. The relative values of the associated absorbed doses to water at secondary electron equilibrium, D200keV , were calculated by multiplication of the spectral energy fluence with the energy-dependent mass energy absorption coefficients of water. The resulting radial distribution of the normalized values of D200keV is shown in Figure 10 for 6 and 15 MV and for various depths in water from 5 to 28 cm at SSD = 90 cm. Each of the radial profiles of D200keV has a central region, radially extending up to about 2 cm, which contains not only scattered, but also primary photons with energies below 200 keV. In this region, the somewhat stronger attenuation of the 6 MV beam with increasing depth can be recognized. At larger off-axis distances, there is an approximately exponential decrease of D200keV with increasing radius, appearing in the semi-log plot
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Fig. 9. Monte Carlo-calculated photon spectra for points of interest on the central axis (x = 0 cm), immediately outside the field border (x = 7 cm, x = 11 cm) and at x = 15 cm from the central axis. a) - d) 6 MV and e) - h) 15 MV, field sizes 5 cm x 5 cm and 10 cm x 10 cm, depth 10 cm. The spectra at 7, 11 and 15 cm from the central axis are analyzed in terms of their beam-head leakage (L) and phantom scatter (S) components.
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Fig. 10. Radial distributions of the dose to water due to photons with energies below 200 keV, for a) 6 MV and b) 15 MV photon beams of radius 1.4 cm at various scoring depths d within the water phantom. The ordinate values have been normalized to the maximum value for d = 5 cm. The curves for depths 10, 20 and 28 cm have been shifted down by scaling factors 0.3, 0.1 and 0.03 respectively for better distinction between the curves which belong to different depths.
as a straight line. The half-value radius of this exponential function, ranging from 6 to 7 cm, is almost depth- and energy independent, and the radial attenuation factor is approximately ␣ ≈ 0.11 cm-1 . This means that in high-energy photon beams there is a wide-ranging lateral transport of the low-energy component of the scattered radiation. As an application example of the wide-ranging lateral transport of the low-energy component of the photon spectrum, Figure 11 shows the Monte-Carlo-calculated depth-dependent values of the dose fraction PD 200keV , attributable to photons with energies not exceeding 200 keV, for points of interest on the central axis of circular photon beams of various radii R of which the equivalent square field side lengths are indicated. The slightly S-shaped, almost linear increase of PD 200keV at points on the beam axis with the side length can be under-
stood by considering the lateral transport of energy-degraded scattered photons (Fig. 10): For a narrow field, the dominating effect is the outward-directed transport of the scattered low-energy photons into the space external to the beam; but with increasing field size more scattered photons are accumulated inside the geometrical region of the beam, and this effect is even enhanced with increasing depth, as shown in Figure 11. In order to complete the picture, Figure 12 shows the MonteCarlo calculated dose contribution by Compton-scattered photons with energies degraded below 200 keV at a point about 2 cm from the field border. The field border was taken as the lateral position at which the dose, normalized to the dose at the beam axis, is reaching 50%. Again at this position and for 6 and 15 MV, the low-energy dose contribution increases
Fig. 11. Dependence of PD 200keV on field size and depth for points of interest on the beam central axis at various depths for 6 MV and 1 cm from the central axis for 15 MV.
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Fig. 12. Dependence of PD 200keV on field size for points at 10 cm depth and 2 cm from the field border, the latter defined by the lateral position of the 50% dose value.
with increasing field size. For 15 MV the effect is smaller than for 6 MV, due to the more forward directed emission of the scattered photon in a Compton process. 3.4 2D profiles of PD 200keV within a water phantom As mentioned in the introduction and in section 2.3, the geometric pattern of parameter PD 200keV is suited to specify absorber regions where detector responses, dose conversion factors and RBE values are likely to vary. Figure 13 illustrates the radial and depth-dependence of PD 200keV for the 5 × 5 cm2 and 30 × 30 cm2 fields with the 6 MV beam (a and b) and the 15 MV beam (c and d) respectively. Within the field borders, the dose fraction due to low-energy components is relatively invariant. In the out-of-field regions PD 200keV is increasing by up to one order of magnitude as compared to the values on the central beam axis, due to the wide spread, already observed in the previous results, of the scattered low-energy photons originating from the irradiated phantom material. For the large field size, the “transition zone” from the field border to the region of the maximum PD 200keV values is much narrower than for the small field size, because for the larger field, the phantomscattered photons are more dominating in comparison with the head leakage radiation.
4 Discussion The aim of the present study has been to investigate the changes of the photon spectrum, especially of its low-energy component, within water phantoms, which may occur in a very similar way in the patient’s body at points in and around radiotherapy treatment fields. This investigation is an extension of the work of several authors who studied the changes of the photon spectrum in body-like phantoms, especially with
regard to the associated changes of detector sensitivities compared with the absorbed dose to water [6,7,9–11,15,32,33,37], or to the associated changes of the RBE for various biological effects, among them cancer induction [16,25,28,45]. The applied Monte-Carlo code BEAMnrc/EGSnrc [22,36] and the accelerator head model representative of the Siemens Primus linac were validated by a comparison of calculated and measured dose distributions, resulting in good agreement inand outside the field limits (see Figs. 2-5). On this basis, the Monte Carlo method was applied to calculate the photon spectra and their typical changes within a large water phantom for 6 MV and 15 MV photon beams. The low-energy portion of the depth-dependent spectra within the beam, Figure 7, reflects the counteracting depth-dependent phenomena of beam hardening, preponderant at small field size, and accumulation of Compton-scattered photons of low energy, which dominates at large field size. Figure 8 illustrates the well-known effect of “beam softening” with increasing off-axis distance, which is most expressed at shallow depths but superposed by phantom scatter at the larger depths. The variation of the photon spectra at the field border or at points in the periphery undergo much larger changes, as shown in Figure 9. Here, we have separated the spectral components into (a) the low-energy contribution from scatter out of the water phantom, S, and (b) the remaining high-energy contribution due to leakage and extra-focal radiation, L. Near the field border, Compton-scattered photons are the main component, superposed with a high-energy component mainly due to extra-focal radiation. In the periphery, the spectrum is furthermore shifted towards lower energies, now consisting of multiply scattered photons and the leakage radiation, filtered by the high-Z shielding materials of the beam head, similar to the results of Edwards and Mountford [9] and Kry et al. [28]. Means for reducing collimator transmission and leakage doses have been investigated recently [4]. The new parameter PD 200keV , i.e. the fraction of the absorbed dose to water under conditions of secondary electron equilibrium, produced by photons with energies below 200 keV (eq. 1 and 2), is then proposed as a simple instrument of characterizing the spatial regions in- and outside the irradiated field where detector responses, dose conversion factors and RBE values are likely to change [2,4,16]. The value 200 keV of the cut-off energy was chosen with regard to the large changes of typical dose conversion factors below 200 keV (Fig. 6). A similar bipartition approach has been applied by Palm et al. [32] and by Eklund and Ahnesjö [11], who have chosen cut-off energies at 100 keV and 5 MeV. Clearly, any choice of a single cut-off energy will be somewhat arbitrary, and other similar values might be more significant in special cases of dosimetrical or radiobiological relevance. Keeping these precautions in mind, we have chosen the cut-off energy of 200 keV in order to demonstrate the general trends of the dose contributions by low-energy photons. Parameter PD 200keV was then applied to characterize the field of low-energy scattered photons associated with narrow
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Table 1 Examples of the response enhancement of dosimetric detectors and biological objects due to exposure to photons of reduced energy. Detector or biol. object
Test radiation quality
Reference radiation quality
Response enhancement factor
Reference
X-Omat film TLD LiF:Mg, Ti Unshielded p-type Si diode Swater,air
112 keV, spectrum 112 keV, spectrum 6 MV X-rays, A = 20x20cm2 d = 25cm 6 MV X-rays* , 3 cm out of field border,d = 5cm 100 keV, spectrum (interpolated value) 6 MV X-rays, only backscattered radiation
6 MV X-rays 6 MV X-rays 6 MV X-rays, A = 10x10cm2 , d = 10 cm 6 MV X-rays* , on axis, d = 5cm Co-60 gamma rays
4.37 1.10 1.05
27 27 11
1.017
10
3.02
13
6 MV X-rays
1.48
45
Human lymphocytes** Human fibroblasts*** * ** ***
A = 10 x 10 cm2 . Yield of dicentric chromosomes, low-dose limit. Yield of DNA dsb at 4 Gy.
Fig. 13. 2D profiles of PD 200keV within water for the Primus 6 MV and 15 MV linear accelerator at field sizes 5 cm x 5 cm and 30 cm x 30 cm. The PD 200keV values are shown in percent of the total dose at the same point.
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primary photon beams. A characteristic exponential lateral distribution of PD 200keV with radial attenuation factor ␣ ≈ 0.11 cm-1 was obtained (Fig. 10). This description is the analytical analogue to the graphic display of the scattered photons published by Eklund and Ahnesjö [10]. The exponential shape of the scattering kernel is similar to the scattering kernel applied by Spies et al. [41] in their analysis of image blurring in portal imaging devices. The wide-ranging radial spread of the scattering kernel was then applied to understand that the low-energy dose fraction at a point on the axis of a circular field increases approximately in proportion with the field radius respectively the corresponding equivalent square field side length (Fig. 11). A dosimetric conclusion to be drawn from the small values of PD 200keV for small field sizes is that in narrow-field dosimetry the dose fraction due to low-energy photons is small, which should be accounted for by special narrow-field calibration conditions for dosimeters with over-response to low-energy photons like Si diodes. Some published examples of measured or calculated detector overresponse to low-energy photons are shown in Table 1. Note that the test radiation in the first two examples was X-rays of 112 keV, whereas in the third example only the field size was varied. The PD 200keV values at the field margin were also shown to increase with field size (Fig. 12), corresponding to the experimental result that the relative peripheral dose at a point 5 cm outside the field border increases with field size due to increases in the scatter contribution [4]. Parameter PD 200keV is also a simple indicator of body regions in which enhanced RBE values for radiobiological effects are to be expected, especially the peripheral region (Fig. 13). Since peripheral doses may reach the order of 5% of the on-axis dose (see Figs. 4 and 5) peripheral doses to be weighted, e.g., by an RBE of two would amount to 10% of the RBE weighted dose on the beam axis. Two examples of the increase of the RBE due to exposure with low-energy photons are given in Table 1. This has a bearing on the discussion of carcinogenic side effects of radiotherapy due to the peripheral doses, because increased organ-specific RBE values for carcinogenesis have to be expected in the peripheral region. The present investigation has been confined to conventional beam-head constructions of electron accelerators for use in photon-beam radiotherapy. The modifications of photon spectra known to occur in the case of flattening-filter free constructions [46] will be studied in further work of this group. The characteristic wide-ranging radial spread of the scattered low-energy photons from each pencil beam of primary photons will however remain unchanged.
5 Conclusions In this paper the typical changes of the photon spectra within and around therapeutic photon beams have been assessed by Monte Carlo calculations. The increase, due to Comptonscattered photons, of the low-energy component within the
field borders with increasing field size and increasing depth, and the build-up of the low-energy component in the periphery of the therapeutic photon beam have been quantified. We propose a method of comprehensively mapping the relative weight of the low-energy component within the total radiation field by using the parameter PD 200keV , the dose fraction due to photons with energies not exceeding 200 keV. Profiles and maps of PD 200keV can be used to identify the regions of a phantom (and similarly of a patient’s body) where the responses of non-water equivalent radiation detectors, the water to tissue dose conversion factors and the RBE values for the induction of radiobiological effects are likely to be influenced by the presence of low-energy photons. Low values of PD 200keV are a characteristic of small-field dosimetry and therefore of the conditions desirable for the calibration of dosimeters for use in small therapeutic photon fields.
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