A . Bouzouita et al .: Radioprotection 2024 , 59 ( 4 ), 296 – 305 297
phantoms greatly enhance the depiction of the human anatomy . Voxel-based phantoms are often used to estimate organ doses in diagnostic radiology and occupational exposures ( Rezaeian et al ., 2022 ; Portugal et al ., 2022 ; Xu et al ., 2023 ). ICRP Publication 144 ( ICRP , 2020 ) proposed a method using voxel phantoms for Monte Carlo calculation of organ DCFs in the special case of planar gamma-ray sources in soil . The Monte Carlo simulation was performed using the radiation transport code PHITS ( ICRP , 2020 ). This calculation serves as basis for estimating organ DCFs corresponding to anthropogenic radionuclides that are distributed exponentially with soil depth . However , given the enormous computational time required to perform Monte Carlo calculations on external exposure to gamma rays from the ground using voxel phantoms , most of previous researches have focused on using simpler , mathematically based phantoms for such calculations .
Askri et al ., ( 2008 ) derived a geometrically optimised model for the Monte Carlo calculation of the gamma radiation field in air due to radioactive sources distributed in the soil , reducing computation time ( Askri et al ., 2008 ; Askri , 2015 , 2016 ). In addition , important advances have been made in CERN ’ s Geant4 Monte Carlo simulation code ( Agostinelli et al ., 2003 ; Allison et al ., 2016 ), which consists in the implementation of an optimised Monte Carlo algorithm for transporting particles in voxel-based geometry .
In the present work , taking advantage of these optimisation techniques , a two-stage Monte Carlo calculation simulation is proposed to estimate human organ DCFs for soil-distributed radioactive sources . In the first stage , gamma photons emitted by sources distributed in the ground are transported in the soilair optimised geometry until reaching a cylindrical surface surrounding a standing human phantom on the ground surface . The second stage uses the ICRP110 reference computational voxel-based male and female phantoms in the Geant4 code to calculate absorbed doses in 141 organs and tissues due to photons originating from the surrounding surface . DCFs for the natural radioactive series of 238 U and 232 Th and for the 40 K and 137 Cs radionuclides are determined and compared with published results in the literature .
2 Material and methods
2.1 The ICRP110 voxel based phantom
The human computational male and female phantoms were created from a set of clinical whole-body CT images : a 38- year-old male ( 176 cm , 70 kg ) and a 43-year-old female ( 163 cm , 60 kg ). These were scaled to match the ICRP adult reference standards ( ICRP , 2009 ), presenting 141 organs / tissues . Each voxel in the phantom is identified by an organ ID , arranged in data files layer by layer , line by line , and column by column , increasing along the x- , y- , and z-axes . Slice numbers increase from the toes to the top of the body , row numbers increase from front to back , and column numbers increase from right to left . The male human phantom is voxelized in x , y , z with 254 127 222 voxels with dimensions 2,137 2,137 8 mm . The female human phantom is voxelized in x , y , z with 299 137 348 voxels with dimensions 1.775 1.775 4.84 mm .
2.2 Soil-air optimised geometry
In the first stage of the Monte Carlo simulation carried out in the present work , gamma photons emitted from sources uniformly distributed in the soil are transported . This process is time-consuming due to the semi-infinite extent of the soil and air media , and the need for a large number of photons to achieve statistical accuracy . The complexity increases when particles are transported inside the phantom , requiring extensive computational time . To address these challenges , an optimised geometry for the soil is proposed , considering only photons likely to reach the exposed human phantom . This geometry is based on physical criteria , including the exponential attenuation law of gamma radiation ( Askri et al ., 2008 ; Askri , 2015 ). Implementing this geometry significantly reduces computational time for photon transport in the soil-air medium ( Askri et al ., 2008 ; Askri , 2015 , 2016 ). For a nominal soil depth d and detection height h above the ground , the useful sources are contained in a soil volume bounded by the surface :
rz ðÞ¼
! ðd þ ^mh Þ 2 ðh � zÞ 2
1 2
� h � z
2 ð^mh � zÞ ð Þ2 þ R d ;
where r ( z ) is the lateral extent as function of the depth z ;
^m ¼ m a m s
; m a the linear attenuation coefficient in the air , m s the linear attenuation coefficient in the soil and R d the radius of a virtual surface detector located at the height h above the ground . As defined in Askri et al . ( 2008 ), the nominal depth of soil is the depth bellow which any emitted radiation is strongly attenuated before reaching the detection location . Considering the phantom dimensions , it is possible to consider the totality of the gamma radiation field reaching the phantom by taking h and R d equal to 2 m in equation ( 1 ).
2.3 Geant4 Nested Parameterisation navigation technique ð1Þ
Geant4 provides various ways to describe geometry , each with a corresponding navigation technique to determine the particle ’ s volume at each step . Traditional navigation in a voxelized human phantom is time-consuming due to high memory demands . To optimise memory use , Geant4 offers the nested parameterization navigation technique via the G4Nested class ( Agostinelli et al ., 2003 ; Allison et al ., 2016 ). The G4Nested class uses parameterization , creating a single volume in memory that appears in multiple locations with different materials at runtime . This technique improves upon the G4Replica tool , which represents multiple volumes as a single volume but requires consistent shape and placement . G4Replica cannot assign different materials to copies when cutting geometry in three directions . G4Nested solves this by using G4Replica for two axes and a one-dimensional parameterization for the third axis , dividing the simulation space into intelligent voxels . Each voxel contains a limited set of geometry volumes , and a map links each volume to its smart voxel . The ComputeMaterial method of G4VNestedParameterization calculates the material for each voxel using the indices from the x , y , and z replicas .