Robust stochastic optimization of needle configurations for robotic HDR prostate brachytherapy

Area of Science:

• Medical Physics
• Radiation Oncology
• Computational Biology

Background:

• Inverse planning for HDR brachytherapy (BT) ideally includes needle pose for source trajectory.
• Robotic needle placement offers enhanced accuracy and freedom in needle positioning.
• Tissue deformation during insertion introduces uncertainty in needle pose, complicating treatment planning.

Purpose of the Study:

• To develop efficient methods for addressing uncertainty in HDR BT inverse planning.
• To robustly optimize needle pose before insertion for robotic placement.
• To facilitate path planning for robotic needle placement under tissue deformation uncertainty.

Main Methods:

• Utilized stochastic linear programming to model inverse treatment planning under uncertainty.
• Simulated tissue deformation by considering random displacements at the needle tip.
• Proposed two efficient stochastic linear programming approaches: averaging dose coefficients and weighting slack variables.
• Compared these approximations against conventional linear programming and full stochastic linear programming.

Main Results:

• Stochastic planning significantly improves treatment robustness against tissue deformation.
• Approximated stochastic linear programming methods better conform to tissue deformation than conventional methods.
• Proposed methods reduced planning runtime by two orders of magnitude compared to full stochastic linear programming.
• Skew needle configurations with weighted stochastic optimization improved mean coverage by 1.77–4.21 percentage points for 4–10 mm deformation.

Conclusions:

• Efficient stochastic optimization enables selection of needle configurations robust to target deformation.
• This approach enhances achievable prescription dose coverage despite tissue displacement.
• The developed method facilitates robust path planning for robotic needle placement in HDR BT.