Fluence optimization

The goal of the fluence optimization is to find a set of bixel/spot weights which yield the best possible dose distribution according to the clinical objectives underlying the radiation treatment.

For mathematical optimization, these clinical objectives have to be translated into mathematical objectives. matRad supports the mathematical optimization of a weighted sum of objetives to help finding an optimal trade-off between adequate target coverage and normal tissue sparing for an individual patent. The individual objectives are defined per structure and can be chosen by the user to be penalizing:

• squared overdosage,
• squared underdosage,
• squared dose deviation,
• mean dose,
• equivalent uniform dose.

The overall fluence optimization process is coordinated by the matRad function matRad_fluenceOptimization.m. The objectives are stored as an dose objective struct within the cst cell array. The objectives can be set including all necessary parameters via the matRad GUI. The objective function and gradient computations are performed in the matRad functions matRad_objFunc.m for physical optimization and matRad_bioObjFunc.m/matRad_bioObjFuncRBExD.m for biological optimization (for carbon ions), respectively. matRad_bioObjFunc.m performs an effect-based optimization based on the linear quadratic model according to Wilkens & Oelfke (2006), matRad_bioObjFuncRBExD.m performs a direct optimization of the RBE-weighted dose according to Krämer & Scholz (2006). The biological effect and the RBE-weighted dose are calculated with α and β base data that has been calculated according to the local effect model IV. α and β tables are available as part of the base data set carbonBaseData.mat which is provided with the matRad release.

For photons, matRad also features an experimental direct aperture optimization that largely follows the implementation described in Wild et al. (2015) which is based on Bzdusek et al. (2009) and (with some modification) Unkelbach & Cassioli (2012).

The objective functions for both physical and biological optimization is minimized using a custom projected Quasi-Newton algorithm for convex optimization. The corresponding matRad function is matRad_projectedLBFGS.m. It applies an L-BFGS update to directly approximate the product of the inverse Hessian with the gradient; a backtracking Armijo line search guarantees sufficient decrease of the objective function value in each iteration. Details about the implementation can be found in Bangert 2011 as well as Bangert 2014 and the references therein. The convergence criteria, i.e. the maximum number of iterations and the precision, can be set via the matRad GUI.