Dose- and LET-dependent changes in mouse skin contracture up to a year after either single dose or fractionated doses of carbon ion or gamma rays

Abstract

Time dependence of relative biological effectiveness (RBE) of carbon ions for skin damage was investigated to answer the question of whether the flat distribution of biological doses within a Spread-Out Bragg peak (SOBP) which is designed based on in vitro cell kill could also be flat for in vivo late responding tissue. Two spots of Indian ink intracutaneously injected into the legs of C3H mice were measured by calipers. An equieffective dose to produce 30% skin contraction was calculated from a dose-response curve and used to calculate the RBE of carbon ion beams. We discovered skin contraction progressed after irradiation and then reached a stable/slow progression phase. Equieffective doses decreased with time and the decrease was most prominent for gamma rays and least prominent for 100 keV/μm carbon ions. Survival parameter of alpha but not beta in the linear-quadratic model is closely related to the RBE of carbon ions. Biological doses within the SOBP increased with time but their distribution was still flat up to 1 year after irradiation. The outcomes of skin contraction studies suggest that (i) despite the higher RBE for skin contracture after carbon ions compared to gamma rays, gamma rays can result in a more severe late effect of skin contracture. This is due to the carbon effect saturating at a lower dose than gamma rays, and (ii) the biological dose distribution throughout the SOBP remains approximately the same even one year after exposure.

Keywords: Fe-Plot; LET; RBE; fibrosis.

Fig. 1.

Dose–response of skin contraction. Distance of two tattoo spots was measured by calipers after 33, 191 and 354 days after single doses of radiation. Skin contraction was calculated by comparing pre- and post-irradiation values in identical mice. Open circle (○) is for gamma rays and closed diamond (♦) for 100 keV/μm carbon ions.

Fig. 2.

Time course of skin contraction after single doses. (a) Skin contraction after 45 Gy of gamma rays (○) or 22 Gy of 100 keV/μm carbon ions (♦). Symbols and bars are mean and standard deviation. (b) Daily reduction of the equieffective dose for 30% skin contraction. It should be noted that the horizontal axis is a logarithmic scale. Gamma rays (○), 100 keV/μm carbon ions (♦). Mean and 95% confidence limit.

Fig. 3.

The logarithmic decrease of the equieffective dose against LET for multifaction schemes. The slopes of the daily reduction for other LETs were also calculated and plotted against LET. The slopes of the daily reduction for single and multifaction schemes were averaged to calculate mean values and plotted against LET. Bars are 95% confidence limit. Slopes of regression lines (i.e. daily-dose reduction/LET) shown in each panel are −0.098, −0.108, −0.145, −0.131, −0.122, −0.091, −0.118 for 1, 2, 3, 4, 5, 6 and 8 fractions, respectively.

Fig. 4.

Change of RBE after single and fractionated irradiation irradiations. RBE was calculated by comparing equieffective doses between reference gamma rays and carbon ions and plotted against days after irradiation. Symbols are mean values for carbon ions of; 14 keV/μm (open circle), 20 keV/μm (closed circle), 40 keV/μm (open square), 50 keV/μm (closed square), 60 keV/μm (open diamond), 80 keV/μm (closed diamond), and 100 keV/μm (open triangle).

Fig. 5.

Fe-plot for skin contraction. Equieffective doses of 30% skin contraction were obtained for 1 through 8 fractions and used to calculate alpha and beta values using Fe-plot. Symbols are: 1 keV/μm (closed triangle), 14 keV/μm (open circle), 20 keV/μm (closed circle), 40 keV/μm (open square), 50 keV/μm (closed square), 60 keV/μm (open diamond), 80 keV/μm (closed diamond) and 100 keV/μm (closed triangle). A value on Y-axis at dose zero extrapolated from the linear regression line is alpha / E while its slope is beta/E.

Fig. 6.

Dependence of survival parameters on time after irradiation. Survival parameters were calculated from Fe-plots shown in Fig. 5 and plotted against days after irradiation. (a) alpha/E, (b) beta/E, and (c) alpha/beta. Symbols are: 1 keV/μm (open circle), 14 keV/μm (closed circle), 20 keV/μm (open square), 40 keV/μm (closed square), 50 keV/μm (open diamond), 60 keV/μm (closed diamond), 80 keV/μm (open triangle), 100 keV/μm (closed triangle).

Fig. 7.

Dependence of alpha and RBE_max on LET. (a) Alpha/E at various days after irradiation was calculated for each LET. (b) RBE_max of carbon ions was calculated by comparing alpha/E of carbon ions to that of gamma rays. Symbols are Day 33 (open circle), Day 64 (closed circle), Day 94 (open square), Day 132 (closed square), Day 191 (open diamond), Day 232 (closed diamond), Day 282 (open triangle), Day 323 (closed triangle), Day 354 (open inverted triangle), Day 384 (closed inverted triangle). Symbol and bar are mean and sem.

Fig. 8.

Biological dose distribution within the SOBP. RBE_max was used to calculate a biological dose at a given depth along with the 6-cm SOBP. LET of two entrance positions are 14 keV/μm and 20 keV/μm whereas the rest of the five positions are for 40, 50, 60, 80 and 100 keV/μm, respectively. Mean and SEM. Upper- and lower curves are respectively biological dose calculated for 10% survival of HSG cells and physical dose.