Determination of the α/β ratio for the normal liver on the basis of radiation-induced hepatic toxicities in patients with hepatocellular carcinoma

Background: The purpose of this study was to determine the alpha/beta ratio for normal liver with hepatitis by analyzing the toxicity data from patients with unresectable hepatocellular carcinoma treated with helical tomotherapy. Methods: Between March 2006 and February 2012, 98 patients were eligible for this study. 66 patients received 45-50 Gy in 4.5-5 Gy fractions (Group A) and 32 patients received 36-60 Gy in 2.5-3 Gy fractions (Group B). Radiation-induced hepatic toxicity was defined as an increase of at least 2 points in the Child-Pugh score within 4 months of completing helical tomotherapy. We attempted to find the statistically significant parameters in the 2 groups using alpha/beta ratios of 2, 4, 6, 8, or 10, and compared the estimated probability curves of each significant parameter. We hypothesized that the alpha/beta ratio associated with the best matches for the curves between the 2 groups would be equivalent to the alpha/beta ratio for the normal liver. Results: When using an alpha/beta ratio of 2 or 4, different parameters were found to be statistically significant in a multivariate analysis (Group A: V-BED30 for alpha/beta ratio = 2 and V-BED25 for alpha/beta ratio = 4, Group B: V-BED25 for alpha/beta ratio = 2 and V-BED20 for alpha/beta ratio = 4). When using an alpha/beta ratio of 6, 8, or 10, V-BED20 was found to be a statistically significant parameter in both groups. Comparison of the estimated probability curve of each significant parameter between the groups revealed that an alpha/beta ratio of 8 resulted in the best matches. Conclusions: We suggest that the alpha/beta ratio of the normal liver with hepatitis is 8. We hope that previously reported parameters and their values can be effectively used in different fractionation schemes by calculating the biologically effective dose using an alpha/beta ratio of 8.