Accurate determination of dose‐point‐kernel functions close to the origin using Monte Carlo simulations

Abstract

Dose-point-kernel (DPK) functions are used extensively for the dosimetry of gamma and beta emitters in many physical problems. These functions are usually obtained from Monte Carlo simulations where the energy deposited in concentric spherical shells around a point source is tallied. The energy scored in a spherical shell divided by the shell mass is taken as the dose at some effective radius R(eff) of the shell. The effective radius R(eff), defined as the distance of a hypothetical zero-thickness scoring region from the source, can be evaluated in different ways for a finite thickness scoring region. For a shell thickness that is very small compared to the distance from the origin, this exact evaluation method becomes unimportant and the arithmetic mean is usually an accurate estimator for R(eff). However, accurately determining R(eff) can be problematic for the innermost regions when the radial dose function D(r) varies considerably over the finite spherical shell thickness. In this work, a new method for determining R(eff) is introduced which yields consistent results for any shell thickness, thus improving on previous Monte Carlo calculations for DPKs at or near the origin. Dimensionless DPK functions for monoenergetic electrons were reevaluated using EGSnrc with an emphasis on accuracy and consistency near the origin using our new method for determining R(eff). These improved functions were implemented in a software code to calculate the DPKs for an exhaustive list of 546 beta emitters, thus extending the compilation from previous works.

An analytical method for computing voxel S values for electrons and photons

“…The emission of the primary monoenergetic electrons or photons was uniformly and isotropically distributed within the central voxel, (0,0,0), while the energy deposition in the voxels was averaged over the eight octants of the 3D space, for symmetry reasons. Each voxel is identified by (i,j,k) indexes ranging from (−5,−5,−5) to (5,5,5).…”

“…On the other hand, the convolution of precalculated electron and photon dose point-kernels with the voxelized spatial distribution of activity has been employed for threedimensional dosimetry in uniform media; 3,4 electron and photon dose point-kernels have been calculated, mainly in water, through the various Monte Carlo codes available, [5][6][7] and approximated analytical models were proposed in order to simplify the convolution algorithms. [8][9][10] The voxel S values (VSVs) approach, introduced in 1999 by the MIRD Committee, 11 has been used more widely than dose point-kernel and direct Monte Carlo computation approaches, due to its recognized simplicity and reliability.…”

An examination of beta dose attenuation effects in coarse grains located in sliced samples

“…Radiation transport simulations performed with a spherical shell model (e.g., Janicki and Seuntjens, 2004) can be used to calculate, for a sphere containing a uniform distribution of sources, the radial dependence of dose within the sphere and extending into the surrounding medium ( Fig. SM4) which is related to the DPK, F(s).…”

Theoretical study of the influence of a heterogeneous activity distribution on intratumoral absorbed dose distribution

“…29 Other studies about short range accuracy and voxel based kernels have been reported. 30,31 These studies will be important for the wide use of the dose point kernel method for performance of microdosimetry.…”