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Inﬂuence of the electron energy and number of beams on the absorbed dose distributions in radiotherapy of deep seated targets H.M. Garnica-Garza n Centro de Investigación y de Estudios Avanzados del IPN Unidad Monterrey, Vía del Conocimiento 201 Parque PIIT, Apodaca, Nuevo León C.P. 66600, Mexico

H I G H L I G H T S

Technical requirements to be met in VHEET are established for the irradiation of prostate tumors. Optimization of beam energy as a function of number of beams is provided. Behavior of the non-tumor integral dose as a function of both energy and number of beams is examined.

art ic l e i nf o

a b s t r a c t

Article history: Received 2 April 2014 Received in revised form 17 June 2014 Accepted 28 July 2014 Available online 7 August 2014

With the advent of compact laser-based electron accelerators, there has been some renewed interest on the use of such charged particles for radiotherapy purposes. Traditionally, electrons have been used for the treatment of fairly superﬁcial lesions located at depths of no more than 4 cm inside the patient, but lately it has been proposed that by using very high energy electrons, i.e. those with an energy in the order of 200–250 MeV it should be possible to safely reach deeper targets. In this paper, we used a realistic patient model coupled with detailed Monte Carlo simulations of the electron transport in such a patient model to examine the characteristics of the resultant absorbed dose distributions as a function of both the electron beam energy as well as the number of beams for a particular type of treatment, namely, a prostate radiotherapy treatment. Each treatment is modeled as consisting of nine, ﬁve or three beam ports isocentrically distributed around the patient. An optimization algorithm is then applied to obtain the beam weights in each treatment plan. It is shown that for this particularly challenging case, both excellent target coverage and critical structure sparing can be obtained for energies in the order of 150 MeV and for as few as three treatment ports, while signiﬁcantly reducing the total energy absorbed by the patient with respect to a conventional megavoltage x-ray treatment. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Radiotherapy Electrons Monte Carlo simulation

1. Introduction The use of electron beams in radiotherapy has been usually conﬁned to the treatment of superﬁcial lesions, namely skin cancer, chest wall irradiation in breast cancer patients, and head and neck cancers. One disadvantage of electrons when compared to other types of charged particles, such as protons or heavy ions, is their relatively low mass, which in turn results in highly irregular trajectories as they scatter through a medium at the energy range currently employed in radiotherapy, namely 4–20 MeV. Although the use of very high energy electron beams in radiotherapy (VHEET), ranging from 150 to 250 MeV, has been suggested by several authors in the last 12 to 14 years (DesRosiers et al., 2000; Yeboah and

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Sandison, 2002), it has not been until more recently, with the advent of compact laser-based electron accelerators, that researchers and clinicians are starting to consider VHEET as a feasible alternative to current radiotherapy technologies based on x-rays and heavy charged particle accelerators (DesRosiers et al., 2008; Fuchs et al., 2009; Moskvin et al., 2010). As the latter technologies are quite established and mature, it is important to fully assess the characteristics of the resultant absorbed dose distributions of VHEET as a function of both beam energy and number of treatment ports in order to establish a baseline of technological requirements to be met if this treatment modality is to be clinically implemented. While several of the previously cited works have explored different aspects of the electron irradiation of deep-seated targets, prostate in particular, a systematic analysis with regards to the effect that a variation in both the electron energy and number of beams has on the absorbed dose distributions for this type of treatment is lacking. In this work, using a realistic patient model and full Monte Carlo

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simulation of the electron transport in such a patient, we evaluate these two important treatment parameters in order to determine their impact on target coverage, sparing of critical structures and the total energy absorbed by the patient, i.e. the non-tumor integral dose (NTID).

2. Materials and methods

voxelized geometries, were used to determine the absorbed dose distributions in the patient model. For each beam, at least 1 108 histories were simulated, achieving an uncertainty at the 1% level for those voxels receiving at least 50% of the maximum dose. Electron and photon cutoff energies were set at 100 keV, while parameters c1 and c2 were both set at 0.1. These latter parameters determine the mean free path between hard elastic collision and the maximum fraction of the electron energy lost in each step respectively.

2.1. Patient model The voxelized Zubal phantom (Zubal et al., 1994) was used to model a prostate radiotherapy treatment. This phantom consists of segmented CT scan images of a male patient and has a voxel resolution of 0.38 cm in each of the main axes. A portion of the phantom at the pelvis level was extracted and the arms were digitally removed. The total number of transverse slices used in this work is 80. The composition of 7 different materials present in the phantom was taken from ICRU Report 44 (1989), the materials being air, bone, skeletal muscle, soft tissue, blood, and bone marrow. Water was used to model the urine and feces. For the prostate treatment, the planning target volume (PTV) was formed by the addition of a 1 cm margin in all directions around the prostate, the gross target volume (GTV), except towards the rectal wall where a margin of 0.5 cm was used, as it is customary in this type of treatment (Bentel, 1996). The PTV thus obtained was used in all the treatments reported in this work. 2.2. Electron beam model It is assumed that a collimation device is available that produces electron beams that conform to the PTV. This collimation could be achieved, for example, by magnetically scanning an electron pencil beam (Fuchs et al., 2009) or by an external collimating device (Ma, 2004; Gauer et al., 2006). A separate computer program was written to determine each beam aperture by means of raytracing through the Zubal phantom using the Siddon algorithm (Siddon, 1984). It is further assumed that the geometry of the accelerating machine is such that it permits an isocentric delivery of the treatment, with the isocenter located at 100 cm from the electron source and that the electrons travel in air before reaching the patient. With regards to the electron energy spectra, it has been previously shown that, for the electron beams produced in laser-based accelerators, the use of a mono-energetic beam or one with the full energy spectrum is virtually indistinguishable in terms of the dose distributions (Fuchs et al., 2009), so in this work we restrict ourselves to the use of mono-energetic electron beams of energies 75, 100, 150, 200, and 250 MeV. Following the work of Fuchs et al. (2009) the electron source is assumed to be a point located at 100 cm from the isocenter, with a Gaussian angular distribution and a divergence of 6 mrad at FWHM. As a reference, a standard 6-ﬁeld 15 MV x-ray prostate 3D conformal radiotherapy treatment (3DCRT) was also calculated in order to make a comparison between the high energy electrons and the current clinical practice with photons, using the same PTV as for the electron beam treatments. The source is placed at 100 cm from the isocenter and again raytracing was used to determine the beam aperture to conform to the PTV for each beam. The x-ray spectrum for these simulations was taken from the literature (Garnica-Garza, 2008). 2.3. Monte Carlo simulations The Monte Carlo code PENELOPE (Salvat et al., 2006) and its auxiliary set of subroutines from the PenEasy suite (Sempau, 2006), which allows the simulation of radiation transport in

2.4. Cimmino optimization algorithm In order to determine each beam weight according to the prescription goals, an in-house optimization program based on the Cimmino algorithm was used (Garnica-Garza, 2011). Table 1 shows the prescription parameters used for the optimization runs. Upon termination, the software delivers each beam weight as well as treatment plan evaluation metrics such as cumulative dose volume histograms (cDVH) for the structures of interest and the NTID. In order to perform a meaningful comparison among all the different treatment plans, after the optimization each plan was renormalized so that the minimum dose imparted to the GTV is the prescribed dose, 72 Gy in this case. In order to assess the inﬂuence of the number of treatment ports on the absorbed dose distributions, the algorithm was separately run with 9, 5 and 3 beams made available to the optimization engine. The beam entrance angles for each beam in ever treatment plan calculated in this work are shown in Table 2.

3. Results and discussion 3.1. GTV dose uniformity and PTV coverage versus beam energy Fig. 1a) and b) shows the cDVH for the GTV, the prostate gland, and the PTV, for the 9 beam treatment technique, normalized to the prescribed dose of 72 Gy, while Fig. 2 shows the relevant data with regards to minimum, maximum and average absorbed doses in these two target structures. With regards to GTV dose uniformity, Figs. 1 and 2a), show that for electron energies at or above 150 MeV, the GTV dose uniformity is virtually the same as that for Table 1 Parameters used in the beam weight optimization algorithm. The structure weight refers to the importance assigned to the dose objectives for each structure, and their sum equals 1. Structure

Minimum dose (Gy) Maximum dose (Gy) Structure weight

GTV PTV Rectal wall Bladder Femoral heads Skin

72.0 65.0 0.0 0.0 0.0

75.0 75.0 65.0 65.0 40.0

0.4 0.4 0.18 0.01 0.005

0.0

40.0

0.005

Table 2 Beam entrance angles in each of the treatment techniques modeled in this work. The 01 beam is deﬁned as the left lateral beam. Treatment technique

Beam entrance angle

VHEET 3 beams VHEET 5 beams VHEET 9 beams 15 MV photons

901, 2351, 3051 451, 901, 1351, 2351, 3051 451, 901, 1351, 1701,2151, 2351, 2701, 3051, 3501 01, 451, 901, 1351, 2251, 3151

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Fig. 1. cDVH for: (a) GTV (the prostate gland) and (b) PTV for the ﬁve different electron energies and the 15 MeV x-ray beam simulated in this work. Continuous line: 75 MeV; dashed line: 100 MeV, dashed-dotted line: 150 MeV; dotted line: 200 MeV, blank circles: 250 MeV; blank diamonds: 15XMeV.

the 15 MV x-ray standard 3DCRT, all of them providing a dose uniformity at or better than 10% of the prescribed dose. The 75 MeV beam performs the worst with regards to this metric, yielding a dose uniformity of 25%. As for the PTV, Figs. 1 and 2b), the situation is basically the same, although it should be noted that both the 200 MeV and 250 MeV electron beams perform slightly better than the x-ray treatment in terms of dose uniformity, with all of them delivering the same PTV average and minimum dose. 3.2. Sparing of organs at risk (OAR) Fig. 3 shows the cDVH for four OARs, namely, the rectal wall, bladder, femoral heads and skin. Again, the normalization dose was chosen to be the prescribed dose of 72 Gy. In the case of the rectal wall, Fig. 3a), a reduction in the amount of volume receiving a given absorbed dose is observed as the electron beam energy is increased. For example, the percent volume receiving at least 80% of the prescribed dose decreases from 20% at 75 MeV down to 10% for the 250 MeV electron energy. The percentage volume receiving an absorbed dose below 40% of the prescribed dose is smaller for the x-ray treatment than for the VHEET treatment, but at doses above this level the difference becomes much less pronounced. For the bladder, the difference between the x-ray and electron beams is negligible at doses above the 20% level. For the femoral heads and skin, Fig. 3c) and d), all treatment results in maximum dose values well below the tolerance values as established by Emami et al. (1991), since the TD5/5 (absorbed dose to the whole structure resulting in a 5% normal tissue complication probability at 5 years) is 52 Gy and 50 Gy for the femoral heads and skin respectively. For the femoral heads an interesting trend is

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Fig. 2. Minimum, average and maximum dose for a 9-ﬁeld electron beam treatment for (a) GTV and (b) PTV. Blank circles: maximum dose; blank squares: average dose; ﬁlled circles: minimum dose. Absorbed doses are normalized to the prescribed dose of 72 Gy.

observed: contrary to the other OARs, the percentage volume receiving a given absorbed dose is reduced as the beam energy decreases. For example, 30% of the irradiated volume receives at least the 20% absorbed dose level for the 250 MeV beam, decreasing to almost 0% at an electron beam energy of 75 MeV. It is important to point out that, according to this ﬁgure, all electron beams result in a reduction in the imparted energy to the femoral heads relative to the x-ray treatment. This could be explained by noting that in bone the collisional stopping power, directly proportional to the absorbed dose, represents 80% to 99% of the total stopping power in the electron energy range of 1–15 MeV, while in the energy range of 70–250 MeV, the VHEET range, it only accounts for 20% to 50% of the total stopping power, the remaining being accounted for by radiative losses. Therefore, the fraction of energy locally available is larger at lower electron energies and therefore the absorbed dose imparted to bone decreases for the very high energies employed in this work. 3.3. Integral dose as a function of beam energy and number of treatment ports Fig. 4 shows the NTID for the three different treatments modeled in this work, namely the 3, 5 and 9 beam techniques, plotted against the electron beam energy. The NTID of the 15 MV x-ray 3DCRT treatment was used for normalization purposes. As the treatment margins are the same in both the x-ray and electron beam treatments, it is clear from this ﬁgure that the latter more efﬁciently target the intended volume resulting in a non-negligible reduction in the total energy absorbed by the patient, particularly at energies above 150 MeV. For the case of x-ray beams the NTID is

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Fig. 3. cDVH for the organs at risk. Continuous line: 75 MeV; dashed line: 100 MeV, dashed-dotted line: 150 MeV; dotted line: 200 MeV, blank circles: 250 MeV; blank diamonds: 15XMeV.

Fig. 4. Integral dose as a function of the number of electron beams. The integral dose of the 15 MeV x-ray 3DCR treatment is used for normalization purposes. Blank circles: 9 beams; blank squares: 5 beams; ﬁlled circles: 3 electron beams.

independent of the treatment technique, i.e. number of beams in 3DCRT and/or the use of Intensity Modulated Radiation Therapy (IMRT) (D’Souza and Rosen, 2003), so it is reasonable to conclude

that the NTID calculated in this work for the 15 MV prostate treatment is representative of all the current external megavoltage x-ray prostate treatment techniques. Therefore, our results show that, in this regard, VHEET is superior to current x-ray radiotherapy techniques. The NTID is an important metric as it has been shown that it correlates with late cancer recurrence after a radiotherapy treatment (Hall and Wuu, 2003). With regards to the effect that the number of treatment ports has on the NTID, Fig. 4 shows that, unlike the case of x-ray radiotherapy, for electron beams there is an important reduction in the total energy absorbed by the irradiated subject as the number of treatment ports decreases, and that the amount of this reduction depends on the beam energy, being higher for higher electron energies. For example, for the 250 MeV energy reducing the number of beams from 9 to 5 decreases the integral dose by about 12%, and further reducing the number of beams to 3 results in turn in a reduction in the total energy absorbed of an additional 7%. This suggests that, at least for the treatment case examined in this work, a smaller number of beams does provide a dosimetric advantage over the use of multiple ports. This is important as this would likely simplify the technological requirements needed for the clinical implementation of this treatment modality, but it remains to be seen whether or not this reduction on the total energy absorbed by the patient while producing the same absorbed dose distributions

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Fig. 5. Dose statistics as a function of the beam energy for the case of electron treatments with 3 and 5 beams. The 15 MeV x-ray treatment is shown as a reference. The 100% dose level corresponds to the 72 Gy prescribed dose. Blank circles: maximum dose; blank squares: average dose; ﬁlled circles: minimum dose.

as a conventional megavoltage x-ray treatment is enough to justify the adoption of high energy electron radiotherapy.

VHEET, this is only possible if the treatment machine is capable of delivering such electron beams with energies in the order of 200 MeV or higher.

3.4. GTV and PTV coverage versus number of beams 3.5. OAR sparing versus number of treatment ports Fig. 5 shows plots of GTV and PTV dose uniformity for the case of electron beam treatments with 3 and 5 beams. The GTV dose uniformity, Fig. 5a) and c), remains invariant against the number of beams, again being better as the beam energy is increased, with 150 MeV being the minimum energy for which acceptable uniformity is achieved. The PTV coverage, however, does get worse as both the number of beams and the electron energy are decreased. For example, for the 100 MeV electron treatment, the minimum PTV dose is 72% of the prescribed dose for the 5-beam treatment compared to only 64% for the 3 beam treatment. At energies at or above 200 MeV the change is negligible. This shows that while it is possible to drastically reduce the number of treatment beams in

In deciding on a suitable treatment scheme, GTV and PTV absorbed dose distributions are not the only parameters to be taken into consideration. OARs are often the limiting factor so it is important to evaluate the resultant absorbed dose distributions in order to determine what treatment strategies are worth pursuing. Both the skin and femoral maximum doses are well below the TD5/5 values, given above, regardless of the number of beams and beam energy; for the femoral heads the maximum observed dose was 24.2 Gy for the 9-beam 250 MeV treatment, while for the skin it was 29.2 Gy for the 3-beam 250 MeV treatment. We could then conclude that neither of these structures are an issue in selecting

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the treatment technique for VHEET of deep-seated targets. We will therefore focus the following analysis on the rectal wall and bladder absorbed dose distributions. In order to gain insight into how the geometric beam arrangement inﬂuences the sparing of the OARs, Fig. 6 shows isodose distributions on the transverse plane through the isocenter, located at the geometric center of the prostate, for the 150 MeV electron treatment as a function of the number of beams used, namely 3, 5, and 9 beams; the 6-ﬁeld 15 MV photon treatment is included in this ﬁgure as a reference. In planning for the 3 and 5 beams care was taken not to include beams that directly traverse through the rectal wall on their way to the target. Fig. 7 shows the maximum and average absorbed doses for these two structures, as a function of the beam energy, again for the 9, 5 and 3-beam treatments. From Fig. 7a) we can see that the maximum rectal wall is independent of the number of beams for energies at or above 150 MeV and that it increases as the number of beam is reduced for energies below 150 MeV. Below this energy, the treatment with 3 electron beams exhibits unacceptable hot spots, larger than 15%, in the rectal wall. The average rectal wall dose on the other hand, Fig. 7b), is shown to decrease with beam energy as the number of treatment ports

increases from 3 to 9 beams. As a reference, the maximum rectal wall for the standard 15 MV x-ray 3DCR treatment is 107% of the prescribed dose while the average dose is 30%, roughly the same as that obtained with VHEET using energies above 150 MeV and at least 5 beams. As for the bladder, Fig. 7c) and d), there are no hot spots regardless of beam energy and number of treatment ports, while the average dose is shown to increase, by 5 percentage points at most, as the number of beams is reduced. Again, the percentages shown in Fig. 6d) are in line with what was obtained with x-ray 3DCRT, a maximum bladder dose of 99% and an average dose of 23% of the prescribed dose of 72 Gy. Considering also the results for GTV and PTV coverage above, indicates that as few as 3 treatment electron beams with an energy of at least 150 MeV are enough to obtain the same absorbed dose distributions as those of the more established and proven x-ray treatment technique.

4. Conclusions In this work, using a realistic patient model and full Monte Carlo simulation, a prostate radiotherapy treatment using high energy

Fig. 6. Isodose distributions superimposed on the segmented Zubal phantom for the 150 MeV electron treatment for (a) 3 beams; (b) 5 beams; (c) 9 beams; the 6-ﬁeld 15 MV photon treatment is shown as a reference in panel (d).

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Fig. 7. Maximum and average absorbed dose statistics as a function of beam energy for the OARs. The 100% dose level corresponds to the 72 Gy prescribed dose. Blank circles: 9 beams; blank squares: 5 beams; ﬁlled circles: 3 beams.

electron beams was modeled. We have determined that for this treatment site, a challenging one due to the depth at which the target is located coupled to the fact that OARs overlap such a target, as few as three treatment ports with an energy of at least 150 MeV are sufﬁcient to produce absorbed doe distributions that are basically the same as those obtained with 15 MV x-ray 3DCR treatments, with the additional advantage of reducing in up to 25% the integral dose in the irradiated subject. We have also shown that neither the skin nor femoral heads receive doses above those imparted with the x-ray treatment regardless of the electron beam energy, provided that at least 3 treatment ports are used, and that therefore they are not a limiting factor in the clinical implementation of this treatment modality.

Acknowledgments This work was funded by the National Council for Science and Technology (CONACyT, México) through contract number CONACyT/SSA/IMSS/ISSSTE 201499.

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