On the measurement uncertainty of microdosimetric quantities using diamond and silicon microdosimeters in carbon‐ion beams

Abstract

Purpose The purpose of this paper is to compare the response of two different types of solid‐state microdosimeters, that is, silicon and diamond, and their uncertainties. A study of the conversion of silicon microdosimetric spectra to the diamond equivalent for microdosimeters with different geometry of the sensitive volumes is performed, including the use of different stopping power databases. Method Diamond and silicon microdosimeters were irradiated under the same conditions, aligned at the same depth in a carbon‐ion beam at the MedAustron ion therapy center. In order to estimate the microdosimetric quantities, the readout electronic linearity was investigated with three different methods, that is, the first being a single linear regression, the second consisting of a double linear regression with a channel transition and last a multiple linear regression by splitting the data into odd and even groups. The uncertainty related to each of these methods was estimated as well. The edge calibration was performed using the intercept with the horizontal axis of the tangent through the inflection point of the Fermi function approximation multi‐channel analyzer spectrum. It was assumed that this point corresponds to the maximum energy difference of particle traversing the sensitive volume (SV) for which the residual range difference in the continuous slowing down approximation is equal to the thickness of the SV of the microdosimeter. Four material conversion methods were explored, the edge method, the density method, the maximum‐deposition energy method and the bin‐by‐bin transformation method. The uncertainties of the microdosimetric quantities resulting from the linearization, the edge calibration and the detectors thickness were also estimated. Results It was found that the double linear regression had the lowest uncertainty for both microdosimeters. The propagated standard (k = 1) uncertainties on the frequency‐mean lineal energy truey¯normalF${\bar{y}}_{\rm{F}}$ and the dose‐mean lineal energy truey¯normalD${\bar{y}}_{\rm{D}}$ values from the marker point, in the spectra, in the plateau were 0.1% and 0.2%, respectively, for the diamond microdosimeter, whilst for the silicon microdosimeter data converted to diamond, the uncertainty was estimated to be 0.1%. In the range corresponding to the 90% of the amplitude of the Bragg Peak at the distal part of the Bragg curve (R90) the uncertainty was found to be 0.1%. The uncertainty propagation from the stopping power tables was estimated to be between 5% and 7% depending on the method. The uncertainty on the truey¯normalF${\bar{y}}_{\rm{F}}$ and truey¯normalD${\bar{y}}_{\rm{D}}$ coming from the thickness of the detectors varied between 0.3% and 0.5%. Conclusion This article demonstrate that the linearity of the readout electronics affects the microdosimetric spectra with a difference in truey¯normalF${\bar{y}}_{\rm{F}}$ values between the different linearization methods of up to 17.5%. The combined uncertainty was dominated by the uncertainty of stopping power o...

Diamond based integrated detection system for dosimetric and microdosimetric characterization of radiotherapy ion beams

“…The water depth distribution of $${\bar{y}_d}\ $$values is plotted in Figure 8 for the 284.7 MeV/u carbon ion beam (upper part of the figure) and the 148.7 MeV proton beam (lower part of the figure). A relative uncertainty of 10% was evaluated for the $${\bar{y}_d}$$ values by applying the error propagation, taking into account the contributions from the lineal energy calibration and density conversion, the statistical fluctuations of the experimental counts as well as the noise level in the energy spectra as also discussed in Reference 41. The microdosimetric spectra for protons at 3 cm water depth is overlapped to the noise background.…”

“…Although both methods strongly encouraged a single linear regression, an inconsistency was observed in the residual plot. The observed heteroscedasticity was overcome via the double linearization proposed by C. Meouchi et al 41 . After the conversion of the channels to the corresponding pulse amplitude in millivolts, each pulse height was assigned to the corresponding energy ε.…”

“…For this purpose, the electronic stopping‐power lookup tables published by ICRU for protons 44 and carbon ions 45 in graphite (lacking data on diamond) were used. The uncertainty associated to the assessment of the maximum lineal energy was assessed by Meouchi et al 41 . to be 7%.…”

“…Although both methods strongly encouraged a single linear regression, an inconsistency was observed in the residual plot. The observed heteroscedasticity was overcome via the double linearization proposed by C. Meouchi et al 41 After the conversion of the channels to the corresponding pulse amplitude in millivolts, each pulse height was assigned to the corresponding energy ε.Indeed,the PHS were calibrated in lineal energy, defined as the energy imparted in one event divided by the mean chord length y = 𝜀 ̄l , using the ion edge method. 42 This method consists, at first, to identify the edge of the spectrum, which corresponds to the maximum energy released by proton and carbon ions in diamond.…”

Microdosimetry for hadron therapy: A state of the art of detection technology

“…A comprehensive, systematic and methodical uncertainty analysis, which is missing in literature at date, would be helpful to obtain improved and more accurate comparisons in future. First interesting works pointing towards this direction have been recently carried out by Hartzell et al [149], and by Meouchi et al, [150].…”