Quantum‐inspired algorithm for radiotherapy planning optimization
Authors: Pakela Julia M. , Tseng Huan‐Hsin , Matuszak Martha M. , Ten Haken Randall K. , McShan Daniel L. , El Naqa Issam 
Published: October 2019

Purpose

Modern inverse radiotherapy treatment planning requires nonconvex, large‐scale optimizations that must be solved within a clinically feasible timeframe. We have developed and tested a quantum‐inspired, stochastic algorithm for intensity‐modulated radiotherapy (IMRT): quantum tunnel annealing (QTA). By modeling the likelihood probability of accepting a higher energy solution after a particle tunneling through a potential energy barrier, QTA features an additional degree of freedom (the barrier width, w) not shared by traditional stochastic optimization methods such as Simulated Annealing (SA). This additional degree of freedom can improve convergence rates and achieve a more efficient and, potentially, effective treatment planning process.

Methods

To analyze the character of the proposed QTA algorithm, we chose two stereotactic body radiation therapy (SBRT) liver cases of variable complexity. The “easy” first case was used to confirm functionality, while the second case, with a more challenging geometry, was used to characterize and evaluate the QTA algorithm performance. Plan quality was assessed using dose‐volume histogram‐based objectives and dose distributions. Due to the stochastic nature of the solution search space, extensive tests were also conducted to determine the optimal smoothing technique, ensuring balance between plan deliverability and the resulting plan quality. QTA convergence rates were investigated in relation to the chosen barrier width function, and QTA and SA performances were compared regarding sensitivity to the choice of solution initializations, annealing schedules, and complexity of the dose‐volume constraints. Finally, we investigated the extension from beamlet intensity optimization to direct aperture optimization (DAO). Influence matrices were calculated using the Eclipse scripting application program interface (API), and the optimizations were run on the University of Michigan's high‐performance computing cluster, Flux.

Results

Our results indicate that QTA’s barrier‐width function can be tuned to achieve faster convergence rates. The QTA algorithm reached convergence up to 46.6% faster than SA for beamlet intensity optimization and up to 26.8% faster for DAO. QTA and SA were ultimately found to be equally insensitive to the initialization process, but the convergence rate of QTA was found to be more sensitive to the complexity of the dose‐volume constraints. The optimal smoothing technique was found to be a combination of a Laplace‐of‐Gaussian (LOG) edge‐finding filter implemented as a penalty within the objective function and a two‐dimensional Savitzky–Golay filter applied to the final iteration; this achieved total monitor units more than 20% smaller than plans optimized by commercial treatment planning software.

Conclusions

We have characterized the performance of a stochastic, quantum‐inspired optimization algorithm, QTA, for radiotherapy treatment planning. This proof of concept study suggests that QTA can be tuned to achieve faster convergence than SA; therefore, QTA may be a good candidate for future knowledge‐based or adaptive radiation therapy applications.