A singular value decomposition linear programming (SVDLP) optimization technique for circular cone based robotic radiotherapy

Abstract

With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP approach is tested and compared with MultiPlan on three clinical cases of varying complexities. In general, the plans generated by the SVDLP achieve steeper dose gradient, better conformity and less damage to normal tissues. In conclusion, the SVDLP approach effectively improves the quality of treatment plan due to the use of the complete beam search space. This challenging optimization problem with the complete beam search space is effectively handled by the proposed SVD acceleration.

Applying pytorch toolkit to plan optimization for circular cone based robotic radiotherapy

“…This method takes full advantage of the treatment space but also means greater computational cost. The second scenario was adopted in our previous work [ 8 ] with a novel technique for beam initialization. The mechanism simulates the process of moving the equivalent dose taper to cover the entire target volume.…”

“…The beam initialization was implemented in C++, and dose was calculated using ray-tracing method on GPU. Plans evaluation was performed on an in-house platform, which was developed and validated in our previous study [ 8 , 20 ]. The MLP plans were also imported to the platform, and all the following mentioned plan evaluation indices were calculated under the same resolution (2 mm × 2 mm × 2 mm) with AD-S plans.…”

“…The need to improve the treatment efficiency means to reduce the number of beams and nodes without jeopardizing the quality of plan. Previously, we presented a singular value decomposition accelerated linear programming (SVDLP) optimization method [ 8 ]. This method used the least absolute shrinkage and selection operator ( lasso ) [ 9 ] for beam reduction.…”

The status of medical physics in radiotherapy in China

“…The top three subspecialties are radiation imaging (218 papers), radiation therapy (70 papers), and magnetic resonance (42 papers). Within the subspecialty of radiation therapy, the number of publications are 15 papers in the field of clinical implementation [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55], 11 papers in the field of plan optimization [56][57][58][59][60][61][62][63][64][65][66], 14 papers in the field of plan evaluation [67][68][69][70][71][72][73][74][75][76][77][78][79][80], and 12 papers in the field of quality assurance [81][82][83][84][85][86][87][88]…”