Robotic path-finding in inverse treatment planning for stereotactic radiosurgery with continuous dose delivery

Physical dose validation of dynamic treatment for Gamma Knife radiosurgery

BACKGROUND

Dynamic treatment in Gamma Knife (GK) radiosurgery systems delivers radiation continuously with couch movement, as opposed to stationary step-and-shoot treatment where radiation is paused when moving between isocenters. Previous studies have shown the potential for dynamic GK treatment to give faster treatment times and improved dose conformity and homogeneity. However, these studies focused only on computational simulations and lack physical validation.

PURPOSE

This study aims conduct dynamic treatment dosimetric validation with physical experimental measurements. The experiments aim to (1) address assumptions made with computational studies, such as the validity of treating a continuous path as discretised points, (2) investigate uncertainties in translating computed plans to actual treatment, and (3) determine ideal treatment planning parameters, such as interval distance for the path discretization, collimator change limitations, and minimum isocenter treatment times.

METHODS

This study uses a GK ICON treatment delivery machine, and a motion phantom custom-made to attach to the machine's mask adapter and move in 1D superior-inferior motion. Phantom positioning is first verified through comparisons against couch motion and computed doses. For dynamic treatment experiments, the phantom is moved through a program that first reads the desired treatment plan isocenters' position, time, and collimator sizes, then carries out the motion continuously while the treatment machine delivers radiation. Measurements are done with increasing levels of complexity: varying speed, varying collimator sizes, varying both speed and collimator sizes, then extends the same measurements to simulated 2D motion by combining phantom and couch motion. Dose comparisons between phantom motion radiation measurements and either couch motion measurements or dose calculations are analyzed with 2 mm/2% and 1 mm/2% gamma indices, using both local and global gamma index calculations.

RESULTS

Phantom positional experiments show a high accuracy, with global gamma indices for all dose comparisons ≥ $\ge $ 99%. Discretization level to approximate continuous path as discrete points show the good dose matches with dose calculations when using 1 and 2-mm gaps. Complex 1D motion, including varying speed, collimator sizes, or both, as well as 2D motion with the same complexities, all show good dose matches with dose calculations: the scores are ≥ $\ge $ 92.0% for the strictest 1 mm/2% local gamma index calculation, ≥ $\ge $ 99.8% for 2 mm/2% local gamma index, and ≥ $\ge $ 97.0% for all global gamma indices. Five simulated 2D treatments with optimized plans scored highly as well, with all gamma index scores ≥ $\ge $ 95.3% when compared to stationary treatment, and scores ≥ $\ge $ 97.9% when compared to plan calculated dose.

CONCLUSIONS

Dynamic treatment computational studies are validated, with dynamic treatment shown to be physically feasible and deliverable with high accuracy. A 2-mm discretization level in treatment planning is proposed as the best option for shorter dose calculation times while maintaining dose accuracy. Our experimental method enables dynamic treatment measurements using the existing clinical workflow, which may be replicated in other centers, and future studies may include 2D or 3D motion experiments, or planning studies to further quantify potential indication-specific benefits.

A linear programming approach to inverse planning in Gamma Knife radiosurgery

PURPOSE

Leksell Gamma Knife® is a stereotactic radiosurgery system that allows fine-grained control of the delivered dose distribution. We describe a new inverse planning approach that both resolves shortcomings of earlier approaches and unlocks new capabilities.

METHODS

We fix the isocenter positions and perform sector-duration optimization using linear programming, and study the effect of beam-on time penalization on the trade-off between beam-on time and plan quality. We also describe two techniques that reduce the problem size and thus further reduce the solution time: dualization and representative subsampling.

RESULTS

The beam-on time penalization reduces the beam-on time by a factor 2-3 compared with the naïve alternative. Dualization and representative subsampling each leads to optimization time-savings by a factor 5-20. Overall, we find in a comparison with 75 clinical plans that we can always find plans with similar coverage and better selectivity and beam-on time. In 44 of these, we can even find a plan that also has better gradient index. On a standard GammaPlan workstation, the optimization times ranged from 2.3 to 26 s with a median time of 5.7 s.

CONCLUSION

We present a combination of techniques that enables sector-duration optimization in a clinically feasible time frame.

Simultaneous optimization of isocenter locations and sector duration in radiosurgery

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^® 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.

Robotic path-finding in inverse treatment planning for stereotactic radiosurgery with continuous dose delivery

PURPOSE

Continuous dose delivery in radiation therapy treatments has been shown to decrease total treatment time while improving the dose conformity and distribution homogeneity over the conventional step-and-shoot approach. The authors develop an inverse treatment planning method for Gamma Knife® Perfexion™ that continuously delivers dose along a path in the target.

METHODS

The authors' method is comprised of two steps: find a path within the target, then solve a mixed integer optimization model to find the optimal collimator configurations and durations along the selected path. Robotic path-finding techniques, specifically, simultaneous localization and mapping (SLAM) using an extended Kalman filter, are used to obtain a path that travels sufficiently close to selected isocentre locations. SLAM is novelly extended to explore a 3D, discrete environment, which is the target discretized into voxels. Further novel extensions are incorporated into the steering mechanism to account for target geometry.

RESULTS

The SLAM method was tested on seven clinical cases and compared to clinical, Hamiltonian path continuous delivery, and inverse step-and-shoot treatment plans. The SLAM approach improved dose metrics compared to the clinical plans and Hamiltonian path continuous delivery plans. Beam-on times improved over clinical plans, and had mixed performance compared to Hamiltonian path continuous plans. The SLAM method is also shown to be robust to path selection inaccuracies, isocentre selection, and dose distribution.

CONCLUSIONS

The SLAM method for continuous delivery provides decreased total treatment time and increased treatment quality compared to both clinical and inverse step-and-shoot plans, and outperforms existing path methods in treatment quality. It also accounts for uncertainty in treatment planning by accommodating inaccuracies.