Chapter 5 Central Axis Depth Dose Calculations

2 Definition of Beam Geometry The accurate delivery of a radiation dose to patient depends on the precise positioning of the patient and radiation source. The geometric parameters linking the source and target (tumor at treatment) are described below (Fig.)

3 SSD and SAD are geometric parameters that can be changed, and the ability to change them leads to two different planning and treatment set-up modalities: Constant SSD technique. Here, the isocenter (the point at which all of the radiation beams cross) of the treatment machine (or simulator) is on the patient’s skin (= nonisocentric technique). Field and dose are defined according to A 0.

4 Constant SAD technique. Here the isocenter of the treatment machine (or simulator) is in the patient (in the tumor) (= isocentric technique; Field and dose are defined according to A d.

5 Build-Up Region The region between the skin and the depth at dose maximum (Dmax) is called the build-up region. This region between the surface and depth d is referred to as the dose build-up region in megavoltage beams, and it results from the kinetic energy deposited in the patient by secondary charged particles (which have relatively long ranges) released inside the patient by photon interactions (photoelectric effect, Compton effect, pair production).

6 Percentage Depth Dose (PDD) The ratio (in percent) of the dose absorbed at a predefined depth (D x ) to D max (the dose maximum) for a predefined SSD and field size is termed the percentage depth dose (PDD or DD%). DD% is also defined as the dose at a specific depth as a function of distance, field and energy in a water phantom. The percentage depth dose curve provides information on the quality of the radiation and its energy. The depth at dose maximum can be calculated. The most probable energy at the surface of the phantom can be found by calculating the range of the electrons. This can give information on X-ray contamination.

7 Dose: Energy transferred per unit mass of target tissue, and its unit is Gray (Gy). The dose in radiotherapy is normalized to the Dmax calculated in the phantom. PDD curves are created by plotting DD% values at different depths from the surface of the phantom.

One way of characterizing the central axis dose distribution is to normalize dose at depth with respect to dose at a reference depth. The quantity percentage (or simply percent) depth dose may be defined as the quotient, expressed as a percentage, of the absorbed dose at any depth d to the absorbed dose at a fixed reference depth d 0, along the central axis of the beam Absorbed dose at any depth: d Absorbed dose at a fixed reference depth: d 0 collimator surface phantom D d0 D d d d0d0 A collimator is a device that narrows a beam of particles or waves.

Effect of Field Size and Shape Field size may be specified either geometrically or dosimetrically. The geometric field size is defined as “the projection, on a plane perpendicular to the beam axis, of the distal end of the collimator as seen from the front center of the source”. This definition usually corresponds to the field defined by the light localizer, arranged as if a point source of light were located at the center of the front surface of the radiation source. The dosimetric, or the physical, field size is the distance intercepted by a given isodose curve (usually 50% isodose) on a plane perpendicular to the beam axis at a stated distance from the source. Unless stated otherwise, the term field size in this course will denote geometric field size. In addition, the field size will be defined at a predetermined distance such as the source to surface distance SSD) or the source to axis distance (SAD). The latter term is the distance from the source to axis of gantry rotation known as the isocenter.

Geometrical field size Dosimetrical or physical field size SAD FS Geometrical field size: the projection, on a plane perpendicular to the beam axis, of the distal end of the collimator as seen from the front center of the source Dosimetric ( Physical ) field size: the distance intercepted by a given isodose curve (usually 50% isodose ) on a plane perpendicular to the beam axis pertaining to zones that receive equal doses of radiation

11 Isodose Curves Isodose curves are prepared by combining the points in the phantom or target tissue that receive the same dose. They are calculated by various dosimetric measurements, and the highest dose is considered 100%. The curves are placed in percentage order, and then used to create the dose distribution graphics for the target tissue and the energy of interest (Fig. 1.55). By the using the isodose curves during treatment planning, the dose distribution of the radiation delivered to the target tissue and neighboring structures can be seen from different angles. In a plot of isodose curves, the y-axis shows the depth below the surface of the skin, while the x-axis shows the range of the field.

Dependence on Source to Surface Distance Photon fluence emitted by a point source of radiation varies inversely as a square of the distance from the source. Although the clinical source (isotopic source or focal spot) for external beam therapy has a finite size, the source to surface distance is usually chosen to be large (≥80 cm) so that the source dimensions become unimportant in relation to the variation of photon fluence with distance. In other words, the source can be considered as a point at large source to surface distances. Percent depth dose increases with SSD because of the effects of the inverse square law. Although the actual dose rate at a point decreases with an increase in distance from the source, the percent depth dose, which is a relative dose with respect to a reference point, increases with SSD.

In clinical radiation therapy, SSD is a very important parameter. Because percent depth dose determines how much dose can be delivered at depth relative to the surface dose or D max, the SSD needs to be as large as possible. However, because dose rate decreases with distance, the SSD, in practice, is set at a distance that provides a compromise between dose rate and percent depth dose. For the treatment of deep-seated lesions with megavoltage beams, the minimum recommended SSD is 80 cm. Let P (d,r,f) be the percent depth dose at depth d for SSD = f and a field size r (e.g., a square field of dimensions r × r). Since the variation in dose with depth is governed by three effects—inverse square law, exponential attenuation, and scattering. where µ is the linear attenuation coefficient for the primary and K s is a function that accounts for the change in scattered dose.

d dmdm f1f1 r d dmdm r f2

d dmdm d dmdm f1 r r PDD increases with SSD the Mayneord F Factor ( without considering changes in scattering )

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18 Dose Profile The characteristics of the delivered radiation can be determined by performing measurements in ionization chamber within a water phantom. These characteristics are the flatness, symmetry, and penumbra for that energy (Fig).

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20 General Features of a Water Phantom System The system can perform three-dimensional computerized controlled analyses of the dose, depth dose, dose ratios [TMR, TPR (measurement and calculation)] and isodose calculations. It has an air scanner capable of making measurements in air, along with an ion chamber, and build-up blocks. There is also a mechanism in these equipments which can be used to mount to the head of actual treatment machines. The system has a specific test apparatus that can be used to test the isocenter point for the treatment machine (an “isocheck”). It has an apparatus that can check the monitor unit controls of a linac teletherapy unit (a “monicheck”). It also has a “linear array” apparatus for dynamic wedge and MLC measurements. Penumbra The penumbra is defined as the region of steep dose rate decrease at the edge of radiation beam, noting that the dose rate decreases as a function of the distance from the central axis

21 Types of Penumbra The physical penumbra is the penumbra measured in the dose profile. It is the distance between the points at which the 20 and 80% isodose curves cross the x-axis at D max. There are several components to the physical penumbra: Geometrical penumbra: This occurs due to the size of the source; large sources have larger geometrical penumbras. Transmission penumbra: This occurs due to the beam emerging from the edges of blocks or collimators. It can be decreased by making sure that the shapes of the focalized blocks take into account the beam divergence.

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23 Inverse Square Law This is the decrease in radiation intensity with the square of distance from the source. In tissues, the depth into the tissue thickness is another factor that must be considered in addition to the distance from the source, and the dose decreases exponentially with depth into the tissue. The inverse square law is very important in both radiotherapy and protection from radiation. Since radiotherapy treatments are applied at a short distance from the source, the dose drops off rapidly with distance due to the inverse square law. This situation is observed for both brachytherapy and external radiotherapy. Most external radiotherapy is delivered as teletherapy (at a distance of 80–120 cm). Thus, the dose fall-off due to distance is relatively small. Brachytherapy isodose curves show a rapid dose decrease → rapid fall-off Here, the isodose curves are narrow, so isodose distances are short Teletherapy isodose curves show a slow dose decrease → slow fall-off Here, the isodose curves are wide, so isodose distances are long Isocentric treatment (constant SAD) is affected more by the inverse square law than the SSD technique.

24 Backscatter Factor (BSF) In a phantom, the ratio of the dose maximum to the dose in air at the same depth is called the backscatter factor (BSF). BSF Increases as the energy increases (gets closer to 1) Increases as the field size increases (gets closer to 1) Is independent of SSD Since the energy of the scattering photon increases as the energy increases, BSF increases. At >2 MV, the BSF approaches 1 The depth at which the BSF is measured depends on the energy The BSF measurement depth at energies below that of Co-60 is the surface, since Dmax is close to the surface

25 Tissue to Air Ratio (TAR) The ratio of the dose at depth d (Dd) in a phantom to the dose at the same depth in air (Dair) for the distance used in SAD is defined as the tissue to air ratio (TAR). The BSF is only defined at Dmax, whereas TAR can be defined at any depth. When d = Dmax, TAR = BSF TAR Increases as the energy increases Increases as the field size increases Is independent of SSD at low megavoltage energies Is dependent on SSD at high megavoltage energies (due to electron contamination) The BSF includes primary radiation and scattered radiation; the TAR only includes scattered and absorbed radiation If Dd = Dmax in the TAR formula → peak scatter factor (PSF).

26 Tissue Maximum Ratio (TMR) The ratio of the dose measured at a depth d (Dd) to Dmax in a phantom is defined as the tissue maximum ratio (TMR) : It is defined by performing two measurements in the phantom (i.e., Dd and Dmax are measured). The TMR is normalized to Dmax, in contrast to the TAR. TMR 1. Increases as energy increases 2. Increases as the field size increases 3. Is independent of SSD at low megavoltage energies 4.Is dependent on SSD at high megavoltage energies (due to electron contamination)

27 The Differences Between TAR and TMR 1. TAR uses the dose in air 2. TMR uses the dose at Dmax in phantom. 3. TAR is used in isocentric treatment technique. 4. TMR calculation is done instead of TAR at energies more than 3 MV. Scatter Air Ratio (SAR) The ratio of dose measured at d depth (Dd-phantom) in phantom to the dose measured at the same depth in air (Dd-air) is defined as SAR. It is used for the calculation of mean scattered dose. It is independent on SSD as TAR, but dependent parameter on energy, depth, and field size.

28 Collimator Scattering Factor (Sc) The ratio of the dose measured in any field at a depth d in air to Dmax measured in a reference field (10 × 10 cm2) in air is called the collimator scattering factor (Sc or CSF)

29 The collimator scattering factor is also termed the output factor. Sc is measured in an ion chamber with a build-up cap. It is: 1. Correlated with field size 2. Correlated with energy (scattering increases as the field size and energy increase). Phantom Scattering Factor (Sp) The ratio of the dose measured in a definite field size at a depth d to Dmax measured in a reference field (10 × 10 cm2) is defined as the phantom scattering factor (Sp). The ratio of the BSF calculated in any field at a depth d to the BSF in a reference field in a phantom is another way of defining Sp. Sp is important for determining scattered radiation from a phantom.

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Relationship between TAR and Percent Depth Dose Tissue-air ratio and percent depth dose are interrelated. The relationship can be derived as follows: Considering Figure 9.9A, let TAR(d,r d ) be the tissue-air ratio at point Q for a field size r d at depth d. Let r be the field size at the surface, f be the SSD, and d m be the reference depth of maximum dose at point P. Let D fs (P) and D fs (Q) be the doses in free space at points P and Q, respectively (Fig. 9.9B,C). D fs (P) and D fs (Q) are related by inverse square law:

Conversion of Percent Depth Dose from One SSD to Another—the TAR Method To convert percent depth dose from one SSD to another the Mayneord F factor, which is derived solely from inverse square law considerations, is used. A more accurate method is based on the interrelationship between percent depth dose and TAR. This TAR method can be derived from Equation 9.23 as follows. Suppose f 1 is the SSD for which the percent depth dose is known and f 2 is the SSD for which the percent depth dose is to be determined. Let r be the field size at the surface and d be the depth, for both cases. Referring to Figure 9.6, let r d,f1 and r d,f2 be the field sizes projected at depth d in Figure 9.6A and B, respectively:

As mentioned earlier, for high-energy x-rays, that is, above 8 MV, the variation of percent depth dose with field size is small and the backscatter is negligible. Equations 9.28 and 9.29 then simplify to a use of Mayneord F factor.

Practical Examples

37 Monitor Unit (MU) Calculation in a Linear Accelerator Monitor units are the units in which the output of a linac is measured. Linacs are calibrated to give 1 cGy at a SAD distance of 100 cm, for a field size of 10 × 10 cm, and at the depth corresponding to Dmax, and this calibration dose is defined as one monitor unit (MU). Percent depth dose is a suitable quantity for calculations involving SSD techniques. Machines are usually calibrated to deliver 1 rad (10 -2 Gy) per monitor unit (MU) at the reference depth t 0, for a reference field size 10 × 10 cm and a source to calibration point distance of SCD.

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TMR is the quantity of choice for dosimetric calculations involving isocentric techniques. Since the unit is calibrated to give 1 rad (10 -2 Gy)/MU at the reference depth t 0 and calibration distance SCD and for the reference field (10 × 10 cm), then the monitor units necessary to deliver isocenter dose (ID) at depth d are given by: 42

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44 Beam Modifiers Bolus Bolus is used for tissue compensation, and is put on the skin at right angles to the beam axis. It is made from a tissue-equivalent density material (Fig.). Bolus use leads to increased effects of radiation scattered into the skin. Thus, the entrance dose to the skin increases. Secondary electrons produced by the bolus also increase the skin dose, since the bolus is in contact with skin ( → the depth corresponding to Dmax gets close to the surface). Compensating Filters The dose distribution is not homogeneous if the surface of the patient is not flat. Therefore, a compensating filter is positioned between the beam source and the skin to reduce the dose delivered to the area with thinner tissue in order to achieve a homogeneous dose distribution in the irradiated volume (Fig.). Compensating filters are made of aluminum–tin or copper–tin mixtures, and are individually designed to compensate for tissue irregularities.

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47 Wedge Filters Metal wedge filters can be used to even out the isodose surfaces for photon beams delivered onto flat patient surfaces at oblique beam angles (Fig.). These wedges can be static, dynamic or motorized. They are most commonly used in tangential irradiation (e.g., the breast, head and neck regions), and they prevent hot spots in vital organs and cold spots in the radiation field. They provide a more homogeneous dose distribution.

48 Shielding Blocks These are manufactured in order to shield the normal critical structures in radiotherapy portals. There are two types of shielding block. Standard blocks come with the teletherapy unit, and have various sizes and shapes. They are designed according to the area that needs to be protected. On the other hand, focalized blocks are individually made in mold rooms to shield the areas of the field that need protecting (according to the simulation procedure). Standard blocks are only used in emergencies.

49 Multileaf Collimator (MLC) Irregular fields cannot be shaped without focalized blocks in conventional radiotherapy machines. The collimator systems in Co-60 and old linac machines provide only a rectangular field. Multileaf collimators, on the other hand, are composed of many leaves, and each leaf can move independently (Fig.). By arranging these leaves appropriately, irregular fields that a required by the treatment plan can easily obtained without using blocks (Table 1).

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61 END OF CHAPTER 5 ANY QUESTIONS