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

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 for reference dosimetry.

The air-filled detectors with sensitive volume less than 0.3 cm3 and air cavity length of 7 mm are preferred for dosimetric measurements for fmsr less than 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 Co<sup>60</sup> radiation beam.

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

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 the accuracy of measurements.

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

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

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

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

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

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

For radiotherapy radiation emitters, where the reference beam size (fref) of 10 cm � 10 cm cannot be obtained, a new concept of machine-specific reference (msr) field size has been proposed. The dimensions of the msr field (fmsr) should be as close as possible to that of fref and must be at least equal to the sum of rLCPE and

3.1 Ionization chambers for reference dosimetry in small and non-reference

An ideal air-filled detector to be used for measurement of dose deposited in water must be equivalent to the water and not perturb the charged particle fluence; its response must not be affected by dose rate or directional dependence; it must show good sensitivity, in terms of signal to noise ratio and time taken to obtain the

ð3Þ

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:

the sum of rLCPE and half of the detector's outer volume.

2.2 The machine-specific reference field (fmsr)

half of the detector's outer volume.

3. Detectors and equipment

fields

44

coordinates of the beam (x and y).

for small beams.

measurements. However, in case of beam profile measurements, the detectors with high spatial resolution, direction-independent response, dose-rate independence, and suitable volume are preferred. Since the selection of detector with suitable volume makes it possible to measure penumbra region accurately, uniformity in directional response may result in accurate measurement of beam profiles; dose rate independence is also important for accurate measurement of beam profiles. Otherwise, correction factors are required for each of these effects for accurate measurement. As in the case of dose-rate dependence, correction factor needs to be applied in case of FFF beams, as these beams have high dose rate per pulse in the center of the beam in comparison to the edges. Otherwise it may lead to overestimation in the region of beam with high dose rate.

due to the difference in mass density relative to water, output correction factors are required when these detectors are used in field sizes below

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

• Plastic and organic scintillators: In these detectors light is produced in the scintillator when it is exposed to radiation. These detectors are almost energy independent, equivalent to water in terms of mass energy coefficient and electron density, and exhibit linear response for measurement of dose

deposition in water [14, 19, 38–40]. Hence, these detectors can be directly used to determine the dose deposited. The corrections are needed to be applied for the production of Cerenkov light in optical fiber, which is used to transport the signals outside the treatment room. Different methods such as the use of hollow core fibers or the use of spectral filtration had been proposed to correct it [41]. Exradin W1 was found to be the only commercially available plastic

• Radiochromic film dosimetry: Radiochromic films are the detectors with superior dimensional resolution. These are self-developing films and do not need chemical processing for development [42]. In case of high-energy photon beams, the radiochromic films are almost equivalent to tissue, resistant to water, and nearly energy independent [42, 43]. These films can be read with the help of suitable flatbed scanner. Before reading the films, it must be calibrated in terms of dose deposited in water, the spatial non-uniformity in the response of film must be carefully considered, and the response of the scanner and effect of orientation of film on the signal must be considered and should be corrected [44]. The radiochromic film can be used for measurements

of lateral beam profiles, penumbra region, and field output factors.

• Thermoluminescent dosimeters (TLDs): TLDs are available in the form of

powder, chips, microchips, rods, and ribbon. The most commonly used TLD material is LiF:Mg,Ti. In order to determine the dose deposited in water from the reading of thermoluminescence response, correction factors must be applied for non-linear relationship with the signal and dose deposited and also fading of the signal and energy correction. In order to accurately perform measurements in small beams of photon, careful handling and control of procedures are required to obtain measurement uncertainty within 2% or

• Optically stimulated luminescence detectors (OSLDs): The linearity in response, dependence on beam energy, and dependence on dose rate are similar to that of TLDs. OSLDs are generally composed of Al2O3:C and are available in the form of rods, chips, and nano-dots. The principle used in measurement of dose is similar to that of TLDs. In OSLD system, laser light is used to eject the energy trapped as luminescence. They can be used both as passive dosimeters and online readout system by connecting them with laser-based readout system

• Radiophotoluminescent (RPL) dosimeters: These are solid-state dosimeters (SSD) based on the principle of radiophotoluminescence. They are accumulation type dosimeters and use silver activated phosphate glass for the measurement to absorbed dose. RPL dosimeters are generally available in the form of glass rods. When this silver-activated glass rod is exposed to radiation, it resulted in formation of stable luminescence centers in silver ions. They can be read using

1 cm [37].

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

scintillator.

better [19].

and optical fiber.

47

There is no ideal detector available for relative dosimetry of small beams. A number of detectors that can be used for relative dosimetry have been described in literature, and each of these detectors has been discussed briefly below:


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

due to the difference in mass density relative to water, output correction factors are required when these detectors are used in field sizes below 1 cm [37].


measurements. However, in case of beam profile measurements, the detectors with high spatial resolution, direction-independent response, dose-rate independence, and suitable volume are preferred. Since the selection of detector with suitable volume makes it possible to measure penumbra region accurately, uniformity in directional response may result in accurate measurement of beam profiles; dose rate independence is also important for accurate measurement of beam profiles. Otherwise, correction factors are required for each of these effects for accurate measurement. As in the case of dose-rate dependence, correction factor needs to be applied in case of FFF beams, as these beams have high dose rate per pulse in the center of the beam in comparison to the edges. Otherwise it may lead to overestimation

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

There is no ideal detector available for relative dosimetry of small beams. A number of detectors that can be used for relative dosimetry have been described in

• Small air-vented ionization chambers: These detectors are also known as

• Micro-ionization chambers: Also known as microchambers. The sensitive

small volume averaging effect, and sensitivity is also reduced due to small

• Liquid ionization chambers (LICs): These chambers are filled with dielectric liquids, which results in higher chamber signal per detector volume than airfilled ionization chambers, due to the higher density of liquid than air. The chambers are almost water equivalent; hence the chamber perturbation effect is reduced. However, the chambers are dose-rate dependent because of its large

• Silicon diodes: The sensitive volume of these detectors is less than 0.2 mm<sup>3</sup>

• Diamond detectors: These detectors exhibit high sensitivity, energy

independence, and uniform response in all directions [31]. However, having dose-rate dependence and substantial pre-irradiation are required. The natural

deposition (CVD) diamonds [32–34]. The bias voltage is not required for these detectors while using them for dosimetric measurements [35, 36]. However,

diamond detectors have been replaced by the artificial chemical vapor

These detectors exhibit angular dependency because of its construction and material composition and small volume averaging effect. The axis of symmetry of these detectors must be placed on the central axis of the beam. These detectors exhibit over-response in the case of low-energy photons due to the non-water equivalence. For small beam measurement, the use of unshielded diodes is preferred over the use of shielded diodes, and for field sizes below 1 cm, output correction factors are needed to be applied [26–30]. For very small beam size measurements, stereotactic diodes can be utilized. The sensitivity of these detectors depends on the accumulated dose, and they have limited lifetime. Therefore, time-to-time checking for constancy of relative

volume of these detectors ranges from 0.002 to 0.01 cm3

minichambers or pinpoint chambers. The sensitive volume of these detectors

beams with size down to 2 cm 2 cm [24, 26]. These detectors are dose-rate independent and have uniform response in all directions and appropriate

. These can be used for measurements in radiation

. These detectors have

.

literature, and each of these detectors has been discussed briefly below:

in the region of beam with high dose rate.

ranges from 0.001 to 0.3 cm3

sensitive volume.

recombination effect.

response must be performed.

46

response for photons of low energy.

the technique of pulsed ultraviolet laser excitation. RPL dosimeters exhibit linear response, flat energy response in the energy range of keV and MeV, good reproducibility, good spatial resolution, and negligible fading of signal [45, 46].

solid-state dosimeter and water is due to the primary component of the beam that remains almost invariant for the given beam quality and does not depend on the volume. On the other hand, the scattered component of the photon beam depends largely on the volume surrounding it; therefore, it depends on dosimeter depth, irradiated field size, etc. Hence, it is convenient to calculate the difference of the response caused by these two components separately and additively combine the two parts at the end of the calculation. To quantify the response rate provided by the primary and scattered components, a scattered factor (SF) could be introduced,

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

SFw <sup>¼</sup> <sup>D</sup>sc w Dpr w

SFSSD <sup>¼</sup> <sup>D</sup>sc

scattered components of photon beam, respectively. A scattered factor of solid-state dosimeter may be defined in the same manner, as shown in Eq. (5). The scattered

factor is dependent on the field size and depth position of the dosimeter. The total dose of water ð Þ Dw or SSD (DSSD) is the sum of the two components, primary and scattered. This can be expressed in terms of scatter

Dw <sup>¼</sup> Dpr

DSSD <sup>¼</sup> <sup>D</sup>pr

The response factor (RF) of SSD dose to water ratio is defined as:

RFSSD

Eq. (8) can also be expressed in terms of scattered factor, combining Eqs. (6)

<sup>w</sup> <sup>¼</sup> <sup>D</sup>pr

RFSSD

ratio between the primary dose of SSD to the dose of water (Dpr

<sup>w</sup> <sup>¼</sup> DSSD Dw

Therefore, the dose response of SSD could be corrected and applied to all SSD

Dpr

considered relatively stable, because once the charged-particle equilibrium (CPE) is established, the local spectra of the primary electrons and photons remain invariant which are independent of irradiation condition variations. Therefore, the RFSSD

variation is due to the difference of the scattered component of both water and SSD.

scattered factors (SFSSD, SFw). However, it could not be easy to evaluate the primary and scattered doses separately in experiments, especially for high-energetic photons, because it needs massive buildup of material, which is necessary to achieve CPE to introduce significant attenuation and wide contribution [51]. Nevertheless, the response factor could be evaluated in a small field where CPE is still achieved. So

In this way, expressing the response factor to fulfill the following objectives: The

SSDð Þ 1 þ SFSSD

<sup>w</sup> ð Þ 1 þ SFw

<sup>w</sup> depends on the determination of the primary dose ratios and

<sup>w</sup> is close to the Dpr

SSD Dpr SSD

<sup>w</sup> correspond to the dose contributions in water by primary and

<sup>w</sup> ð Þ 1 þ SFw (6)

SSDð Þ 1 þ SFSSD (7)

<sup>w</sup> before the measurement implementation.

SSD=Dpr

SSD=Dpr

<sup>w</sup> ) can be

w

<sup>w</sup> since the main

(4)

(5)

(8)

(9)

defined as follows:

where Dsc

factor as follows:

and (7):

As a result, RFSSD

49

<sup>w</sup> and Dpr

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

measurement by the evaluation of RFSSD

in small-field dosimetry, the evaluated RFSSD

• Alanine: Its macroscopic interaction coefficients and density are close to that of water. The exhibit volume averaging effect because of its large size, low sensitivity, and high doses of radiation is needed to be delivered to obtain reproducibility of less than 0.5%.
