Average stopping powers for electron and photon sources for radiobiological modeling and microdosimetric applications

Dose-mean lineal energy values for electrons by different Monte Carlo codes: Consequences for estimates of radiation quality in photon beams

BACKGROUND

The microdosimetric quantity lineal energy and its mean values have proven useful for quantifying radiation quality in many situations. The ratio of dose-mean lineal energies is perhaps the simplest quantity for quantifying differences between two radiation qualities. However, published dose-mean lineal energy values from different codes may differ significantly with potential influence on radiation quality estimates.

PURPOSE

The purpose was to compare dose-mean lineal energy values from different track-structure data sets for condensed water vapor and liquid water, and to evaluate the influence on radiation quality estimations for some photon sources.

METHODS

Published dose-mean lineal energy values for 0.1 keV to 1 MeV electrons in spheres with diameters 2 nm to 1 μm, calculated with water vapor and liquid water track structure codes and proximity functions, were collected, analyzed, and compared. Data for cylinders were converted to spheres using a theoretical transformation published by Kellerer. A new set of dose-mean lineal energy values was calculated to cover the whole range of volumes of interest here using the GEANT4-DNA code. The influence from the differences between codes on radiation quality calculations was estimated using dose-mean lineal energy ratios for the photon sources ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co.

RESULTS

The theoretical relation for converting the dose-mean lineal energy between different geometrical volumes, results in differences up to 10% between cylinders and spheres depending on electron energy and target size, in agreement with published simulated results. For spheres with diameter above 100 nm, dose-mean lineal energy values for condensed water vapor and liquid water are with few exceptions within ±10%. Below 100 nm, the difference increases with decreasing diameter reaching a factor of two at 2 nm. The values from water vapor codes are in general larger than from liquid water codes. If the dose-mean lineal energy ratio is based on condensed water vapor instead of liquid water, the ratio differs less than 9% for the nuclides ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co independent of the volume simulated. However, a specific value of the dose-mean lineal energy ratio, is found at a larger target diameter in liquid water than in condensed water vapor.

CONCLUSIONS

When ratios of the dose-mean lineal energy are used as a measure of the radiation quality it is important to compare values for geometrically equal target shapes. A practical method of converting values for cylinders of equal diameter and height to spheres was demonstrated. Although dose-mean lineal energy values calculated with water vapor and liquid water codes may differ significantly, the radiation quality, in terms of ratios of dose-mean lineal energy, for the three photon sources ¹⁹² Ir, ¹⁶⁹ Yb, and ¹²⁵ I relative to ⁶⁰ Co, agree within 9%. The same ratio appears at a larger diameter when a liquid water code is used. It is therefore important to use the same code in radiation quality investigations. The present findings may be of special interest in studies related to the relative biological effectiveness (RBE).

On calculation of the average linear energy transfer for radiobiological modelling

Applying the concept of linear energy transfer (LET) to modeling of biological effects of charged particles usually involves calculation of the average LET. To calculate this, the energy distribution of particles is characterized by either the source spectrum or fluence spectrum. Also, the average can be frequency-or dose-weighted. This makes four methods of calculating the average LET, each producing a different number. The purpose of this note is to describe which of these four methods is best suited for radiobiological modelling. We focused on data for photons (x-rays and gamma radiation) because in this case differences in the four averaging methods are most pronounced. However, our conclusions are equally applicable to photons and hadrons. We based our arguments on recently emerged Monte Carlo data that fully account for transport of electrons down to very low energies comparable to the ionization potential of water. We concluded that the frequency average LET calculated using the fluence spectrum has better predictive power than does that calculated using any of the other three options. This optimal method is not new but is different from those currently dominating research in this area.

A simple model for calculating relative biological effectiveness of X-rays and gamma radiation in cell survival

OBJECTIVES

The relative biological effectiveness (RBE) of X-rays and γ radiation increases substantially with decreasing beam energy. This trend affects the efficacy of medical applications of this type of radiation. This study was designed to develop a model based on a survey of experimental data that can reliably predict this trend.

METHODS

In our model, parameters α and β of a cell survival curve are simple functions of the frequency-average linear energy transfer (L_F) of delta electrons. The choice of these functions was guided by a microdosimetry-based model. We calculated L_F by using an innovative algorithm in which L_F is associated with only those electrons that reach a sensitive-to-radiation volume (SV) within the cell. We determined model parameters by fitting the model to 139 measured (α,β) pairs.

RESULTS

We tested nine versions of the model. The best agreement was achieved with [Formula: see text] and β being linear functions of [Formula: see text] .The estimated SV diameter was 0.1-1 µm. We also found that α, β, and the α/β ratio increased with increasing [Formula: see text] .

CONCLUSIONS

By combining an innovative method for calculating [Formula: see text] with a microdosimetric model, we developed a model that is consistent with extensive experimental data involving photon energies from 0.27 keV to 1.25 MeV.

ADVANCES IN KNOWLEDGE

We have developed a photon RBE model applicable to an energy range from ultra-soft X-rays to megaelectron volt γ radiation, including high-dose levels where the RBE cannot be calculated as the ratio of α values. In this model, the ionization density represented by [Formula: see text] determines the RBE for a given photon spectrum.