2.1.1 Definition of small field

radiation fields (4 cm 4 cm up to 40 cm 40 cm) in terms of their size. Due to their small size, the penumbra region generated from the edges of the fields overlap, resulting in apparent field widening of the fields [2]. As a result the traditional detectors used for dosimetry become large relative to the size of the field, and this may lead to unintended errors while performing measurements for small field [3]. The widely accepted Code of Practices (COPs) reported in the Technical Reports Series No.398 of IAEA have procedures to determine absorbed dose to water from measurements made with an ionization chamber in photon, electron, proton, and heavy-ion beams [4–7]. The ionization chambers are used to perform the measurement using the calibration coefficients obtained from primary standard dosimetry laboratories (PSDL) in terms of absorbed dose to water under reference conditions. However, these COPs do not consider the conditions deviating from reference

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

As a result of technological improvements and introduction to new radiation therapy techniques, the small static radiation beams are rapidly used, which is achieved by using standard or add-on MLCs or by the design of the radiation equipment. Consequently, the uncertainties related to the clinical dosimetry based on traditionally used COPs have been considerably increasing, and errors related to dosimetry have been growing larger. The main causes of this increase in the size of dosimetric errors are that it is not possible to achieve the reference conditions as recommended by traditional COPs on some radiation equipment and non-

standardization of dose measurement procedures in small and composite radiation fields. Hence, many accidents have been reported that have occurred due to the use

The dosimetry of small fields is quite important. The beam data once configured during commissioning will be used for treatment in the future, so there should be high accuracy in the dosimetry of these small fields. To achieve high accuracy in beam data measurement in small fields and to be able to measure the dose in small fields with high precision, it is quite important to understand the physical aspects of the small fields. The measurement of output factors, beam profiles, and depth dose data is highly influenced by the beam energy, scattering, and field dimensions at the level of detector. The knowledge of the important characteristics of small fields is required to measure the dose parameters and to collect data for treatment. Hence, in 2017 a joint working group from the International Atomic Energy Agency (IAEA) and American Association of Physicists in Medicine (AAPM) proposed a new COP, Technical Report Series (TRS) No. 483 (Dosimetry of Small Static Fields Used in External Beam Radiotherapy). [9] This COP provides recommendations related to the relative and reference dosimetry of small and composite fields. Hence, this chapter discusses the concepts related to the dosimetry of small and composite field sizes.

In general, two types of field sizes have been defined by the International Electrotechnical Commission. The first is called the geometric field size; it is defined as two-dimensional projection by the source of radiation of the collimator opening on a plane orthogonal to the central axis of the primary photon beam. The second is called the irradiation field size; it is defined as the two-dimensional area bounded by specific isodose lines in a plane orthogonal to the central axis of the radiation beam. An alternative way to define irradiation field size is by using full width at half maximum (FWHM) of radiation beam profiles obtained along the lateral direction (in-line or crossline profiles) at isocenter depth. This FWHM is equal to the opening of the collimating jaws at the isocenter. Therefore, at isocenter the geometrical and irradiation fields are in consonance with each other. Hence, this agreement can be

of recommendations of traditional COPs in dosimetry of small fields [8, 9].

conditions in detail [8].

2. Field size definition

40

Any radiation beam which fulfills at least one of the following conditions can be named as small field:


Conditions I and II are related to the size of the radiation beam, whereas condition III refers to the size of the detector. If all the above mentioned conditions are fulfilled, then the penumbra region overlaps with the volume of the detector.

#### Figure 1.

Schematic illustration of the definition of geometrical and irradiation field size using the concept of geometrical projection and FWHM of radiation beam profile for both broad and small beam conditions: (a) for large field sizes, where condition of LCPE is fulfilled and radiation source is not blocked, the full width at half maximum (FWHM) of the lateral dose profiles is equal to the opening of the collimating jaws at the isocenter. Hence, for large field sizes at isocenter, geometrical field size and irradiation field size are in agreement with each other; (b) for the field sizes of the order of the range of secondary charged particles, the penumbra region of opposite jaws. It results in small error in determining the field size from the FWHM of lateral beam profiles; (c) however, for small field sizes due to the reduction in the radiation output along the central axis, the value of maximum dose is reduced. Hence, the FWHM of lateral beam profile is pushed outward and agreement between the geometrical and irradiation fields is lost.

less than 5 mm, as it can be observed from Figure 2, the loss of LCPE also starts for radiation beams with a radius of 5 mm. Therefore, the partial blockage of radiation source starts when loss of charge equilibrium starts [1]. The partial blockage of radiation source results in a decrease in the beam output. Hence, result in the sharp dose gradient, as a consequence of which the response of the detector is affected. Therefore, the absence of LCPE and partial blockage of small beams of photon radiation source is the main cause of the decrease in the radiation output along the beam axis. This effect gets more dominant with increase in the energy of the

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field…

The last condition is related to the size of the detector relative to the size of the

A schematic representation of volume averaging effect along the central axis of the beam. The Gaussian curve in black represents the actual beam profile; the measured profile obtained using the detector (5 mm long) is given represented by dashed line; the dimensions of the detector along the scanning axis is represented by double arrow;

the variation between the measured profile and Gaussian curve is given by dash-dotted line.

radiation beam. The signal produced by the detector on irradiation is directly proportional to the average of the deposited dose within the detector's sensitive volume. The signal obtained from the detector is responsive to the uniformity of deposited radiation dose over the sensitive volume of the detector, also known as volume averaging as illustrated in Figure 4 [13]. Hence, in order to obtain dose

radiation beam and decrease in the density of the medium.

2.1.1.2 Conditions related to detector size

DOI: http://dx.doi.org/10.5772/intechopen.89150

A schematic illustration of the source occlusion effect.

Figure 4.

43

Figure 3.

#### Figure 2.

The ratio of collisional kerma in water and absorbed dose in water at a depth of 5 cm. Source to surface distance (SSD) of 80 cm is used for Co60 and SSD of 100 cm was used for photon beam. X axis represents the radius of the beam and the Y axis represents the ratio of the quantities.

#### 2.1.1.1 Conditions based on field size

For the radiation beams with FWHM lesser than the maximum range of the secondary electrons, the LCPE is absent. The absence of LCPE makes it difficult to perform measurements for absorbed dose to water for detectors made of non-water equivalent material. In order to find a relation between the size of the beam and the size of the detector for which the LCPE exists, LCPE range (rLCPE) has been proposed. rLCPE can be defined as the minimum radius of circular photon field for which the ratio of collisional kerma in water and dose deposited in water is equal to 1 at the center of the beam. Figure 2 illustrates the concept of LCPE, where the ratio of collisional kerma in water and dose deposited in water are calculated using Monte Carlo simulations at a depth of 5 cm along the central axis of the radiation beam [11].

rLCPE (in cm) can be manifested as a function of beam quality of photon beam, Tissue Phantom Ratio (TPR), TPR20,10(10):

$$r\_{LCPE} = 8.369 \times TPR\_{20,10}(10) \, - \, 4.382 \, \tag{1}$$

In the case of beam quality defined in terms of percentage depth dose at a depth of 10 cm, %dd(10,10)x, rLCPE can be calculated using the correspondence between %dd(10,10)x and TPR20,10(10) [12]:

$$r\_{LCPE} = 77.97 \times 10^{-3} \times \text{ }\% \, dd(10, 10) \, \_\text{x} - 4.382 \tag{2}$$

The second condition related to the partial blockage of the primary radiation source is illustrated in Figure 3. It is based on the finite size of the extended focal spot, which can be determined by FWHM measurement of bremsstrahlung spectrum emitted by the radiation source. The partial shielding of the radiation source by the beam modifier, used for the definition of small beam, results in decrement of radiation output along the central axis of the radiation beam relative to the unshielded condition. The radiation beams with size equal to or less than the FWHM of the emission spectra emitted from the source, the effect of partial occlusion of radiation source becomes more dominant. Since the source size is generally

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field… DOI: http://dx.doi.org/10.5772/intechopen.89150

less than 5 mm, as it can be observed from Figure 2, the loss of LCPE also starts for radiation beams with a radius of 5 mm. Therefore, the partial blockage of radiation source starts when loss of charge equilibrium starts [1]. The partial blockage of radiation source results in a decrease in the beam output. Hence, result in the sharp dose gradient, as a consequence of which the response of the detector is affected.

Therefore, the absence of LCPE and partial blockage of small beams of photon radiation source is the main cause of the decrease in the radiation output along the beam axis. This effect gets more dominant with increase in the energy of the radiation beam and decrease in the density of the medium.

### 2.1.1.2 Conditions related to detector size

The last condition is related to the size of the detector relative to the size of the radiation beam. The signal produced by the detector on irradiation is directly proportional to the average of the deposited dose within the detector's sensitive volume. The signal obtained from the detector is responsive to the uniformity of deposited radiation dose over the sensitive volume of the detector, also known as volume averaging as illustrated in Figure 4 [13]. Hence, in order to obtain dose

Figure 3. A schematic illustration of the source occlusion effect.

#### Figure 4.

A schematic representation of volume averaging effect along the central axis of the beam. The Gaussian curve in black represents the actual beam profile; the measured profile obtained using the detector (5 mm long) is given represented by dashed line; the dimensions of the detector along the scanning axis is represented by double arrow; the variation between the measured profile and Gaussian curve is given by dash-dotted line.

2.1.1.1 Conditions based on field size

the beam and the Y axis represents the ratio of the quantities.

Tissue Phantom Ratio (TPR), TPR20,10(10):

%dd(10,10)x and TPR20,10(10) [12]:

beam [11].

42

Figure 2.

For the radiation beams with FWHM lesser than the maximum range of the secondary electrons, the LCPE is absent. The absence of LCPE makes it difficult to perform measurements for absorbed dose to water for detectors made of non-water equivalent material. In order to find a relation between the size of the beam and the size of the detector for which the LCPE exists, LCPE range (rLCPE) has been proposed. rLCPE can be defined as the minimum radius of circular photon field for which the ratio of collisional kerma in water and dose deposited in water is equal to 1 at the center of the beam. Figure 2 illustrates the concept of LCPE, where the ratio of collisional kerma in water and dose deposited in water are calculated using Monte Carlo simulations at a depth of 5 cm along the central axis of the radiation

The ratio of collisional kerma in water and absorbed dose in water at a depth of 5 cm. Source to surface distance (SSD) of 80 cm is used for Co60 and SSD of 100 cm was used for photon beam. X axis represents the radius of

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

rLCPE (in cm) can be manifested as a function of beam quality of photon beam,

In the case of beam quality defined in terms of percentage depth dose at a depth of 10 cm, %dd(10,10)x, rLCPE can be calculated using the correspondence between

The second condition related to the partial blockage of the primary radiation source is illustrated in Figure 3. It is based on the finite size of the extended focal spot, which can be determined by FWHM measurement of bremsstrahlung spectrum emitted by the radiation source. The partial shielding of the radiation source by the beam modifier, used for the definition of small beam, results in decrement of

radiation output along the central axis of the radiation beam relative to the unshielded condition. The radiation beams with size equal to or less than the FWHM of the emission spectra emitted from the source, the effect of partial occlusion of radiation source becomes more dominant. Since the source size is generally

ð1Þ

ð2Þ

deposited to the water from the signal produced by the detector, the correction factor must be used for the volume averaging. It can be defined as a ratio of dose deposited in water at the point of reference in the nonexistence of the detector to the average of the dose deposited over the detection volume of the detector in the nonexistence of the detector. It can be acquired by integrating the threedimensional distribution of dose over the detector's sensitive volume [14–19].

The general expression that can be used in calculation of correction factor for averaging of the signal over the detector's sensitive volume is:

$$k\_{vol} = \frac{\int \int\_{A} \, ^{W(x,y)} \, d\mathbf{x} dy}{\int \int\_{A} \, ^{W(x,y)} OAR(x,y) \, d\mathbf{x} dy} \tag{3}$$

signal; the detector signal must be beam energy independent and directly proportional to the dose deposited in water; and it must show minimum fluctuations,

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field…

The detector size must be such that it fulfills rLCPE criteria. The positioning of the air-filled detector must be such that the charged particle fluence remains

Modern radiotherapy linear accelerators are available in two general models, that is, with flattening filter (WFF) and flattening filter free (FFF). For WFF radiation emitters, air-filled detectors with sensitive volume range between 0.3 and

, since these detectors are often water resistant and easy to use for in-phantom measurements have negligible leakage effect and good signal to noise ratio [20]. In the case of FFF radiation emitters, air-filled detectors with sensitive volume lying in the range of 0.1–0.3 cm<sup>3</sup> are preferred over the commonly used Farmer type airfilled detectors [21]. In case the Farmer type air-filled detectors is used in FFF beam, then the beam profiles must be corrected for their non-uniformity; the factor

A comparative study was performed by Le Roy et al. [24] using 24 small volume air-filled detectors of 8 different types, to study the probability of their use in highenergy photon beams for reference dosimetry, with beam size ranging down to 2 cm 2 cm. The authors reported that out of eight different types of air-filled detectors only three types of chambers were found suitable for small beam dosimetry, which includes CC04, CC01 models from IBA, and AISL from Exradin.

In case of very small circular msr fields as that of Gamma Knife machine having the diameter of the radiation beam 1.6 or 1.8 cm. It is found that these fields exhibit LCPE, rLCPE was found to be 0.6 cm for 60Co [25]. The chambers fulfilling the condition of rLCPE in msr fields are suitable for use in these very small circular fields

The air-filled detectors with sensitive volume less than 0.3 cm3 and air cavity

6 cm 6 cm. The criteria used for selection of detector volume and air cavity length can be demonstrated by relating it with the size of the radiation beam and beam energy. The detector with air cavity of 7 mm satisfies rLCPE condition for field sizes down to 4 cm in 10 MV beam, down to 3 cm in 6 MV beam, and down to 2 cm for

3.2 Different types of detectors for relative dosimetry in small radiation beams

For the measurements of output factor, volume averaging effect, dependence on the: size of the radiation beam; beam energy; dose rate; equivalence to water and overall perturbation are the deciding factors to find the suitable detector for

The concept of relative dosimetry is based on the determination of various dosimetric beam parameters, such as measurement of dose distribution with depth along central axis of the beam, lateral beam profiles, etc. as a function of the size of the radiation beam and its shape. The choice of appropriate detector is based on the specific type of parameter being measured. Hence, two or more suitable detectors of different kinds can be used to perform the same measurement to be sure about

length of 7 mm are preferred for dosimetric measurements for fmsr less than

approximately uniform over the sensitive volume of the detector.

3.1.1 The square equivalent msr field (fmsr) greater than 6 cm 6 cm

for correction can be 1.5% for FFF photon beam of 6 MV [22, 23].

3.1.2 The square equivalent msr field (fmsr) less than 6 cm 6 cm

leakage, and no effect of cable irradiation.

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1 cm3

for reference dosimetry.

Co<sup>60</sup> radiation beam.

the accuracy of measurements.

45

where (x,y) are the positions of the points on the axis orthogonal to the beam axis, A is the projected area of the detector's sensitive volume in a plane perpendicular to the central axis of the beam, OAR (x,y) gives the off-axis ratio at position (x,y), and w(x) is the weighting function that represents extension of cavity of the air-filled detector along the central axis (z) of the beam in relation to the lateral coordinates of the beam (x and y).

The volume averaging effect and the disturbance caused by the existence of detector to the fluence of the charged particles are two main effects observed in small beam dose measurement. As discussed above, due to the presence of dose gradients and absence of LCPE, the perturbation effect becomes dominant and cannot be modeled easily. Along with this, the errors related to the averaging of the detector signal along its volume become larger. Consequently, the dose gradients and nonexistence of LCPE make it difficult to perform dosimetric measurements for small beams.

The radiation fields, having the distance between the edges of the field and outer surface of the detector volume less than the rLCPE within a medium, satisfy the small beam condition. In order to prevent such condition and perform dosimetric measurements accurately, the FWHM or the radius of the photon beam must be equal to the sum of rLCPE and half of the detector's outer volume.
