Stereotactic lung radiotherapy (SLRT) is an effective treatment option for malignant pulmonary tumours that measure 6 cm or less [1, 2]. In SLRT a high dose of radiation is given with few treatment fractions and a high probability of tumour control can be achieved when compared to the conventional fractionation [3, 4]. Clinical outcomes of SLRT for peripheral primary lung tumours are comparable to surgery and this is one of the reasons that SLRT is rapidly increasing in the treatment of small lung tumours [5, 6]. The use of intensity-modulated radiotherapy (IMRT) and volumetric modulated arc treatments (VMAT) has been evaluated and proposed over 3D-CRT techniques for the delivery of SLRT [7–9]. However, with the increased complexity in beam shaping a large number of narrow field shapes are needed in the dose delivery. This situation becomes a clinical concern when the irradiated volume is located in lung tissue, where the secondary Compton electrons have a wider range. Dose rebuild-up and rebuild-down effects occur in the tumour periphery and the effects become steeper when the field size is decreased [10]. As a result underdosing effects take place at the lung-tumour interface potentially decreasing the minimum dose delivered to the tumour, which in turn can decrease the tumour control probability [11].

The inadequacy of the most common, type-a algorithms, such as pencil beam convolution (PBC) to calculate the dose accurately inside heterogeneous media is well documented [12, 13]. The type-b calculation algorithms, such as collapsed cone (CC) and anisotropic analytic algorithms (AAA) are able to approximate the electron transport in heterogeneous media more accurately than the PBC algorithm [14–16]. The dosimetric accuracy of these algorithms is, however, controversial and depends on field size, beam energy and density of lung investigated. Monte Carlo simulation is assumed to be the best representation of the real dose distribution. Recently new Monte Carlo codes have been developed, which allow the simulations of complex IMRT and VMAT delivery techniques [17]. Unfortunately, full Monte Carlo have not gained widespread clinical use yet since the simulations with high spatial resolution are laborious and time-consuming.

The accuracy of different dose calculation algorithms has been studied in the treatments of SLRT mainly with the conventional 3D-techniques with relatively large field sizes as compared to the effective field sizes used in intensity modulated techniques [12, 18, 19]. Numerous studies have also compared the calculated doses of type-a and type-b algorithms but unfortunately the measurements with IMRT dose delivery methods have been sparse [20, 21]. To our knowledge, dose accuracy of IMRT or RapidArc, a form of VMAT, in a heterogeneous phantom has been performed only once [22]. However, studies to investigate the effect of small MLC apertures of the IMRT or RapidArc to the surface doses of small tumours have not been conducted. The aim of this work was to evaluate the dosimetric accuracy of IMRT and RapidArc techniques in SLRT using heterogeneous phantoms. Another purpose of this study was to define the smallest sliding window aperture (SWA) that can be used in SLRT without compromising the peripheral doses of the treated lung tumours.

The effect of lung heterogeneities on tumour central and peripheral doses was studied with a Novalis Tx linear accelerator (Varian Medical Systems, Palo Alto, CA and BrainLAB, München, Germany) with a photon energy of 6 MV. Higher energies were neglected since the dosimetric advantages of lower photon energies have been well documented in SLRT [15, 23]. The Novalis Tx is equipped with a high-definition multileaf collimator (HD-MLC) with a total of 60 leaf pairs with central leaves of width 2.5 mm and the peripheral leaves 5 mm in the isocentre.

Phantoms

Two heterogeneous phantoms, made of polymethyl methacrylate (PMMA, ρ = 1.18 g/cm³), polycarbonate and cork, were designed for this study (Figure 1). Spherical polycarbonate inserts of Ø1.5 cm and Ø4.0 cm mimicked the lung tumours with an average density of 50 HU. Tumours were surrounded by cylindrical cork (average density of −550 HU) with a diameter of 14 cm. The phantoms were cut in half so that an EBT2 film (Gafchromic; ISP, Wayne, NJ) could be placed in the middle of the tumour (Figure 1B). The cylinders were designed so that they were reproducibly insertable to a cylindrical outer ring mimicking thoracic wall with a thickness of 3 cm constructed from PMMA. In addition to be able to accurately repeat the film positioning in the phantoms, two wooden pins were attached into the cork with fixed distances (Figure 1C). The films had the corresponding holes to fit these pins.

Two additional phantoms made of solid PMMA were constructed to execute measurements in homogeneous media with two ionization chambers (Farmer NE 2571 and PTW Micro chamber). The solid PMMA inserts had tailored cavities in the middle of the phantom to fit the chambers inside.

The use of IMRT and VMAT techniques is increasing in SLRT and thus the effective field sizes are smaller compared to conventional 3D-CRT. Data evaluating the dosimetric accuracy of modulated techniques applied in SLRT is sparse and possible underdosage of the central or peripheral parts of the tumour may compromise optimal tumour control [26]. The purpose of this study was to evaluate the actual doses of small lung tumours irradiated by intensity-modulated techniques to understand the risk for dose calculation errors in precision RT such as SLRT. The experimental set-up used in this study was chosen such way that the impact of aperture size on the surface doses of simulated tumours could be quantified.

Although our findings are not directly comparable to previous studies it is relevant to relate them to existing data. Sikora et al.[18] studied stereotactic lung IMRT dose distributions with radiographic film measurements, Monte Carlo simulations and PBC calculations with tumour sizes of 2.7, 4.2 and 5.0 cm in diameter. The measurements, however, were performed only for a conformal plan consisting of one vertical beam. The central doses were underestimated by PBC approximately by 5% and 6% with 6 MV with tumour sizes of 2.7 cm and 4.2 cm, respectively. In our study, on the contrary, PBC algorithm overestimated the central dose on average 5% for the smaller tumour studied and underestimated the central dose by 1% with the larger tumour. Dobler et al.[12] used a conventional treatment plan to irradiate a tumour insert of 2 cm diameter and 4 cm height with 6 MV photons. In their report PBC overestimated the dose up to 5.4% while CC algorithm underestimated the dose by 5.0%. In our study the difference between measured and AAA calculated dose with the 3D-CRT-treatment plan was less than 2%. In a study of Panettieri et al.[19] spherical tumours of 2 cm and 5 cm in diameter were studied with conventional treatment fields. Central doses of the tumours were calculated accurately with PBC and CC algorithms but in the target periphery the doses were overestimated up to 10%. In general, PBC tends to overestimate the target dose of small tumours surrounded by lung [27], which is apparent in the smaller tumour of our study (Figure 2). However, with the studied larger tumour (Ø4 cm) PBC algorithm calculated the dose in the central parts of the tumour accurately, but again the peripheral doses were overestimated.

AAA is a more advanced calculation algorithm than the PBC algorithm. Although, there are also limitations in the accuracy of AAA as the divergent scatter of heterogeneities from upper levels is not correctly taken into account and the use of a discrete number of angular sectors might cause smoothening out of the calculated dose distribution near heterogeneous interfaces [28]. With the studied heterogeneous phantoms AAA was able to predict the tumour dose accurately. The difference between the calculated and the measured doses was generally in the range of ±3% except for the very small SWAs and the small tumour, where the difference tended to increase as a function of decreasing SWA (see Figure 2). The main reason for this discrepancy is probably due to the rounded leaf end transmission (dosimetric leaf separation, DLS) and leaf transmission values, which were optimized for conventional treatment plans and for the junction areas of dynamically split IMRT fields. The beam hardening effect becomes also more pronounced by decreasing the SWA because more radiation is penetrating the MLC. Beam hardening effect cannot be modelled in the Eclipse beam configuration since it uses a constant-value model. The values of DLS and leaf transmission used in this study were 0.6 mm and 2.0%, respectively. Chang et al.[29] measured the DLS of the HD-MLC to be 0.84 mm for the energy of 6 MV with leaf leakage of 1.0%. From Figure 2 it is evident that very small target volumes are sensitive to the dosimetric settings of the HD-MLC. When the target volume gets larger (in this study Ø4.0 cm) the calculation errors decreases, although the percentage of dose coming from leaf transmission increases. Future studies of the discrepancies between the calculated and measured dose are required to minimize the dose calculation errors in small targets.

The typical values of individual leaf separations with dynamic IMRT treatments are usually between 5 and 15 mm depending on the beam modulation. The average leaf openings with the IMRT treatment plans studied were 12 and 15 mm for the small and large tumour, respectively. With the RA1 treatment plans the corresponding values were 7.9 and 23.7 mm and with the RA2 plans the related values were 7.0 and 13.6 mm. The PBC algorithm underestimated the dose in the centre of the Ø4.0 cm target with the studied IMRT treatment plan by 4% (Figure 2). The main reason for this is that the leaf transmission and DLS values were optimized for the treatment plans calculated with AAA. The optimal values for the PBC calculated treatment plans would be different since the PBC models only the primary photon source and not the scattered photons or electrons from the accelerator head.

The largest deviation of the central doses of the tumours with the IMRT and RapidArc treatment plans was observed with the RA2 treatment plan of the small tumour. AAA underestimated the central dose by 4%, while in the larger tumour the dose was overestimated by 1% (Figure 2). Fog et al.[30] observed the same effect in homogeneous phantom with a small target (0.4 cm³). In their study the measured doses delivered by RapidArc and HD-MLC were 20% greater than the calculated ones for the small PTV while for the larger PTV there was good agreement between calculated data and measurements. In our study, we also noticed that with greater beam intensity modulation (RA2) the measured dose distribution was less homogenous than the calculated one, which is visible in Figure 3.

The quantity of dose build-up in the vicinity of lung equivalent heterogeneities is proportional to the width of the MLC leaf pairs: the smaller the aperture, the bigger the build-up region at the lung-tumour interface. Indeed, we observed a more than a 2 mm decrease in isodose line width with SWAs of 2 mm and 4 mm to the direction of leaf travel and beam direction (Figure 5). The decrease in tumour peripheral doses was not modelled by the AAA or the PBC. The maximum difference of 4.2 mm in isodose line diameter with the nine field treatment plans was recorded with a SWA of 2 mm and with the Ø4.0 cm tumour, respectively. The highest deviations were recorded with the 85% and 90% isodose lines as can be seen in Figure 5. When the difference was converted to dose difference, the deviation in dose was on average 6%. Surprisingly the difference in isodose line width was smaller with the Ø1.5 cm tumour, which showed a maximum difference of 2.6 mm. With a SWA larger than 6 mm the maximum difference between isodose line radius of open and modulated treatment plan was decreased down to 1 mm. The main reason for the surface dose difference between the open and modulated fields is probably due to the increased rebuild-up and rebuild-down effects at the mimicked tumour and lung interfaces with the small apertures.

The dosimetric inaccuracy of a single EBT2 film measurement has been reported to be 3.8% in the dose range of 0–4 Gy [25]. We repeated the measurements three times to increase the overall accuracy of the used EBT2 dosimeter. The individual film measurements were presumed to be normally distributed and the SD of the film measurements was used to estimate the measurement inaccuracy, which was on average 1.6%.

Our study is impeded by few limitations. We neglected the movement of the tumour caused by breathing and the setup of the study is thus best comparable to treating patients with active breath hold techniques or having tumours with a very limited movement. Alternatively respiration-correlated 4D-CT can be used to visualize tumour motion and treatment plan optimization can be realised with average CT or maximum intensity projection (MIP) CT [31]. It has been shown that calculation algorithms overestimate the peripheral doses of moving tumours and the underdosing effect is not noticed in the central parts of the targets [19]. Accordingly, we can conclude that if the studied tumours were not stationary, the peripheral doses were likely to decrease even more than reported in this study.

The dose calculation accuracy in the patient geometry does not only depend on the used calculation algorithm but also on patient anatomy, used energy, and effective field size. This study was based on the assumption that the entire tumour is surrounded by lung. However, tumours might be situated close to the thoracic wall or even attached to it, which would result in a decrease of dose build-up effects.

Narrow field sizes produced by HD-MLC were studied to find the possible limitations of using small dynamic apertures in SLRT. The surface doses of the mimicked lung tumours decreased with decreasing the sliding window aperture. The largest deviation between measured and calculated isodose lines was 4.2 mm, which was recorded with a SWA of 2 mm and with the larger tumour size studied. With a larger than 6 mm SWA the difference in the isodose line radius between the open and modulated field was less than 1 mm. AAA was able to calculate the peripheral doses of the tumours accurately with an average error of 1.1 mm as the measured and calculated isodose lines of 80-95% were compared. The PBC algorithm failed to model the peripheral doses of the small lung tumours correctly and thus should be used with caution in the treatments of SLRT.