SU‐E‐T‐04: A Generalized Linear‐Quadratic Model Incorporating Reciprocal Time of Radiation Damage Repair

Abstract

Purpose: It is well known that repair of sublethal damage plays an important role in radiation therapy. The repair rate has been conventionally assumed to be constant during the entire radiation course. However, there is increasing evidence from animal modes showing that the repair process may slow down with time and the experimental data does not fit an exponential pattern. To address this enigma, we presented a generalized linear‐quadratic (gLQ) model incorporating a reciprocal time of damage repair and applied it to fit published experimental data. Methods: In the gLQ model, the parameter G in the surviving fraction represents the repair process of sublethal damage with Tr as the repair half‐time. When a reciprocal pattern of repair process was adopted, a generalized form of G was derived analytically for arbitrary radiation schemes. The published animal data was used to test the reciprocal formulas. Results: The gLQ model incorporating a reciprocal pattern to describe the repair process was presented. Subsequently, formulas for special cases including constant dose rate were derived from this general form. The reciprocal model showed better fit to the animal data than the exponential model, particularly for the ED50 data, resulting in the following parameters: alpha/beta=2.6–4.8 Gy, Tr= 3.2–3.9 h for rat feet skin, and alpha/beta=0.9 Gy, Tr =1.1 h for rat spinal cord. Conclusions: These modeling results suggest that the gLQ model incorporating the reciprocal time of sublethal damage repair facilitates the interpretation of complex experimental designs, especially for irregular dose delivery schedules. These formulas can be used to analyze experimental and clinical data, where a slowing‐down of the repair process occurs during the radiation therapy course.