Quantitative analysis of in-air output ratio.

Output factor (Scp) is one of the important factors required to calculate monitor unit (MU), and is divided into two components: phantom scatter factor (Sp) and in-air output ratio (Sc). Generally, Sc for arbitrary fields are calculated using several methods based on Sc determined by the absorbed dose measurement for several square fields. However, there are calculation errors when the treatment field has a large aspect ratio and the opening of upper and lower collimator are exchanged. To determine Sc accurately, scattered photons from the treatment head and backscattered particles into the monitor chamber must be analyzed individually. In this report, a simulation model that agreed well with measured Sc was constructed and dose variation by scattered photons from the treatment head and by backscattered particles into the monitor chamber was analyzed quantitatively. The results showed that the contribution of scattered photons from the primary collimator was larger than that of the flattening filter, and backscattered particles were affected by not only the upper jaw but also the lower jaw. In future work, a new Sc determination algorism based on the result of this report will be proposed.

INTRODUCTION

Determination of the monitor unit (MU) is required to deliver a prescribed absorbed dose to planning target volume (PTV). The output factor is one of the important parameters required to determine MU. According to Kahn et al., the output factor is derived from two components [1, 2]: one is the phantom scatter factor (Sp)—the ratio of the dose rate of a given field to the dose rate of a reference field at the same depth. The other is the collimator scatter factor (Sc)—the ratio of output in air of a given field to that of a reference field. The collimator scatter factor is also called the ‘head scatter factor’ or the ‘in-air output ratio’, but the term ‘in-air output ratio’ and ‘Sc’ are used to describe the factor in this report.

According to the report of AAPM TG-74, Sc is defined as the ratio of collision water kerma in the free space of an arbitrary field to that of a reference field [3]. When charged particle equilibrium is established, collision water kerma may be an approximation of the absorbed dose. Generally, Sc is determined by absorbed dose measurement using miniphantom and ionization chambers for several square fields.

In clinical studies, Sc for arbitrary fields are calculated using the A/P [4] or other methods [5-7]. However there are calculation errors for both open and wedge fields with large aspect ratios [8, 9]. Furthermore Sc differs when the opening of the upper and lower collimator jaws is exchanged. This phenomenon is called collimator exchange effect (CEE) [9], and could be corrected using the ‘field mapping method’ [9]. However, the field mapping method might overestimate Sc when the upper jaw is fixed and underestimate Sc when the lower jaw is fixed for the Varian machines.

To determine Sc accurately, scattered photons from the flattening filter, the primary collimator, jaws and backscatter to monitor chamber should be considered. Chaney et al. reported the fluence and energy spectrum of scattered photons from the treatment head [10]. However, they evaluated Sc using photon fluence instead of the absorbed dose or collision kerma so that the calculated Sc and the measured Sc did not agree well for the arbitrary field. On the other hand, some authors have experimentally evaluated the effect of backscattered particles to the monitor chamber. Duzenli et al. reported ‘relative chamber reading’ as the effect of backscattered particles using the telescope method [11]. Lam et al. calculated monitor backscatter factor based on the measurement of charge deposited in the target [12]. However, these reports gave nothing but backscatter phenomenon and are insufficient in terms of supplying quantitative evidence to agree with the actual Sc. Ding simulated Sc considering the variation of backscattered particles to the monitor chamber and compared this with measured data [13]. The report showed good agreement between simulated and measured Sc for not only square fields but also rectangular fields. However the Monte Carlo simulation was performed comprehensively and did not give individual information of scattered photons from head component and backscattered particles. In addition, it is time consuming and impractical for clinical use.

To calculate Sc for clinical fields with high accuracy and less computing time, a new Sc determination algorism considering the CEE phenomenon and the complex field shaped by a multi leaf collimator (MLC) is required. We assumed that Sc can be expressed with the next two functions. Dose variation by scattered photons from the treatment head can be regarded as a function of upper jaw, lower jaw and MLC opening. On the other hand, dose variation by backscattered particles into the monitor chamber can be regarded as a function of upper jaw opening. Therefore two functions must be analyzed individually. In this report, a simulation model that agreed well with measured Sc was constructed. And furthermore, dose variation by scattered photons from the treatment head and by backscattered particles into the monitor chamber was analyzed quantitatively.

MATERIALS AND METHODS

Measurement of Sc

Figure 1 shows the geometry of the Sc measurement. Ionization charges for several square fields were measured using a farmer type ionization chamber (TN-30013; Physikalisch-Technische Werkstätten, Germany) mounted in miniphantom. The miniphantom is cylindrical in shape, 4 cm in diameter and 20 cm in height, and set on the beam axis. The sensitive volume of the chamber was set at SCD = 100 cm and 10 cm in physical depth. Variation of the quality correction factor, kQ, by field size can be ignored, therefore Sc for arbitrary field A is calculated using the following equation when the electrometer reading is M (A):

Fig. 1.

Measurement geometry of in-air output ratio, Sc

where Aref is the reference field (A = 10 cm × 10 cm).

Treatment head modeling and beam commissioning

Figure 2 shows the geometry of the treatment head of the Clinac 600C (Varian medical systems, USA), which generates 4 MV X-rays. Head components from the target to the isocenter were precisely coded using BEAMnrc [14]. The initial electron energy and spatial distributions on the target were adjusted by comparison between measured and calculated dose distributions. Their agreement was judged objectively using the method and criteria of Venselaar et al. [15].

Fig. 2.

Schematic diagram of treatment head of Clinac 600C (Varian)

Simulation of photons generated from the treatment head

Photons from the treatment head were sampled within a 0.5-cm radius circular region on the central axis at 100 cm from the target. Sampled photons were categorized by each accelerator head component where interaction took place using the ‘latch’ option.

Collision water kerma for the arbitrary field colK(A) was calculated using information from sampled photons as follows:

where Φ (A) is the photon fluence at energy E for field size A, and μen(E)/ρ is the mass energy absorption coefficient of water, respectively.

To analyze the contribution of scattered photons to the collision water kerma, positions (x′, y′) of interaction between photons and the head component were calculated using the following equations:

where SSD is the distance from the target to the sampling plane (= 100 cm); zlast is the distance of the Z axis from the target to the position where the photon interaction took place; u, v, w is the direction cosine of scattered photons to the X, Y, Z axes; and (x, y) is the position on the sampling plane shown in Fig. 3.

Fig. 3.

Schematic diagrams to calculate positions of interaction between photon and head components

Simulation of backscatter particles from jaws and mirror

Absorbed doses to air of monitor chamber for various jaw openings were calculated using the Monte Carlo simulation to analyze variation of the monitor chamber response by backscattered particles from jaws and mirror.

Calculation of S′c, Sb and Sc

The ratio of collision water kerma S′c (A) for the arbitrary field A to the reference field Aref is calculated using the following equation:

where colKp and colKs are the collision water kerma of primary photons and that of scattered photons, respectively. colKs was calculated as follows:

where colKspcol, colKsff colKsjaws colKsothers are the collision water kerma of scattered photons from the primary collimator, flattening filter, jaws and other head components, respectively.

Sb is the variation of monitor chamber response by jaw opening, and is defined by the following equation:

where Dfront is the absorbed dose to the air in the monitor chamber deposited by particles from the target, primary collimator and flattening filter. Dback is the sum of the absorbed dose to air deposited by backscattered particles from the upper jaws , lower jaws and mirror as per the following equation:

On the other hand, Dfront does not depend on jaw position, namely, field size A. Therefore Dfront(A) is constant and equal to Dfront(Aref). Thus, equation (7) can be converted into the following equation:

Considering the interaction between photons and treatment head components, Sc can be used to calculate the variation in collision water kerma in free space from scattered photons, and the monitor chamber response from backscattered particles. Therefore, the in-air output ratio by simulation Sccalc can be calculated with the following equation:

For all simulations, 1.2 × 1011 incident electrons on the target were used to obtain statistical uncertainty of less than 2.0%.

RESULTS AND DISCUSSION

Commissioning results of beam model

Measured and simulated dose distributions are shown in Figs 4 and 5, and the confidence limit and distance to agreement (DTA) for each region is shown in Table 1. When incident electron energy was 4.0 MeV with 1.5% of full width half maximum (FWHM) energy spread and 0.3 cm of spatial FWHM, the confidence limit and DTA satisfied the criteria at all evaluation regions. Therefore, it is confirmed that the following simulation faithfully reproduced the actual beam.

Fig. 4.

Measured and simulated PDD in water for 10 cm × 10 cm field

Fig. 5.

Measured and simulated OAR at 10 cm depth in water for 40 cm × 40 cm field

Table 1.

Criteria (confidence limit or DTA) of objective judgement for beam commissioning

	PDD		OAR
Region	1	2	2	3	4
Venselaar et al.	2.0%	2.0 mm	2.0 mm	3.0%	30%
This report	1.1%	0.6 mm	1.3 mm	1.9%	25%

Region numbers were defined as: 1, points on the central beam axis beyond the depth of dmax; 2, points in the build-up region and penumbra; 3, points beyond dmax, within the beam but outside the central beam axis; 4, points off the geometrical beam edges and below shielding blocks.

Analyses of photons from head components

Collision water kerma of primary and scattered photons calculated by equation (2) for a square field are shown in Fig. 6(a). Collision water kerma of primary photons accounted for over 95.5% of the total, and did not depend on field size. On the other hand, collision water kerma of scattered photons increased slightly as the field size enlarged. Collision water kerma of scattered photons from each head component are shown in Fig. 6(b), and the percentage of collision water kerma from head components to total scattered photons are shown in Table 2. Collision water kerma from the primary collimator and flattening filter accounted for from 53.7–59.9 % and 38.2–46.3 % of total scattered photons, respectively. However, collision water kerma from collimator jaws and others were small amounts so could be ignored. Thus, it was obvious that scattered photons from the primary collimator and flattening filter affect Sc.

Fig. 6.

Collision water kerma as a function of field size divided into (a) primary and scattered photons; (b) scattered photons from the primary collimator and flattening filter

Table 2.

Percentage of collision water kerma from head components to total scattered photons

	A side of square field (cm)
Components	5	10	20	40
Primary collimator	59.9	53.2	53.6	53.7
Flattening filter	38.2	43.7	46.2	46.3
Others	0.19	0.31	0.20	0.00

The spatial distribution of the interaction coordinate of scattered photons at the primary collimator and flattening filter as calculated by equations (3) and (4) is shown in Fig. 7 for the primary collimator and Fig. 8 for the flattening filter. The Interaction coordinate was distributed throughout and the shapes of the primary collimator and flattening filter were clearly discernible.

Fig. 7.

Spatial distribution of interaction points of scattered photons at primary collimator (a) X–Y coordinate; (b) X–Z coordinate

Fig. 8.

Spatial distribution of interaction points of scattered photons at flattening filter (a) X–Y coordinate; (b) X–Z coordinate

The S′c calculated using equation (5) is shown in Fig. 9. S′c increases from 0.981 for 5 cm × 5 cm to 1.002 for 15 cm × 15 cm. For this field range, S′c depends on fluence of scattered photons from the primary collimator and flattening filter. On the other hand, in the field larger than 15 cm × 15 cm, the primary collimator and flattening filter can be seen fully from the point of calculation because they are not concealed by jaws.

Fig. 9.

S′c as a function of field size

Analyses of backscattered particles into the monitor chamber

The absorbed dose to air deposited by particles from the target side and back side in the monitor chamber is shown in Fig. 10(a). The contribution of particles from the target side was constant, however, the contribution of backscattered particles decreased as the jaws moved away from the central beam axis. The absorbed dose from backscattered particles accounted for 5.0% for 5 cm × 5 cm, and 1.0% for 40 cm × 40 cm fields of the total absorbed dose to air in the monitor chamber.

Fig. 10.

Absorbed dose to air in monitor chamber as a function of field size divided into (a) particles from target and back side; (b) backscattered particles from upper and lower jaws

The absorbed dose to air by backscattered particles from the upper and lower jaws are shown in Fig. 10(b), and the percentage of total for several fields are shown in Table 3. Percentage of absorbed dose by the upper jaws compared with that of total backscattered particles decreased linearly as field size enlarged from 97.3% for 5 cm × 5 cm to 72.4% for 40 cm × 40 cm. On the other hand, the percentage of absorbed dose from lower jaws to that of total backscattered particles increased from 2.6% for 5 cm × 5 cm to 27.6% for 40 cm × 40 cm. Th absorbed dose from the mirror was a small amount and could be ignored.

Table 3.

Percentage of absorbed dose of backscattered particles from head components to total dose

	A side of square field (cm)
Components	5	10	20	40
Upper collimator jaws	97.3	91.9	82.6	72.4
Lower collimator jaws	2.6	8.1	17.4	27.6

Sb calculated using equation (9) is shown in Fig. 11. Sb increased from 0.956 to 1.033 as field size enlarged.

Fig. 11.

Sb as a function of field size

Evaluation of Sccalc

Comparisons of measured and calculated Sc using equation (10) are shown in Fig. 12. The calculated and actual Sc agreed within 0.5% for several square fields. There are some reports about calculation of Sc based on scattered photons from the flattening filter [9, 16]. However, it is obvious that an accurate Sc cannot be calculated without scattered photons from the primary collimator and backscattered particles from jaws into the monitor chamber. Furthermore, the amount of scattered photons from the primary collimator is larger than that from the flattening filter. On the other hand, Sc is affected by variation of Sb for fields larger than 15 cm × 15 cm as is shown in Table 4.

Fig. 12.

Measured and simulated Sc as a function of field size

Table 4.

Comparison of each scatter factor for various square fields

	A side of square field (cm)
Scatter factor	5	10	20	40
S′c	0.981	1.000	1.002	1.002
Sb	0.996	1.000	1.010	1.033
Simulated Sc	0.977	1.000	1.013	1.034
Measured Sc	0.974	1.000	1.017	1.031

CONCLUSION

To express Sc with two different functions, a Monte Carlo simulation model that agreed well with measured Sc was constructed. And dose variation by scattered photons from the treatment head and by backscattered particles into the monitor chamber was analyzed quantitatively.

The results showed that the contribution of scattered photons from the primary collimator was larger than that of the flattening filter, and backscattered particles were affected not only by the upper jaw but also the lower jaw. In future work, a new Sc determination algorism based on the result of this report will be proposed.