Fast modelling of spectra and stopping-power ratios using differentiated fluence pencil kernels

Abstract

Modern radiotherapy steadily utilizes more of the available degrees of freedom provided by radiotherapy equipment, raising the need for the dosimetric methods to deliver reliable measurements for situations where the spectral properties of the radiation field may also vary. A kernel-based superposition method is presented for which the spectra from any field modulation can be instantly calculated, thus facilitating the determination of dosimetric quantities at arbitrary locations. A database of fluence pencil kernels describing the fluence resulting from point monodirectional monoenergetic beams incident onto a water phantom has been calculated with the PENELOPE-2005 Monte Carlo package. Spectra calculated by means of the kernels are presented for various 6 MV fields. The spectra have been used to investigate depth and lateral variations of water-to-air stopping-power ratios. Results show that the stopping-power ratio decreases with depth, and that this effect is more pronounced for small fields. These variations are clearly connected to spectral variations. For a 10 x 10 cm(2) field, the difference between the stopping-power ratio at 2.5 cm depth and 30 cm depth is less than 0.3% while for a 0.3 x 0.3 cm(2) field this difference is 0.7%. Ratios outside the field were found to be sensitive to the collimator leakage spectral variations.

Dosimetry of small static fields used in external photon beam radiotherapy: Summary of TRS‐483, the IAEA–AAPM international Code of Practice for reference and relative dose determination

“…This increase can also affect the stopping‐power ratio. However, it turns out that the charged particle spectrum produced in water is much less affected so that the water‐to‐air stopping‐power ratio has been found to decrease by no more than 0.5% at the depth of 10 cm in a 6 MV photon beam from 10 cm × 10 cm reference fields down to 0.3 cm × 0.3 cm square fields and 0.3 cm diameter circular fields . Even over a range of depths, from the depth of dose maximum to a depth of 30 cm, the variation is not more than 1% .…”

“…However, it turns out that the charged particle spectrum produced in water is much less affected so that the water‐to‐air stopping‐power ratio has been found to decrease by no more than 0.5% at the depth of 10 cm in a 6 MV photon beam from 10 cm × 10 cm reference fields down to 0.3 cm × 0.3 cm square fields and 0.3 cm diameter circular fields . Even over a range of depths, from the depth of dose maximum to a depth of 30 cm, the variation is not more than 1% . However, the increased average photon energy of the beam does affect the response of, for example, silicon‐based diode detectors because of the large variation in the water‐to‐silicon mass energy‐absorption coefficient ratio for photon energies below 100 keV.…”

Report of AAPM Therapy Physics Committee Task Group 74: In‐air output ratio, , for megavoltage photon beams

“…where S c is defined in Eq. ͑3͒, ⌿ is the energy fluence free in air, ͑ en / ͒ is the mean ͑energy fluence weighted͒ mass energy transfer coefficient for the miniphantom material, SF K = K / K p is the total-to-primary kerma ratio ͑or kerma scatter factor͒ that accounts for miniphantom scatter, S det,med S-A is the mean ͑secondary electron fluence weighted͒ Spencer-Attix stopping power ratio of electrons between the detector and the miniphantom medium for the detectors sensitive volume, 116 d is the effective depth of the detector, is the mean attenuation coefficient ͑energy fluence weighted͒, ␤ is the dose-to-collision kerma ratio, ͑ en / ͒ wat med is the mass energy transfer coefficient ratio for the miniphantom material and water, and the variables with a subscript "ref" denotes the corresponding variables for the reference geometry. Correction factors can be used to mitigate eventual spectral/ material induced shifts caused by measurement technique as to convert the reading from the measurement geometry to the "water kerma in free-space" conditions of definition for S c .…”

Review of fast Monte Carlo codes for dose calculation in radiation therapy treatment planning

“…[86–90] Considering the detailed discussion of MMC, SMC, and VMC, fast MC codes take two general approaches to accelerate dose calculations. In one approach, the transport parameters and algorithms of the particles are formulated in an efficient form, considering the specific conditions that one encounters in clinical situations.…”