Correction factors to convert microdosimetry measurements in silicon to tissue in ¹²C ion therapy

Silicon microdosimetry is a promising technology for heavy ion therapy (HIT) quality assurance, because of its sub-mm spatial resolution and capability to determine radiation effects at a cellular level in a mixed radiation field. A drawback of silicon is not being tissue-equivalent, thus the need to convert the detector response obtained in silicon to tissue. This paper presents a method for converting silicon microdosimetric spectra to tissue for a therapeutic 12C beam, based on Monte Carlo simulations. The energy deposition spectra in a 10 μm sized silicon cylindrical sensitive volume (SV) were found to be equivalent to those measured in a tissue SV, with the same shape, but with dimensions scaled by a factor κ equal to 0.57 and 0.54 for muscle and water, respectively. A low energy correction factor was determined to account for the enhanced response in silicon at low energy depositions, produced by electrons. The concept of the mean path length (lPath) to calculate the lineal energy was introduced as an alternative to the mean chord length (l) because it was found that adopting Cauchy's formula for the (l) was not appropriate for the radiation field typical of HIT as it is very directional (lPath) can be determined based on the peak of the lineal energy distribution produced by the incident carbon beam. Furthermore it was demonstrated that the thickness of the SV along the direction of the incident 12C ion beam can be adopted as (lPath). The tissue equivalence conversion method and (lPath) were adopted to determine the RBE10, calculated using a modified microdosimetric kinetic model, applied to the microdosimetric spectra resulting from the simulation study. Comparison of the RBE10 along the Bragg peak to experimental TEPC measurements at HIMAC, NIRS, showed good agreement. Such agreement demonstrates the validity of the developed tissue equivalence correction factors and of the determination of (lPath).