Simultaneous optimization of isocenter locations and sector duration in radiosurgery

Abstract

Stereotactic radiosurgery is an effective technique to treat brain tumors for which several inverse planning methods may be appropriate. We propose an integer programming model to simultaneous sector duration and isocenter optimization (SDIO) problem for Leksell Gamma Knife R Icon TM (Elekta, Stockholm, Sweden) to tractably incorporate treatment time. We devise a Benders decomposition scheme to solve the SDIO problem to optimality. The performances of our approaches are assessed using anonymized data from eight previously treated cases, and obtained treatment plans are compared against each other and against the clinical plans. The plans generated by our SDIO model all meet or exceed clinical guidelines while demonstrating high conformity.arXiv:1807.02607v1 [physics.med-ph] 7 Jul 2018 IntroductionStereotactic radiosurgery (SRS) is an effective method for treatment of brain tumors, vascular malformations, and other conditions such as tremors. During SRS, a large amount of radiation is delivered to tumors through the intact skull without damaging the surrounding normal brain tissue.SRS aims to obtain highly conformal dose distributions so that dose is delivered to target structures with high precision while sparing the surrounding healthy tissues, thus increasing the patient's survival chance and improving the quality of life after the treatment. One advanced SRS system is Leksell Gamma Knife R (LGK) (Elekta, Stockholm, Sweden) Icon TM . Icon TM has a single collimator with eight detached sectors that can either be robotically driven to three different collimator sizes (4, 8, and 16 mm) or be blocked. During SRS, the patient lies on a couch and radiation is emitted by 192 cobalt-60 sources to the targets where the intersection point of all the beams is called the isocenter. The radiation delivery follows a step-and-shoot manner, i.e., the couch is stationary during delivery of radiation at each isocenter location, and only moves when the beam is blocked. To fully leverage the robotic capability of the delivery system, an automated approach for planning is required. The clinical goals for such an automated approach are: (1) satisfy or exceed the dosimetric clinical objectives (e.g., coverage, conformality, healthy tissue dose); (2) achieve (1) with minimal irradiation time (i.e., beam-on time); and (3) achieve (1) and (2) with a plan as efficient as possible, including minimizing the number of isocenters and shots required.Most of the current literature has separated the task of isocenter placement from the task of sector duration optimization (SDO). In SDO, as in fluence map optimization in Intensity Modulated Radiation Therapy, the aim is to find the intensities (or irradiation times) of each beamlet in a fixed set of beams. Previous studies on SDO mainly focus on variants of convex quadratic penalty models (Oskoorouchi et al., 2011;Ghobadi et al., 2012;Ghaffari, 2012). In order to determine the isocenter locations, Ghobadi et al. (2012) propose an algorithm that combines the well-known

Knowledge‐based isocenter selection in radiosurgery planning

“…It is also important to note, since the treatment planning is done in two steps (isocenter selection and SDO), it is possible to remedy some of the errors made in the isocenter selection phase through SDO as indicated in previous studies. 9,16 Another limitation of the present work is the scarcity of the available data and its homogeneity. That is, the entire dataset comes from single institution and consists mainly of brain metastases cases.…”

“…Some other studies attempt to simultaneously optimize isocenter locations and sector durations. 9,16 The proposed methods involve selecting a subset of the isocenters from the candidate set by solving a mixed-integer linear program (MILP). Since MILPs are generally NP-hard, this approach is limited in terms of the size of the candidate set.…”

A preliminary study on a multiresolution‐level inverse planning approach for Gamma Knife radiosurgery

“…There are two existing studies that consider the simultaneous optimization of isocenter locations and sector durations. 15,29 Both studies employed the GSP algorithm to preselect a large number of isocenter candidates (eg, 50~100 isocenter candidates per target), by either adjusting the parameters of the GSP algorithm 15 or employing random sampling to further increase the number of isocenter candidates. 29 Compared with the conventional sequential planning strategy, these two studies have more degrees of freedom in finding optimal solutions because of their larger amount of isocenter candidates fed into the optimization.…”

“…15,29 Both studies employed the GSP algorithm to preselect a large number of isocenter candidates (eg, 50~100 isocenter candidates per target), by either adjusting the parameters of the GSP algorithm 15 or employing random sampling to further increase the number of isocenter candidates. 29 Compared with the conventional sequential planning strategy, these two studies have more degrees of freedom in finding optimal solutions because of their larger amount of isocenter candidates fed into the optimization. Unlike these two studies, our study present a new feasible solution to realize the optimization of both isocenter locations and sector duration, without using the GSP method to preselect the isocenter candidates based on the geometry only.…”

Tuning-Target-Guided Inverse Planning of Brain Tumors With Abutting Organs at Risk During Gamma Knife Stereotactic Radiosurgery

“…The Inverse Planning (IP) technique for GK SRS was proposed by multiple groups [1][2][3][4] and was not commercially available until Elekta released the GammaPlan® version 10.0 in 2010 [5]. The IP feature allowed the users to iteratively optimize desired target dose.…”