Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams

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Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams Impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie M. Hamdi a , M. Mimi a , M. Bentourkia b,∗ a b

Department of electrical engineering, university of Mostaganem, BP188/227, Mostaganem 27000, Algeria Department of nuclear medicine and radiobiology, université de Sherbrooke, 3001, 12th, avenue North, Sherbrooke (Qc), J1H 5N4, Canada

a r t i c l e

i n f o

Article history: Received 12 August 2016 Received in revised form 24 December 2016 Accepted 9 January 2017 Keywords: Dosimetry Monte Carlo Small animal Tumor X-rays Photon interaction

a b s t r a c t Purpose. – Radiotherapy treatments to local tumors are always associated with dose deposit in surrounding tissues and even in distant tissues not traversed by the radiation beams. In the present work, we demonstrate by Monte Carlo simulations the impact of radiation energy on absorbed dose in a lung tumor and in other secondary organs in a digital mouse. We also report the energy difference between simulations of monoenergetic and spectral radiations, and between CT-based and atlas-made digital mouse. Materials and methods. – We simulated seven monoenergetic and spectral radiation beams from 50 keV (or kVp) to 450 keV (or kVp). For each energy mode, the beams were generated along seven angles converging on the tumor. We assessed the absorbed dose in ten volumes including the lungs, the heart and the spine. Results. – The results showed an increase of absorbed dose as a function of energy with a lowest dose at 100 keV. In the secondary organs not traversed by the beams, the spinal cord received doses of 0.78% and 0.07%, and the spinal bone received 2.36% and 0.35% relative to those in the tumor, respectively at 50 keV and at 450 keV. A region in the heart not traversed by the beams received 2% of the dose to the tumor. Conclusions. – The optimal energy to the tumor with relatively reduced doses to other organs was achieved at energies around 200 keV. At these energies, the surrounding of the tumor received lesser doses. Monoenergetic radiations were found to be more appropriate to target the tumor than spectral radiations produced by X-ray tubes, and CT-based digital mouse was more realistic than atlas-based mouse since it accounts for tissue heterogeneity. ´ e´ franc¸aise de radiotherapie ´ oncologique (SFRO). Published by Elsevier Masson SAS. All © 2017 Societ rights reserved.

r é s u m é Mots clés : Dosimétrie Monte Carlo Petits animaux Tumeur Rayons X Interaction des photons

Objectif. – Les traitements de tumeurs locales par irradiation sont toujours associés avec des dépôts de dose dans les tissus environnants et même dans les tissus proches non irradiés par les faisceaux de rayonnement. Dans le présent travail, nous démontrons par des simulations Monte Carlo l’impact de l’énergie du rayonnement sur les doses absorbées dans une tumeur pulmonaire d’une souris numérique et dans d’autres organes secondaires. Nous présentons également l’impact de l’énergie dans les simulations de radiations monoénergétiques et spectrales, et entre la souris numérique produite par les images de tomodensitométrie et par un atlas.

∗ Corresponding author. E-mail address: [email protected] (M. Bentourkia). http://dx.doi.org/10.1016/j.canrad.2017.01.008 ´ e´ franc¸aise de radiotherapie ´ 1278-3218/© 2017 Societ oncologique (SFRO). Published by Elsevier Masson SAS. All rights reserved.

Please cite this article in press as: Hamdi M, et al. Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. Cancer Radiother (2017), http://dx.doi.org/10.1016/j.canrad.2017.01.008

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Matériel et méthodes. – Nous avons simulé sept faisceaux monoénergétiques de 50 keV à 450 keV et sept faisceaux polyénergétiques de 50 kVp à 450 kVp. Pour chaque énergie, quel que soit le mode, nous avons simulé une balistique à sept faisceaux isocentriques. Nous avons analysé les doses absorbées dans dix volumes dont les poumons, le cœur et la colonne vertébrale. Résultats. – Les résultats ont montré une augmentation de la dose absorbée en fonction de l’énergie avec les effets les plus faibles constatés à l’énergie de rayonnement de 100 keV. Pour les tissus secondaires non traversés par les faisceaux, la moelle épinière a rec¸u des doses de 0,78 % et 0,07 %, et la colonne vertébrale a rec¸u 2,36 % et 0,35 % relativement à celles de la tumeur, respectivement, à 50 keV à 450 keV. Une région du cœur non traversée par les faisceaux a rec¸u une dose de 2 % de celle de la tumeur. Conclusions. – Une énergie proche de 200 keV semble optimale pour irradier la tumeur tout en épargnant les tissus sains environnants. Les faisceaux monoénergétiques ont paru plus appropriés que les faisceaux polyénergétiques produits par des tubes à rayons X. La souris numérique basée sur des images de tomodensitométrie était plus réaliste que la souris obtenue à partir d’un atlas. ´ e´ franc¸aise de radiotherapie ´ oncologique (SFRO). Publie´ par Elsevier Masson SAS. Tous © 2017 Societ ´ ´ droits reserv es.

1. Introduction The goal of external radiation therapy in cancer treatment is to treat the malignant tissue while preserving the normal tissues. For this reason, high precision of tissue targeting and radiation beam shape and energy are required. The provided three-dimensional anatomical structures by tomographic imaging serve as a guide for the radiation oncologist to precisely locate and calculate the depth of the disease inside the patient’s body, together with the nature of tissues located on the beam trajectory. The beam flux, intensity, energy and orientation are then estimated to optimize the penetration of the beam until the targeted tissue. To avoid or limit dose deposit in certain organs at risk like bone marrow, spinal cord and even bones and achieve a sufficient dose in the tumor, multiple beams from different irregularly spaced angles are used [1–3]. To calculate dose distributions, Monte Carlo simulations are the predominant preclinical dosimetry methods due to their capacity to model physical processes and complex geometries [4–8]. However, the calculations are time, disk space and memory demanding which limit their application in clinical dosimetry. This constraint is overcome by using high memory and fast clusters of computers in conjunction with improved algorithms [9–12]. Experimental preclinical small animal models are used to investigate tumor response to radiation therapy that can be translated to clinical applications [13]. Even though, some limitations restrain the use of small animal irradiators to mimic clinical radiotherapy treatments, including scaling of radiation energy from kilovoltage to megavoltage and the guidance precision from submillimeters to a few millimeters by exploring high resolution small animal imaging technologies like microcomputed tomography (micro-CT) [14–17]. Monte Carlo simulations are essential tools for imaging and for the assessment of the transferred energy and absorbed dose especially in small animal models. The simulations also allow understanding specific effects separately from several phenomena occurring in an experiment, which cannot be independently described experimentally. Small animal phantoms are generally created from high-resolution anatomical imaging such as magnetic resonance imaging (MRI), CT or from digital atlases [18–20]. The aims of the present work were to assess the impact of energy on the absorbed dose in a primary tumor and preserving other secondary organs of a mouse phantom using multiple beam angles and energies targeting the tumor [18]. We report the statistics of the transferred energy in the tumor and in the other tissues and the types of interactions. We also compared the simulations as a function of energy using monoenergetic radiations and spectral radiations as those produced by X-ray tubes, and the simulations in CT-based mouse phantom versus atlas-made mouse phantom. To achieve these calculations, we used Geant4 Applications for Tomographic Emission (GATE) based on Monte Carlo simulations

Fig. 1. Whole mouse atlas phantom with ten tissue regions used to assess the impact of X-ray energy on absorbed dose during irradiation with kilovoltage X-ray beams. Region 1 is the targeted tumor. The circles around the digits indicate the actual spherical shapes of the regions with 1.4 mm in diameter except for regions 9 and 10 which were manually drawn. The seven radiotherapy beams (beam numbers are outside the mouse image) focused on the tumor only. The image intensity was adjusted to clearly highlight the bones and the volumes of interest in 3D display. The beams were sketched as parallel beams. Mire de l’atlas de la souris entière avec les dix régions tissulaires utilisée pour évaluer l’impact de l’énergie sur la dose absorbée lors de l’irradiation par un faisceau de rayons X de basse énergie. La région 1 représente la tumeur. Les cercles autour des chiffres indiquent les volumes des sphères autour des régions avec 1,4 mm de diamètre, à l’exception des régions 9 et 10 qui ont été tracées manuellement. Les sept faisceaux de radiothérapie (les numéros des faisceaux sont indiqués à l’extérieur de l’image de la souris) convergent vers la tumeur. L’intensité des images a été ajustée afin de favoriser l’apparence des os et des volumes d’intérêt en affichage tridimensionnel. Les faisceaux ont été illustrés comme faisceaux parallèles.

code [21]. The findings in this work are expected to be of interest for energy type and model selection in imaging and dosimetry in either human or small animal models. 2. Materials and methods 2.1. Heterogeneous mouse phantom The three-dimensional micro-CT image of a 28 g normal nude male mouse provided by the Digimouse project with spatial resolution of 0.1 mm was used as input to our simulations (Fig. 1) [18]. We also used the atlas of the same digital mouse that provided segmented tissue structures and their densities. Since the Digimouse data were provided as gray scale levels, we converted them to Hounsfield units (HU) [22–24]. In fact, GATE utilizes Hounsfield units, and within GATE, there exists an algorithm to convert tissue structures expressed in Hounsfield units to densities. This calibration was based on the stoichiometric calibration introduced by Schneider et al. [25]. To convert mouse

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image from gray scale levels to Hounsfield units, we chose four volumes of interest (VOI) on the Digimouse in air, lung, heart and in spinal bone [23,26,27]. We then evaluated the mean intensity values in the Digimouse of each volume of interest as 0 for air, 37.33 for lung, 101.56 for heart, and 241.37 for spinal bone. For the calculation of Hounsfield units values, we extracted the mass attenuation coefficients for these four materials from the tables of photon cross sections and attenuation coefficients (http://atom.kaeri.re.kr:8080/cgi-bin/w3xcom, the densities of the media are also given therein) by supposing 33 keV monoenergetic photon beam (in ref [18], the authors used a spectrum of 50 kVp,  and we took  33 keV here as the effective energy): HUm = 1000 ×

m H O 2

− 1 , where m and H2 O are the linear attenuation

coefficients of the specified material and water and HUm is the corresponding Hounsfield unit of the material. Once Hounsfield units values were calculated for air, lung, heart and spinal bone, these were plotted against their respective intensities in the image and parameters of a linear regression were calculated from which all voxels in the mouse image were converted into Hounsfield units. This procedure is similar to that implemented in [28], except we used air, lung, heart and spinal bone as reference materials for the linear regression instead of air, water and polytetrafluoroethylene in [28]. Our calculations through Hounsfield units allowed us to retrieve the bone density as provided in the mouse atlas with a ratio 1.0132 at 50 kVp. In the mouse phantom, we modeled a lung tumor having 60 HU [29] with a spherical volume of 1.4 mm in diameter [30] (Fig. 1). The mean difference between the tumor and lung tissue was about 625 HU. For dosimetry analyses, we used seven radiation beams focusing on the tumor and we evaluated photon interactions, energy transfer and the related absorbed dose in ten volume regions including the tumor (Fig. 1). Volume 1 (VOI1) was around the tumor. In addition to the actual volume of the tumor, i.e. 1.4 mm of diameter, the tumor volume was defined by two other regions of different diameters to assess the energy transfer and absorbed dose at larger volumes than intercepted by the beams, at diameters of 1.6 mm, VOI2, and 1.8 mm, VOI3. These assessments were made to estimate the dose to the boundaries of the tumor and to nearest tissues as the real limits of the tumor are not always accurately known from the images in clinical situations. The other volumes were VOI4 and was in lung tissue, VOI5 was in lung tissue intercepted by beam 1, VOI6, partially intercepted by beam 2, and VOI7 were in the heart, VOI8 was located in the lung at the level of the tumor but horizontally translated by 1.8 mm, VOI9 was manually drawn around the spinal bone including bone marrow, and VOI10 was located around the spinal cord excluding the bone. Volumes VOI9 in the spine and VOI10 in the spinal cord were respectively 6.23 and 1.09 times greater than the tumor volume VOI1. All these regions were identified by means of the indications on the Digimouse atlas (http://neuroimage.usc.edu/neuro/Digimouse Download) [18]. Furthermore, we also used the digital mouse atlas where the organs are originally segmented in tissue densities and this 3D image including the tumor in the lung was supplied to our Monte Carlo simulations. 2.2. Simulation procedure A monoenergetic X-ray beam was simulated from a point source and focalized on the volume of the tumor of 1.4 mm in diameter located at 121 mm in a conic emission [31]. The beam source was rotated around the mouse phantom at seven angles of emission irregularly spaced to avoid irradiating bone marrow and the spinal cord [32] (Fig. 1). As in clinical radiotherapy, the dose was delivered to the tumor with several converging radiation beams [33–35]. To

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investigate the influence of the X-ray energies on the absorbed dose within the tumor, in its surrounding tissues and in the neighboring organs, the X-ray radiation spanned the following energies of 50, 100, 150, 200, 250, 350 and 450 keV. We also performed the simulations with seven radiation spectral energies as to be produced in an X-ray tube with 50, 100, 150, 200, 250, 350 and 450 kVp. One can compare the absorbed dose from radiations with energy spectra against those with an effective energy of these energy spectra. The simulation with spectral energies is useful when comparing to experimental data, but it does not allow accurate understanding of individual physical phenomena since the effects of several energies are merged; in addition, the energy spectra contains the characteristic X-rays of the anode. In this work, we simulated the energy spectra by accelerating electrons on an anode made of tungsten with the respective filters for each kVp energy of 1 mm Al, 2 mm Al, 3 mm Al, 4 mm Al, 4 mm Al + 0.25 mm Cu, 4 mm Al + 0.75 mm Cu, and 4 mm Al + 1 mm Cu. Such filtering allowed the validation by reproducing published energy spectra [35,36]. The effective energies of the energy spectra were calculated based on the reference [37]. In summary, we considered an energy spectrum as a number of photons N0 plotted as a function of energy, and for each energy in the spectrum we evaluated the transmitted photon counts N, then knowing the total photons for all energies of the spectrum and their corresponding total transmitted photons, we estimated a single attenuation coefficient, then deduced the corresponding energy used as the effective energy. These effective energies can also be calculated using half value thickness as in [38]. The calculated effective energies corresponding to the above energy spectra were 29.5, 41, 49.5, 57, 68, 88, 104 keV. The absorbed dose assessed with the energy spectra and with their corresponding effective energies was compared. The two energy sequences, 50 keV to 450 keV and 50 kVp to 450 kVp were not to be compared with each other but to show their effects as a function of energy in the mouse. For GATE simulations, the standard physical model was used for all photon and electron interactions except Rayleigh scattering where the low energy model was used. Since the volume of the tumor and the volumes of interest were relatively small, the particles were tracked down to 1 ␮m which corresponded to 250 eV for photons and 281 eV for electrons. To achieve statistically significant results, a total of approximately 5 × 109 , 4 × 109 , 2.4 × 109 , 1.7 × 109 , 1.3 × 109 , 9 × 108 , 7.4 × 108 photons were respectively simulated for 50 keV, 100 keV, 150 keV, 200 keV, 250 keV, 350 keV and 450 keV. These numbers of photons correspond to the expected absorbed dose, around 60 mGy, in a small volume of a mouse tissue [39]. The same number of photons was simulated for the respective spectral beams. We obtained the absolute absorbed dose directly with GATE, with the dose actor tool. The simulations were conducted on a supercomputer having 2464 CPUs and 308 SGI XE320 compute nodes each with 2 Intel Xeon E5462 four core processors at 2.8 GHz and 16 to 32 Gigabytes of memory per node (http://www.calculquebec. ca/en/resources/compute-servers/mammouth-serie-ii). Each simulation was distributed on 300 computer processing units (CPU). For example, the simulation with 5 × 109 photons at 50 keV was split onto 300 CPUs, each computing 17 × 106 photons and a single CPU calculation took 6 h. This time duration did not include the waiting time in the tasks queue. The simulated photons were tracked for photoelectric and Compton interactions. The results of the simulations were saved for each photon with the type and position of interaction and the energy transfer. The mean radiation dose was calculated in each volume of the ten regions (Fig. 1). We also concentrated our efforts here on energy transfer and absorbed dose in specific volume regions instead of lines of isodoses [40]. It is also possible

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to assess absorbed doses in whole organs instead of limited volumes. All parts of our calculations were validated against published works. Moreover, we reproduced the absorbed dose as reported with 5 Monte Carlo codes in AAPM Task Group 195 [41]. This consisted in simulating a voxelized human atlas irradiated with a 120 kVp beam. We specifically reproduced the reported case 5. 2.3. Data analysis The results of particle tracking were obtained in ROOT file format [42], then the data, i.e. photon identifier number, type of interaction, position of interaction, and energy transferred were extracted for further analysis. In addition, two 3D matrices (0.1 mm resolution) storing the energy transferred and the related absorbed dose in the whole mouse thorax were provided in two files in Analyze format [22,43]. For each VOI, the relative importance for elementary interactions (Compton and photoelectric), the energy spectra, the total transferred energy and its related absorbed dose were also calculated. 2.4. Statistical analysis We conducted the statistical analysis of the absorbed dose in tissues following the description in [33] in accordance with GATE simulations. In this reference, the authors reported statistical uncertainties in Monte Carlo based treatment planning. The approach consists in counting the absorbed dose deposited by each event in each voxel of the tissue. The events history is obtained from the simulations. We note that, in our simulations, the volumes of interest were small and except the tumor, the other volumes of interest were not on the path of the radiation beams which gave low counts and high uncertainties. Also the simulations with GATE returned the uncertainty values in percentage.

Fig. 2. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: Energy spectra in the tumor volume of interest 1 for the seven monoenergetic radiation beams in logarithmic scale. Note that despite the small size of the tumor, the photopeak is present at all simulated energies. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : spectre d’énergie dans la tumeur VOI1 pour les sept faisceaux monoénergétiques à l’échelle semi-logarithmique. Malgré les petites dimensions de la tumeur, le photopic apparaît pour toutes les énergies simulées.

3. Results The spectra of the energy transfer in the tumor VOI1 of 1.4 mm diameter and for each of the seven monoenergetic beams are shown in Fig. 2. It appears in this figure that the photopeak exists even for the highest energy of 450 keV and for such a small tumor. Meanwhile, Compton interactions formed the major energy transfer in the tumor for all energies including subsequent Compton interactions following previous interactions before the primary photons penetrate the tumor. On the other hand, only a small fraction of photons from those emitted by the source was counted in the tumor as shown by the intensity (y-axis) in Fig. 2. Fig. 2 also depicts Compton edge respectively located for the seven energies at 8, 28, 55, 88, 124, 202 and 287 keV. These values were obtained as the maximal transferred in a single interaction  photon energy  Emax = 2E02 / m0 c 2 + 2E0 , with E0 being the incident energy and m0 c2 the electron rest mass. The photopeak counts in the tumor VOI1 were found, respectively for each radiation energy, 8,620,029, 739,725, 121,919, 33,644, 12,652, 3075 and 1452 photons, and similarly for Compton interactions: 6,106,013, 1,435,021, 412,010, 174,808, 93,400, 97,900 and 21,730. These numbers can be compared to the number of simulated photons from the source giving ratios between 1.7 × 10−3 and 2 × 10−6 . The values of photoelectric effect did not include the photoelectric interaction after Compton interactions, as these did not deposit the whole energy of the original emission. The ratio of Compton interactions in the tumor VOI1 of all radiation energies with respect to those at 50 keV were: 1, 0.24, 0.067, 0.029, 0.015, 0.016 and 0.004. We recall that some photons

Fig. 3. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: Relative number of interactions, with respect to VOI1 at 50 keV, in the ten volumes of interest and for the seven monoenergy simulations. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : rapport d’interactions relativement à VOI1 à 50 keV, dans les dix volumes d’intérêt et pour les sept simulations monoénergétiques.

interacted in their path before reaching the tumor which reduced their energy and raised their probability to interact in the tumor. We also observed that the highest Compton interactions in the tumor were at 50 keV, and the ratio appeared still appreciable even at 450 keV. Fig. 3 depicts the number of interactions in the ten volumes of interest and for the seven monoenergetic beams. From this figure, it is shown that there were photons interactions in all the ten simulated volumes of interest. The total energy transferred in the tumor VOI1 and for each of the seven radiation monoenergies together with the absorbed dose are reported in Fig. 4A. Even if the number of simulated photons was decreasing with energy to maintain a normal dose, both the energy transfer and the absorbed dose showed a slight decrease at

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Fig. 4. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. A. Energy transfer and absorbed dose in the tumor VOI1 as a function of energy. The energy transfer and the absorbed dose increase as a function of energy with a depression at 100 keV. B. Absorbed dose in the tumor volumes VOI1, VOI2 and VOI3. At 200 keV the dose to the tumor VOI1 increases with energy while the dose to the neighboring tissue decreases. We recall that the number of photons was lowered with energy increase in order to maintain a constant dose to the tumor. C. Absorbed dose in ten volumes of interest and for seven energies. Data normalized to the absorbed dose in VOI1 at 50 keV (see Table 1). D. Absorbed dose in ten volumes of interest and for seven energies obtained with the same number of simulated photons of 5 × 109 for each energy as for VOI1 at 50 keV. The absorbed dose appears continuously increasing with energy. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie. A. Transfert d’énergie et dose absorbée dans la tumeur VOI1 en fonction de l’énergie. Le transfert d’énergie et la dose absorbée augmentent en fonction de l’énergie avec un abaissement à 100 keV. B. Dose absorbée dans les volumes de la tumeur VOI1, VOI2 et VOI3. À 200 keV la dose à la tumeur VOI1 augmente en fonction de l’énergie alors que la dose aux tissus entourant la tumeur baisse. Rappelons que le nombre de photons primaires émis lors de la simulation a été réduit lorsque l’énergie augmente afin de préserver la même dose à la tumeur. C. Dose absorbée dans les dix volumes d’intérêt et pour les sept énergies. Les données ont été normalisées à la dose absorbée dans la tumeur VOI1 à 50 keV (voir Tableau 1). D. Dose absorbée dans les dix volumes d’intérêt et pour les sept énergies obtenue avec le même nombre de photons primaires simulés 5 × 109 pour chaque énergie comme pour VOI1 à 50 keV. La dose absorbée paraît augmenter uniformément avec l’énergie.

100 keV in comparison to the other energies (Fig. 4A, Table 1). This decrease is very marginal when considering the uncertainties. The surroundings, VOI2 and VOI3, of the tumor VOI1 presented a slight decrease of the absorbed dose as a function of energy (around 3% for VOI2 and 6% for VOI3 when comparing the absorbed dose at 50 keV and 450 keV) when the absorbed dose was nearly maintained in

VOI1 with energy (Fig. 4B). The decline is more apparent starting at 200 keV. This energy level can be assumed as an optimal energy for dose deposit in the target tumor and preserving its neighboring. The absorbed dose in all volumes of interest and for all energies is displayed in Fig. 4C as normalized absorbed dose obtained with monoenergies, and in Fig. 4D as absorbed dose obtained with

Table 1 Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a digital mouse phantom irradiated with kilovoltage X-ray beams: absorbed dose in milligrays in the ten volumes of interest for the seven monoenergetic radiations. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une souris numérique irradiée par un faisceau de rayons X de basse énergie : dose absorbée en milligrays dans les dix volumes pour les sept faisceaux monoénergétiques. Radiation energy (keV) 50 VOI1 VOI2 VOI3 VOI4 VOI5a VOI6a VOI7 VOI8 VOI9b VOI10b a b

66.89 61.8 56.48 0.08 6.95 13.89 1.15 0.27 1.58 0.52

100 ± ± ± ± ± ± ± ± ± ±

0.82 1.05 1.23 61.6 2.1 1.32 2.4 12.3 0.72 6.82

66.78 61.56 56.1 0.05 6.77 12.48 1.15 0.18 0.49 0.17

150 ± ± ± ± ± ± ± ± ± ±

0.72 0.97 1.16 76.3 2.75 1.44 2.08 13.4 1.33 14.3

66.94 61.57 56.01 0.04 6.78 12.24 1.13 0.15 0.29 0.1

200 ± ± ± ± ± ± ± ± ± ±

0.88 1.13 1.31 67.7 3.31 1.83 2.55 17 1.62 18.4

67.35 61.47 55.76 0.04 6.85 12.3 1.14 0.13 0.23 0.07

250 ± ± ± ± ± ± ± ± ± ±

1.01 1.23 1.36 15.6 3.64 2.11 2.91 16.5 1.86 19.6

67.61 61.1 55.17 0.04 6.95 12.4 1.15 0.13 0.21 0.06

350 ± ± ± ± ± ± ± ± ± ±

1.08 1.26 1.35 84.8 3.7 2.22 3.09 12.3 2.08 24.3

67.94 60.4 54.09 0.08 7.14 12.85 1.25 0.19 0.21 0.05

450 ± ± ± ± ± ± ± ± ± ±

1.08 1.21 1.27 56.1 3.55 2.18 3.01 6.31 2.23 29.3

68.02 59.8 53.26 0.16 7.42 13.56 1.45 0.42 0.24 0.05

± ± ± ± ± ± ± ± ± ±

1.04 1.13 1.17 23.6 3.33 2.05 2.82 4.83 2.2 28.3

VOI5 and VOI6 were partially crossed at a single angle by the beam. VOI9 and VOI10 were manually drawn and were respectively 7.32 and 1.09 times larger than the tumor.

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Fig. 5. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: Investigation of the decreased absorbed dose at 100 keV with respect to the other radiation energies. The sphere was moved at different positions of (4,2), (4,3), (2,4) (−4,3), (−4,2), (−4,0), and the beam was directed on the water phantom lying on the x-axis. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : investigation de la diminution de la dose absorbée à 100 keV par rapport aux autres énergies. La sphère a été déplacée à différentes positions à (4,2), (4,3), (2,4), (−4,3), (−4,2), (−4,0), et le faisceau a été dirigé sur la mire de l’eau se trouvant sur l’axe des x.

monoenergies and with the same number of photons, 5 × 109 , as for VOI1 at 50 keV. By considering the same number of photons in each simulation, the absorbed dose continuously increases in all volumes of interest with a notable depression at 100 keV (Fig. 4D). We have observed that the absorbed dose in the mouse tumor at 50 keV was higher than that at 100 keV, and then the absorbed dose uniformly increased with radiation energy in tissues mostly

Fig. 6. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: Example of two energy spectra of 100 kVp and 350 kVp obtained by simulation. The characteristic X-rays of tungsten are also apparent at 59 keV and 67 keV [33]. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : exemple des deux spectres d’énergies à 100 kVp et 350 kVp obtenus avec les simulations. Les rayons X caractéristiques du tungstène apparaissent à 59 keV et 67 keV [33].

laterally located with respect to the radiation beam. This effect has also been reported in other works [40]. To confirm this behavior, we have then simulated an X-ray line beam of energies from 50 keV to 250 keV at steps of 50 keV impinging on a thin water cylinder of

Fig. 7. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. A. Absorbed dose in the ten volumes of interest and at the seven spectral energies in kVp. B. Same in (A) by accounting for the same number of simulated photons as for VOI1 at 50 kVp. C. Ratio of monoenergy on spectral energy absorbed dose for the tumor VOI1 and its surroundings VOI2 and VOI3. D. Ratio of the absorbed dose from the CT-made mouse on the atlas-made mouse models evaluated in the tumor and its surroundings in spectral energy. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie. A. Dose absorbée dans les dix volumes d’intérêt et pour les sept énergies spectrales en kVp. B. Même chose qu’en (A) en calculant pour le même nombre de photons simulés comme dans le cas de VOI1 à 50 kVp. C. Rapport de la dose absorbée monoénergétique sur la dose absorbée spectrale pour la tumeur VOI1 et les tissus l’entourant VOI2 et VOI3. D. Rapport de la dose absorbée dans le modèle de souris basé sur les images de tomodensitométrie à la dose absorbée dans le modèle de souris basé sur l’atlas pour les énergies spectrales (tumeurs et tissus environnants).

Please cite this article in press as: Hamdi M, et al. Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. Cancer Radiother (2017), http://dx.doi.org/10.1016/j.canrad.2017.01.008

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Fig. 8. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: Absorbed dose in uniform and separate phantoms for the seven polyenergetic beams. Data assessed along beam path as a function of depth in the phantoms. (A) water; (B) lung; (C) blood; (D) bone. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : dose absorbée simulée dans des mires uniformes séparées pour les sept faisceaux polyénergétiques. Les valeurs ont été obtenues le long de la trajectoire du faisceau en fonction de la profondeur dans les mires. (A) eau ; (B) poumon ; (C) sang ; (D) os.

length 9 mm and diameter 1 mm, and we recorded the absorbed dose in a 1 mm diameter heart tissue spherical phantom located at repeated positions in mm (4,2), (4,3), (2,4) (−4,3), (−4,2) and (−4,0) as depicted in Fig. 5. Therefore, for the lateral positions (4,2) and (4,3) with respect to all incident beams, the 100 keV beam was found to provoke less energy deposit at these positions relatively to the other simulated positions. The preceding results were obtained with monoenergetic radiations in the CT-based mouse phantom in order to evaluate photon interaction types and absorbed dose. We also simulated the absorbed dose provoked by energy spectra for the seven radiations mimicking radiations produced by an X-ray tube (Fig. 6). Fig. 7A depicts the absorbed dose obtained in the CT-based mouse phantom with spectral radiations (kVp). Contrary to the monoenergy simulations, here the absorbed dose appeared decreasing with energy. When using the same number of simulated photons of 5 × 109 , the shape of the absorbed dose became as in Fig. 7B. By comparing the monoenergy and the spectral energy simulations in the tumor volumes of interest, it appeared that below 100 keV, the spectral energy provoked more absorbed dose than the monoenergy, then the pattern was reversed for higher energy (Fig. 7C). The absorbed dose in the tumor provoked by the seven effective energies with respect to their counterparts in spectral energies (100 × doseEeffective /doseEspectral ) were 97, 92, 82, 69, 66, 66 and 62. These ratios confirm the high absorbed dose at higher spectral energies. Also we compared the simulations with the CT-made mouse and the atlas-made mouse, and the results are displayed in Fig. 7D as ratios of absorbed doses for VOI1, VOI2 and VOI3. These data clearly showed that the densities in the two mouse models could

be originally different in order to produce such discrepancies in terms of ratios and in terms of variation with energy. As shown in Fig. 7D, the ratios were more pronounced at low energy. This effect was also reported in [44]. To assess the absorbed dose as a function of depth in separate uniform media, we simulated a single polyenergetic (X-ray spectrum) beam in water, lung, blood and bone all of depth 25 mm. The simulated energies were as described earlier, 50, 100, 150, 200, 250, 350 and 450 kVp. We assessed the absorbed dose on the beam line and on a line parallel to the beam distant of 4 mm. This distance is comparable to the position of the organs in the mouse not traversed by the beams. Figs. 8 and 9 shows the absorbed dose along and parallel to the beam, respectively. As expected, the absorbed dose decreased with depth on beam line in all media but in different ways with respect to energy, while, on the line parallel to the beam, the absorbed dose presented a maximum deeper in all media and was energy dependent. The statistical uncertainties on the absorbed dose were directly calculated with GATE for all energies and in all volumes of interest. Table 1 shows the uncertainties for the monoenergetic beams. Mostly in the organs not traversed by the beams, the absorbed dose was too low due to the secondary scattered photons only and, accordingly, the uncertainties were high. 4. Discussion Monte Carlo simulations in small animal radiotherapy treatment are accessible and handy tools to guide for better designing treatment planning, not only to the target tumors and to the tissues along the beam paths, but also to distant organs of interest.

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Fig. 9. Study on the impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams: absorbed doses for depths along a line parallel to beam path located at 4 mm, to represent absorbed dose in mouse organs not traversed by the beams. (A) water; (B) lung; (C) blood; (D) bone. Étude de l’impact de l’énergie sur la dose absorbée évaluée par des simulations Monte Carlo dans une tumeur de souris et dans les organes voisins irradiés par un faisceau de rayons X de basse énergie : dose absorbée simulée à des profondeurs le long d’une ligne parallèle au faisceau et distante de 4 mm représentant les doses absorbées dans les organes de la souris non traversés par les faisceaux. (A) eau ; (B) poumon ; (C) sang ; (D) os.

It has been reported that doses of more than 5 Gy could be considered as lethal in mice [14,45]. It is recognized that exposure to repeated radiations during follow-up studies can have biological effects on the animal models and thus can affect the experimental results. Monte Carlo simulations can therefore help in selecting the appropriate radiation energies, beam directions and intensity and duration of experiment. It is preferable to study each beam direction separately in order to determine its optimal parameters. Instead of using monoenergetic photons in the simulations, an energy spectrum resembling the one produced by an X-ray tube can be generated reproducing also its shape and intensity. The doses obtained in these simulations at lower energies (50–100 keV) were in the same range as those for microCT/radiotherapy or for radiotherapy previous studies at an effective energy around 50 keV [35,46–48]. The volumes determined within the spinal cord received around 0.78% of the absorbed dose in the tumor at 50 keV, knowing that this volume was not on the path of any beam, and it was surrounded by bones. The spinal bone received a dose of 2.36% and 0.35% of those of the tumor at 50 keV and 450 keV. We note however that the volume of VOI9 was 6.23 times that of the tumor. In real treatments, the number of photons is also governed by beam application duration among other parameters. The two extra volumes around the lung tumor directly received the beam from some angles, but they were not directly exposed to the beams from some other angles. Also, the tissue density of these extra volumes was less than that of the tumor. Because of these differences, photons interactions in these volumes VOI2 and VOI3 were decreasing with radiation energies in comparison to VOI1, and their average ratios of absorbed dose (average over radiation

energies) were VOI2/VOI1 = 0.91 and VOI3/V1 = 0.82. Apart from uncertainty on tumor volume definition, the X-ray focal spot on the anode could also cause a penumbra that can have an impact on tumor neighboring tissues [47,48]. 5. Conclusion The goal of this study was to primarily assess the optimal energy to the tumor as a function of radiation beam and to concurrently preserve other organs from the direct and indirect radiations. These results showed that the optimal radiation energy should be greater than 200 keV in order to efficiently irradiate the tumor while lowering the dose to the other organs. For polyenergetic beams, the absorbed dose continuously declined with energy with an average around 16% at 450 kVp with respect to 50 kVp in the tumor and its surrounding tissue. We also assessed photon interaction types, energy transfer and absorbed dose in tissues distant from the radiation beams as a function of radiation energy. The spinal cord, being protected by the bones and not traversed by the beams, received in average 0.78% of the dose to the tumor. The dose to tumor surrounding tissue was shown to be dependent of radiation energy and had average ratios of 0.91 and 0.82 for volumes of diameters 1.6 mm and 1.8 mm with respect to the lung tumor of diameter 1.4 mm. In addition to these results that can apply to monoenergetic beams like in isotopic radiation sources, the spectral energies produced by X-ray tubes appear less appropriate for an optimal dosimetry as they contain a few high energy photons and a high number of low energy photons which generate Compton scattering in the whole mouse. Finally, the CT-based mouse phantom was assumed more realistic than the atlas-based mouse phantom for Monte Carlo simulations

Please cite this article in press as: Hamdi M, et al. Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. Cancer Radiother (2017), http://dx.doi.org/10.1016/j.canrad.2017.01.008

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Please cite this article in press as: Hamdi M, et al. Impact of X-ray energy on absorbed dose assessed with Monte Carlo simulations in a mouse tumor and in nearest organs irradiated with kilovoltage X-ray beams. Cancer Radiother (2017), http://dx.doi.org/10.1016/j.canrad.2017.01.008