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Title: BReP-SNAP-T-54: Efficient Stochastic Optimization Accounting for Uncertainty in HDR Prostate Brachytherapy Needle Placement
Written by: S. Gerlach and F. Siebert and A. Schlaefer
in: Medical Physics 2020
Volume: 47 Number: 6
on pages: e458
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DOI: https://doi.org/10.1002/mp.14316
URL: https://aapm.onlinelibrary.wiley.com/doi/abs/10.1002/mp.14316
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Abstract: Purpose: Uncertainty due to tissue deformation affects treatment planningfor HDR prostate brachytherapy. Hence, position and orientation of the nee-dles are typically not optimized in inverse planning. Stochastic linear pro-gramming (SLP) has been proposed to consider uncertainty duringoptimization. Conventionally, it draws samples from a probability distribu-tion but increases the problem size substantially. We propose an efficientscheme allowing for fast identification of robust needle configurations. Methods: We account for uncertainty along the needle axis by deformingthe target using B-Spline interpolation and a random displacement of thevoxel at the needle tip. Conventional SLP adds constraints for each sample.The new weighted SLP (WSLP) scheme first creates all spatial distributionsand then establishes one discretized optimization problem where weights inthe objective function represent the likelihood of voxels falling into grid ele-ments. Both approaches and the original deterministic problem are comparedon a set of 5 patient cases. Moreover, we use WSLP on a large set of ran-domly generated needles to select a robust subset of needles. Evaluations aredone on 100 independently sampled deformations. Results: Depending onthe deformation and needle count, SLP and WSLP improve the target cover-age by 1.5 to 10.9 percentage points compared to deterministic optimization.There is no significant difference in target coverage between plans for SLPand WSLP (p = 0.98) but WLSP is substantially more efficient, taking belowten seconds instead of more than four hours when considering 100 sampleddeformations. Using WSLP to identify robust needle configurations, cover-age can be improved 0.7 to 3.3 percentage points over the most promisingneedle configurations identified by deterministic optimization. Conclusion: WSLP allows for fast optimization considering a dense sample of possibledeformations. Using WSLP, it is feasible to realize inverse planning incorpo-rating uncertainty in needle placement and to identify robust needle sets

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