Heterogeneous phantom geometries. Gray slabs correspond to water equivalent plastic, dotted slabs correspond to cortical bone equivalent plastic, and white areas correspond to air gaps. All thicknesses are geometric and given in centimeter. The diagonal lines indicate the section of the phantom that was irradiated by the 15×15 cm2 field.
An equivalent thickness map through the anthropomorphic phantom calculated at the level of the EPID detector. Note that the outline indicates the anatomical location of the irradiated area, which in this example is the thorax.
The MC calculated attenuation of the primary beam CP signal as a function of homogeneous water equivalent phantom thickness. In order to replicate the physical measurement setup, the virtual phantom material position was simulated such that the exit surface was 100 cm from the source and the MC scoring plane was at 135 cm from the source. The first HVL is 14.8 cm and the second is 16.1 cm.
The EPID measured attenuation along the beam’s CP as a function of homogeneous phantom thickness. This measurement includes broad beam scatter conditions as well as the detector dependent response, unlike the primary beam calculation of Fig. 3. The plots are normalized such that the measured signal at thickness = 0 cm is 100%. Only a limited set of the measured FS’s are shown for clarity. The hollowed points represent the measured data and are replicated in each plot. There is a best-fit exponential attenuation curve, (qt+r)e−μt, for each FS within a given HVL zone. These zones are highlighted in white in the plots above. In (a) the curves are optimized to match the data points within the first (0 ≤ t ≤ 15 cm) HVL. Similarly, in (b) and (c) the curves correspond to the data points within the second (15 < t ≤ 30 cm) and third (t > 30 cm) HVLs, respectively.
The q values from the (qt+r)e−μt fits, examples of which are shown in Fig. 4, plotted as a function of field size. The hollowed points represent the measured data. The dark solid lines represent the best-fit quadratic curves of the form q = α*(FS)2 + β*(FS) + γ. The light dotted lines represent the 95% confidence interval limits.
mPDIs acquired over the entire imager at 135 cm SDD behind (a) 1 cm, (b) 10 cm, and (c) 30.2 cm of water equivalent phantom material. The axes labels refer to distances scaled to the isocenter plane. Each image is normalized to a value of 1.0 at its own central pixel. It can be observed that as the thickness increases, the difference between the OAP and CP values increases with increasing distance from the CP. Cross-plane line profiles through the center of the imager are shown in (d) A limited set thicknesses are displayed for the purposes of clarity. Note that the grid pattern in the images and periodic dips in the line profiles are caused by the linac couch netting.
The c values from the Δ(x,y,t) = exp − [[x2 + y2]/[ c(t)2]] expression in Eq. (7), plotted as a function of homogeneous phantom thickness. The hollowed points represent the measured data. The dark solid line represents the best-fit power function of the form c(t) = η*t−λ +κ. The light dotted lines represent the 95% confidence interval limits. The thickness = 1, 2, and 3 cm data points were important for specifying the appropriate power function.
The EPID measured attenuation along the beam’s CP as a function of homogeneous phantom thickness. The lines represent data collected for the algorithmic commissioning, where the field size was defined at the exit surface of the phantom, 100 cm from the source, and the EPID was at 135 cm SDD. The points represent data collected for the situation where both the phantom and the EPID were moved further from the beam source, as is more likely to occur in a patient treatment scenario. For these points, a CS of 10×10 cm2, defined at 100 cm from the source, was used. The location of the data points along the commissioning curves indicates that scaling the collimator setting to the field size at the phantom exit surface may be an appropriate method to calculate the correct FS to use in Eq. (4).
Gamma maps for three of the heterogeneous slab phantom geometries. (a) The 2 cm slab of bone shown in Fig. 1(f) was shown in Table III to have the greatest area passing the 3%, 3 mm criteria, 97.1%. There are no discontinuities in the field. (b) The phantom shown in Fig. 1(i) where the middle layer is half bone (left side) and half air (right side) is a field that represents the median of the areas passing the gamma criteria, 95.1%. Failure along the junction is observed. (c) The phantom shown in Fig. 1(d) where there is a slab of phantom 5 cm wide and 24.7 cm tall with just air on either side represents a geometry where the algorithm totally breaks down. In Table III only 66.7% of the pixels pass the criteria and these are at the left and right sides of the field, relatively far from the dual discontinuities. The square pattern on each image is caused by the beam traversing the netting of the Varian Exact Couch which is supporting the phantoms.
A sample of the images associated with the transit dose verification for a representative field from the data in Table IV. (a) The Van Esch pPDIair calculated using Eclipse. (b) The mPDIair acquired with the EPID. The scale is the same for both (b) and (c) and is given in terms of “Calibrated Units” (CU), Varian’s unit of dose to the EPID. (c) The 3% of local value, 3 mm gamma evaluation comparing the through-air predicted and measured images. 98.6% of the pixels passed the gamma criteria. (d) The 2DTD pPDItx created using the calculated thickness map, the pPDIair in (b), and Eq. (4). (e) The mPDItx acquired through the anthropomorphic phantom. The scale is the same for (e) and (f) and is also reported in CU. (f) The gamma evaluation comparing the through-phantom predicted and measured images. 97.6% of the pixels passed the gamma criteria. It is evident that the conversion from the pPDIair in (b) to the pPDItx in (e) is not a simple rescaling of the dose, rather it also accounts for the effect of the anthropomorphic phantom’s inhomogeneities.
Summary of measurements performed for the commissioning and verification of the 2DTD algorithm. In the commissioning phase, each field size was delivered through each of the phantom thicknesses. This data was used to model the central pixel (CP) response. The data for the largest, 22.2×29.6 cm2, field was also used to model the off-axis pixel (OAP) response. Additional data points for the OAP modeling were acquired through homogeneous slab thicknesses of 1, 2, and 3 cm. If an open field was used for either commissioning or verification, 300 MU was delivered. IMRT fields used in the verification of the algorithm were delivered with the MU calculated from the planning system.
Summary of gamma comparison results for the 49 IMRT treatment fields delivered to the flat, homogeneous phantoms and to the heterogeneous slab phantom shown in Fig. 1(j). A criteria of 3% of the pPDIair local pixel value and 3 mm was used for the gamma comparison. The max and min rows correspond to the IMRT field within each phantom irradiation that had the most and least area, respectively, passing the gamma criteria. The p-value corresponds to the level of statistical significance in the difference between the results for a given phantom irradiation versus the through-air (t = 0 cm) irradiation using the student’s t-test.
Summary of gamma comparison results for the open 15×15 cm2 fields delivered to the flat, heterogeneous slab phantoms. A criteria of 3% of the pPDIair local value and 3 mm was used for the gamma comparison. The identifiers (a)–(j) correspond to the phantom schematics shown in Fig. 1. While most of the comparisons are very good, the thickness correction fails along severe, non-anatomical, discontinuities, such as that drawn in Fig 1(d).
Summary of gamma comparison results for the 33 IMRT fields delivered to the anthropomorphic phantom. A criteria of 3% of the pPDIair local value and 3 mm was used for the gamma comparison. The max and min rows correspond to the IMRT field within each irradiation that had the most and least area, respectively, passing the gamma criteria. The p-value corresponds to the level of statistical significance in the difference between the results for the anthropomorphic phantom irradiation versus the through-air irradiation using the student’s t-test.
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