Real-time inverse high-dose-rate brachytherapy planning with catheter optimization by compressed sensing-inspired optimization strategies

Abstract

This paper demonstrates that optimization strategies derived from the field of compressed sensing (CS) improve computational performance in inverse treatment planning (ITP) for high-dose-rate (HDR) brachytherapy. Following an approach applied to low-dose-rate brachytherapy, we developed a reformulation of the ITP problem with the same mathematical structure as standard CS problems. Two greedy methods, derived from hard thresholding and subspace pursuit are presented and their performance is compared to state-of-the-art ITP solvers. Applied to clinical prostate brachytherapy plans speed-up by a factor of 56-350 compared to state-of-the-art methods. Based on a Wilcoxon signed rank-test the novel method statistically significantly decreases the final objective function value (p < 0.01). The optimization times were below one second and thus planing can be considered as real-time capable. The novel CS inspired strategy enables real-time ITP for HDR brachytherapy including catheter optimization. The generated plans are either clinically equivalent or show a better performance with respect to dosimetric measures.

A fast multitarget inverse treatment planning strategy optimizing dosimetric measures for high‐dose‐rate (HDR) brachytherapy

“…Based on our empirical stability test and the comparison with the expected upper bound retrieved using the relaxed version of the MILP, we conclude that the retrieved solutions are near the global optimum (< 10%). This deviation is acceptable and also in the range of what we have observed for other ITP approaches for brachytherapy . Further we conclude that an initial solution with all dwell times set to zero is a valid initial guess that yields a high plan quality.…”

“…This deviation is acceptable and also in the range of what we have observed for other ITP approaches for brachytherapy. 17,27 Further we conclude that an initial solution with all dwell times set to zero is a valid initial guess that yields a high plan quality. An extension of the approach with multiple starting points to further increase the quality of the optimization is not necessary and may even lead a deterioration in quality.…”

“…In addition, are weighting factors and is a function evaluating the number of dose points that are above a given dose threshold for a given dwell‐time vector x ; is a respective function evaluating the number of dose points that are below a given dose threshold. The function Q ( x ) can be optimized with a variety of different optimization techniques such as probabilistic methods, the reformulation into a linear programming problem, or compressed sensing inspired methods . The final optimization problem reads as:where s is the number of possible dwell positions.…”

“…The function Q(x) can be optimized with a variety of different optimization techniques such as probabilistic methods, 10 the reformulation into a linear programming problem, 8 or compressed sensing inspired methods. 17 The final optimization problem reads as:…”

A fast inverse treatment planning strategy facilitating optimized catheter selection in image‐guided high‐dose‐rate interstitial gynecologic brachytherapy

“…Two other methods addressing catheter optimization based on pure geometric optimization are needle planning by integer program (NP) and the centroidal Voronoi tessellation (CVT) for fast needle selection. Recently a real‐time catheter optimization strategy inspired by compressed sensing that allows catheter optimization based on the DBOF . The presented splitting inspired subspace pursuit algorithm (SISA) is a greedy‐based approach that decouples dwell time from catheter optimization.…”