Repair Kinetics Deduced from Multi-fractioned Irradiation Regimen in Mouse Lung – Application of the gLQ Model

Model Introduction With the advancement of image-guided radiation therapy (RT), SRS, SBRT and HDR brachytherapy, there is increasing interest in the use of large dose fractions to irradiate human cancer. The dose prescription has been guided by clinical experience accumulated from conventional RT (2Gy fractions) and low-dose-rate (LDR) brachytherapy using the classic LQ model. However, concerns have been raised that extension of the LQ model to high doses would overestimate cell killing and lead to significant underdosing. In 2007, Wang et al. (1) developed a gLQ model to address the dilemma of the LQ model in the high-dose-fraction domain, and to bridge the RT regimens from the conventional schedule to hypofractionated SRS, SBRT and HDR brachytherapy. In 1985, Vegesna and colleagues (2, 3) published a well designed animal study to investigate the fractionation effect of radiation. The authors investigated the response of mouse lung to the repeated dose with different fraction sizes ranging from 1.15 Gy to 13.43 Gy. The time interval between fractions was 3 hours assuming sufficient time for complete repair of cellular injury. The endpoint was the death due to radiation pneumonitis. The reciprocal of LD50 (lethal dose for 50% mortality) as a function of dose per fraction shows a downward curvature (Fig. 1), deviated from the linear line predicted by the conventional LQ model with complete repair. Thames et al. (4) presented a study to interpret the downward curvature with incomplete repair. However, the repair half-time required to fit the data was 1.5 hours that was much longer than those derived from the experiments designed to examine the radiation repair kinetics of the mouse lung [e.g. (5-10)]. When Vegesna et al. (3) published their data, they noted that the non-linear feature and suggested that the LQ dose response model might not be appropriate or that the repair of cellular injury in lung was not complete in 3 hours, or both. In this study, we present our analysis of this dataset using both the LQ and the gLQ models, investigate the discrepancy of the repair half-time and provide a consistent interpretation of the downward curvature of the LD50 plot in the entire dose range. Methods and Materials Many experiments with different dose fractionations had been performed to measure the repair half-time of mouse lung for radiation injury (5-10). The data indicated that the repair half-time ranges from 0.3 to 0.8 hour, faster than the repair half of 1.5 hours used by Thames et al. (4). In the latest two studies, van Rongen et al. reported the repair half-time of 0.4 hour (5) , and it might contain two components: a major component (80%) of 0.4 hour and a small slow component (20%) of 4.0 hours (6). These repair half-times were adopted in our study to analyze the mouse lung LD50 data and test the data-modeling ability of both the LQ and gLQ models. In the conventional LQ model, the radiation effect E of dose D is E =aD+bGD2 , Where a and b are intrinsic radiosensitivity parameters and G is the dose-rate factor. Because the 50% mortality due to pneumotitis is an isoeffect, we assume it corresponds to a constant radiation effect E, with D=LD50, then we have 1 /LD50 =a E +bGd E. This formula was used to fit the LD50 data of mouse lung study. In the LQ model, if the separation time of split-doses is long enough, and repair is complete, G=1, therefore a linear relationship between the reciprocal of LD50 and dose fraction d is expected; in case of incomplete repair, G has the format shown in Eq. (7) of Ref. (11) with N=2. In the gLQ Model, G is calculated by the equation presented in Ref. (1). Both equations present the downward curvature in the 1/LD50 vs. d plot shown in Fig. 1. The 2 min χ fitting method was adopted to fit the data and to evaluate the figure of merit for the two models (12). Results The fitting of the results are shown in Fig. 1(a) for the full range of fraction dose. The dashed and dashdotted curves represent the best fits of the LQ model with the single repair half-time (Tr = 0.4 hour) and with two component repair half-times (Tr =0.4 and 4 hours with a ratio of 4 to 1). The solid curve represents the best fit of the gLQ model. The gLQ model fits the data ( 2 min χ /v = 0.39) better than the LQ model ( 2 min χ /v = 0.66) with two repair-components and much better than the LQ model ( 2 min χ /v = 2.8) with single repair component. The latter one could not well reproduce the downward curvature presented in the data. The fitting parameters are a/b =2.4 Gy for the gLQ model, and a/b = 3.0 Gy for the two-component LQ model. In the gLQ model fit, we adopted the repair kinetics with two components. With a single repair component (Tr=0.4 hour), the gLQ could also well fit the LD50 data ( 2 min χ /v = 0.43) with slightly different model parameters (a/b = 2.4 Gy). The fitting curve is very similar to the solid curve. Data are not shown in Fig. 1(a). To demonstrate the difference of LQ Model and gLQ Model in addressing the large-fraction dose, we performed fitting in the low dose range with the two models, and then extended the model fit to the high-dose region to compare with the LD50 data. In the low dose fitting, we focused on the first 8 data points with d < 3.25 Gy. The fitting curves are plotted in Fig. 1(b). While the fitting curve and parameters of the gLQ Model remained similar to those obtained in the entire dataset, the results for the LQ model changed significantly. This test demonstrated, as shown in the figure, that the gLQ model can well predict the LD50 in large-dose fraction domain, with a deviation of 2% for single fraction irradiation (d=13.43 Gy), whereas the LQ model presented large discrepancies (6% for two-component LQ model and 26% for single-component LQ model). Fig. 1 Isoeffect data for lung pneumonitis of mouse – Reciprocal of total dose with 50% lethality (LD50) vs dose per fraction (3). Both the conventional LQ and the gLQ models were used to fit the animal data: (a) full dose range 0-11.5 Gy; (b) only low dose data (< 3.25 Gy). The curves above 3.25 Gy in (b) represent the model predictions based on low-dose data. Dashed and dash-dotted curves represent LQ model fits with repair half-times of 0.4h and 0.4h + 4.0h respectively; solid curves represents gLQ model fits with repair half-times of 0.4h + 4.0h.