Treatment Planning for Volumetric-Modulated Arc Therapy: Model and Heuristic Algorithms

In this paper, we study the radiation treatment planning optimization for Volumetric-Modulated Arc Therapy (VMAT). A nonlinear mixed integer programming model is formulated, then the linearization technique is used, and the resulting mixed integer programming model is solved by a heuristic approach based on the Nested-Partitions framework. The approach partitions the feasible region iteratively and constructs a feasible solution by solving the LP relaxation of the original problem. We design two partition strategies: partition by column and expansion from center of aperture. Numerical results with clinical cases show the efficiency of the proposed model and algorithm. Note to Practitioners-VMAT delivers a dose in a continuous manner which requires the dose intensity and aperture shape to be optimized simultaneously. The resulting treatment planning problem becomes very difficult to solve. In this paper, we develop a nonlinear mathematical model based on control points. The frequently used clinical setting such as dose-limit and dose volume constraints as well as multi-leaf collimator (MLC) constraints are considered in the model. We then use a linearization technique to transform the nonlinear treatment planning model to an equivalent mixed integer linear programming (MILP) model. The objective of the MILP model is a penalty function of target underdose and organ at risk (OAR) overdose. Based on the property of the MILP treatment planning problem, an effective heuristic method based on Nested-Partitions framework is developed to solve the MILP problem. The output of the model includes the dose intensity and aperture at each control point. As the prescription dose limit and feasibility of change between adjacent control points are ensured in the model, the output is deliverable through a planning system.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000347705600012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Automation & Control SystemsSCI(E)EI1ARTICLEsongjie@coe.pku.edu.cn; zhongshun@pku.edu.cn; sunbofei@foxmail.com; leyuan@coe.pku.edu.cn1116-1261