Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods D. Henzen, P. Manser, D. Frei, W. Volken, H. Neuenschwander, E. J. Born, K. Lössl, D. M. Aebersold, M. F. M. Stampanoni, and M. K. Fix Citation: Medical Physics 41, 031712 (2014); doi: 10.1118/1.4866227 View online: http://dx.doi.org/10.1118/1.4866227 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/41/3?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Delivery validation of an automated modulated electron radiotherapy plan Med. Phys. 41, 061715 (2014); 10.1118/1.4876297 Monte Carlo-based treatment planning system calculation engine for microbeam radiation therapy Med. Phys. 39, 2829 (2012); 10.1118/1.4705351 Radiotherapy with laser-plasma accelerators: Monte Carlo simulation of dose deposited by an experimental quasimonoenergetic electron beam Med. Phys. 33, 155 (2006); 10.1118/1.2140115 Evaluation of the first commercial Monte Carlo dose calculation engine for electron beam treatment planning Med. Phys. 31, 142 (2004); 10.1118/1.1633105 Monte Carlo evaluation of 6 MV intensity modulated radiotherapy plans for head and neck and lung treatments Med. Phys. 29, 2705 (2002); 10.1118/1.1517291

Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods D. Henzen,a) P. Manser, D. Frei, and W. Volken Division of Medical Radiation Physics and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Berne, Switzerland

H. Neuenschwander Clinic for Radiation-Oncology, Lindenhofspital Bern, CH-3012 Berne, Switzerland

E. J. Born, K. Lössl, and D. M. Aebersold Division of Medical Radiation Physics and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Berne, Switzerland

M. F. M. Stampanoni Institute for Biomedical Engineering, ETH Zürich and Paul Scherrer Institut, CH-5234 Villigen, Switzerland

M. K. Fix Division of Medical Radiation Physics and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Berne, Switzerland

(Received 26 September 2013; revised 5 February 2014; accepted for publication 7 February 2014; published 26 February 2014) Purpose: This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). Methods: As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the inhouse developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. Results: The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V95% increased from 90% to 96% and V107% decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. Conclusions: MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4866227] Key words: modulated electron radiotherapy, forward planning, Monte Carlo

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0094-2405/2014/41(3)/031712/10/$30.00

© 2014 Am. Assoc. Phys. Med.

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1. INTRODUCTION Due to the characteristics of an electron beam, in particular the high dose at the surface and the steep dose fall-off at larger depths,1 electron radiotherapy is well suited for superficially located lesions. However, as clinical routine electron beam treatment usually still involves the manual handling of heavy applicators and the production of individualized irregular cutouts, electron radiotherapy can be a rather time consuming and cumbersome treatment option. This limitation becomes even more emphasized if a distal modulation of the electron beam is considered, which could improve the conformality of the dose distribution and thus reduce dose to healthy tissue. One approach for such a modulation is the use of a customized, patient-specific bolus. The technique of manufacturing an individualized bolus has been commercialized as the product BolusECT (.decimal, Sanford, FL), based on the work of Low et al.2, 3 An alternative method to modulate the distal shape of the electron dose distributions is the use of many, possibly irregular fields with different electron beam energies. As the collimation of these fields using patient specific, individually manufactured cut-outs is not efficiently realizable, the feasibility of modulated electron radiotherapy (MERT) employing multi or few leaf collimators and corresponding treatment planning strategies were investigated during the last years by various research groups: AlYahya et al.4 used a few leaf electron collimator (FLEC) as an add-on device on their linear accelerators to shape irregular electron fields. The FLEC forms an irregular field shape by a superposition of rectangular fields. The dedicated electron MLC (eMLC) is another add-on device of which prototypes and even commercially available devices were built and investigated by Lee et al.,5 Hogstrom et al.,6 Olofsson et al.,7 Gauer et al.,8 and Vatanen et al.9 A third possibility to collimate irregular electron fields involves the use of the photon MLC (pMLC) that is already available on most linear accelerators for photon beam treatments. While du Plessis et al.10 and Salguero et al.11 investigated electron fields collimated by the pMLC of a Siemens (Siemens Medical Systems, Erlangen) accelerator, Klein et al.12 used the Millennium 120 pMLC of a Varian (Varian Medical Systems, Palo Alto, CA) accelerator. Different treatment planning procedures and different treatment sites were investigated by the above-mentioned groups: For three different breast cancer patients Ma et al.13 created MERT plans using an inverse planning strategy. Using forward planning, Klein et al.14 generated treatment plans for a chest wall and a scalp treatment. This forward planning technique was further elaborated by Surucu et al.,15 who also investigated mixed photon and electron beam treatment plans for four chest wall cases. Using an inverse treatment planning strategy Olofsson et al.7 created plans for postoperative breast cases. Gauer et al.16 published a study about inversely planned MERT for breast and chest wall tumors. Head and neck cases as well as chest wall cases were planned using an inverse planning strategy by Salguero.17 A further improvement of this inverse planning strategy was the implementation of mixed electron and photon beams by Palma et al.18 to treat Medical Physics, Vol. 41, No. 3, March 2014

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breast cancer. Furthermore, Alexander et al.19, 20 developed an inverse planning technique and created plans for a spinal cord irradiation as well as for breast cases. In a recent publication they were using a mixed beam technique and investigated the treatment for a head and neck rhabdomyosarcoma case.21 With the exception of the methods employing inverse planned mixed beam techniques, all investigations resulted in a degraded dose homogeneity in the PTV when MERT treatment plans were compared with photon treatment plans. For pure MERT treatment plans, inverse planning generally leads to a more homogenous dose in the PTV than forward planning for similar tumor sites. On the other hand, the reduction of dose to distal OARs is similar for both planning techniques. Thus, a forward planning process applying methods to improve the dose homogeneity in the PTV would represent a rather intuitive way to yield state of the art MERT results. Therefore, in this work the MERT forward planning strategy proposed by Surucu et al.15 is extended by implementing a feathering process and an automated weight optimization algorithm to reduce dose inhomogeneities in the PTV. For the forward planning process neither time consuming MC calculations prior to the optimization nor long computation times during the optimization are necessary. However, even if the forward planning process requires fewer MC calculations, the efficiency of the MC calculations will highly influence the efficiency of the forward planning process. As currently no commercially available treatment planning system (TPS) incorporates the possibility to calculate electron fields shaped by a pMLC, a MC based beam model22 was developed that accurately reconstructs the pMLC collimated electron beam. However, in order to apply the forward planning process on a large scale, the MC part of this beam model had to be made more efficient by substantially improving the transport of electrons through the pMLC, which is the main factor regarding the computation time of the beam model. Together with a macro Monte Carlo23–25 (MMC) code for the dose calculations this beam model allows an efficient implementation of our forward-planning approach to MERT. The forward planning strategy for MERT treatments developed in this work was evaluated for an academic situation and two different clinical situations. All plans were created for a Varian linear accelerator equipped with a Millennium 120 pMLC for an SSD of 70 cm.

2. MATERIALS AND METHODS The previously developed beam model22 as well as the MMC (Refs. 23–25) dose calculation code are available in the Swiss Monte Carlo Plan (SMCP).26 This framework allows including features of the Eclipse TPS (Varian Medical Systems, Palo Alto, CA) in the forward planning process shown in Fig. 1. For this work, all MC calculations were carried out using the electron beam model22 with a modified pMLC transport (see Sec. 2.D) and the MMC (Refs. 23–25) dose calculation algorithm.

Henzen et al.: Forward planning MERT

Initial beam set up

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The initial electron beams are set up such that the projection of the PTV in the beams eye view is fully encompassed by the beams, and the maximal PTV depth in direction of the electron beams is within the therapeutic range of the highest available electron beam energy. If a field smaller than 15 × 35 cm2 is sufficient to cover the PTV, the user may restrict the area for the upcoming segmentation process.

Import CT into Eclipse

Set electron beam

In a first step the distal extension of the target projection in beams eye view is determined similar to the method proposed by Low et al.2 The initial electron beams or the restricted area (Sec. 2.A), where the segmentation process is initiated, are divided into a pixel grid. The resolution of this grid is defined by the user (Fig. 2). For the cases considered in this work a pixel size of 5 mm in the direction perpendicular to the leaves (corresponding to the width of the central leaves) and 5 mm in direction of leaf travel is used. Using ray tracing along lines originating from the virtual focus of the electron beam and intersecting the center of a pixel, the distal depths of the planning target volume (PTV) are determined for each pixel. To account for the dependence of the electron beam range on the density of the material, the distance the ray travels in a voxel is weighted with the density of that voxel. The lowest available electron energy is assigned to each pixel such that the weighted depth is still covered by the therapeutic range (depth of 95% isodose) of the electron beam for a pMLC shaped 5 × 5 cm2 field. The user is free to change

Scan PTV depth

Assign energies

Create segments

Look up values

Create feathered segments

Dose calculation

Weight optimization

Load dose into Eclipse

Adjust segments

Calculation, optimization, evaluation

Feathering

Segmentation

2.B. Segmentation

F IG . 1. Flow chart illustrating the different steps of the forward planning strategy starting with the beam set up in Eclipse until the evaluation of the dose distribution in Eclipse. The steps in between are performed externally.

2.A. Initial electron beam

The planning process of the proposed forward planning strategy starts with the import of CT data into Eclipse. After contouring the relevant structures on the CT data set and prescribing the dose, an initial electron beam is manually set, defined by gantry angle, collimator rotation and if possible an SSD of 70 cm on the beam axis in order to minimize the inair scattering of the electrons.12 If an SSD of 70 cm cannot be achieved, the shortest SSD possible is used. The secondary collimator jaw positions are set to 15 × 35 cm2 (in the isocenter plane), which is a constraint of the beam model. This jaw setting guarantees that the motion of pMLC leaves is never restricted because of the mechanical limitations of the device. For fields larger than 15 × 35 cm2 adjacent beams with the same gantry angle are used and in this case more than one field is initially defined in Eclipse. Medical Physics, Vol. 41, No. 3, March 2014

F IG . 2. Shown in the middle is the area where the segmentation process is carried out, formed by the pMLC and the projection of the PTV in beams eye view. For each pixel of the grid the depth of the distal boundary of the PTV is determined.

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this assignment in a postprocessing step to correct for the field size dependence of the therapeutic range. The initial beam is then divided into segments, which are defined as contiguous pixels with the same assigned electron beam energy. For an efficient delivery and for the upcoming optimization steps a large number of tiny segments, e.g., containing only one or a few pixels, should be avoided. The user is therefore given the possibility of changing the size of the segments.

2.C. Feathering

Due to the energy and depth dependence of the electron beam penumbra, abutting segments of different energies lead to a highly inhomogeneous dose distribution in the region of abutment. In order to achieve a better homogeneity of the dose distribution across segments, a feathering procedure is implemented. For an eMLC, Eley et al.27 proposed a discrete Gaussian edge feathering to overcome the above described issues with abutting segments for electron beams. For two abutting segments they subdivide the higher energy segment into five equally weighted individual segments. The borders of these segments, i.e., the final positions of the eMLC leaves for each of the five segments, are defined by so-called feathering positions. These positions are determined by matching the dose penumbras of abutting segments at 1 cm depth in a homogenous water phantom. The penumbras are calculated analytically using a pencil beam algorithm.28 In our work the procedure of the Gaussian edge feathering is adapted: the penumbras of the abutting pMLC shaped electron beam segments are calculated using MC methods to accurately model the particle transport through the pMLC and the water phantom. MC dose distributions of 5 × 5 cm2 electron segments with different energies are calculated in a water phantom. For each combination of energies of two abutting segments, the depth in the water phantom, where the largest dose inhomogeneities occur, is determined. At these depths the dose profiles in leaf travel direction are extracted and the corresponding penumbras are determined. For all energy combinations of abutting segments a match of the penumbras is performed using a deconvolution27 technique, and the resulting feathering positions are written into a look-up table. As shape and width of these pre-calculated penumbras are dependent on field-size and patient geometry (e.g., inhomogenities), the feathering positions in the look up table are used as initial positions only and can be adapted by the user for each specific case, either by modifying the look-up table or the leaf positions directly. The feathering process for the data presented in this work is carried out only in the direction of leaf travel. It should be noted that in the perpendicular direction only certain discrete feathering positions would be allowed due to the widths of the pMLC leaves. Providing the energy and shape of a segment together with its neighbors in leaf travel direction as input, an automatic feathering process is implemented, which creates the corresponding expanded or contracted segments using the values from the look up table. Medical Physics, Vol. 41, No. 3, March 2014

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2.D. Calculation, optimization, and evaluation

Following the creation of the expanded and contracted segments, the input files for the MC calculation are automatically generated and the calculations are launched. The statistical uncertainty (1 std. dev.) of the MC calculations is determined using a history by history method.29 For all calculations presented here the mean statistical uncertainty of the dose distribution is below 2% (Refs. 30 and 31) and is calculated by considering voxels with a dose deposition larger than 50% of the dose maximum. For an efficient treatment planning, our in-house pMLC transport code PIN was modified by means of implementing an extended range rejection and a particle recycling method. The range rejection method discards an electron in the pMLC if the distance to exit the pMLC is larger than the electron range. This method has been extended in the following way: a border, which corresponds to an enlarged (+5 mm) pMLC opening is defined. All particles that impinge on the pMLC outside this border are rejected. Furthermore, all particles, which reach a plane directly below the MLC are recycled29, 32 25 times before being passed to the dose calculation algorithm. After the dose calculation, the weights of the dose distributions for the different segments are optimized by a simulated annealing algorithm33 in order to improve the dose homogeneity in the target volume. In each step of the weight optimization, the optimizer randomly selects a segment and varies the weight of its dose distribution by a random factor, which is sampled from a Gaussian distribution defined by a standard deviation σ [see Eq. (1)] and mean value (=1). The width of the Gaussian distribution decays according to σ = 1 + (σ0 − 1) ∗ e− log(nac +1)/T0 , σ

(1)

where σ 0 is the initial width, nac the number of accepted changes, and T0σ the cooling rate for the step size. At each step, a cost function, defined as the variance of the dose values in the target volume, is evaluated. The new weight is accepted if the cost function value decreases. The simulated annealing algorithm allows the acceptance of a weight change even for an increasing cost function value with a passing probability P, which is defined according to the standard Boltzman simulated annealing cooling schedule:34 P = 2 ∗ P0 ∗

1 1+

P elog(nac +1)/T0

,

where P0 is the initial passing probability and T0P is the cooling rate for the passing probability. The convergence of the optimization algorithm depends on the selection of the abovementioned parameters. There is a trade-off between a fast convergence and the possibility to overcome local minima of the cost function. Performing test cases lead to the following valp ues: σ0 = 5%, P0 = 5%, Tσ0 = 2, and T0 = 2. Bogner et al.35 used the following stopping criteria for a simulated annealing driven algorithm: 2 ∗ |cfn − cfn−1 | < |cfn + cfn−1 | ∗ 10−X and σ < threshold,

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where cfn represents the cost function value at an iteration step n and X is the digit up to which cf remains unchanged. In this work X is set to 4 and a threshold of 0.75% is used. Analogous to the work of Bogner et al.35 both criteria have to be fulfilled for at least five consecutive iterations. Finally, the dose distributions for all optimized segments are loaded back into Eclipse, which provides the tools to display dose distributions and calculate dose volume histograms (DVHs). The evaluation process verifies that the dose constraints for the PTV of 95% minimal dose and 107% maximal dose with reference to the prescribed dose are fulfilled. In addition, the DVH tools in Eclipse allow a quick comparison of dose distributions with respect to all contoured structures (PTV, OARs). If the evaluation of the dose distribution does not lead to satisfying results, treatment planning is repeated using modified parameters in order to achieve a better result. For example, beam angles, segment sizes, and feathering positions can be adjusted. Thus, the forward treatment planning is an iterative process driven by experience. 2.E. Academic situation

For testing purposes of the forward treatment planning strategy, an academic situation and two clinical situations are planned and evaluated with MERT. The academic situation consists of a 40 × 40 × 32 cm3 water phantom with a PTV and a distal OAR (Fig. 3) where different electron beam energies are expected to be necessary to adequately cover the PTV while simultaneously sparing the OAR. Two different voxel sizes are investigated: 0.2 × 0.2 × 0.1 cm3 and 0.1 × 0.2 × 0.1 cm3 . The smaller voxel size is used in order to determine whether the feathered dose distribution is sensitive to the dose grid resolution. The dimensions of the PTV and OAR structures are shown in Fig. 3. Both structures have an extent of 8 cm in the direction perpendicular to the shown plane. To evaluate the dif-

1 cm 6.4 cm 3.8 cm

F IG . 3. Geometry of the academic situation, which consists of a water phantom containing a PTV and an elliptical OAR. The thick line on the top corresponds to the surface of the phantom. Medical Physics, Vol. 41, No. 3, March 2014

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ferences between the dose distributions of electron plans with and without energy modulation and to investigate the impact of the feathering procedure on the dose distribution, three different treatment plans are investigated: The first plan uses a single 20 MeV segment representing the current status of electron treatments, the second treatment plan is a forward MERT plan consisting of three adjacent segments with electron energies of 20, 12, and 9 MeV without feathering and the third treatment plan corresponds to the second one but including feathering. For the feathered MERT treatment plan, segment sizes are optimized in order to get a more homogenous dose distribution in the PTV. The three dose distributions are compared with regard to the above-mentioned aspects. 2.F. Clinical situations

MERT plans are also created for two different clinical situations. They are compared to standard plans using photon beams and BolusECT treatment plans. The standard treatment plans are 3D-CRT plans without any inverse optimization. These plans are calculated in Eclipse using the analytical anisotropic algorithm (AAA) algorithm (Varian Medical Systems, Palo Alto, CA) for photon beams and the electron Monte Carlo algorithm (eMC) (Varian Medical Systems, Palo Alto, CA) for electron beams. The treatment planning procedure for the BolusECT plans requires the use of the p.d – software (.decimal, Sanford, FL). This program allows the creation of a bolus and the optimization of its shape, such that the resulting dose distribution covers the target as conformal as possible. At the end of that process, the bolus is exported as part of the patient’s structure set and loaded back into Eclipse, where the treatment plan including the bolus is calculated using eMC. Figure 4 shows single CT slices of both clinical cases including the contoured structures. For the first patient, a breast boost treatment, the dose of 16 Gy was delivered using a standard plan with a 12 MeV electron beam and two tangential wedged 15 MV photon beams. The corresponding MERT plan consists of a single initial electron beam. The forward planning process led to a total of 7 feathered segments using electron beam energies of 9, 12, and 16 MeV. The BolusECT treatment plan for this case employs a 15 MeV electron beam. For the second clinical case the standard treatment plan consists of two tangential wedged 6 MV photon beams treated to a total dose of 50 Gy. For the MERT plan two initial electron beams are needed to cover the tumor. The forward planning process divided these beams into a total of 7 feathered segments using 6 and 9 MeV. A 9 MeV electron beam is used for the BolusECT treatment plan. Because of the tangential field setup in the standard plan, the margin between the CTV and the PTV in direction of the lung was extended to cover the effects of respiratory motion. On the other hand, the MERT plan consists of electron segments that impinge approximately in the direction of the chest movement. Hence, the respiratory motion has to be considered differently for the MERT plans compared to the standard photon plan. To account for this, Gauer et al.16 introduced a second PTV with reduced margins in the direction of the lung, while Ma et al.13 optimized their

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F IG . 6. DVH comparison for the different plans generated for the academic case. The single segment plan DVHs are represented by the dashed-dotted line, the nonfeathered MERT plan DVHs by the dashed lines, and the feathered MERT plan by the full lines.

3.A. Academic situation

F IG . 4. CT slice of the two clinical situations in Eclipse. Contoured are the PTV for the breast boost case (top), the CTV for the whole breast case (bottom) and the lungs, which are taken into account as OARs.

MERT planning for the CTV instead of the PTV. In a similar way, in this work the MERT planning for the second clinical case is optimized for the CTV. For both patients a voxel size of 0.2 × 0.2 × 0.2 cm3 is used for the MERT and BolusECT dose calculations. The standard plans are calculated using a voxel size of 0.25 × 0.25 × 0.25 cm3 .

3. RESULTS For a meaningful comparison, the dose distributions for the plans are normalized such that the median dose of the PTV is equal to the prescribed dose36 and all percentage dose values are relative to the prescribed dose, which is set to 100%.

110%

80%

95%

30%

80%

30%

First, the dose distributions for the calculations using a voxel size of 0.2 × 0.2 × 0.1 cm3 are analyzed. In Fig. 5 isodose lines in one slice containing the PTV and the OAR are shown for the three different treatment plans. Only for the nonfeathered MERT plan dose values of more than 110% are present in the PTV. The 80% isodose line encompasses the OAR for the single segment plan, whereas for the MERT plans only a very small volume receives more than 80% of the prescribed dose. The DVHs for all treatment plans are compared in Fig. 6. As expected, the dose in the OAR is reduced if MERT is used, e.g., D80% of the OAR drops from 93% for the single segment plan to 17% for the MERT plans. In order to assess the impact of the feathering procedure on the dose distribution, the dose homogeneity in the PTV is analyzed for the two MERT plans. Without feathering, a V95% value of 90% and a V107% value of 8% is reached. If feathering is applied, V95% rises to 96% and V107% decreases to 80%) area in the lung for the standard photon treatment plan. On the other hand, the 30% isodose line encompasses a smaller volume of the lung for the standard treatment plan compared to the MERT plan. The hot spots (>105%) are located inside the CTV for the MERT plan, whereas for the standard plan those regions are mostly located in normal tissue outside the CTV. In contrast to the standard plan, the 95% isodose line for the MERT plan does not fully encompass the CTV. The DVHs for both plans (Fig. 10) confirm these observations: The lung volume receiving more than 45% of the prescribed dose is reduced for the MERT plan, whereas the low-dose lung volume is larger than for the standard plan. Also, the MERT plan results in a degraded dose homogeneity for the CTV. Despite adjustments of the segment sizes, the feathering positions and the final weight optimization, the CTV homogeneity of the MERT plan could not be further improved without simultaneously increasing the dose to the OARs. The BolusECT plan results in a dose distribution nearly as homogeneous as for the standard photon plan. However, the low-dose lung volume is much larger than for the other plans. For the presented MERT treatment plans, the segments and feathering positions were changed iteratively to improve the quality of the plans. In this work a maximum of four

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iterations were used for the clinical cases. The dose calculation for the presented MERT plans, calculated to 2% statistical uncertainty, requires between 15 and 24 min on a single core Pentium 2.66 GHz system with 6 GB RAM. This computation time is highly dependent on the segment sizes and the electron beam energies, which leads to different calculation times for the cases considered. It is worth noting that without the modifications regarding the pMLC particle transport model, namely, the rejection and recycling methods, the time to reach a 2% statistical uncertainty is between 630 and 1000 min (depending on the case). For the weight optimization, the time to reach the termination criteria was approximately 1 min. In addition, the first iteration step (including initial setup, segmentation, and generation of the feathered segments) takes about 15 min. Furthermore, depending on the complexity of the iterative adjustments, an additional 5–10 min are necessary for each additional iteration step. 4. DISCUSSION AND CONCLUSIONS

F IG . 9. Screenshot of a CT slice in Eclipse for the whole breast case withisodose lines (105% full line, 95% dotted line, 80% dashedline, 30% dasheddotted line). (Top) Dose distribution of the standardplan (tangential wedged photon beams); (bottom) dose distribution of theMERT plan. The percentage values of the dose are relative to the prescribeddose of 100%.

F IG . 10. DVH comparison for the whole breast case. The full lines represent the DVHs for the MERT plan, the dashed lines represent the DVHs for the photon plan, and the connected dots correspond to the DVHs for the BolusECT plan. Medical Physics, Vol. 41, No. 3, March 2014

In this work an efficient and intuitive forward treatment planning process for MERT is developed using pMLC shaped electron beam segments and MC methods. This forward planning process is highly automated, but still allows the user to change the size and shape of the segments iteratively if needed and to restart the dose calculation for the updated segments. For the results presented here up to four iterations were used. The MERT planning process was evaluated for three different irradiation situations. First, a MERT plan for an academic situation was created (Fig. 3). The use of MERT leads to lower doses in the OAR and the feathering procedure is able to improve the dose homogeneity in the PTV. The reduction of the voxel size in leaf travel direction, i.e., using 0.1 × 0.2 × 0.1 cm3 instead of 0.2 × 0.2 × 0.1 cm3 voxels does not lead to changes exceeding 1% in PTV DVH values. The final results for the feathered MERT plan (Figs. 5 and 6) are in accordance with published data by Alexander et al.19 where an inverse treatment planning strategy was applied. For the clinical breast boost treatment, the MERT technique results in dose distributions of similar quality as the standard plan, which consists of an electron beam and two tangential 15 MV photon fields. However, with MERT there is no need to fabricate an individual cut-out and to mount the electron applicator during treatment. For the clinical whole breast treatment, the MERT plan reduces the high-dose volume in the lung, while the low-dose volume is increased compared to the standard plan. Also the dose homogeneity in the CTV is worse for the MERT treatment plan. These findings are in accordance with the results found by Ma et al.13 and Gauer et al.16 However, the possibility of using multiple beam angles, which is difficult to implement in the forward planning process, could help to further reduce the dose to the lungs. For both patients BolusECT plans result in a more homogenous target coverage at the cost of higher doses to the OARs compared to the MERT plans. However, the BolusECT technique requires out-sourced manufacturing including the delivery of the patient-specific bolus whereas the presented

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MERT technique promises an efficient treatment option using devices already available without any consumables. Generally, MERT treatment plans for the clinical situations considered in this work result in a less homogenous dose distribution to the target compared to the rather simple academic situation. There are several reasons that may explain this observation, e.g., inhomogeneities in the patient’s anatomy or oblique beam incidence on the curved patient surface. It is worth noting that the level of homogeneity achieved with the methods developed in this work is in agreement with published data using various approaches in inverse treatment planning. Another important aspect for treatment planning is the required computation time. In this work special efforts are undertaken to improve the efficiency of the treatment planning process. Employing the developed electron beam model with the modified pMLC transport code PIN leads to maximal calculation times of 100 min (four iterations) for the presented cases. Regarding a typical clinical environment with many computation nodes on which the dose calculations for multiple segments can be distributed, an efficient and intuitive alternative to a complex inverse treatment planning procedure is presented in this paper. The forward planning process presented here is independent of a special model of linear accelerator and MLC, as long as an efficient beam model is available that is able to correctly calculate dose distributions for MLC shaped electron beams. ACKNOWLEDGMENT This work was supported by Varian Medical Systems. a) Authors

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