The effect of different lower detection thresholds in microdosimetric spectra and their mean values

Highlights

• The influence of data analysis on microdosimetric results in clinical beams.

• Definition of a standard microdosimetric procedure for clinical applications.

• How to linearly extrapolate microdosimetric spectra to allow data intercomparison.

Abstract

Research on the applications of microdosimetry to particle therapy is spreading worldwide with a rapid increase of publications in the last years. In order to be able to perform an intercomparison of data acquired with different detectors in different clinical centres it is important to analyse data with a standard procedure. Often microdosimetric spectra are presented with different lower detection thresholds, in relation with different detection sensitivity and noise levels. The purpose of this paper is to analyse the influence of the lower detection threshold on the dose-mean lineal energy values, which are used as an assessment of the average LET of the radiation field. Furthermore, the dose distribution of the lineal energy can be used in combination with biological weighting functions to estimate the biological RBE at different positions along the penetration depths of therapeutic proton or carbon ion beams. Microdosimetric spectra cut at different lower thresholds lead in principle to different RBE values. It was an additional purpose of this work to analyse and discuss this effect both for proton and carbon ion irradiations.

Spectra in proton and carbon ion beams gathered with a miniaturized TEPC developed at the Legnaro National Laboratories of the Italian Institute for Nuclear Physics (LNL-INFN) have been used to perform this study.

Linear extrapolation of the microdosimetric spectra to a common value of 0.01 keV/μm significantly reduces the deviations in the mean values due to different lower thresholds. It is advisable to perform this procedure to have uniformity in data analysis and facilitate the intercomparison of data.

Introduction

Microdosimeters measure the stochastic process of energy deposition in a micrometric target aiming to mimic the radiation interaction process in a cell. The stochastic nature of the interaction is likely related to the biological effectiveness of different radiation fields, with densely ionizing radiation more effective than sparsely ionizing radiation, for a given absorbed dose [Rossi, 1966; Durante, 2009].

The interest in microdosimetry for potential application in hadron therapy, as a tool to measure the radiation quality of complex radiation fields, is growing worldwide, as documented by the increasing number of publications on this topic. Several detectors, both typical Tissue Equivalent Proportional Counters (TEPCs) and solid-state microdosimeters are currently being used to study the radiation quality of different clinical centres [Conte et al., 2020]. In order to make the intercomparison of results between each other and with meaningful simulated data, it is important to set a standard procedure for data analysis.

In particular, the dose-mean lineal energy, ${\bar{y}}_{\text{D}},$is defined in the ICRU Report 36 [Booz J., 1983] as the mean value of the dose distribution $d\left(y\right)$ of the lineal energy over the whole range of lineal energy values. However, electronic noise and detection system sensitivity pose a limit on the lowest detectable signal, the signal that can be detected over the background electronic noise of the detection system. The main source of noise is the preamplifier, with typical noise levels of 500 electrons RMS. The minimum detectable signal ε_m (or Lower Level Discriminator (LLD)) should be set to about 5 times the RMS noise to avoid the conversion of background noise pulses and freezing of the acquisition system [H. Rossi and M. Zaider, 1996; D. Srdoc, 1970]:

$${\epsilon }_{min}=\frac{5\cdot e_{\text{rms}}\cdot W}{G}$$

where W is the average energy required to produce an ion pair (electron-hole pair in case of solid state detectors), approximately 10/3.6/28 eV for diamond/silicon/propane gas respectively, and G is the amplification factor of the detector, which is 1 for solid state detectors and about 500 for gas proportional counter. When this rule is followed most of the noise is suppressed with 1 count per second as counting rate for the background noise. According to equation (1) and with e_rms = 500, the minimum detectable energy in diamond and silicon microdosimeters results to be ${\epsilon }_{\text{min}}=25\text{keV}$ and ${\epsilon }_{\text{min}}=9\text{keV}$ respectively. In terms of lineal energy, these ${\epsilon }_{\text{min}}$ values correspond to $y_{\text{min}}={\epsilon }_{\text{min}}/\bar{l}$, being $\bar{l}$ the mean chord length of the sensitive volume. Therefore, for a given RMS noise, the actual value $y_{\text{min}}$ decreases with increasing simulated site size. For instance, if $\bar{l}=10\mathrm{\mu m}$ one gets $y_{\text{min}}=2.5\text{keV}/\mathrm{\mu m}$ and $y_{\text{min}}=0.9\text{keV}/\mathrm{\mu m}$ ion correspondence of the previous values of ${\epsilon }_{\text{min}}$.

For a spherical TEPC simulating a water site of 1 μm, having a typical gas gain G = 500, the minimum detectable energy is ${\epsilon }_{\text{m}}=0.14\text{keV}$ and the minimum lineal energy is $y_{\text{min}}=0.21\text{keV}/\mathrm{\mu m}$.

To minimize the dependency on the lower detection threshold of the average lineal energy values, the lineal energy distributions can be linearly extrapolated down to a common threshold of 0.01 keV/μm, corresponding to the ionization threshold of 10 eV in water. This extrapolation procedure is described in [Lindborg and Waker, 2017], [Lindborg, 1975] [Beck and Appendix, 2004] and it has been normally applied in other publications of the mini-TEPCs [Conte et al., 2020] [Bianchi et al., 2020] together with a discussion on the uncertainties related to this procedure [Moro, 2003a] [Moro, 2003b]. However, this extrapolation procedure is not applied often by experimental groups (see for example Missiaggia et al., 2020; Verona et al., 2020; Debrot et al., 2018), leading to a heterogeneity of results that strongly depend on the electronic noise level during the irradiation and on the specific detector sensitivity. When the lineal energy mean values are calculated from microdosimetric distributions that are cut above the lowest detectable signal without performing the extrapolation to 0.01 keV/μm, the low lineal energy fraction of the microdosimetric spectrum is completely neglected resulting in artificially higher values of the calculated mean values. The yd(y) distributions measured with thick silicon detectors or with diamond microdosimeters, often show a cut at about 1 keV/μm (see for example Debrot et al., 2018; Verona et al., 2020). The lowest detectable signal, in terms of lineal energy, for thin silicon devices can be up to 10 times higher [Agosteo et al., 2010].

In this work, we studied the influence of the lower detection threshold on the calculated dose-mean lineal energy values and also on the assessment of the Relative Biological Effectiveness (RBE) for clonogenic survival of asynchronized normoxic V79 cells, calculated with a new Biological Weighting Function by [Parisi, 2020]. The analysis was performed on microdosimetric spectra measured in protons and carbon ion beams with a miniaturized TEPC.