TU-EE-A2-01: A Linear-Quadratic-Linear Formulation to Model Radiation Dose-Response
Purpose: Recent technological advances enable radiotherapy to be delivered in a highly conformal manner almost anywhere in the body. This has renewed interest in hypofractionation wherein the tumor is delivered a few fractions of large dose/fraction. Extrapolating clinical experience with conventional fractionations to fractions of high dose is important when designing hypofractionated regimens. Method and Materials: The concept of biologically effective dose (BED) based on the linear‐quadratic (LQ) formulation e −(α D + β D 2 ) is useful for intercomparing conventional fractionations but is suspect at high dose because the LQ curve bends continuously on the log‐linear plot. A linear‐quadratic‐linear (LQ‐L) formulation which better fits the final exponential response of experimental dose‐response studies at high dose is described. This new formulation requires only one new term, the dose DT at which the LQ curve transitions to a linear tail. LQ‐L is applied to published dose‐response curves and the clinical implications of LQ‐L are examined across a wide range of fractionations. Results: For fractions of high dose, the LQ formulation underestimates the dose per fraction required to maintain equivalency with conventional regimens. The LQ‐L model fits a wide variety of experimental survival data over a wide range of dose. When D T = 2α/β Gy , the line tangent to the LQ curve at DT intersects the e−αD and e−βD2 curves at dose α/β and also closely fits the linear response in the high dose region of many in vitro studies. Conclusion: For fractions of high dose LQ‐L gives better estimates of BED than LQ because LQ‐L better fits experimental dose‐response in the high dose region. This is particularly important when planning hypofractionated regimens for reactions with low α/β such as prostate cancer or late sequelae because D T ≈ 2α/β Gy for these reactions falls within the contemplated range of hypofractional doses.