Biological equivalent dose prediction in pion irradiation using pion star density and the mixed beam lesion additivity model

Abstract

The biological equivalent dose profile of the pion beam was predicted with one parameter (gamma) using physical dose and pion star density. The value of the relative biological effectiveness (RBE) at each depth was given as a linear function of pion star density (PSD): RBE = 1.0 + gamma PSD, assuming (i) the mixed beam lesion additivity model and (ii) the linear relationship between the ratio of high LET dose to total dose and pion star density. The predicted depth-survival curve fitted well with the pooled biological data of the gel technique using Chinese hamster cells (CHO). The predicted RBE were consistent with previously published results through the flat dose peak, except at the decreasing portion of the dose profile. The practical usefulness of this model in clinical treatment is stressed.

Reply to 'On the use of distributions of stopping pions as an indicator of spatial distribution of the high-LET dose in negative pion radiotherapy'

“…The basic principle of the scheme is to separate conceptually the local dose into different dose components whose spatial distribution can be differentially correlated with physical measurements and then to compute their local combined effect using the mixed radiation lesion additivity concept (Lam 1988). The formulation recently published (Shirato 1989, Lam 1990) represents the first step in this approach, which does not include the effects of neutrons that are generated from pion interactions. In his letter to the Editor, Dr Brenner suggested that this neutron dose may play a major role in pion treatment planning in such a scheme.…”

“…I welcome this opportunity to respond since the topic has important implications for clinical pion therapy. The model which I suggested has been straightened by Dr Lam and is called the LA-SD model in this reply (Shirato 1990).…”

“…The Editor, Sir, I acknowledge with interest the letter from Dr Brenner commenting on our modified star density model or LA-SD model for biological equivalent dose prediction in pion irradiation (Shirato 1989, Lam 1990). I welcome this opportunity to respond since the topic has important implications for clinical pion therapy.…”

“…A possible advantage of the LA-SD model compared with the microdosimetric approach is that 2 or 3 dimensional distributions of R B E could be visualized by autoradiography and by PET scan (Shirato et al 1989a, b). Problems associated with activity measurements have been discussed already (Shirato 1989).…”

On the effect of neutron dose in pion treatment planning

“…The basic principle of the scheme is to separate conceptually the local dose into different dose components whose spatial distribution can be differentially correlated with physical measurements and then to compute their local combined effect using the mixed radiation lesion additivity concept (Lam 1988). The formulation recently published (Shirato 1989, Lam 1990) represents the first step in this approach, which does not include the effects of neutrons that are generated from pion interactions. In his letter to the Editor, Dr Brenner suggested that this neutron dose may play a major role in pion treatment planning in such a scheme.…”