**2. Characteristics of physical or nonphysical wedges in clinical implementation**

#### **2.1. Fundamental properties of physical and nonphysical wedges**

In radiation therapy, wedge filters are commonly used to improve dose uniformity toward the target volume [2]. A physical wedge is usually constructed from a high-density material, such as lead or steel, which attenuates the beam progressively across the entire field. A nonphysical wedge generates a sloping dose distribution by moving one of the jaws with variable speed, while the opposite jaw remains steady. Nonphysical wedges inherently have no beam attenuation or beam hardening effect and thus offer more flexibility than physical wedges [3, 4]. According to the International Commission on Radiation Units and Measurements, the wedge angle is defined as the angle at which an isodose curve is tilted at the central axis of the beam at a specified depth (usually 10 cm) [5].

Before deciding on physical or nonphysical wedges during clinical treatment planning, the treatment planning system (TPS) requires obtaining a number of measurements from each wedge system. In general, the TPS requires data on the percentage depth-dose (PDD), beam profiles, and wedge factors of the X-ray beams [6]. As an example, **Figure 1** shows the profile curve measurements when physical or nonphysical wedges at 30° and 60° were used (field size 10 × 10 cm<sup>2</sup> ).

The results show that nonphysical wedges have straighter profile curve lines than physical wedges, which are desirable in clinical practice. These results are consistent with those previously described [7, 8]. Ahmad et al. reported that differences in profiles between physical and nonphysical wedges were most evident in larger fields, shallow depths, thicker wedges, and when using a low-energy beam [8].

On the other hand, the presence of a wedge filter in the path of a radiation beam decreases its intensity; this must be taken into account when calculating treatment doses. When physical wedges were used, photon energy fluence is reduced in the wedged beam compared to the open beam; this effect is more pronounced when increasing the wedge angle [9]. It has also been shown that a physical wedge factor has a stronger depth dependence than a nonphysical wedge factor owing to beam hardening [2].

**Figure 1.** The profile curves of 10 MV X-ray beams using (a) 30° or (b) 60° of physical or nonphysical wedges under a source-surface distance of 100 cm and depth of 10 cm in water. The red line indicates profile curves of nonphysical wedges; the black line indicates that of physical wedges.

#### **2.2. Comparison between calculation data and measurement data**

with linear accelerators. Such wedges are usually mounted externally or internally in the gantry head of the linear accelerators. Nonphysical wedges, first proposed in the late 1970s by Kijewski et al., produce modulated dose distributions that were similar to those of physical wedges [1]. They rely on the dynamic movements of a pair of independent collimating jaws during treatment and have been widely implemented in modern radiotherapy machines. Both modalities possess unique advantages and limitations in terms of dosimetric character-

In this chapter, we discuss and compare the clinical implementation and application of wedge

In radiation therapy, wedge filters are commonly used to improve dose uniformity toward the target volume [2]. A physical wedge is usually constructed from a high-density material, such as lead or steel, which attenuates the beam progressively across the entire field. A nonphysical wedge generates a sloping dose distribution by moving one of the jaws with variable speed, while the opposite jaw remains steady. Nonphysical wedges inherently have no beam attenuation or beam hardening effect and thus offer more flexibility than physical wedges [3, 4]. According to the International Commission on Radiation Units and Measurements, the wedge angle is defined as the angle at which an isodose curve is tilted at the central axis of the beam

Before deciding on physical or nonphysical wedges during clinical treatment planning, the treatment planning system (TPS) requires obtaining a number of measurements from each wedge system. In general, the TPS requires data on the percentage depth-dose (PDD), beam profiles, and wedge factors of the X-ray beams [6]. As an example, **Figure 1** shows the profile curve measurements when physical or nonphysical wedges at 30° and 60° were used (field

The results show that nonphysical wedges have straighter profile curve lines than physical wedges, which are desirable in clinical practice. These results are consistent with those previously described [7, 8]. Ahmad et al. reported that differences in profiles between physical and nonphysical wedges were most evident in larger fields, shallow depths, thicker wedges, and

On the other hand, the presence of a wedge filter in the path of a radiation beam decreases its intensity; this must be taken into account when calculating treatment doses. When physical wedges were used, photon energy fluence is reduced in the wedged beam compared to the open beam; this effect is more pronounced when increasing the wedge angle [9]. It has also been shown that a physical wedge factor has a stronger depth dependence than a nonphysical

**2. Characteristics of physical or nonphysical wedges in clinical** 

**2.1. Fundamental properties of physical and nonphysical wedges**

istics, treatment accuracy, and efficiency.

at a specified depth (usually 10 cm) [5].

).

when using a low-energy beam [8].

wedge factor owing to beam hardening [2].

techniques in radiation therapy.

**implementation**

252 Radiotherapy

size 10 × 10 cm<sup>2</sup>

Before wedge filters are installed in clinical practice, several measurements must be incorporated into the TPS for beam modeling. The modeling method for the TPS varies between manufacturers and also between calculation algorithms, as the mechanism of motion of the nonphysical wedges is different for every manufacturer. In this section, the Eclipse planning system (Varian Medical Systems, Palo Alto, CA, USA) and the Enhanced Dynamic Wedge (EDW, Varian Medical Systems, Palo Alto, CA, USA) are mainly described.

A physical wedge changes the beam energy fluence of the primary X-ray beam through the insertion of a metallic filter at the gantry head. This effect is modeled via a wedge transmission curve; specifically, depth doses, wedge profiles, and longitudinal profiles are used for such modeling. In the Eclipse system, the energy fluence of the primary X-ray beam is modeled as a two-dimensional spectrum that considers the mass-energy attenuation coefficient, which is calculated based on the wedge filter material and thickness. Furthermore, the physical wedge produces secondary radiation when interacting with the primary X-ray beam. Eclipse hence considers the wedge a source of scatter, and modeling is performed using a dual Gaussian plane. Moreover, when physical wedges are used in the Eclipse system, a separate electron contamination source model is applied to the calculation; it is necessary to verify the precision of the final model by comparing it to the acquired data before the wedge filters are installed in clinical practice.

Fogliata et al. compared the calculation models and measurement data using the analytical anisotropic algorithm (AAA) [10–13] and the Acuros XB (AXB) [14–16], which is built into Eclipse (version 10.0) [17]. Six and 15 MV X-rays were validated in their study; measurements were performed in water using the PTW-MP3 phantom with a 0.125 cm<sup>2</sup> cylindrical ionization chamber (Semiflex, PTW). Next, depth-dose curves were investigated for several field sizes. In the wedged field along the central axis, the difference in absolute dose between calculated vs. measured values revealed deviations (including standard deviations) smaller than 1%. Moreover, the profile curves were investigated in some field sizes at depths of dmax, 5, 10, 20, and 30 cm. In the central beam region, the average difference in profile curves between calculations and measurements was smaller than 1%, with a standard deviation lower than 1%. Output factor and monitor unit (MU) calculations were also investigated in some field sizes at a source-surface distance (SSD) of 90 cm and a depth of 5 cm in water. The difference between the calculated and measured MUs to deliver a fixed dose to the isocenter exhibited a maximum deviation of 0.2%. Therefore, when using AAA or AXB under reference conditions, it is possible to model correctly. However, when considering clinical use, validation in non-reference conditions is also necessary. Van Esch et al. validated depth-dose curves at SSDs of 80, 90, and 100 cm to verify the accuracy of modeling of the electron contamination as a function of source-to-skin distance [18]. For depth-dose curves involving different SSDs, they reported that the disagreement between calculated and measured data in the buildup region was high under conditions of higher energy and small SSD. In wedge profiles for 60° physical wedges using 18 MV for the selection of asymmetric fields (X = 15 cm, Y1 = 7.5 cm, Y2 = −5 cm), deviations up to 4% in the absolute dose at the center of the field were observed. Hence, accurate modeling using this method is difficult because the wedge produces numerous scattered photons and electrons. For tolerance settings at the time of modeling, please refer to Refs. [19, 20].

The nonphysical wedge produces a distribution similar to that of a physical wedge by moving the collimator jaw and/or modifying the dose rate. In the Varian EDW, only a single jaw is moved; moreover, the dose rate for the Siemens virtual wedge is varied. The EDW uses the segmented treatment table (STT) when planning the position of the moving jaw and corresponding doses. The golden STT (GSTT) is used for a wedge angle of 60°, which controls all other wedge fields (i.e., all the field sizes and the wedge angles) as well as the center axis dose of the open field [21]. In other words, EDW settings do not require any input data for beam configuration other than the open beam data. The movement of the collimator in the EDW affects the primary radiation and scatter components, as well as the backscatter of the collimator. Therefore, it is necessary to verify the accuracy of the modeling by comparing calculated estimates to the measured data.

A physical wedge changes the beam energy fluence of the primary X-ray beam through the insertion of a metallic filter at the gantry head. This effect is modeled via a wedge transmission curve; specifically, depth doses, wedge profiles, and longitudinal profiles are used for such modeling. In the Eclipse system, the energy fluence of the primary X-ray beam is modeled as a two-dimensional spectrum that considers the mass-energy attenuation coefficient, which is calculated based on the wedge filter material and thickness. Furthermore, the physical wedge produces secondary radiation when interacting with the primary X-ray beam. Eclipse hence considers the wedge a source of scatter, and modeling is performed using a dual Gaussian plane. Moreover, when physical wedges are used in the Eclipse system, a separate electron contamination source model is applied to the calculation; it is necessary to verify the precision of the final model by comparing it to the acquired data before the wedge filters are

Fogliata et al. compared the calculation models and measurement data using the analytical anisotropic algorithm (AAA) [10–13] and the Acuros XB (AXB) [14–16], which is built into Eclipse (version 10.0) [17]. Six and 15 MV X-rays were validated in their study; measurements

chamber (Semiflex, PTW). Next, depth-dose curves were investigated for several field sizes. In the wedged field along the central axis, the difference in absolute dose between calculated vs. measured values revealed deviations (including standard deviations) smaller than 1%. Moreover, the profile curves were investigated in some field sizes at depths of dmax, 5, 10, 20, and 30 cm. In the central beam region, the average difference in profile curves between calculations and measurements was smaller than 1%, with a standard deviation lower than 1%. Output factor and monitor unit (MU) calculations were also investigated in some field sizes at a source-surface distance (SSD) of 90 cm and a depth of 5 cm in water. The difference between the calculated and measured MUs to deliver a fixed dose to the isocenter exhibited a maximum deviation of 0.2%. Therefore, when using AAA or AXB under reference conditions, it is possible to model correctly. However, when considering clinical use, validation in non-reference conditions is also necessary. Van Esch et al. validated depth-dose curves at SSDs of 80, 90, and 100 cm to verify the accuracy of modeling of the electron contamination as a function of source-to-skin distance [18]. For depth-dose curves involving different SSDs, they reported that the disagreement between calculated and measured data in the buildup region was high under conditions of higher energy and small SSD. In wedge profiles for 60° physical wedges using 18 MV for the selection of asymmetric fields (X = 15 cm, Y1 = 7.5 cm, Y2 = −5 cm), deviations up to 4% in the absolute dose at the center of the field were observed. Hence, accurate modeling using this method is difficult because the wedge produces numerous scattered photons and electrons. For tolerance settings at the time of modeling, please

The nonphysical wedge produces a distribution similar to that of a physical wedge by moving the collimator jaw and/or modifying the dose rate. In the Varian EDW, only a single jaw is moved; moreover, the dose rate for the Siemens virtual wedge is varied. The EDW uses the segmented treatment table (STT) when planning the position of the moving jaw and corresponding doses. The golden STT (GSTT) is used for a wedge angle of 60°, which controls all other wedge fields (i.e., all the field sizes and the wedge angles) as well as the center axis dose

cylindrical ionization

were performed in water using the PTW-MP3 phantom with a 0.125 cm<sup>2</sup>

installed in clinical practice.

254 Radiotherapy

refer to Refs. [19, 20].

For the EDW, Fogliata et al. also compared the calculations to the measurements using the AAA and AXB [17]. Moreover, depth-dose curves were investigated in field sizes of 20 × 20 cm<sup>2</sup> . In wedge fields along the central axis, the difference in absolute dose between the calculations and measurements presented deviations (including standard deviations) smaller than 1%. Furthermore, profile curves were investigated in a field size of 20 × 20 cm<sup>2</sup> at depths of dmax, 5, 10, 20, and 30 cm. In the central beam region, the average differences of profile curves between calculations and measurements were smaller than 1%; standard deviations were lower than 1%. Furthermore, output factors and MU calculations were investigated in some field sizes at SSDs of 90 cm and a depth of 5 cm in water. The difference between the calculated and measured MUs when delivering a fixed dose to the isocenter presented a maximum deviation of 0.2%. Validation in a selection of asymmetric fields (X = 15 cm, Y1 = 7.5 cm, Y2 = −5 cm) indicated deviations up to 1.5% in the absolute dose at the center of the field [18]. Furthermore, in a Monte Carlo simulation study, the surface dose of TPS produced large errors of up to 40% compared to Monte Carlo simulation in depthdose curves [22]. This was attributed to two reasons: First, the calculation of PDDs with TPS is based on ionization chamber measurement data; the measurements of this chamber could be affected by contaminated electrons produced by the moving collimators. Second, the measured surface dose may be averaged incorrectly owing to the erroneous calculation of the ion chamber volume because of the partial volume effect. Monte Carlo simulation indicated that there are significant TPS errors at the outer regions of the field; the maximum relative error of the position difference between TPS and the actual measurements is 20%. Lateral electronic disequilibrium exists in the penumbra regions of the dose profile, especially for smaller field sizes. As mentioned in the American Association of Physicists in Medicine report, TPS cannot accurately calculate backscatter, multiple scattering, or electron disequilibrium in AAA [23]. It is necessary to take into account the calculation precision in the region indicated by the black arrows in **Figure 2**.
