L-curve analysis of radiotherapy optimization problems.
We attempt to select an optimal value of regularization parameter in the optimization problems for intensity-modulated radiotherapy which are solved using a variational regularization technique. We apply to inverse treatment planning the L-curve method which was developed to determine the regularization parameter in the discrete ill-posed problems. The L-curve method is based on finding the regularization parameter which minimizes the residual norm which is a measure of accuracy of fit and the solution norm which is a measure of smoothness of solution. The main idea of the L-curve method is to plot the smoothing norm as a function of the residual norm for all values of the regularization parameter. This characteristic curve has an L-shaped dependence and the optimal value of regularization parameter can be found at the "corner" of the L-curve. We plot the L-curves for the optimization problems which simulate prostate radiotherapy cancer treatment with intensity-modulated beams. Different numerical methods are applied to calculate the point of maximum curvature of the L-curves which is a criterion to locate the corner. We show that the point of maximum curvature can be located in a most robust way using a formula derived from the singular value decomposition analysis.
Chvetsov
Alexei V
AV
Department of Radiation Oncology, Case Western Reserve University and University Hospitals of Cleveland, 11100 Euclid Avenue, Cleveland, Ohio 44106-6068, USA. alexei.chvestov@cwru.edu
D000465:Algorithms; D001822:Body Burden; D006801:Humans; D008297:Male; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D009928:Organ Specificity; D011471:Prostatic Neoplasms / Q000503:physiopathology* / Q000532:radiotherapy*; D011874:Radiometry / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D020266:Radiotherapy, Conformal / Q000379:methods*; D012062:Relative Biological Effectiveness; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity