Monte Carlo study of voxel S factor dependence on tissue density and atomic composition

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Abstract

Voxel dosimetry is a common approach to the internal dosimetry of non-uniform activity distributions in nuclear medicine therapies with radiopharmaceuticals and in the estimation of the radiation hazard due to internal contamination of radionuclides.

Aim of the present work is to extend our analytical approach for the calculation of voxel S factors to materials different from the soft tissue.

We used a Monte Carlo simulation in GEANT4 of a voxelized region of each material in which the source of monoenergetic electrons or photons was uniformly distributed within the central voxel, and the energy deposition was scored over the surrounding 11×11×11 voxels. Voxel S factors were obtained for the following standard ICRP materials: Adipose tissue, Bone cortical, Brain, Lung, Muscle skeletal and Tissue soft with 1 g cm−3 density. Moreover, we considered the standard ICRU materials: Bone compact and Muscle striated.

Voxel S factors were represented as a function of the “normalized radius”, defined as the ratio between the source–target voxel distance and the voxel side. We found that voxel S factors and related analytical fit functions are mainly affected by the tissue density, while the material composition gives only a slight contribution to the difference between data series, which is negligible for practical purposes.

Our results can help in broadening the dosimetric three-dimensional approach based on voxel S factors to other tissues where diagnostic and therapeutic radionuclides can be taken up and radiation can propagate.

Introduction

The continuous improvement of the multi-modality tomographic imaging devices in nuclear medicine has triggered the development of more sophisticated approaches to internal dosimetry, such as the three-dimensional dosimetry at the voxel level.

The voxel S factors approach to three-dimensional dosimetry, introduced in Ref. [1], has been more widely used than other methods (such as dose point-kernel convolution and direct Monte Carlo computation methods), due to its recognized simplicity and reliability.

Recalling the updated MIRD nomenclature [2], the average dose to the target voxel can be calculated as:D¯t=sA˜sStswhere A˜s is the time-integrated activity in the generic source voxel, and Sts is defined as:Sts=Δiϕi(ts)mtwhere Δi is the mean energy emitted as radiation i per decay, ϕi is the absorbed fraction in t of the radiation i emitted in s, and mt is the mass of the target voxel.

In the MIRD Pamphlet no. 17 [1], voxel S factors were given for five radionuclides (32P, 89Sr, 90Y, 99mTc and 131I) and two cubic voxel sizes (3 and 6 mm).

The need to generalize the approach to different beta–gamma emitting radionuclides and voxel sizes led to computation methods exploiting direct Monte Carlo computations or convolution of dose point kernels.

In particular, Lanconelli et al. [3] presented a website providing voxel S factors for seven radionuclides and several voxel sizes in soft or compact bone tissues; data available from such a repository were obtained starting from the simulation, through the EGSnrc code, of monoenergetic sources of electrons and photons. The obtained voxel S factors, for each radionuclide and voxel size, underwent to a quality check through a comparison with the results of other Monte Carlo codes, before being published on the website.

Furthermore, a method to calculate voxel S factors for a generic voxel size was introduced by Dieudonné et al. [4]. They used a resampling procedure that started from nuclide-specific fine-resolution voxel S factors, previously calculated through Monte Carlo simulation.

In a previous work [5], we proposed an analytical calculation method for voxel S factors for a generic beta–gamma emitting radionuclide, valid in a model of soft tissue with 1.04 g cm−3 density. There, we pointed out the inaccuracies which arise when using, in bone tissue, voxel S factors evaluated for soft tissue.

In the present work, we aimed to extend our analytical approach to tissue materials of different density and atomic composition. Such generalization is of potential clinical relevance, since it solves the systematic biases affecting the three-dimensional dosimetric approach at the voxel level in tissues whose density and atomic composition is significantly different from that of the soft tissue. The proposed methodology allows to obtain data for several tissues and voxel sizes in a simple way, without direct Monte Carlo calculations.

Section snippets

Materials and methods

In order to study the dependence of voxel S factors on tissue density and atomic composition, we used a Monte Carlo simulation in GEANT4 [6], a simulation toolkit originally developed for high energy physics, currently applied also in the field of medical radiation physics [7], [8], [9], [10]. We adapted a simulation code previously developed for calculating dose factors for electrons and photons in soft tissue [11], [12], [13], [14]. We considered an infinite volume of homogeneous absorbing

Results and discussion

Fig. 1, Fig. 2 report the average energy deposition per event (monoenergetic photon or electron, respectively) emitted in the central voxel, for the eight materials studied. The analysis of photon data reveals that density influences the steepness of Edep(Rn) curves for all energies, while materials with the same or similar densities and different atomic composition show differences in the Edep(Rn) curves which decrease as the energy increases.

Electron data series show the usual trend composed

Conclusions

In this work, we developed a Monte Carlo simulation in GEANT4 which allowed us to study the dependence of voxel S factors on tissue density and atomic composition. We simulated eight standard materials and applied a previously proposed analytical formulation in order to fit Edep(Rn) curves for monoenergetic electrons and photons. Following the approach introduced in Ref. [5], the knowledge of the fit parameters allows to calculate voxel S factors for a generic beta–gamma emitting radionuclide

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