A 3D pencil-beam-based superposition algorithm for photon dose calculation in heterogeneous media

Abstract

In this work, a novel three-dimensional superposition algorithm for photon dose calculation is presented. The dose calculation is performed as a superposition of pencil beams, which are modified based on tissue electron densities. The pencil beams have been derived from Monte Carlo simulations, and are separated into lateral and depth-directed components. The lateral component is modeled using exponential functions, which allows accurate modeling of lateral scatter in heterogeneous tissues. The depth-directed component represents the total energy deposited on each plane, which is spread out using the lateral scatter functions. Finally, convolution in the depth direction is applied to account for tissue interface effects. The method can be used with the previously introduced multiple-source model for clinical settings. The method was compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities. Comparisons were made for several field sizes for 6 and 18 MV energies. The deviations were generally within (2%, 2 mm) of the field central axis d(max). Significantly larger deviations (up to 8%) were found only for the smallest field in the lung slab phantom for 18 MV. The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes.

Dosimetric comparison of Acuros XB with collapsed cone convolution/superposition and anisotropic analytic algorithm for stereotactic ablative radiotherapy of thoracic spinal metastases

“…Heterogeneity corrections are accomplished longitudinally by radiological depth scaling along ray directions and laterally by combining a radiological distance scaling to exponential absorption functions. The heterogeneity corrections are approximate and have been shown to underestimate (or overestimate) dose at bone/air/tissue interfaces 10 , 11 , 12 …”

Dosimetry of oblique tangential photon beams calculated by superposition/convolution algorithms: a Monte Carlo evaluation

“…( 14 , 15 ) The pencil beam used MC simulations with adjustment based on measurement to consider the primary photons, scattered extrafocal photons and scattered electrons. The longitudinal distribution of the pencil beam is scaled using the equivalent path length method, and the lateral distribution of the pencil beam is scaled according to the equivalent path length to the calculation point based on the densities relative to water in the previous layer of the irradiated volume.…”

“…In all superposition/convolution methods, the collapsed cone convolution (CCC) algorithm ( 13 ) and anisotropic analytical algorithm ( 14 , 15 ) (AAA) are popular, and have a good accuracy in heterogeneous media. There were a number of evaluations concerning dose calculations of the AAA and CCC in the heterogeneous media using various heterogeneous and homogeneous phantoms.…”

Radiobiological evaluation of dose calculation algorithms in RapidArc planning of esophageal cancer treatment plans

“…The AAA is based on a pencil-beam convolution/superposition technique, and the primary photons, scattered photons and electrons scattered from the beam limiting devices are modeled separately in AAA [18] . The tissue heterogeneity in the AAA is handled by scaling of primary photons and photon scatter kernel scaling in lateral directions according to local electron density [18][19][20] . A more detailed description of the AAA is presented elsewhere [18][19][20] .…”

“…The tissue heterogeneity in the AAA is handled by scaling of primary photons and photon scatter kernel scaling in lateral directions according to local electron density [18][19][20] . A more detailed description of the AAA is presented elsewhere [18][19][20] . The AXB solves numerically Linear Boltzmann Transport Equation which describes the macroscopic behavior of radiation particles as they travel through and interact with matter [14] .…”