Configuration space analysis of common cost functions in radiotherapy beam-weight optimization algorithms

Area of Science:

• Medical Physics
• Computational Biology
• Radiotherapy Optimization

Background:

• Downhill search algorithms offer speed advantages in radiotherapy optimization but risk local minima entrapment.
• Local minima can hinder the efficiency and success of optimization algorithms in treatment planning.

Purpose of the Study:

• To investigate the presence of local minima in the cost function landscape for radiotherapy beam-weight optimization.
• To evaluate the impact of different cost function terms on the existence of local minima.

Main Methods:

• Applied configuration space analysis to examine the search space of radiotherapy cost functions.
• Utilized a downhill-simplex beam-weight optimization algorithm, running it repeatedly to generate cost value frequency distributions.
• Analyzed common cost functions including PTV dose deviation, OAR integral dose, and OAR dose-volume/threshold constraints.

Main Results:

• Simple cost functions like quadratic PTV dose deviation and integral OAR dose were found to be free of local minima.
• Dose-threshold and dose-volume constraints for organs-at-risk (OARs) were identified as sources of local minima in the studied case.
• Combinations of cost functions were also assessed for their susceptibility to local minima.

Conclusions:

• The choice of cost functions significantly impacts the presence of local minima in radiotherapy optimization.
• Dose-threshold and dose-volume constraints require careful consideration to avoid potential entrapment in local minima during optimization.
• Further research into robust optimization strategies is warranted for complex cost functions in radiotherapy planning.