Toward semi-automatic biologically effective dose treatment plan optimisation for Gamma Knife radiosurgery.

Objective.Dose-rate effects in Gamma Knife radiosurgery treatments can lead to varying biologically effective dose (BED) levels for the same physical dose. The non-convex BED model depends on the delivery sequence and creates a non-trivial treatment planning problem. We investigate the feasibility of employing inverse planning methods to generate treatment plans exhibiting desirable BED characteristics using the per iso-centre beam-on times and delivery sequence.Approach.We implement two dedicated optimisation algorithms. One approach relies on mixed-integer linear programming (MILP) using a purposely developed convex underestimator for the BED to mitigate local minima issues at the cost of computational complexity. The second approach (local optimisation) is faster and potentially usable in a clinical setting but more prone to local minima issues. It sequentially executes the beam-on time (quasi-Newton method) and sequence optimisation (local search algorithm). We investigate the trade-off between time to convergence and solution quality by evaluating the resulting treatment plans' objective function values and clinical parameters. We also study the treatment time dependence of the initial and optimised plans using BED95(BED delivered to 95% of the target volume) values.Main results.When optimising the beam-on times and delivery sequence, the local optimisation approach converges several orders of magnitude faster than the MILP approach (minutes versus hours-days) while typically reaching within 1.2% (0.02-2.08%) of the final objective function value. The quality parameters of the resulting treatment plans show no meaningful difference between the local and MILP optimisation approaches. The presented optimisation approaches remove the treatment time dependence observed in the original treatment plans, and the chosen objectives successfully promote more conformal treatments.Significance.We demonstrate the feasibility of using an inverse planning approach within a reasonable time frame to ensure BED-based objectives are achieved across varying treatment times and highlight the prospect of further improvements in treatment plan quality.

The impact of unscheduled gaps and iso-centre sequencing on the biologically effective dose in Gamma Knife radiosurgery.

PURPOSE: Establish the impact of iso-centre sequencing and unscheduled gaps in Gamma Knife® (GK) radiosurgery on the biologically effective dose (BED). METHODS: A BED model was used to study BED values on the prescription iso-surface of patients treated with GK Perfexion™ (Vestibular Schwannoma). The effect of a 15 min gap, simulated at varying points in the treatment delivery, and adjustments to the sequencing of iso-centre delivery, based on average dose-rate, was quantified in terms of the impact on BED. RESULTS: Depending on the position of the gap and the average dose-rate profiles, the mean BED values were decreased by 0.1% to 9.9% of the value in the original plan. A heuristic approach to iso-centre sequencing showed variations in BED of up to 14.2%, relative to the mean BED of the original sequence. CONCLUSION: The treatment variables, like the iso-centre sequence and unscheduled gaps, should be considered during GK radiosurgery treatments.

The influence of the α/ß ratio on treatment time iso-effect relationships in the central nervous system.

Purpose: To investigate the influence of changes in α/ß ratio (range 1.5-3 Gy) on iso-effective doses, with varying treatment time, in spinal cord and central nervous system tissues with comparable radio-sensitivity. It is important to establish if an α/ß ratio of 2 Gy, the accepted norm for neuro-oncology iso-effect estimations, can be used.Methods: The rat spinal cord irradiation data of Pop et al. provided ED50 values for radiation myelopathy for treatment times that varied from minutes to ∼6 days. Analysis using biphasic repair kinetics, allowing for variable dose-rates, provided the best fit with repair half-times of 0.19 and 2.16 hr, each providing ∼50% of overall repair; with an α/ß ratio 2.47 Gy (CI 1.5-3.95 Gy). Using the above data set, graphical methods were used to investigate changes in the repair parameters for differing fixed α/ß ratios between 1.5 and 3.0 Gy. Two different intermittent dose delivery equations were used to evaluate the implications in a radiosurgery setting.Results: Changes in the α/ß ratio (1.5-3.0 Gy) have a minor effect on equivalent doses for radiation myelopathy for treatment durations of a few hours. Changing the α/ß value from 2 Gy to 2.47 Gy, modified equivalent single doses by < 1% when overall treatment times ranged from 0.1 to 5.0 hr. Significant changes were only found for treatment times longer than 5-10 hr. These two α/ß ratios were also compared in a practical radiosurgery situation, using two different models for estimating BED, again there was no significant loss of accuracy.Conclusions: It is reasonable to use an α/ß ratio of 2 Gy for CNS tissue, with the same repair half-times as published in the original publication by Pop et al., in situations where the assessment of the BED in radiosurgery is used with other form of radiotherapy. In radiosurgery, the variation in BED with treatment duration (for a fixed physical dose) is very similar, but absolute BED values depend on the α/ß value. In radiosurgery, clinical recommendations obtained using BED calculations using the originally proposed α/ß ratio of 2.47 Gy are still appropriate. For calculations involving a combination of radiosurgery and other modalities, such as fractionated radiotherapy, it would be appropriate in all cases to apply a value of 2 Gy, the accepted norm in neuro-oncology, without significant loss of accuracy in the radio-surgical component. This may have important applications in retreatment situations.

Development of the open-source dose calculation and optimization toolkit matRad.

PURPOSE: We report on the development of the open-source cross-platform radiation treatment planning toolkit matRad and its comparison against validated treatment planning systems. The toolkit enables three-dimensional intensity-modulated radiation therapy treatment planning for photons, scanned protons and scanned carbon ions. METHODS: matRad is entirely written in Matlab and is freely available online. It re-implements well-established algorithms employing a modular and sequential software design to model the entire treatment planning workflow. It comprises core functionalities to import DICOM data, to calculate and optimize dose as well as a graphical user interface for visualization. matRad dose calculation algorithms (for carbon ions this also includes the computation of the relative biological effect) are compared against dose calculation results originating from clinically approved treatment planning systems. RESULTS: We observe three-dimensional γ-analysis pass rates ≥ 99.67% for all three radiation modalities utilizing a distance to agreement of 2 mm and a dose difference criterion of 2%. The computational efficiency of matRad is evaluated in a treatment planning study considering three different treatment scenarios for every radiation modality. For photons, we measure total run times of 145 s-1260 s for dose calculation and fluence optimization combined considering 4-72 beam orientations and 2608-13597 beamlets. For charged particles, we measure total run times of 63 s-993 s for dose calculation and fluence optimization combined considering 9963-45574 pencil beams. Using a CT and dose grid resolution of 0.3 cm3 requires a memory consumption of 1.59 GB-9.07 GB and 0.29 GB-17.94 GB for photons and charged particles, respectively. CONCLUSION: The dosimetric accuracy, computational performance and open-source character of matRad encourages a future application of matRad for both educational and research purposes.