Verification of Varian eMC

Introduction

The introduction of electron Monte Carlo (eMC) into clinical practice was over a decade ago (~2006). Many clinics have adopted eMC as the standard calculation algorithm over less accurate algorithms like Gaussian Pencil Beam. Surprisingly, however, not all clinics that use eMC use the MU that it provides. A 2016 survey of the MedPhys listserve showed that nearly half of the respondents used the MU generated from hand calculations for delivering the patient’s treatment. Yet, the physician was presented the isodose curves based on the MU generated by eMC in ~75% of those clinics.

In my clinic, we were using the hand calculated MU for treatments and were not generating isodose plans at all. EMC usually gave MU that were 5-15% higher than the hand calculated MU. We were reluctant to use the eMC MU. One day, the radiation oncologist noted that the electron patients were not getting “red enough” and we had an “aha” moment. We figured if she wanted them redder, we should use higher MU. EMC was giving higher MU and we thought let’s just use the higher MU from eMC.

Her comments prompted the following study to show that eMC was delivering the correct dose with the higher MU.

Methods

Highly Irregular Electron Cutout:

Using Eclipse, we drew a representation of the athletic logo for Wheaton College in an electron block cutout for a 10×10 cone. We poured the cutout from Cerrobend using standard techniques. A depiction of the drawn and poured cutout is shown in Figure 1. The greyed area shows the mismatch between the two.

Figure 1: Beam’s eye view of the cutout drawn in Eclipse (dotted-dash line) overlayed with the poured cutout (solid line). The mismatch between the two is highlighted in grey.

We measured various dose planes using an IBA Dosimetry MatriXX (2009 vintage) placed on the couch on top of 5 cm of plastic water backscatter. We recorded the dose planes with the IBA Omnipro IMRT software. We produced a depth dose curve for the open 10×10 12 MeV electron beam for depths ranging from 0.33 to 7.33 cm. The MatriXX does not have a central axis chamber. Therefore, we offset the MatriXX by centering the first ion chamber in the first quadrant along the central axis (CAX). We label this the CAX chamber. The MatriXX calibration gives a value of 100 for a 10×10 12 MeV beam delivering 100 MU at 100 cm and depth of 2.85 cm (D_Max). However, this is not a dose in cGy because there is no correction for the changing stopping powers built into the OmniPro software. To get the dose in cGy, we calculated the stopping powers using the FORTRAN routine of Section X.D from TG-51. We multiplied the stopping power by the value recorded in OmniPro for the CAX chamber for the given depth. We divided the resulting values by the maximum recorded value to produce a percent depth dose (PDD). Finally, we calculated a factor to convert OmniPro CAX chamber values directly to dose in cGy for each depth by dividing the PDD by the original OmniPro CAX chamber values. Multiplying these correction factors by any value recorded by the MatriXX for a given depth then gives the dose in cGy. The process above was repeated with the Wheaton logo cutout in place.

We used Eclipse to calculate dose planes for five different depths with the logo as the block. The calculation settings were Accuracy: 2 %, Calculation Grid Size: 0.25 cm, Number of Particle Histories: 160 million, Smoothing Method: “No Smoothing”, and Smoothing Level: “Low”.

We exported the dose planes in DICOM format with a resolution equal to that of the MatriXX, 0.76 cm. In the OmniPro software, we resampled the measured and imported dose planes to 0.1 cm using the built-in linear interpolation. The measured data was shifted by 0.38 cm in the negative x and negative y directions to correct the CAX offset. Each dose plan was rescaled so that the dose at the CAX represented 100 %. We calculated a relative γ with 3 % dose agreement and 3 mm distance to agreement in the OmniPro IMRT software.*This was before TG-218

Heterogeneous phantom

We simulated a realistic heterogeneous phantom using a short rack of baby back ribs in cryovac packaging purchased from the grocery store. We secured three CC-13 Scanditronix Wellhöffer ionization chambers to the cryovac packaging using water-resistant tape. We aligned the chambers perpendicular to the beam with offsets as given in Table 1.

Setup	Chamber Serial Number	X offset (cm)	Y offset (cm)
Ribs Low Water and Ribs High Water	7701	0.4	0
	7702	1	3.4
	3498	1.2	-1.2
Lucy	7701	-0.1	0
	3498	2.4	0

We placed everything in a rectangular plastic container with dimensions ~(37 cm × 25 cm × 13 cm) and added water to the container to cover the ribs. We denote this setup as Ribs Low Water because the surface of the ribs was even with the surface of the water. We scanned the whole assembly using our CT simulator with standard settings and 1.25 mm slice thickness. Then we moved the whole assembly to the treatment machine. We connected the chambers to either a SuperMax or Max 4000 and applied a voltage of 300 V across the electrodes. We delivered 1000 MU with both 9 MeV and 12 MeV beams using the open 10×10 cone with the 10×10 cm² standard cutout. We recorded the ionization, M_Raw, for each chamber.

After irradiating the Ribs Low Water setup and before moving the container, we added more water so that approximately 2 cm of water was above the surface of the ribs. We measured the depth using a ruler placed on the surface of the ribs. We denote this setup as Ribs High Water. We irradiated this new setup as mentioned before. We moved the Ribs High Water setup back to the CT simulator and rescanned with the higher water level.

We imported and contoured both scans in Eclipse. We contoured the chambers and assigned each the material water. We measured the depth to each chamber using the “WED and Distance” tool. We calculated the dose using the “Calculate Volume with Preset Value” option with 1000 MU selected. The algorithm calculation settings were the same as those used for the logo test above. We recorded the minimum, mean, and maximum dose to the chambers as reported in the “Dose Statistics” tab of Eclipse for each energy and setup.

Anatomical Phantom

We secured two CC-13 ion chambers to the large cavity hemisphere of a Standard Imaging Lucy phantom. We taped CC-13 3498 inside the cavity along with a lightly packed damp washcloth. We placed CC-13 7701 between two pieces of 1 cm sticky bolus. We draped the sticky bolus with the chamber over the Lucy phantom and positioned the Lucy phantom, ion chambers, and bolus on 5 cm of plastic water backscatter. We acquired a CT scan of the phantom. Figure 2 shows the setup described above. Measurements, CT scan, contouring, and calculations mirrored those presented in the previous sections. The offset for each chamber in the beam’s eye view is provided in Table 1.

Figure 2:  Transverse view of the Lucy phantom on the backscatter plate with the bolus and chambers.

Ion chamber dose calculations

We collected all the data into a spreadsheet for easy manipulation. We corrected the ionization readings as prescribed in the TG-51 protocol. For k’_R50 we used Equation 19 in TG-51 to calculate two k’_R50 values. One is based on the R₅₀ of the energy and the other is based on an R₅₀ of 0.5 cm. The difference in these two values divided by two gives an estimated maximum uncertainty. k_ecal is from Table III of TG-51 and we assume the CC-13 is equivalent to the Wellhofer IC-10/IC-5 presented there. With the uncertainty in k_ecal we assumed the dominant component was Pfl which can range from 0.95 to 1.00 (see Figure 9-26 in Rogers). For the measurements presented here we assumed the uncertainty in Pfl and thus k_ecal was 5 % for the low energy measurements and 3 % for the high energy measurement. L/ρ was calculated using equation 12.9 from Milhadis, which has an inherent uncertainty of 1% and we used that uncertainty directly. For \(N_{D,W}^{^{60}Co}\), NIST special publication 250-74 gives a relative combined standard uncertainty of 0.47 %. However, the calibration certificates for all the chambers was older than two years. Therefore, an on-site measurement of the \(N_{D,W}^{^{60}Co}\), using a recently calibrated A19 reference chamber for inter-comparison resulted in deviations from the ADCL value of up to 2 %. To get a maximum uncertainty in all measurements we used 2 % for all chambers. It would be impossible to measure \(P_{Gr}\) in this setup. Therefore, \(P_{Gr}\) was only estimated by reading the PID for each beam at the point of measurement and 0.15 cm deeper. For example, for the 7701 chamber in the 9 MeV Ribs Low measurement the PID was 90.9 % at the measured depth and 85.51 % at depth plus 0.5 r cavity. The PIDs were originally measured with the 7701 chamber and all chambers have the same characteristics. The uncertainty in this method is unclear and so we have assumed that the maximum uncertainty (3 σ) was 3 % for the low energy beam and 2 % for the high energy beam. Figure 9-24 of Rogers shows a variation in \(P_{Gr}\) between different protocols and calculation methods for photon beams. We have used this variation to define the uncertainty for these electron beams. The uncertainty budget for these measurements is given in Table 2. Other correction factors affecting the dose have not been considered because their contribution to the dose is small i.e. \(P_{ion}\) and \(P_{pol}\), or the value can be calculated almost exactly, i.e. \(P_{TP}\).

Parameter	Uncertainty Type	Value for 9 MeV	Value for 12 MeV
\(k’_{R_{50}}\)	B	0.017	0.023
\(k_{ecal}\)	B	5 %	3 %
L/ρ	B	1 %	1 %
\(N_{D,W}^{^{60}Co}\)	A, B	2 %	2 %
\(P_{Gr}\)	B	3 %	2 %

Results

Highly Irregular Electron Cutout:

Figure 3 shows the PDD measured using the Matrixx and plastic water slabs. The \(χ^2\) probability distribution for this data is 0.002. Therefore, the Matrixx with the corrections we have applied can be used for measuring a depth dose.

Figure 3: PDD measured with Matrixx and plastic water (diamonds) as well as PDD measured with a Farmer-type chamber in water (dashed-dot line). Both PDDs has been corrected for changes in stopping power with depth. Horizontal error bars on the Matrixx measurements are estimated at 1 mm for depth. Vertical error bars are not shown because the estimated 1 % uncertainty for dose is within the size of the marker. The PDD measured in water is assumed to be exact.

Figure 4 shows the depth dose measured using the Matrixx along the CAX for the Wheaton College logo. The Matrixx values have been corrected using the correction factors described above. The grey region represents the uncertainty of 1 % in the Matrixx dose and 1 mm in the depth. The error bars on the eMC dose are 2 %. The positional uncertainty in the eMC is 0.125 mm, half of the grid resolution.

Figure 4: Depth dose curve for the Wheaton College logo cutout measured with the Matrixx (solid line) and the dose calculated by Eclipse at the depths shown (open squares). The grey region represents the uncertainty in depth (1 mm) as well as the dose (1 %) for the Matrixx measurement. The horizontal error bars for the Eclipse data are 1.25 mm which represents half of the grid resolution. The vertical error bars on the Eclipse data are 2 % which represents the accuracy level based on results of the commissioning process.

Table 3 shows the dose measured using the Matrixx when the Wheaton College logo cutout was in place. The correction factor converts the Matrixx CAX reading to dose and is described above. A relative γ was calculated in the OmniPro software using the % dose difference of 3 and distance to agreement of 3 mm.

Depth Matrixx (cm)	Depth eMC (cm)	Matrixx CAX Measurement (Rdg)	Correction Factor (cGy/Rdg)	Matrix Dose (cGy)	eMC Dose (cGy)	% difference	γ1 Pass Rate (%)	γ2 Pass Rate Centered (%)
0.83	0.9	197.5	0.956	188.7	189.3	0.3	83.8	86.1
2.13	2.25	204.8	0.972	199.1	200.1	0.5	85.7	91.7
2.83	2.95	205.0	0.981	201.2	202.6	0.7	95.6	99.0
3.83	4	179.0	0.996	178.2	172.8	3.1	94.1	99.8

Heterogeneous and anatomical Phantom

The chamber properties are given in Table 4. The factors were read from TG-51 or determined by appropriate methods using the TG-51 formalism.

CC-13 S/N	\(N_{D,W}^{^{60}Co}\)	\(k’_{R_{50}}\)	\(k’_{R_{50}}\)	\(k_{ecal}\)	\(P_{ion}\)	\(P_{pol}\)
		9 MeV	12 MeV
7701	2.68×108	1.0179	1.0086	0.904	1.006	1.000
7702	2.69×108
3498	2.64×108

Table 5presents the measured readings for the Ribs Low Water, Ribs High Water, and Lucy phantoms, along with the correction factors necessary to convert to dose. The temperature and pressure of the Ribs Low Water and Ribs High Water measurements were 21.5 °C and 98.76 kPa respectively. For the Lucy measurement, the temperature and pressure were, 22 °C and 99.34 kPa respectively.

Phantom	Energy (MeV)	Chamber S/N	Mraw (nC)	Pgr	PTP	Depth (cm)	L/ρ	Dose (cGy)	2 σ	eMC (cGy)
Ribs Low	9	7701	33.94	0.941	1.024	2.63	1.099	8.9	0.7	8.9
		7702	31.8	1.012	1.024	0.00	1.048	8.6	0.7	8.1
		3498	34.28	1.016	1.024	0.42	1.055	9.2	0.7	8.7
	12	7701	36.7	1.000	1.024	2.63	1.076	9.9	0.7	9.7
		7702	34.15	1.009	1.024	0.00	1.040	9.1	0.6	8.7
		3498	36.64	1.010	1.024	0.42	1.046	9.6	0.7	9.2
Ribs High	9	7701	12.19	0.659	1.024	4.17	1.135	2.3	0.2	2.8
		7702	36.45	1.016	1.024	1.25	1.071	10.1	0.8	9.2
		3498	39.26	1.009	1.024	1.63	1.078	10.7	0.9	9.8
	12	7701	33.15	0.938	1.024	4.17	1.101	8.6	0.6	8.3
		7702	36.8	1.006	1.024	1.25	1.054	9.9	0.7	9.3
		3498	38.81	1.005	1.024	1.63	1.062	10.3	0.7	9.6
Lucy	9	7701	33.63	1.015	1.020	0.8	1.062	9.2	0.7	9.0
		3498	2.469	0.804	1.020	4.9	1.155	0.57	0.05	0.80
	12	7701	36.05	1.006	1.020	0.8	1.050	9.6	0.7	9.4
		3498	21.9	0.858	1.020	4.9	1.113	5.2	0.4	5.6

Discussion

Highly Irregular Electron Cutout

The Wheaton College athletic logo was chosen for two reasons. One of the authors gave a lecture on electron Monte Carlo dose calculations to the physics department at Wheaton and wanted to engage the students with something they were familiar. Second, the logo presents areas where the full lateral scatter of the beam cannot be assumed. The superior region has “fingers” that are less than 1 cm in some parts and the inferior region goes down to a point. This test is like the tests performed by (cygler papers). However, instead of film, we have used the Matrixx for the dose plane measurements.

Measuring the agreement between the measured and calculated dose planes at various depths shows that eMC is calculating the dose distribution in a homogeneous phantom correctly. The calculated γ for the for the dose planes presented have excellent pass rates for all but the plane closest to the surface. The disagreement here can be explained by the mismatch between the drawn cutout in Eclipse and the poured cutout used for the measurement. Figure 4 shows the γ analysis plane for the 0.83 cm dose plane. The red regions indicate where γ fails with a value greater than 1. The regions of failure correspond well with the regions of mismatch seen in Figure 1. The deeper dose planes are less affected by the mismatch because the scattering is greater with depth, smearing out the mismatch.

Figure 4: γ analysis plane for the 0.83 cm dose plane. The red region indicates points where γ is greater than 1.0. The red regions correspond to the mismatch seen in Figure 1.

Ion chamber dose measurements with heterogeneous and anatomical Phantoms

Testing eMC for heterogeneity and anatomical corrections was problematic in our clinic because we did not have any anthropomorphic phantoms. Most of the electron calculations in our clinic were for breast or chest wall scar boosts. It was assumed that an accurate representation of a chest wall could be found in a rack of pork baby back ribs. The cryovac wrapped ribs have all the anatomy of a human, muscle, fat, bone, etc. but could be easily manipulated. Ion chambers attached to the anterior and posterior surfaces of the ribs would give the dose above and below the ribs. A representation of the curvature of the breast was found in the Lucy phantom. Measured doses that agreed with the eMC calculations for these phantoms would verify that the heterogeneity and anatomy corrections in eMC are right.

The measured dose values shown in Table 5 do agree, 95 % confidence interval, with the eMC dose values within the uncertainty of both the measured and eMC values for all but the 9 MeV Lucy measurement with the 3498 chamber. The depth of the chamber for this measurement was 4.9 cm, a depth beyond the practical range of the 9 MeV beam. Including other sources of uncertainty can account for this discrepancy. For example, the calculations assume an electron beam but at this depth the dominant contributor to the dose is Bremsstrahlung photons.

Conclusions

Stop screwing around and use the mu calculated by eMC. TG-70 says, “If you have performed all the tests there is no reason not to.” The test presented here can be done in any clinic and do not require expensive phantoms, film processors, or equipment that is not part of a standard practice. It is troubling to see that sites still rely on hand calculations. This reminds us of the switch from homogeneous to heterogeneous calculations a few years ago.