A new variable was proposed based on which normal tissue sparing was quantitatively evaluated, comparing different prescription IDLs in SRS.

Purpose Half‐beam block is a field matching technique frequently used in radiotherapy. With no setup error, a well calibrated linac, and no internal organ motion, two photon fields can be matched seamlessly dosimetry‐wise with their central axes passing the match line. However, in actual clinical situations, internal organ motion is often inevitable. This study was conducted to investigate its influence on radiation dose to patient internal points directly under the matching line. Methods A clinical setting is modeled as two half‐space (x<0 and x<0) radiation fields that are turned on sequentially with a time gap of integer times of the patient internal organ motion period (T0). Our point of interest moves with patient internal organs periodically and evenly in and out of the radiation fields, resulting in an average location at x=0. When the fields are delivered without any motion management, the initial phase of the point's movement is unknown. Statistical methods are used to compute the expected value () and variance (σ) of the point dose given the uncertainty. Results Analytical solutions are obtained for and s of dose received by a point directly under the match line. is proportional to the total beam‐on time (T1), and σ demonstrates previously unknown periodic behavior. /

Purpose: To evaluate the target positional differences between 3D/4D planning CTs (pCTs) and daily CBCTs, and assess ITV coverage of daily GTVs, for lung SBRT patients with misaligned tumor positions between the 3D and 4D pCTs. Methods: Simulation 3D and 4D pCTs, both under free breathing, were acquired on a Sensation Open (Siemens) with RPM (Varian). ITV_All is the union of the GTVs delineated on the 3D pCT (GTV_3D) and on all phases of the 4D pCT (ITV_4D). While for most patients GTV_3D is included in ITV_4D, for some patients GTV_3D shows a substantial misalignment in the axial plane from ITV_4D with spine‐based rigid registration. Under IRB approval, pCTs of 51 patients were retrospectively reviewed to assess the frequency of such misalignments. For one patient with daily kV CBCTs available, all planning and treatment CTs were rigidly registered. GTV_3D, ITV_4D, GTV_F1 through GTV_F5 (on daily CBCTs of Fractions 1–5) were delineated. ITV_All and ITV_5mm (5mm uniform expansion of GTV_3D) were generated. Volumes and centers‐of‐mass (COMs) of all structures were analyzed. The inclusion relations (percentage of Structure‐A included in Structure‐B) were studied between GTV_F1 to GTV_F5 (Structure‐As) and GTV_3D, ITV_4D, ITV_All, ITV_5mm (Structure‐Bs). Results: Three patients showed substantial target misalignments between the 3D and 4D pCTs. For the analyzed patient, daily GTV positions agreed better with GTV_3D than with ITV_4D, with a median (range) COM vector difference of 2.45mm (1.00–4.58) and 16.06mm (15.39–17.44), respectively. The average inclusion of daily GTVs was 99.47% and 69.53% in ITV_5mm and ITV_All, respectively; although ITV_5mm was ∼35% larger than ITV_All for the ∼2cc tumor (GTV_3D). Conclusion: Substantial lung tumor misalignments were observed between 3D and 4D pCTs for some patients. For one such patient, daily tumor positions agreed better with the 3D pCT. Using spinebased localization for SBRT, ITV_All may provide insufficient internal margin.

Purpose: To examine the effectiveness of the coefficient of variation, skewness (third central moment), and kurtosis (fourth central moment) in quantifying and characterizing the target dose distribution in brain stereotactic radiosurgery (SRS) cases. Methods: Twenty‐one brain lesions in eighteen SRS patients treated using non‐coplanar dynamic conformal arcs were randomly selected. Setup errors of these patients were extracted from clinical ExacTrac data. Retrospective plans were generated based on the ExacTrac data to simulate the effects of patient positioning errors. The coefficient of variation, skewness, and kurtosis were used to analyze the dose distribution of the planning target volume (PTV). These variables were computed from the dose‐volume histogram of the PTV. For each patient, the ratios of the variables were calculated between treatment plans with and without setup errors. Results: The magnitude of patient setup errors ranged from 0.28 mm to 2.78 mm, with an average of 1.35 ±0.67 mm. The average ratio of coefficient of variation was 1.63 ±1.25, the ratio of the skewness was 1.40 ±0.41, and the ratio of the kurtosis was 1.26 ±0.33. These ratios were in accordance with the fact that when setup errors existed, the PTV dose distribution generally became broader, more asymmetric, and less uniform. The values of the skewness were negative, reflecting that upon setup errors part of the PTV fell into regions of lower doses. Anova analysis showed significant differences between the coefficient of variation (p=0.037), the skewness (p=0.02), and the kurtosis (p=0.01) with and without patient setup errors. Conclusion: The coefficient of variation, skewness, and kurtosis were introduced to PTV dose distribution analysis. It was found that those variables were good measures of the characteristics of the PTV dose distribution. They may be useful parameters in the evaluation of treatment plan quality.

Purpose: To study the effect of limited angular resolution of pencil beam calculation (PBC) on dynamic conformal arc plan (DCAP) in iPlan (BrainLab) using the ArcCHECK sytem and 3DVH software (Sun Nuclear Corporation). Methods: Four DCAPs were generated in iPlan RT Dose 4.5 treatment planning system on the ArcCHECK cylindrical phantom with central planning target volume (PTV). A cylindrical shell structure (SHELL) 2.85cm from phantom surface and 1.5 mm thickness was created to simulate the ArcCHECK diode array. Planned doses were calculated using both Monte Carlo calculation (MCC) and PBC algorithms, and exported to 3DVH software for global and target based comparisons using the 3Dgamma index. Four additional DCAPs were created and calculated on patient CT images and mapped onto the ArcCHECK phantom for measurement using a Varian TrueBeam STx. The measurements were compared against both MC and PB calculation using gamma index analysis. Results: For the ArcCHECK phantom, the dose distribution agreement quantified with 3D‐gamma index is better (average‐gamma (<γ>)=99.9%vs.79.1% and 96.8%vs45.7%, p=0.0294, 0.0286 for gamma (2mm,2%) and (1mm,1%) criteria respectively using Mann‐Whitney U test) in the PTV than in the SHELL. The measurements show better agreement with MCC than the PB (<γ>=100%vs.86.7%, 99.6%vs.72.3%, 85.5%vs.50.8%, p=0.021, 0.026, 0.029 for gamma (3mm,3%), (2mm,2%) and (1mm,1%) criteria using Mann‐Whitney U test respectively). The effect due to limited (10 degree) angular resolution of the PBC was observed, and it can be one of the possible reasons for poor agreement between measurement and PB calculation. Conclusion: The PBC of iPlan shows poor peripheral dose calculation accuracy for dynamic conformal arc plans due to limited angular resolution, but it performs well in the area close to target volume without considering heterogeneity. Since the user cannot change the 10 degree angular resolution of PBC, MCC is more appropriate for dynamic conformal arc plans.

Purpose: Randomness in patient internal organ motion phase at the beginning of non‐gated radiotherapy delivery may introduce uncertainty to dose received by the patient. Concerns of this dose deviation from the planned one has motivated many researchers to study this phenomenon although unified theoretical framework for computing it is still missing. This study was conducted to develop such framework for analyzing the effect. Methods: Two reasonable assumptions were made: a) patient internal organ motion is stationary and periodic; b) no special arrangement is made to start a non ‐gated radiotherapy delivery at any specific phase of patient internal organ motion. A statistical ensemble was formed consisting of patient's non‐gated radiotherapy deliveries at all equally possible initial organ motion phases. To characterize the patient received dose, statistical ensemble average method is employed to derive formulae for two variables: expected value and variance of dose received by a patient internal point from a non‐gated radiotherapy delivery. Fourier Series was utilized to facilitate our analysis. Results: According to our formulae, the two variables can be computed from non‐gated radiotherapy generated dose rate time sequences at the point's corresponding locations on fixed phase 3D CT images sampled evenly in time over one patient internal organ motion period. The expected value of point dose is simply the average of the doses to the point's corresponding locations on the fixed phase CT images. The variance can be determined by time integration in terms of Fourier Series coefficients of the dose rate time sequences on the same fixed phase 3D CT images. Conclusion: Given a non‐gated radiotherapy delivery plan and patient's 4D CT study, our novel approach can predict the expected value and variance of patient radiation dose. We expect it to play a significant role in determining both quality and robustness of patient non‐gated radiotherapy plan.

Purpose: To evaluate dose fall‐off in normal tissue for lung stereotactic body radiation therapy (SBRT) cases planned with different prescription isodose levels (IDLs), by calculating the dose dropping speed (DDS) in normal tissue on plans computed with both Pencil Beam (PB) and Monte‐Carlo (MC) algorithms. Methods: The DDS was calculated on 32 plans for 8 lung SBRT patients. For each patient, 4 dynamic conformal arc plans were individually optimized for prescription isodose levels (IDL) ranging from 60% to 90% of the maximum dose with 10% increments to conformally cover the PTV. Eighty non‐overlapping rind structures each of 1mm thickness were created layer by layer from each PTV surface. The average dose in each rind was calculated and fitted with a double exponential function (DEF) of the distance from the PTV surface, which models the steep‐ and moderate‐slope portions of the average dose curve in normal tissue. The parameter characterizing the steep portion of the average dose curve in the DEF quantifies the DDS in the immediate normal tissue receiving high dose. Provided that the prescription dose covers the whole PTV, a greater DDS indicates better normal tissue sparing. The DDS were compared among plans with different prescription IDLs, for plans computed with both PB and MC algorithms. Results: For all patients, the DDS was found to be the lowest for 90% prescription IDL and reached a highest plateau region for 60% or 70% prescription. The trend was the same for both PB and MC plans. Conclusion: Among the range of prescription IDLs accepted by lung SBRT RTOG protocols, prescriptions to 60% and 70% IDLs were found to provide best normal tissue sparing.

Purpose: To study gain calibration variation over time for an MV flat‐panel‐detector (FPD). Methods: Gain calibration images (1024×1024 pixels) of a FPD (PerkinElmer AN‐9 on a Siemens ARTISTE) acquired in 40 consecutive months were studied. Using Python programming language, the images were processed to analyze the central 900×900 pixels with a threshold applied to exclude dead pixels. Month1 was set as the base image, then the difference images between it and the following months were calculated. The pixel intensity mean and standard deviation of the difference images were used to study the gain variation over time. Two other months’ images were also randomly selected as the base image and the above analyses were repeated. Finally, to investigate the equivalence of monthly calibration and quarterly calibration, the results from comparing neighboring months’ images, such as (month2‐month1), (month3 ‐month2) et al, were compared with those from comparing images taken in 3‐month intervals, such as (month4‐month1), (month7‐month4) et al, using Welch's t‐test. Results: For most months’ gain calibration images, the differences (mean and standard deviation) from base images were constant. In three months, the differences were relatively larger compared to other months but seemed instantaneous without any worsening trend. In those 3 months no clinical portal image quality degradation was observed. The difference between monthly and quarterly calibration tested by Welch's t‐test were insignificant for both means (p=0.9) and standard deviations (p=0.8). Conclusion: Long term stability of the FPD gain calibration images was observed. Therefore, the vendor‐recommended calibration frequency of 2–4 weeks is unnecessary. Less frequent, such as quarterly, calibration is sufficient.