5.1.1 Calibration coefficient for fmsr is available

In situations where calibration coefficient in terms of absorbed dose to water ( ) is available for machine-specific reference field (fmsr) and beam quality similar to that of the user beam (Qmsr), the absorbed dose to water at depth of reference (zref) in the nonexistence of detector in water can be determined using the following relation:

$$D\_{\
u,Q\_{\
u\nu r}}{}^{f}{}\_{\
u r} = \mathbf{M}\_{Q\_{\
u\nu r}}{}^{f}{}\_{\
u} \mathcal{N}\_{D,\mathbf{w}} \; \mathcal{Q}\_{\
u \nu r}{}^{f \, \mkern-1.1mu \; \nu} \tag{29}$$

where is the detector reading fmsr beam corrected for influential quantities, such as temperature, pressure, perturbation factors, etc.

## 5.1.2 Calibration factor available for fref (10 cm � 10 cm) and beam quality (Q0) correction factor

In conditions where calibration coefficient ( ) is provided by calibration laboratory in terms of fref and correction factor quality of beam Q0. The absorbed dose to water can be calculated using the following relation:

$$D\_{\text{w, }Q\_{msr}}{}^{f}{}\_{msr} = M\_{\mathcal{Q}\_{msr}}{}^{f}{}\_{msr} N\_{D, w, Q\_0}{}^{f}{}\_{w}{}^{ref} k\_{\mathcal{Q}\_{msr}, Q\_0}{}^{f}{}\_{ref} \tag{30}$$

where is the detector reading reworked for influential quantities and is the correction factor for difference in beam quality and field size.

### 5.1.3 Calibration factor available for fref (10 cm � 10 cm) without beam quality (Q0) correction factor

In the situation where the correction factor for the generic quality of beam, correcting for the difference in beam quality and effect of difference in field size, is not provided by the calibration laboratory, the dose deposited can be determined using the following relation:

$$D\_{\text{w},Q\_{\text{msr}}}{}^{\;f\;\;\;\text{msr}} = \mathcal{M}\_{Q\_{\text{msr}}}{}^{\;f\;\;\;\;\text{var}}N\_{D,\text{w},Q\_{0}}{}^{\;f\;\;\;\;ref\;k}k\_{Q,Q\_{0}}{}^{\;f\;\;\;\;\;\text{ref}}k\_{Q\_{\text{msr}},Q}{}^{\;f\;\;\;\;\text{var}}N\_{\text{ref}}\tag{31}$$

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

where is the detector reading for fmsr reworked for influential quantities, is the detector calibration factor in terms of absorbed dose to water in fref beam and Q0 quality of beam, is the correction factor for difference in detector response of detector in beam quality Q0 in field size fref and response of detector in beam quality Q in fref beam size, and is the beam quality correction factor to account for the difference between the response of detector in beam quality Q, fref beam size and beam quality Qmsr, and beam size of fmsr.

In order to determine the dose deposited in water for FFF radiation beam, the following relation can be used:

$$\dot{D}^{f\_{\text{npr}}}\_{\text{w, \dot{Q}}, \dot{Q}\_{\text{min}}, \dot{P}\_{\text{inf}}} = \dot{M}^{f\_{\text{npr}}}\_{\text{w, \dot{Q}}, \dot{P}\_{\text{min}}, \dot{Q}\_{\text{w, \dot{W}}, \dot{Q}\_{\text{max}}}} \dot{N}\_{\text{D, w, \dot{W}}, \dot{Q}\_{\text{tot}}} \dot{Q}\_{\text{w, \dot{W}}, \dot{Q}\_{\text{inf}}} \dot{Q}\_{\text{w, \dot{W}}, \dot{P}\_{\text{inf}}} \dot{Q}\_{\text{min}} \dot{Q}\_{\text{min}} \dot{Q}\_{\text{inf}} \quad \text{(32)}$$

where is the correction for beam quality for difference in response of the detector in beam QWFF, beam size fref and response of detector in quality of beam Q0, and beam size of fref. It can be taken from the international dosimetry protocols [1, 2, 7], and is the factor of correction for variation in response of the detector in the FFF and WFF radiation fields. It can be obtained from Monte Carlo studies. Figure 16 summarizes the different conditions discussed above for the determination of dose deposited in water.

#### Figure 16.

Schematic summary of the determination of absorbed dose in case of small beams considering the case of machine specific reference field according to the formalism given by TRS 483. The arrows and formulas labeled (1), (2) and (3) refer to Section 6.1.1, 6.1.2 and 6.1.3, respectively.

recommendation provided by task group series (TRS) 398 and other equivalent protocols [1–7]. However, in radiation equipment where fref setting is not

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

condition.

the following relation:

correction factor

correction factor

using the following relation:

64

5.1 Measurement of absorbed dose in fmsr

5.1.1 Calibration coefficient for fmsr is available

feasible, fmsr is used. The full width at half maximum of fmsr must satisfy small-field

In situations where calibration coefficient in terms of absorbed dose to water ( ) is available for machine-specific reference field (fmsr) and beam quality similar to that of the user beam (Qmsr), the absorbed dose to water at depth of reference (zref) in the nonexistence of detector in water can be determined using

where is the detector reading fmsr beam corrected for influential

5.1.2 Calibration factor available for fref (10 cm � 10 cm) and beam quality (Q0)

In conditions where calibration coefficient ( ) is provided by calibration laboratory in terms of fref and correction factor quality of beam Q0. The absorbed

where is the detector reading reworked for influential quantities and

5.1.3 Calibration factor available for fref (10 cm � 10 cm) without beam quality (Q0)

In the situation where the correction factor for the generic quality of beam, correcting for the difference in beam quality and effect of difference in field size, is not provided by the calibration laboratory, the dose deposited can be determined

is the correction factor for difference in beam quality and field size.

quantities, such as temperature, pressure, perturbation factors, etc.

dose to water can be calculated using the following relation:

ð28Þ

ð29Þ

ð30Þ

ð31Þ

## 5.2 Measurement of field output factors

To measure the dose deposited by clinical radiation beams with respect to the msr field in Ref. dosimetry, field output factors ( ) are determined. They are also known as relative dose factors [91] or total scatter factors [1, 56, 79]. It is defined as the ratio of dose deposited in water by clinical beam (fclin) with the quality of beam (Qclin) to the dose deposited in water in msr field (fmsr) with quality of beam Qmsr:

ð33Þ

1.The generation of particles is based on the distribution function used to

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

3.The probability distribution functions are sampled using interaction cross

4.The step of a particle is defined as the distance between two consecutive

5."Scoring" for each and every outcome is performed to calculate quantities,

There are various Monte Carlo codes available which can be used in radiation dosimetry of stereotactic fields. The most commonly used MC codes are Electron Gamma Shower [106], GEANT4 [107], and the Monte Carlo N-Particle code [108]. Due to highly accurate radiation transport algorithm for electrons and photons and easy to use BEAM package, EGSnrc is one of the most frequently used Monte Carlo

Heydarian et al. [109] performed a study using diamond detectors, diodes, films, and EGS4 Monte Carlo code, for field sizes ranging from 7 to 23 mm on Siemens Mevatron linac. Scielzo et al. [110] investigated the application of Monte Carlobased calculation algorithm for treatment planning in stereotactic radiosurgery for Varian 2100C. Authors reported large difference between the treatment planning system (TPS) and MC calculation, especially near the inhomogeneous regions. Verhaegen et al. [92] performed a dosimetric study using the BEAM/EGS4 Monte Carlo code for 6 MV SRS unit for circular field sizes with diameter ranging from 1.25 to 5 cm at isocenter. The authors reported a good agreement between the measurement and computational results for most of the detectors in terms of cone factor. De Vlamynck et al. [111] performed clinical dosimetry using Markus parallel plate ion chamber and diamond detector in 6 MV photon beam of SL 25 (Elekta) linac and compared the results with Monte Carlo calculations. The depth dose distributions for measured and calculated data were found in good agreement with each other; however slight discrepancies were reported for lateral beam profiles. Cheung et al. [112] verified the accuracy of treatment planning system (Leksell GammaPlan) using Gafchromic films and Monte Carlo methods for field sizes ranging from 4 to 18 mm on a Gamma Knife unit. Variations up to 10% were observed for Gafchromic films which were attributed to the energy dependency of films. Westermark et al. [113] performed a comparative study using diamond detector, liquid ion chamber, plastic scintillator, silicon diode, and Monte Carlo techniques for small-field sizes (φ > 4 mm) of 6 and 18 MV photon beams in order to study the response of various dosimeters. Deng et al. [114] generated a multiple source model by following the procedure of beam commissioning for Cyberknife unit for Monte Carlo-based treatment planning. Authors reported largest variation of 9.5% for ionization

6. In order to reduce the statistical uncertainty in the calculation, it is recommended to perform simulations using a large number of particles

2.The random numbers are obtained in the range of (0, 1) using the

describe the radiation source.

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

events (collision/scatter).

).

codes for small-field dosimetry.

sections.

(<sup>1</sup> <sup>10</sup><sup>9</sup>

67

pseudorandom number generators.

such as dose deposited in a medium.

6.2 Monte Carlo studies for small-field dosimetry

The output factors are utilized to calculate the dose deposited to water in clinical beams (fclin) from the dose deposited to water in machine-specific reference beams (fmsr). can be determined using the detector readings by using the following relation:

$$
\Omega\_{\mathcal{Q}\_{clto}^{I}\mathcal{Q}\_{mmr}^{I}} \stackrel{\mathcal{F}\_{clto}^{I}\mathcal{F}\_{mmr}}{\sim} = \frac{\mathcal{M}\_{\mathcal{Q}\_{clto}^{I}}}{\mathcal{M}\_{\mathcal{Q}\_{mmr}}} k\_{\mathcal{Q}\_{clto}^{I}\mathcal{Q}\_{mmr}} \stackrel{\mathcal{F}\_{clto}^{I}\mathcal{F}\_{mmr}}{\sim} \tag{34}$$

where is the output correction factor; it can be determined either by direct measurements or using Monte Carlo techniques.

### 6. Monte Carlo simulation in small-field dosimetry

Monte Carlo techniques are widely used as an alternative in situations where measurements are either difficult or are not possible. Many authors have reported about the possibility of using MC techniques for small-field dosimetry [92–98]. Monte Carlo techniques can be used to calculate the correction factors as discussed in Section 6 of this chapter. It can also be used as a reference or standard with respect to different techniques of relative and absolute dose measurements with acceptable accuracy. With the use of Monte Carlo techniques, the dosimetry in lowdensity materials can be understood where it is difficult to perform measurements due to the presence of non-equilibrium conditions [99–105]. In radiation dosimetry two approaches are followed for the use of MC techniques. First approach is to calculate correction factors for the dosimeters to be used for dosimetric measurements. In the second approach, the dosimetric quantities are directly calculated, which is equivalent to performing measurements in ideal conditions. However, it is important to verify the MC model against the beam modeling parameters before using it for radiation dosimetry calculations.

#### 6.1 General purpose of Monte Carlo codes for radiation dosimetry

It is possible to explicitly model the interaction of every particle using Monte Carlo techniques. The main characteristics of Monte Carlo techniques used for radiation dosimetry are:

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


There are various Monte Carlo codes available which can be used in radiation dosimetry of stereotactic fields. The most commonly used MC codes are Electron Gamma Shower [106], GEANT4 [107], and the Monte Carlo N-Particle code [108]. Due to highly accurate radiation transport algorithm for electrons and photons and easy to use BEAM package, EGSnrc is one of the most frequently used Monte Carlo codes for small-field dosimetry.

### 6.2 Monte Carlo studies for small-field dosimetry

Heydarian et al. [109] performed a study using diamond detectors, diodes, films, and EGS4 Monte Carlo code, for field sizes ranging from 7 to 23 mm on Siemens Mevatron linac. Scielzo et al. [110] investigated the application of Monte Carlobased calculation algorithm for treatment planning in stereotactic radiosurgery for Varian 2100C. Authors reported large difference between the treatment planning system (TPS) and MC calculation, especially near the inhomogeneous regions. Verhaegen et al. [92] performed a dosimetric study using the BEAM/EGS4 Monte Carlo code for 6 MV SRS unit for circular field sizes with diameter ranging from 1.25 to 5 cm at isocenter. The authors reported a good agreement between the measurement and computational results for most of the detectors in terms of cone factor. De Vlamynck et al. [111] performed clinical dosimetry using Markus parallel plate ion chamber and diamond detector in 6 MV photon beam of SL 25 (Elekta) linac and compared the results with Monte Carlo calculations. The depth dose distributions for measured and calculated data were found in good agreement with each other; however slight discrepancies were reported for lateral beam profiles. Cheung et al. [112] verified the accuracy of treatment planning system (Leksell GammaPlan) using Gafchromic films and Monte Carlo methods for field sizes ranging from 4 to 18 mm on a Gamma Knife unit. Variations up to 10% were observed for Gafchromic films which were attributed to the energy dependency of films. Westermark et al. [113] performed a comparative study using diamond detector, liquid ion chamber, plastic scintillator, silicon diode, and Monte Carlo techniques for small-field sizes (φ > 4 mm) of 6 and 18 MV photon beams in order to study the response of various dosimeters. Deng et al. [114] generated a multiple source model by following the procedure of beam commissioning for Cyberknife unit for Monte Carlo-based treatment planning. Authors reported largest variation of 9.5% for ionization

5.2 Measurement of field output factors

of beam Qmsr:

following relation:

To measure the dose deposited by clinical radiation beams with respect to the msr field in Ref. dosimetry, field output factors ( ) are determined. They are also known as relative dose factors [91] or total scatter factors [1, 56, 79]. It is defined as the ratio of dose deposited in water by clinical beam (fclin) with the quality of beam (Qclin) to the dose deposited in water in msr field (fmsr) with quality

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

The output factors are utilized to calculate the dose deposited to water in clinical beams (fclin) from the dose deposited to water in machine-specific reference beams (fmsr). can be determined using the detector readings by using the

where is the output correction factor; it can be determined

Monte Carlo techniques are widely used as an alternative in situations where measurements are either difficult or are not possible. Many authors have reported about the possibility of using MC techniques for small-field dosimetry [92–98]. Monte Carlo techniques can be used to calculate the correction factors as discussed in Section 6 of this chapter. It can also be used as a reference or standard with respect to different techniques of relative and absolute dose measurements with acceptable accuracy. With the use of Monte Carlo techniques, the dosimetry in lowdensity materials can be understood where it is difficult to perform measurements due to the presence of non-equilibrium conditions [99–105]. In radiation dosimetry two approaches are followed for the use of MC techniques. First approach is to calculate correction factors for the dosimeters to be used for dosimetric measurements. In the second approach, the dosimetric quantities are directly calculated, which is equivalent to performing measurements in ideal conditions. However, it is important to verify the MC model against the beam modeling parameters before

either by direct measurements or using Monte Carlo techniques.

6. Monte Carlo simulation in small-field dosimetry

using it for radiation dosimetry calculations.

radiation dosimetry are:

66

6.1 General purpose of Monte Carlo codes for radiation dosimetry

It is possible to explicitly model the interaction of every particle using Monte Carlo techniques. The main characteristics of Monte Carlo techniques used for

ð33Þ

ð34Þ

of the dose distribution or its contribution to the procedure of inverse optimization. Hence, the dose distribution obtained from TPS is expected to be inaccurate in regions beyond the edges of the primary field. The predictions in low-dose regions near the primary field by TPS have been shown to be inaccurate as well. Jang et al. [126] investigated the inaccuracies in dose calculation in low-dose regions for intensity-modulated radiotherapy (IMRT) and reason behind these inaccurate calculations by comparing their results against Monte Carlo methods. Authors

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

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

reported error up to 25% in low-dose regions and found that the inadequate modeling of transmission through MLC leaves and leaf scatter in TPS to be the main cause of error. In the treatments performed using IMRT techniques, doses of 2 Gy per fraction is delivered over large fractions to deliver a total dose of 60–70 Gy to the tumor volume. However, stereotactic radiotherapy follows hypofractionated regime, in which doses of 10–20 Gy per fraction is delivered. Hence, the dose deposited out-of-field due to each fraction is of concern. Petti et al. [127] investigated the doses outside the treatment field and cause of it for treatment using Cyber Knife and compared them against the doses obtained using Gamma Knife and IMRT for similar treatment. The out-of-field doses were found higher by a factor of two to five for Gamma Knife and by a factor of four for IMRT treatments. According to the authors, the leakage radiation is the main cause of out-of-field doses. Chuang et al. [128] investigated for the reduction in out-of-field doses after installation of shielding upgrade and reported the reduction of 20–50% in out-of-field doses. Comparison of difference in peripheral doses absorbed using different equipment for stereotactic treatment was made by Di Betta et al. [129] and used the data for estimation of risk of stochastic effects. Authors reported that the risk of adverse side effects for treatment using 5 Gy per fraction due out-of-field doses is negligible. Lastly, there are relatively fewer studies available on out-of-field doses due to the small fields. More studies are required on it, which can be helpful to investigate the

Considering the importance of accurate small-field dosimetry, this chapter discusses all important aspects related to it in details. It includes the physics of small radiation fields, cavity theory, and methodology of small-field dosimetry to understand the response of dosimeters and brief discussion on several dosimeters. It also discusses the recommendations of COP for dosimetry of small radiation fields. Moreover, it discusses the small and long cavity theories for computing the accurate dose response. In addition, pencil beam algorithms as a tool for the dose response evaluation is reported, and uses of Monte Carlo simulation in categorizing the primary and scattering components of the radiotherapeutic photon beam are handled. Also this chapter focuses on the application and importance of Monte Carlo techniques in small-field dosimetry and treatment methods that are based on small

fields, such as stereotactic treatments and IMRT. Available general purpose Monte Carlo codes used for applications in radiotherapy is also mentioned.

Such Monte Carlo codes have the ability to simulate transport of radiation within a medium in great details. EGSnrc, Geant4, PENELOPE, and MCNP are some of the most commonly used Monte Carlo codes for small-field dosimetry studies. Its accurate algorithm to model the transport of radiation and easy-to-use graphical user interface of BEAM code of EGSnrc makes it one of the most widely used MC code. A thorough recent literature review is performed on the small-field dosimetric studies performed using Monte Carlo codes. The studies on out-of-field doses, limitation of contemporary treatment planning systems, use of Monte Carlo codes

effects of out-of-field doses.

7. Conclusion

69

chamber IC-10 and attributed this variation to the volume averaging effect of the chamber. Paskalev et al. [115] investigated the dose distribution for circular field (1.5 and 3 mm) for 10 MV photon beam using Varian Clinac-18 and reported maximum variation of 0.3 mm between the measured and calculated 50% isodose surface. Tsougos et al. [116] performed a Monte Carlo-based dosimetric study for in-house developed 6 MV SRT unit and compared it against conventional dosimetric techniques. Francescon et al. [117] investigated total scatter factor for Cyberknife unit for three different collimator opening diameters ranging from 5 to 10 mm. Comparison was made between the experimental and Monte Carlo results. Heydarian et al. [118] investigated the dosimetric parameters of a SRS linac using experimental measurements and Monte Carlo methods and reported good agreement between the Monte Carlo and experimental data. Scott et al. [29] investigated the effect of source occlusion on output of the linac for small-field sizes and large focal spot sizes and found that output factors are sensitive to the dimensions of the electron spot size hitting the target. Sargison et al. [119] proposed a methodology for measurement and reporting of relative output factors for small fields using both experimental and Monte Carlo methods. In 2014, Sargison et al. [120] presented two scientific quantitative definitions of very small-field size and reported that careful methodology is required for setting of field sizes and placement of detectors for field sizes less than 12 mm for 6 MV photon beams. In 2019, Francescon et al. [121] investigated the sensitivity of dosimetric correction factors to interunit variation and reported variation up to 9% between the measured data corrected using the recommendations of TRS-483 and Monte Carlo results. Casar et al. [122] provided detector-specific output correction factors for small-field sizes using the recommendations of TRS-483.
