The investigations of this study are based on real patient data: ten consecutive patients (age 67 ± 6 years, female 3, male 7) treated with SBRT for early stage non-small cell lung cancer or pulmonary metastases. Written informed consent was obtained from all patients.
For all ten patients a respiratory correlated 4D-CT study was acquired for treatment planning (Siemens Sensation Open; Siemens Medical Solutions, Erlangen, Germany). Details about 4D-CT image acquisition and image reconstruction have been described previously [24
]. The motion range of the pulmonary target was evaluated after reconstruction of CT series in peak-inhalation and peak-exhalation. The motion of the tumor in the predominant direction was chosen for one-dimensional (1D) simulations: this was the superior-inferior direction in all patients. A pressure sensor placed in an elastic belt around the patient's abdomen generated the external breathing signal (Anzai AZ-733V; Anzai Medical Solutions, Japan). The external breathing signal recorded during acquisition of the 4D-CT study was the basis for the calculation of the tumor PDF; the range of the PDF was equated with the maximum motion range of the tumor measured in the 4D-CT (Figure ).
Figure 1 Probability density functions of the pulmonary tumor for the 10 patients (exhalation and inhalation position have negative and positive numbers). The zero position is the geometrical centre of the PDF and the mean target position (PMean) is marked with (more ...)
The patient specific parameters are listed in table ; breathing motion was quantified by the range of the PDF (AMax), standard deviation (Eq. 1) of the PDF (σPDF) and the time-weighted mean target position (PMean). The standard deviation of the motion signal P was calculated using the position sample (Pi), the mean target position (PMean) and the number of elements in the sample (n).
Overview of patient data derived from 4D-CT imaging and the external breathing signal
A 1D convolution model was used to investigate the dosimetric influence of breathing induced tumor motion. The model was implemented in Matlab™ (The MathWorks, Inc., Natick, MA, USA) and allowed the variation of the following parameters: dose profile, field size, target size, motion range and shape of the PDF.
Dose profiles were generated by convolving an intensity profile with a pencil beam kernel while a homogeneous medium was assumed [26
]. The intensity profile was a square profile simulating an open field shape. To ensure the correctness of the computed dose profiles, a comparison with measured profiles in a water phantom was performed with the following parameters: field size 24 × 24 mm, depth 50 mm, machine Elekta Synergy S equipped with the BeamModulator with 4 mm leaf width (Elekta Oncology Systems, Crawley, UK) and photon energy 6 MV. The calculated and measured dose profiles were in good agreement with 0.07% mean error normalized to maximum value. The resolution of the simulated dose profiles was 0.1 mm.
Assuming no breathing motion, a minimum dose of 100% was prescribed to the edge of the static target in the time-weighted average position PMean
. The centre of the target in this time-weighted average position was the isocentre as suggested by Wolthaus et al. [27
]. According to the SBRT, different degrees of dose inhomogeneity in the target volume were simulated. The maximum dose in the tumor was varied between 102% and 150%. The dose inhomogeneity was achieved by variation of the field size only, no step-and-shoot segments for intensity modulation were used. Figure displays the prescription types P105, P125 and P150 while P105 corresponds to a plan with a minimum dose of 100% and a maximum dose of 105% within the target volume.
Illustration of three different dose prescriptions P105, P125 and P150. The minimum dose was set to 100% at the edges of the target with maximum doses of 105%, 125% and 150%.
The time accumulated dose profile Dacc was calculated by convolving the static reference dose profile D0(x) with the variation kernel PDF(x).
This resulted in a blurring of the dose gradient and consequently reduced the accumulated dose to the target volume (Figure ). For quantification of the motion effect, the dose to the static target was compared with the dose after motion simulation. The minimum dose to the target (DMin) was considered as the treatment dose. Then, field sizes were symmetrically enlarged in steps of 0.1 mm until the dose reduction due to breathing motion was completely compensated (Figure ). The position of the dose profile was shifted and optimized until the tumor received equal doses to the edges. A margin was defined as the increase in field size in one direction; the total increase in field size is consequently twice the one-sided margin. This target volume concept for compensation of breathing motion was termed as "optimization of the surrounding isodose" (OSI concept). Additional blurring of the dose profile due to setup errors were not considered in this work.
Figure 3 Workflow of convolution simulation for patient #5 for prescription type P125 (the shaded area represents the target in the time weighted mean position 5.6 mm). (a) The dose to the target without (dashed line) and with consideration of motion (solid line). (more ...)
Additionally, the influence of motion on the dose to the region surrounding the tumor (organs-at-risk lung or liver) was investigated. This region corresponds to the pulmonary/hepatic tissue superior and inferior to the target in a 1D patient model, because target motion in superior-inferior direction was modelled. In real patient treatment, a significant dose is delivered to healthy tissue in the entrance and exit regions of the beam (axial direction) assuming a predominant coplanar beam set-up. This is not considered in a 1D model. Consequently, doses to the surrounding organ-at-risk were transformed into a 2D model in a sagittal plane: with a coplanar opposing field design, the dose distribution in superior-inferior direction was extrapolated in anterior-posterior direction. Doses in a 2D sagittal plane with extensions of 15 cm in superior-inferior and 12 cm anterior-posterior direction were calculated, respectively; the dose inside the target (equal tumor size in superior-inferior and anterior-posterior direction) was excluded for dose calculation to this organ-at-risk. As the mean lung dose was shown to be predictive for radiation induced pulmonary toxicity [28
], the mean dose in this region was calculated (DMean Surr
The simulation in this study was divided into four parts to analyse the influence of the parameters motion range, dose inhomogeneity and motion pattern, separately.
Range of breathing motion
The first part of the study systematically quantified the influence of the motion range on the dose to target. For a single breathing pattern (PDF#1) and a target size of 20 mm, the motion range AMax was varied ranging from 2 mm to 30 mm. These simulations were performed based on dose prescriptions P105, P125 and P150, which are most frequently used in pulmonary and hepatic SBRT. Margins necessary for compensation of the dose loss due to breathing motion were calculated.
The second part of the study systematically evaluated the influence of the breathing pattern. For one single target size of 20 mm and AMax of 15 mm the breathing pattern was varied with the ten clinically observed PDFs. The simulation was performed for P105, P125 and P150 and margins for motion compensation were calculated.
The third part of the study systematically evaluated the influence of the dose inhomogeneity in the target on margins necessary for compensation of breathing motion. Dose prescriptions from P102 to P150 were simulated. This was done exemplary for three different patients (#1, #5, #8) and the corresponding tumor PDF, AMax and tumor size. Simulations for P105, P125 and P150 were performed using all ten patient data (Table ). Additionally, the influence of dose inhomogeneity on DMean Surr, the mean dose to the tumor surrounding region, was evaluated.
ITV versus OSI target volume concept
The internal target volume (ITV) concept was evaluated as this is most commonly used in SBRT treatment: the ITV encompassed the target during the whole breathing cycle and the 100% dose was prescribed to cover the ITV. Results of the OSI and ITV concepts were compared with dose prescriptions of P105, P125 and P150.