An Almost Linear Time Algorithm for Field Splitting in Radiation Therapy

Area of Science:

• Medical Physics
• Computational Geometry
• Operations Research

Background:

• Intensity-Modulated Radiation Therapy (IMRT) uses multi-leaf collimators (MLCs) to deliver precise radiation doses.
• MLC maximum leaf spread constraints can necessitate splitting large Intensity Maps (IMs) into smaller, overlapping sub-IMs for delivery.
• This splitting process impacts treatment efficiency and delivery time.

Purpose of the Study:

• To develop a computationally efficient algorithm for the optimal field splitting problem in IMRT.
• To minimize the total complexity of sub-IMs generated during field splitting.
• To simultaneously minimize the maximum beam-on time for the delivered sub-IMs.

Main Methods:

• Formulated the field splitting problem as a shortest path computation in a directed acyclic graph with a Monge property.
• Utilized the Monge property to develop a close-to-linear time algorithm for solving the shortest path problem.
• Addressed the min-max beam-on time objective by solving a min-max slope path problem in a monotone polygon in linear time.

Main Results:

• Developed a close-to-linear time algorithm for optimal field splitting.
• The algorithm effectively minimizes the total complexity of sub-IMs.
• Experimental results demonstrate fast performance and high-quality splitting on real and generated Intensity Maps.

Conclusions:

• The proposed algorithm offers an efficient and effective solution for the optimal field splitting problem in IMRT.
• This advancement can lead to improved treatment delivery efficiency and reduced beam-on times.
• The underlying shortest path and min-max slope path algorithms may have broader applications.