B represents the transmission factor of the x rays beam through the shielding wall calculated using the tenth value layer of the shielding material and the shielding thickness. Knowing the later, the transmission factor for all the barriers were calculated using the following equation:

$B={10}^{-\left\{1+\left[\frac{t-\text{TVL}1}{\text{TVLe}}\right]\right\}}$ (1)

where TVL1 and TVLe are respectively the first and equilibrium Tenth Value Layer which is defined as the absorber thickness which attenuates the beam intensity to 10% and t is the thickness of the wall which we want to calculate the transmission factor. In this study, the material for radiation shielding is concrete.

Protective barriers are designed to ensure that the dose equivalent received by any individual does not exceed the applicable maximum equivalent value. Hence the design dose (P) equivalent limit (some fraction 1/20 of the annual regulatory limit) for the site being protected start with the following equation:

$P=\frac{B\ast W\ast U\ast T}{d^2}$ (2)

here B is the barrier transmission factor calculated above, W is the radiation workload in term of total dose delivered at the isocenter (1 m from the X ray target) per year (Gy/year), d is the distance from the X ray target to the point protected (meters), U is the use factor or fraction of the workload that the primary beam is directed at the barrier in question and T is the occupancy factor for the protected location or fraction of time that a person is present beyond the barrier.

The direct workload receives contributions from the conventional treatment delivery and the quality assurance activities which include calibration and other physics research activities. In average 60 patients are treated every day in around 250 working day with 2.5 Gy in average to account for larger dose per fraction for some palliative treatments. The occupancy factors T were taken from NCRP 151 for the concerned areas as shown in Table 1 .

$W_{dir}=\left(\frac{2.5\text{Gy}}{\text{patient}}\ast 250\text{working}\text{day}\ast 60\text{patients}/\text{day}\right)+20\%\text{QC}$ (3)

Similar formulas for determining the dose for secondary barrier thickness requirement stemming from the leakage and patient scatter are also proportional to the workload.

$P=\frac{B\ast W_L\ast L\ast T}{d^2}$ (4)

The IMRT treatment delivery technique contributes more to the leakage per unit dose at the isocenter than the direct radiation by a factor C which ranges from 2 to 10. A factor of 5 is often used in calculations.

$W_L=W_{dir}+5\ast W_{IMRT}$ (5)

A hypothesis that 30% of the patients will be treated with IMRT was done. The leakage attenuation factor L is by regulation not to exceed 0.1% (IEC Safety standard). The use factor was taken equal to 1 since scatter and leakage are assumed with isotropic emission. The occupancy factors T were taken from NCRP 151 for the concerned areas as shown in Table 2 [4] .

The equivalent dose for scatter from the patient shielding is given by the following equation:

$P=\frac{F}{400}\ast \frac{a\ast W\ast B\ast T}{d_{scat}^2\ast d_{sec}^2}$ (6)

F is the area of the beam at the scattering point at mid-depth of the patient at 1 m (cm²), d_scat and d_sec are respectively the distance from the source to the patient and the distance from patient to point of interest, $a$ represents the scatter fraction at 1 m from a human-size phantom, target-to-phantom distance of 1 m, and field size of 400 cm² [15] [16] .The scatter workload is determined by the dose at the isocenter received by the patient or phantom. A conservative and simplifying procedure would be to set:

$W_{sca}=W_{dir}$ (7)

The following table ( Table 3 ) summarizes the different parameters used to estimate the workload for the scatter radiation.

The total dose rate at the entrance of the maze arises from the scattered primary beam from the bunker wall, the scatter from the patient, the scatter of the head leakage radiation from the bunker walls and from the transmission of head leakage radiation through the maze wall when the beam is pointed at the wall B which is in front of the maze. It was calculated using the following equation:

$H_B=f{S}_S+S_p+L+L_d$ (8)

with f the fraction of beam transmitted by the patient body (»0.26 for 6 - 10 MV). Adding the contributions when the beam is pointing in all 4 directions, the total dose rate to the maze entrance is obtained. As a rule (from NCRP151) total dose rate is obtained with this following equation:

$H_{Tot}=2.64\ast H_B$ (9)

And the required door shielding design dose is given by:

$P=B\ast H_{Tot}$ (10)

The dose rate at the maze entrance (S_s) arises from the scattered primary beam from the Bunker Wall (the nearest to the maze) and is given by:

$S_s=\frac{W\ast U_B\ast {\alpha }_1\ast A_1\ast {\alpha }_2{A}_2}{{\left(d_i\ast d_{r1}\ast d_{r2}\right)}^2}$ (11)

where W is the radiation workload, U is the use factor toward the wall B, α₁ is the reflection coefficient at first scattering surface (the wall A₁), α₂ is the reflection coefficient for second surface (the wall A₂), A is the area filled by the beam at each reflection and d is the distances as shown in Figure 2(a) .

The dose rate at the maze entrance (S_p) from the patient scatter was calculated using the following equation:

$S_p=\frac{a\ast W\ast U_B\ast \frac{F}{400}\ast {\alpha }_1\ast A_1}{{\left(d_{sca}\ast d_{sec}\ast d_s\right)}^2}$ (12)

where a is the patient scatter fraction, W is the radiation workload, U is the use factor toward the wall B, F is the area of the beam in the plane of the patient, α is the reflection coefficient at the wall, A is the area filled by the beam at the reflection and d are distances as shown by Figure 2(b) .

The dose rate at the maze entrance (L) from the scatter of head leakage radiation from the Bunker Walls was calculated using this formula:

$L=\frac{L_0\ast w\ast U_B\ast {\alpha }_1\ast A_1}{{\left(d_s\ast d_1\right)}^2}$ (13)

where L₀ is the leakage factor, W is the radiation workload, U is the use factor toward the wall B, α is the reflection coefficient at the wall, A is the area filled by the beam at the reflection and d are distances as shown in Figure 2(c) .

The dose rate at the maze entrance (L_d) from the transmission of head leakage radiation through the maze wall is given by this equation:

$L_d=\frac{L_0\ast W\ast U_B\ast {10}^{-\left(t/\text{TVL}\right)}}{{\left(d_1-d\right)}^2}$ (14)

But it was not computed because the transmission of scatter radiation has the lowest mean energy compared to leakage radiation.

In this study, all the calculations were done using the empirical equation and factors from NCRP151 to meet the requirements for designing the shielding.

Microsoft excel software was used to handle the data and R statistical software for the comparison of means and to calculate the p values. Statistical significance was defined as p < 0.05.

To verify the method and validate the calculations, the results were evaluated by a comparison with measured doses in all the concerned areas using a detector.

Measurements have been done using a Fluke Biomedical ion chamber survey meter. The maximum field size (40*40 cm²) was used with a solid phantom (PMMA) on the table to simulate the scatter.

The results show that the primary barrier are sufficiently wide, that’s means they will also shield small angle scattered radiation and no additional thickness is needed to shield the scatter radiation. In this case the calculated doses for scatter exceed the leakage for these areas technical room, secretary office and waiting room but are below the leakage dose for console, physicist room and street. These differences can be explained by the fact that the scatter fraction is higher for the three first areas. The scatter fraction increases when the scatter angle decreases and here we use small scatter angle for the areas which don’t face the primary beam and higher scatter angle for the one that face the primary beam to be more conservative. The barrier for the primary beam is wider than the barrier for secondary.

The measurements were done in the worse condition to be more conservative using the biggest open field (40*40 cm²) with the highest dose rate (600 UM/min). The tests performed on the data between the calculated and the measured equivalent dose show that there is no significant difference between the means value for the following areas: patient waiting room and console with p values greater than 0.05. For the other areas, the results show a significant difference with p values less than 0.05. Figure 3 shows the equivalent dose comparison in terms of histogram for all the areas.

An investigation was performed to examine the equivalent dose in a radiotherapy room when a new technique has to be started. The results show that the secondary radiation could not exceed the primary one. For console, physicist room and street, the equivalent doses were estimated considering these areas as primary and secondary barrier at the same time and the found value for the latter are negligible compared to the primary one.

These calculations indicated that primary shielding for conventional therapy is already conservative, with conformal-therapy size fields yielding relative exposure rates outside the room a factor of two less than inside the room. The use of 40*40 cm² broad-beam transmission data to determine barrier thickness, even if appropriate considerations are made for the tumor dose, may yield overestimates in the required barrier thickness. This is consistent with a common understanding that a 40*40 cm² field size is a conservative estimate used for shielding calculations.

For all barriers considered as secondary in this study, the scatter doses exceed the leakage doses, this can be explained by the fact that the Linac head is well shielded by the manufacturer.

The secondary shielding barrier thickness will increase due to the increase in monitor units required to deliver IMRT treatments. Followill et al. [6] estimated that the MUs required for IMRT treatments are about a factor of two greater than those required for conventional therapy [17] . In this study, a factor of 5 was used to be more conservative. The increase in shielding requirements will be proportional to the increase in total delivered monitor units which is a function of the mix of conventional and IMRT patient loads.

An estimate of the barrier thickness must account for the expected distribution of IMRT and conventional patients. MUTIC et al. found that conventional primary barriers are adequate for both dynamic MLC and serial tomotherapy IMRT [11] . All the equivalent doses presented here are lower than their corresponding annual limit for workers and for public except the secretary who should be considered as public. This can be explained by the fact that the equivalent dose used in design calculations was occupational since that office was occupied first by the therapist. There are different shielding design goals for controlled and uncontrolled areas. Shielding design goals (P) are levels of dose equivalent (H) used in design calculations and evaluation of barriers constructed for the protection of workers and public. The design dose from the annual dose limit for occupational and public exposure, the workload of the department, the occupancy and use factors and the distances between the target isocenter and the different walls should be taken depending on the surrounded areas. Due to the fact that the machine used in this study is monoenergetic with 6MV, neutron shielding for high-energy photon IMRT was not investigated.