^{1}, Ren-Dih Sheu

^{2}, Cynthia S. Polvorosa

^{3}and Cheng-Shie Wuu

^{3}

### Abstract

**Purpose:**

A method to perform transit dosimetry with an electronic portal imaging device(EPID) by extending the commercial implementation of a published through-air portal doseimage (PDI) prediction algorithm Van Esch*et al.* [Radiother. Oncol. **71**, 223–234 (2004)] is proposed and validated. A detailed characterization of the attenuation, scattering, and EPID response behind objects in the beam path is used to convert through-air PDIs into transit PDIs.

**Methods:**

The EPIDdetector response beyond a range of water equivalent thicknesses (0–35 cm) and field sizes (3×3 to 22.2×29.6 cm^{2}) was analyzed. A constant air gap between the phantom exit surface and the EPID was utilized. A model was constructed that accounts for the beam’s attenuation along the central axis, the presence of phantom scattered radiation, the detector’s energy dependent response, and the difference in EPID off-axis pixel response relative to the central pixel. The efficacy of the algorithm was verified by comparing predicted and measured PDIs for IMRT fields delivered through phantoms of increasing complexity.

**Results:**

The expression that converts a through-air PDI to a transit PDI is dependent on the object’s thickness, the irradiated field size, and the EPID pixel position. Monte Carlo derived narrow-beam linear attenuation coefficients are used to model the decrease in primary fluence incident upon the EPID due to the object’s presence in the beam. This term is multiplied by a factor that accounts for the broad beam scatter geometry of the linac-phantom-EPID system and the detector’s response to the incident beam quality. A 2D Gaussian function that models the nonuniformity of pixel response across the EPIDdetector plane is developed. For algorithmic verification, 49 IMRT fields were repeatedly delivered to homogeneous slab phantoms in 5 cm increments. Over the entire set of measurements, the average area passing a 3%/3mm gamma criteria slowly decreased from 98% for no material in the beam to 96.7% for 35 cm of material in the beam. The same 49 fields were delivered to a heterogeneous slab phantom and on average, 97.1% of the pixels passed the gamma criteria. Finally, a total of 33 IMRT fields were delivered to the anthropomorphic phantom and on average, 98.1% of the pixels passed. The likelihood of good matches was independent of anatomical site.

**Conclusions:**

A prediction of the transit PDI behind a phantom or patient can be created for the purposes of treatment verification via an extension of the Van Esch through-air PDI algorithm. The results of the verification measurements through phantoms indicate that further investigation through patients during their treatments is warranted.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Overview of the Van Esch pretreatment through-air verification algorithm

II.B. Monte Carlo simulation to account for the addition of attenuating material

II.C. Measurement of the detector response behind phantom material

II.D. 2DTD algorithmic verification

III. RESULTS

III.A. Detector response behind phantom material

III.B. 2DTD algorithmic verification

IV. DISCUSSION

V. CONCLUSION

### Key Topics

- Image guided radiation therapy
- 63.0
- Dosimetry
- 32.0
- Intensity modulated radiation therapy
- 26.0
- Medical imaging
- 20.0
- X-ray scattering
- 15.0

## Figures

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 cm^{2} field.

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 cm^{2} 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.

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 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 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.

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.

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 − [[x^{2} + y^{2}]/[ 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 c values from the Δ(x,y,t) = exp − [[x^{2} + y^{2}]/[ 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 cm^{2}, 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).

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 cm^{2}, 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.

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 pPDI_{air} calculated using Eclipse. (b) The mPDI_{air} 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 pPDI_{tx} created using the calculated thickness map, the pPDI_{air} in (b), and Eq. (4). (e) The mPDI_{tx} 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 pPDI_{air} in (b) to the pPDI_{tx} in (e) is not a simple rescaling of the dose, rather it also accounts for the effect of the anthropomorphic phantom’s inhomogeneities.

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 pPDI_{air} calculated using Eclipse. (b) The mPDI_{air} 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 pPDI_{tx} created using the calculated thickness map, the pPDI_{air} in (b), and Eq. (4). (e) The mPDI_{tx} 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 pPDI_{air} in (b) to the pPDI_{tx} in (e) is not a simple rescaling of the dose, rather it also accounts for the effect of the anthropomorphic phantom’s inhomogeneities.

## Tables

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 cm^{2}, 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 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 cm^{2}, 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 pPDI_{air} 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 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 pPDI_{air} 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 cm^{2} fields delivered to the flat, heterogeneous slab phantoms. A criteria of 3% of the pPDI_{air} 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 open 15×15 cm^{2} fields delivered to the flat, heterogeneous slab phantoms. A criteria of 3% of the pPDI_{air} 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 pPDI_{air} 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.

Summary of gamma comparison results for the 33 IMRT fields delivered to the anthropomorphic phantom. A criteria of 3% of the pPDI_{air} 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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