A generalized linear-quadratic model incorporating reciprocal time pattern of radiation damage repair.

Purpose: It has been conventionally assumed that the repair rate for sublethal damage (SLD) remains constant during the entire radiation course. However, increasing evidence from animal studies suggest that this may not the case. Rather, it appears that the repair rate for radiation-induced SLD slows down with increasing time. Such a slowdown in repair would suggest that the exponential repair pattern would not necessarily accurately predict repair process. As a result, the purpose of this study was to investigate a new generalized linear-quadratic (LQ) model incorporating a repair pattern with reciprocal time. The new formulas were tested with published experimental data.

Methods: The LQ model has been widely used in radiation therapy, and the parameter G in the surviving fraction represents the repair process of sublethal damage with T(r) as the repair half-time. When a reciprocal pattern of repair process was adopted, a closed form of G was derived analytically for arbitrary radiation schemes. The published animal data adopted to test the reciprocal formulas.

Results: A generalized LQ model to describe the repair process in a reciprocal pattern was obtained. Subsequently, formulas for special cases were derived from this general form. The reciprocal model showed a better fit to the animal data than the exponential model, particularly for the ED50 data (reduced χ(2) (min) of 2.0 vs 4.3, p = 0.11 vs 0.006), with the following gLQ parameters: α/β = 2.6-4.8 Gy, T(r) = 3.2-3.9 h for rat feet skin, and α/β = 0.9 Gy, T(r) = 1.1 h for rat spinal cord.

Conclusions: These results of repair process following a reciprocal time suggest that the generalized LQ model incorporating the reciprocal time of sublethal damage repair shows a better fit than the exponential repair model. These formulas can be used to analyze the experimental and clinical data, where a slowing-down repair process appears during the course of radiation therapy.