An iterative convex relaxation method for proton LET optimization

Abstract

Abstract Objective: A constant relative biological effectiveness of 1.1 in current clinical practice of proton radiotherapy (RT) is a crude approximation and may severely underestimate the biological dose from proton RT to normal tissues, especially near the treatment target at the end of Bragg peaks that exhibits high linear energy transfer (LET). LET optimization can account for biological effectiveness of protons during treatment planning, for minimizing biological proton dose and hot spots to normal tissues. However, the LET optimization is usually nonlinear and nonconvex to solve, for which this work will develop an effective optimization method based on iterative convex relaxation (ICR). Approach: In contrast to the generic nonlinear optimization method, such as Quasi-Newton (QN) method, that does not account for specific characteristics of LET optimization, ICR is tailored to LET modeling and optimization in order to effectively and efficiently solve the LET problem. Specifically, nonlinear dose-averaged LET term is iteratively linearized and becomes convex during ICR, while nonconvex dose-volume constraint and minimum-monitor-unit constraint are also handled by ICR, so that the solution for LET optimization is obtained by solving a sequence of convex and linearized convex subproblems. Since the high LET mostly occurs near the target, a 1 cm normal-tissue expansion of clinical target volume (CTV) (excluding CTV), i.e. CTV1cm, is defined to as an auxiliary structure during treatment planning, where LET is minimized. Main results: ICR was validated in comparison with QN for abdomen, lung, and head-and-neck cases. ICR was effective for LET optimization, as ICR substantially reduced the LET and biological dose in CTV1cm the ring, with preserved dose conformality to CTV. Compared to QN, ICR had smaller LET, physical and biological dose in CTV1cm, and higher conformity index values; ICR was also computationally more efficient, which was about 3 times faster than QN. Significance: A LET-specific optimization method based on ICR has been developed for solving proton LET optimization, which has been shown to be more computationally efficient than generic nonlinear optimizer via QN, with better plan quality in terms of LET, biological and physical dose conformality.