Multiple local minima in radiotherapy optimization problems with dose-volume constraints

被引:109
作者
Deasy, JO
机构
[1] Department of Radiation Oncology, James Graham Brown Cancer Center, University of Louisville, Louisville
关键词
optimization; local minima; convex; beam weights; intensity modulation; TCP;
D O I
10.1118/1.598017
中图分类号
R8 [特种医学]; R445 [影像诊断学];
学科分类号
1002 ; 100207 ; 1009 ;
摘要
The cause of multiple local minima in beam weight optimization problems subject to dose-volume constraints is analyzed. Three objective functions were considered: (a) maximization of turner control probability (TCP), (b) maximization of the minimum target dose, and (c) minimization of the mean-squared-deviation of the target dose from the prescription dose. It is shown that: (a) TCP models generally result in strongly quasiconvex objective functions; (b) maximization of the minimum target dose results in a strongly quasiconvex objective function; and (c) minimizing the root-mean-square dose deviation results in a convex objective function. Dose-volume constraints are considered such that, for each region at risk (RAR), the volume of tissue whose dose exceeds a certain tolerance dose (D-Tol) is kept equal to or below a given fractional level (U-Tol). If all RARs lack a ''volume effect'' (i.e., U-Tol = 0 for all RARs) then there is a single local minimum. But if volume effects are present, then the feasible space is possibly nonconvex and therefore possibly leads to multiple local minima. These conclusions hold for all three objective functions. Hence, possible local minima come not from the nonlinear nature of the objective functions considered, but from the ''either this volume or that volume but not both'' nature of the volume effect. These observations imply that optimization algorithms for dose-volume constraint types of problems should have effective strategies for dealing with multiple local minima. (C) 1997 American Association of Physicists in Medicine.
引用
收藏
页码:1157 / 1161
页数:5
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