Shielding Volume Reduction in a High Dose Rate Brachytherapy Room

This paper describes a method to reduce the shielding thickness in a high dose brachytherapy treatment room, with an Iridium-192 source, using the protocols established by the International Atomic Energy Agency in its Safety Report No. 47; calculating the volume of shielding material, without failing to comply with the radiation safety para-meters established by the General Radiation Safety Regulations and regulations in force by the Comisión Nacional de Seguridad Nuclear y Salvaguardias , which acts as the regulatory body for the use of radioactive sources in Mexico. The shielding of the walls was determined as a function of room design, source activity, workload, use factor, number of weekly treatments, treatment time, and shielding material properties. The results show that the shielding volume can be reduced by 19.592% and 20.727% for five-point and eleven-point fractionation, respectively, for a Brachytherapy room with a maze.


INTRODUCTION
Radiation protection (RP) focuses on the prevention of stochastic and deterministic damage caused by ionizing radiation to workers, the public, and the environment, without interfering with the exposure processes associated with a benefit, ranging from electric power generation to applications in medicine, industry, and agriculture [1] [2] [3] .
RP is the responsibility of each country; however, there are international organizations such as the International Atomic Energy Agency (IAEA) and the International Commission on Radiological Protection (ICRP), which issue recommendations on radioprotection to reduce risks and prevent accidents, respond to emergencies associated with radioactive sources and seek to mitigate harmful effects associated with radiological exposure practices; environmental, occupational, or public [3] [4] .
It is important to mention that the RP is based on the principles of: • Justification: Any practice involving exposure to ionizing radiation should produce more benefit than harm [1] .
• Optimization: All radiation exposure should be kept As Low As Reasonably Achievable (ALARA Principle) [1] .
• Dose limits: applicable for planned and justified radiation exposure [1] .
The first two are aimed at the use of the radioactive source, and the third one, for exposed personnel and the public [5] , regulating the dose limits in force. In  Table 1.
Also, there are RP factors or practical RP methods [6] , which are: • Time: The less time an individual is exposed to a radiation source, the lowest dose absorbed [7] .
• Distance: Every individual should be as far away as possible from the radiation source, according to the inverse square law of distance, which indicates that it is inversely proportional to the square of the distance from the source [4] [ 7] .
• Shielding: Barrier between the source and the individual that reduces the intensity of ionizing radiation [7] .
These factors should be considered to optimize the RP design [6] . Regarding shielding, it depends on activity, type of radiation and energy emitted by the source, which is directly related to the type of particles released by the radionuclide (emissions α, β+, β-, γ, etc.) [7] , as well as the density and thickness of the material.
Nowadays, the most used materials are concrete, lead, and steel [7] [10] , whose description and density are shown in Table 2. Regarding medical use, radioactive sources are used in diagnosis, treatment [1] , and theragnostic [12] .
Particularly in treatments, there are teletherapy and brachytherapy.
Brachytherapy is a treatment in which radioactive sources are placed at a short distance from the tumor.
It is classified according to dose rate or how quickly the dose is delivered to the patient: low, medium, and high [13] . In the case of High Dose Rate Brachytherapy (HDR-B), the most radioactive isotopes used are Cobalt-60 ( 60 Co) and  Ir) [11] . Particularly, 192 Ir has a half-life of 73,829 days and decays 95.35% by particle emission β and 4.65% by Electronic Capture (EC) to excited states of   Pt) and Osmium-192 ( 192 Os) respectively. Afterwards, they decay by emission γ until they reach stability ( Figure   1) [14] [15] . Exposure to high levels of γ-rays cause harmful effects (for example cancer), which is why a barrier is used to attenuate them (mainly by photoelectric effect and Compton effect) [16] .
Shielding depends on the design of the HDR-B treatment room. Therefore, the IAEA suggests a room design with a doorless maze for 60 Co radioactive source, includes a control area, preparation/procedure room, recovery area, sluice room, and image processing area ( Figure 2) [17] . The dimensions for the width of the maze should be 1.8 meters (m), the internal ones 4 m long by 4 m wide (Figure 2), and a height of 3 to 3.6 m.
The above, assuming the use of fluoroscopy equipment for applicator placement [11] , although Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) simulation is also used [17] . FIGURE 1. 192 Ir decay diagram by particle emission and EC [15] . dimensions and adjoining areas [17] .

Calculation of primary barriers
IAEA Safety Report Series No. 47 (SRS-47) describes a method for calculating shielding thicknesses in walls, floor, and roof and considerations as primary barriers (shielding where useful radiation beam hits directly).
This method starts from the calculation of the attenuation required by the barrier (B) given a dosimetry shielding point that is at a certain distance from the source (d) [4] [11] [18] . Thus, B is determined from Equation (1) Where P is the design limit measured in µSv week -1 , W is the workload in micro grays per square meter week -1 (µGy m2 week -1 ), U is the use factor, and T is the occupancy factor of adjacent areas [11] .
Concerning P, it must ensure compliance with the permissible exposure dose limits for adjacent areas.
The classification of the adjacent areas is: • Controlled: areas with specific protective measures to control potential exposures under normal working conditions. The limit is P equal to 120 microsievert per week (µSv week -1 ) [11] [16] .
• Uncontrolled (public): areas that are not designated as controlled but are under review. The design limit is 6 µSv week -1 [11] [16] .
About W, it refers to the dose administered per treatment each time (usually in one week) [4] [11] . It is calculated by the Equation (2) [11] : Where RAKR is the Reference Air Kerma Rate for a source of unit activity at one-meter distance modified by attenuation and scattering in the air [16] ; A is the total source activity measured in becquerels (Bq); t is the average treatment duration in hours, and n is the number of treatments per week [11] .
According to the American Association of Medical Where S k is the air kerma strength of the source in units of U o (µGy m 2 )/h and it is equivalent to the product of RAKR times A [19] .
For the T factor, it indicates the average fraction of time that a person is mostly exposed to adjacent area where the source is in use. Table 3 shows the value for each area according to NCRP Report No. 49 (NCRP-49) [4] [10] [11] . It is important to mention that for HDR-B, the sources are isotropic, i.e., they are not collimated, and their emissions are in all directions. In this sense, the U factor will always be equal to 1 [4] [11] .
It is also recommended the use of the Tenth Value Layer (TVL) and Half Value Layer (HVL), which reduce the radiation intensity by a factor of one tenth and one half of the initial intensity, respectively, whose thickness is specific for each material and radionuclide [11] .
The number of TVL that produces a transmission factor B is calculated from the Equation (4) [11] : So, the barrier thickness (Et) is obtained by multiplying the TVL times the TVL value of the material (TVLm) [11] , as shown in the Equation (5):

Calculation of secondary barriers
In addition, secondary radiation must be considered, especially that transmitted into the maze. For which, the factor B for the secondary barriers (barriers not in direct contact with the radiation beam from the source), is calculated from Equation (6) [11] :

MATERIALS AND METHODS
The method consists of three stages: the first is to identify the room design data, source characteristics,   For this case, we consider the use of an 192 Ir source with a nominal activity of 370 Gigabecquerel (GBq), RAKR of 0.111 µGy · MBq -1 ·m 2 ·h -1 [11] , total activity (A) of 555 GBq [20] , a workload (n) of 30 treatments per week, with an average treatment duration (t) of 10 minutes (0.167 hours) to deliver an absorbed dose of 7.5 Gy, to the prescription point per treatment and concrete as shielding material, whose TVL value for this source is 0.152 m [11] .
Also, the value for the factor T and the design limit P is established according to the adjacent area and NCRP Table 3) [10] . The assignment of these values is shown in Table 4.   First, the distances of the points to the source (distance between two points) are calculated, using the Equation (7) [21] .

(values shown in
For this purpose, the positions (x, y, z) of the dosimetric points on the cartesian plane, represented by the HDR-B room, are considered. Which has origin (0, 0) at the lower left and the source position at (x 0 = 3, y 0 = 2.5, z 0 = 1.1) (Figure 4).
Then, the W factor is calculated by substituting the values of RAKR, A, t, and n, in the Equation (2), which results:  For this case, we considered the d sca value of 1.5 m and a maximum F of 400 cm 2 and a reflection angle of 45° for 60Co (α) of 0.0037 [11] ; these values and the values of T, P, and W (calculated previously) are substituted in Equation (6) to obtain the factor B, resulting:   Then, for each of the distances obtained, the thickness is calculated using the Equations (1), (4), and (5).
To obtain the area, Equation (8)

RESULTS AND DISCUSSION
From the previous study, Tables 5 and 6 (Table 7).

Shielding for barriers A, B, D and E, for 11 points.
A similar case is barrier D, the volume decreased from 8.036 m 3 for one point to 7.459 m 3 for 5 points and 7.396 m 3 for 11 points (Figure 8), representing a decrease of 7.180% and 7.964% (Table 7), respectively.
For barrier E, the volume calculated for one point is 8.036 m 3 , while for 5 points it is 7.644 m 3 and for 11 points it is 7.630 m 3 (Figure 8), representing a percentage decrease of 4.878% and 5.052% (Table 7) respectively.   In the case of barrier C, it represents the best reduction in shielding, since a single point requires 8.932 m 3 of concrete, while with the proposed method the volume required is 3.084 m 3 (Table 8). This difference represents a 65.472% of reduction in the shielding volume (Table 7). The calculation of the geometric mean of the reduction percentages per wall at 5 points yielded a reduction percentage of 11.070%, while for 11 points it was 11.526%.
In addition, the shielding volume required for the HDR-B room at one point is 70.676 m 3 , while for fractionation at 5 points requires 56.829 m 3 and at 11 points 56.027 m 3 , representing a percentage decrease of 19.592% and 20.727%, respectively (Table 10).   [25] . However, knowing that gamma-ray attenuation is related to the interaction with matter, represented by the Equation (10) Where I(x) is the intensity of gamma-rays as a function of distance x in the material and µ is the linear attenuation coefficient which depends on the energy of the gamma rays and the material which they interact with [26] [27] , it is possible to compare an analysis based on fractionation of the barriers (proposed in Figure 3), derived from the fact that it is known that increasing the distance between the focal point (source) and the interaction point (dosimetric point) the amount of radiation is decreased by the inverse square law of the distance [7] [18] [26] [28] [29] .
In this sense, a reduction in the volume of shielding was obtained in all barriers calculated with the proposed method (Figure 8), the most significant reduction percentage is 65.472% in the C barrier (Table 7). In the other barriers, the reduction was lower because the distances from the points to the source do not present much difference between them. One example is barrier B, divided into 11 points (  (Table 9).
Also, IAEA document SRS-47 recommends that for HDR-B room the shielding barriers should be primary because when the source is in use, it is isotropic and without collimation [11] [17] [31] [33] . However, it was analyzed that both in the second section of the C barrier ( Figure 5) and in the second section of the roof ( Figure   7) there is no primary radiation, but the radiation transmitted through by the E barrier and the scattered radiation, product of the reflection on barrier B. Therefore, and considering the cost-benefit, it is possible to consider these sections as secondary barriers, otherwise; it implies calculating an excessively and unnecessary thickness, which implies the requirement of more material, space, and economic resources [30] [34] [35] .
It should be noted that there is no specific recommendation or method for the analysis of secondary radiation. Even estimating the absorbed dose at the entrance of the maze is difficult, so in practice, various methods have been adopted, ranging from considering only direct radiation or scattered radiation [4] [11] .
In the case of the secondary radiation analysis, the value used for α corresponds to 60 Co, because in the IAEA SRS-47 report, it is not available for 192 Ir. In addition, 60 Co has a gamma-ray energy value (of 1.25 MeV) higher than that of 192 Ir (0.375 MeV), thus ensuring that the calculation is effective [11] [26] [36] .
It is important to mention that this study does not contemplate the affectation of rear shielding derived from the elimination of part of it to install ducts and boxes embedded in walls, roofs and floors, hardware in lead-lined doors or concrete block joints, since these adaptations are specific to each HDR-B room [30] [37] .
Similarly, it does not include the shielding analysis for the floor, because it is assumed that the HDR-B room is on the ground level does not affect any piping or drainage [32] . However, if necessary, it can be performed in the same way as for the roof.
Although the design of the HDR-B room is related to space and available resources, this method is intended as a strategy to reduce construction costs without failing to comply with national and international regulations regarding exposure dose limits for exposed personnel and the public, and also, to optimize resources to be allocated to other expenses such as the cost of equipment, radioactive sources, auxiliary equipment, service and maintenance costs, training and salaries of personnel [26] [31] [34] [37] [38] .
In this sense, a cost-benefit analysis of the fractional shielding calculation could be expected to be effective in RP and cheaper in shielding material cost with respect to the IAEA SRS-47 methodology. However, the option of having an RP surveillance program is not ruled out [32] [34] [39] .
As for the geometric mean calculated for the percentages reduced in each barrier (Table 7), it was obtained that, for the fractionation in 5 points, it was 11.070%, meanwhile for 11 points it was 11.526%. This indicates that the shielding reduction in the DHR-B room barriers is reduced by at least 11%.
Thus, the proposed method for the calculation of shielding for HDR-B rooms, which starts from the RP and optimizes space and economic resources allocated, a concrete reduction of 19.592% and 20.727% was obtained for the fractionation in 5 and 11 points respectively (Table 10), which makes it more beneficial compared to conventionally method using the IAEA 47.