Repair Kinetics of Sublethal Damage in Rat Cervical Spinal Cord - Application of the gLQ Model Incorporating Reciprocal Time

Pattern Introduction Repair of sublethal damage plays an important role during radiation therapy (RT). Based on the published data on the kinetics of repair in animal data (1-6), the understanding of the repair mechanisms and patterns is a critical component of radiation treatment design and optimization. The repair process is directly associated with the approach of dose delivery and the dose effectiveness on tumor control and normal tissue toxicity. Our current understanding is based on the theory that the sublethal damage is repaired exponentially with a characteristic repair half-time (Tr). However, many studies have indicated that repair after each fraction does not proceed at a constant rate, suggesting that a multi-exponential processes may play a role in the process (7-13). More and more animal data demonstrated that repair slows down during the recovery process (5, 9-10, 14-16). These data cannot fit into a single exponential form, and two or multiple exponential-components are needed to interpret the data (17). In other words, the repair of radiation damage does not represent the first order, as expressed in the exponential pattern, but instead a second order with a slowing-down of the repair pattern. Dale et al. proposed a new repair form with a reciprocal time (15). Fowler demonstrated that the reciprocal repair pattern could closely match the biexponential pattern within several repair half-times (16). This repair feature, with a slowing-down rate as a function of time interval between dose fractions, has a significant impact on the fractionation approach, especially for accelerated fractionation schemes radiation with two or three fractions per day (BID or TID). For an exponential repair pattern, only 3% of sublethal damage is left unrepaired after 5 repair half-times. However, if the repair follows a reciprocal pattern, there would be 1/6 (=17%) of the sublethal damage left unrepaired in the same time interval of 5 repair half-times. Because typical repair half-times of tissues are in the range of hours, a tissue repair kinetic following a reciprocal pattern may have a significant effect on the BID/TID radiation schedules. If the repair half-time is even longer, e.g. 4-5 hours, once-daily fractionation schedules would also be impacted. This “leftover” unrepaired damage would enhance radiation effect on tumor, if tumor follows such slow-repair pattern, but would also cause more severe complications, if the normal tissues follow such pattern. Fowler presented a simplified method to analyze the animal data with reciprocal repair pattern (16). However, this simplified form could not be used to directly analyze the survival or complication data collected in experiments or clinical practice. Furthermore, during the data conversion/simplification process, useful information is lost. It is necessary to develop a linear-quadratic-based model with a reciprocal time to simplify the interpretation of experimental and clinical data. Because the linear-quadratic (LQ) model can accommodate an unlimited range of fraction durations and inter-fraction intervals, the development of the LQ-based model would offer the possibility of a reassessment of a wide range of clinical data (15). The LQ model has been a widely used mathematical model to describe cell killing by radiation therapy and to represent various radiation fractionation schemes, however it generally fails in the region of large doses due to ignoring conversion of sublethal damage to lethal damage. We recently developed the generalized linear-quadratic (gLQ) model by considering the conversion of sublethal to lethal damage, and showed that this model can cover the entire large range of doses (18). In this study, based on the basic form of the gLQ model, we derived a closed form with reciprocal-time repair, which can be used to directly calculate the cell surviving fractions for radiation courses with arbitrary dose rates and delivery patterns. Furthermore, animal data published in the literature were analyzed with the newly developed formulas to investigate the feasibility of the gLQ model with reciprocal-time of radiation damage repair for interpreting the in vitro, animal and clinical data with a direct analysis.