Room: AAPM ePoster Library
Uncertainty due to tissue deformation affects treatment planning for HDR prostate brachytherapy. Hence, position and orientation of the needles are typically not optimized in inverse planning. Stochastic linear programming (SLP) has been proposed to consider uncertainty during optimization. Conventionally, it draws samples from a probability distribution but increases the problem size substantially. We propose an efficient scheme allowing for fast identification of robust needle configurations.
We account for uncertainty along the needle axis by deforming the target using B-Spline interpolation and a random displacement of the voxel at the needle tip. Conventional SLP adds constraints for each sample. The new weighted SLP (WSLP) scheme first creates all spatial distributions and then establishes one discretized optimization problem where weights in the objective function represent the likelihood of voxels falling into grid elements. Both approaches and the original deterministic problem are compared on a set of 5 patient cases. Moreover, we use WSLP on a large set of randomly generated needles to select a robust subset of needles. Evaluations are done on 100 independently sampled deformations.
Depending on the deformation and needle count, SLP and WSLP improve the target coverage by 1.5 to 10.9 percentage points compared to deterministic optimization. There is no significant difference in target coverage between plans for SLP and WSLP (p = 0.98) but WLSP is substantially more efficient, taking below ten seconds instead of more than four hours when considering 100 sampled deformations. Using WSLP to identify robust needle configurations, coverage can be improved 0.7 to 3.3 percentage points over the most promising needle configurations identified by deterministic optimization.
WSLP allows for fast optimization considering a dense sample of possible deformations. Using WSLP, it is feasible to realize inverse planning incorporating uncertainty in needle placement and to identify robust needle sets.