Radial secondary electron dose profiles and biological effects in light-ion beams based on analytical and Monte Carlo calculations using distorted wave cross sections.

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.

Impact of dose and sensitivity heterogeneity on TCP.

This present paper presents an analytical description and numerical simulations of the influence of macroscopic intercell dose variations and intercell sensitivity variations on the probability of controlling the tumour. Computer simulations of tumour control probability accounting for heterogeneity in dose and radiation sensitivity were performed. An analytical expression for tumor control probability accounting for heterogeneity in sensitivity was also proposed and validated against simulations. The results show good agreement between numerical simulations and the calculated TCP using the proposed analytical expression for the case of a heterogeneous dose and sensitivity distributions. When the intratumour variations of dose and sensitivity are taken into account, the total dose required for achieving the same level of control as for the case of homogeneous distribution is only slightly higher, the influence of the variations in the two factors taken into account being additive. The results of this study show that the interplay between cell or tumour variation in the sensitivity to radiation and the inherent heterogeneity in dose distribution is highly complex and therefore should be taken into account when predicting the outcome of a given treatment in terms of tumor control probability.

Limitations (and merits) of PENELOPE as a track-structure code.

PURPOSE: To outline the limitations of PENELOPE (acronym of PENetration and Energy LOss of Positrons and Electrons) as a track-structure code, and to comment on modifications that enable its fruitful use in certain microdosimetry and nanodosimetry applications. METHODS: Attention is paid to the way in which inelastic collisions of electrons are modelled and to the ensuing implications for microdosimetry analysis. RESULTS: Inelastic mean free paths and collision stopping powers calculated with PENELOPE and two well-known optical-data models are compared. An ad hoc modification of PENELOPE is summarized where ionization and excitation of liquid water by electron impact is simulated using tables of realistic differential and total cross sections. CONCLUSIONS: PENELOPE can be employed advantageously in some track-structure applications provided that the default model for inelastic interactions of electrons is replaced by suitable tables of differential and total cross sections.

A Monte Carlo program for the analysis of low-energy electron tracks in liquid water.

A Monte Carlo code for the event-by-event simulation of electron transport in liquid water is presented. The code, written in C++, can accommodate different interaction models. Currently it implements cross sections for ionizing collisions calculated with the model developed by Dingfelder et al (1998 Radiat. Phys. Chem. 53 1-18, 2008 Radiat. Res. 169 584-94) and cross sections for elastic scattering computed within the static-exchange approximation (Salvat et al 2005 Comput. Phys. Commun. 165 157-90). The latter cross sections coincide with those recommended in ICRU Report 77 (2007). Other included interaction mechanisms are excitation by electron impact and dissociative attachment. The main characteristics of the code are summarized. Various track penetration parameters, including the detour factor, are defined as useful tools to quantify the geometrical extent of electron tracks in liquid water. Results obtained with the present microdosimetry code are given in the form of probability density functions for initial electron kinetic energies ranging from 0.1 to 10 keV. The sensitivity of the simulated distributions to the choice of alternative physics models has been briefly explored. The discrepancies with equivalent simulations reported by Wilson et al (2004 Radiat. Res. 161 591-6) stem from the adopted cross sections for elastic scattering, which determine largely the spatial evolution of low-energy electron tracks.

The influence of dose heterogeneity on tumour control probability in fractionated radiation therapy.

Theoretical modelling of tumour control probability (TCP) with respect to non-uniformity in the dose to the tumour, alternate fractionation schemes and tumour kinetics is a very useful tool for assessment of the influence of changes in dosimetric or radiobiological factors on the outcome of the treatment. Various attempts have been made to also include effects from non-uniform dose to the tumour volume, but the problem has not been fully solved and many factors were totally neglected or not accurately taken into account. This paper presents derivations of analytical expressions of TCP for macroscopic inter-cell dose variations and for random inter-fractional variations in average tumour dose, based on binomial statistics for the TCP and the well-known linear quadratic model for the cell survival. Numerical calculations have been performed to validate the analytical expressions. An analysis of the influence of the deterministic and stochastic heterogeneity in dose delivery on the TCP was performed. The precision requirements in dose delivery are discussed briefly with the support of the presented results. The main finding of this paper is that it is primarily the shape of the cell survival curve that governs how the response is affected by macroscopic dose variations. The analytical expressions for TCP accounting for heterogeneity in dose can quite well describe the TCP for varying dose from cell to cell and random dose in each fraction. An increased TCP is seen when a large number of fractions are used and the variations in dose to the cells are rather high for tissues with low α/ß.