Purpose: Gamma Knife (GK) radiosurgery treatments exhibit considerable variations in treatment times, influencing the delivered radiation's biological effectiveness. We investigate the feasibility of generating semi-automated treatment plans based on the biologically effective dose (BED) to tackle this issue. We thus create high-quality iso-effective treatment plans through the optimisation of per iso-centre beam-on times and delivery sequence.
Methods: Using a BED model considering bi-exponential repair during treatment delivery leads to a non-convex optimisation problem, and optimising the shot order poses a combinatorial problem. Therefore, we implemented two optimisation algorithms. One accurate but slow, based on mixed-integer linear programming (MILP) using a purposely developed convex under-estimator for the BED. The other utilising two established local methods (L-BFGS-B and an adapted 2-opt) alternatively, significantly faster but more prone to local minima issues. We evaluated the post-optimisation results to determine if the more rapid approaches could produce results close to those from the more demanding MILP approach.The different approaches were executed on 14 cases of Vestibular Schwannoma, using the iso-centre configurations from the original physical dose treatment plans and using a 60 min treatment as a BED reference.
Results: In terms of the final objective function values, the faster optimisations came within 1.2% (0.02-2.08%) of the convex MILP approach while requiring significantly less computation time (minutes vs hours-days).The issue of reduced biological effectiveness with increasing treatment times, which was evident in the initial BED95 values, was resolved by the BED optimisations. Overall, the Paddick Conformity Index (PCI) for the BED distribution was improved, both in average and range, from initially 0.81 (0.58-0.9) to 0.88 (0.78-0.93) with negligible differences between the optimisation approaches.
Conclusion: We demonstrate the feasibility of efficient BED-based treatment planning to ensure iso-effective treatments across varying treatment times and highlight the prospect of further improvements in treatment plan quality.
Funding Support, Disclosures, and Conflict of Interest: Funding Support: UCL CDT in Medical Imaging [EP/L016478/1], Wellcome/EPSRC Centre for Interventional and Surgical Sciences [NS/A000050/1], Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z], NIHR BRC based at Guys and St Thomas Trust CRUK ARTNET Network Accelerator Award [A21993]. Disclosure: J.McClelland/I.Paddick: grants/personal fees from Elekta outside scope of submitted work