Microdosimetric calculation of relative biological effectiveness for design of therapeutic proton beams 

Abstract

The authors attempt to establish the relative biological effectiveness (RBE) calculation for designing therapeutic proton beams on the basis of microdosimetry. The tissue-equivalent proportional counter (TEPC) was used to measure microdosimetric lineal energy spectra for proton beams at various depths in a water phantom. An RBE-weighted absorbed dose is defined as an absorbed dose multiplied by an RBE for cell death of human salivary gland (HSG) tumor cells in this study. The RBE values were calculated by a modified microdosimetric kinetic model using the biological parameters for HSG tumor cells. The calculated RBE distributions showed a gradual increase to about 1cm short of a beam range and a steep increase around the beam range for both the mono-energetic and spread-out Bragg peak (SOBP) proton beams. The calculated RBE values were partially compared with a biological experiment in which the HSG tumor cells were irradiated by the SOBP beam except around the distal end. The RBE-weighted absorbed dose distribution for the SOBP beam was derived from the measured spectra for the mono-energetic beam by a mixing calculation, and it was confirmed that it agreed well with that directly derived from the microdosimetric spectra measured in the SOBP beam. The absorbed dose distributions to planarize the RBE-weighted absorbed dose were calculated in consideration of the RBE dependence on the prescribed absorbed dose and cellular radio-sensitivity. The results show that the microdosimetric measurement for the mono-energetic proton beam is also useful for designing RBE-weighted absorbed dose distributions for range-modulated proton beams.

Characterization of proton pencil beam scanning and passive beam using a high spatial resolution solid‐state microdosimeter

“…These few high lineal energy events can significantly change the values downstream of the BP and can lead to substantial uncertainties, which has been noted in Ref. using TEPC.…”

“…This RBE value was slightly less than 1 because the dose‐mean lineal energy used for α simulation according to the MKM [Eq. ] for protons at those depths is less than 4.3 keV/μm corresponding to the X‐ray radiation reference used for the RBE derivation [Eq. ].…”

“…Detailed considerations of the MKM's theory can be found in Hawkins . The RBE calculation method used in this study is based on the modified MKM as introduced by Kase et al . This is a combined model of microdosimetry and repair of radiation‐induced lesions .…”

“…The RBE is proton dose‐dependent and related to particular survival fractions S ( D p ) and can be obtained from using the following formula:where α p is a linear function of y ∗ , D p and D X are protons and reference X‐ray radiation doses necessary for the same cell survival S, respectively. X‐rays (200 kVp) are used as a reference radiation for HSG cells for which α X = 0.164 Gy −1 and βp = β X = 0.05 Gy −2 …”

Designing a ridge filter based on a mouse foot skin reaction to spread out Bragg-peaks for carbon-ion radiotherapy

“…The mixed absorbed dose, D m (x), and mixed y ⁄ value, y ⁄ m (x), at the depth of x in the SOBP beam were calculated from the original dose distribution of the mono-energetic beam by the following mixing calculation [13]:…”