3-D superposition for radiotherapy treatment planning using fast Fourier transforms

Area of Science:

• Medical Physics
• Radiotherapy
• Computational Dosimetry

Background:

• Current radiotherapy planning algorithms lack electron scatter modeling.
• Superposition/convolution techniques model electron scatter but are computationally intensive.
• Electron scatter is significant at higher linear accelerator energies.

Purpose of the Study:

• To present a 3D dose calculation method using fast Fourier transforms (FFTs) for superposition in radiotherapy treatment planning.
• To improve the speed of superposition calculations while maintaining accuracy.
• To evaluate the accuracy of the FFT-based convolution method for various field sizes and energies.

Main Methods:

• Developed a 3D dose calculation method using FFTs for superposition.
• Calculated dose spread arrays using the EGS Monte Carlo code.
• Convolved dose spread arrays with TERMA (total energy released per unit mass) in Fourier space.
• Modeled a 10 MV nominal beam energy using a 10-component spectrum and compared with monochromatic energy.

Main Results:

• The FFT technique significantly accelerates superposition calculations compared to standard convolution for medium to large datasets.
• The method demonstrates high accuracy for small fields in homogeneous media.
• For larger fields, central axis depth dose remains accurate, though penumbral region profiles show minor distortion.

Conclusions:

• The FFT-based convolution method is a computationally efficient and accurate approach for radiotherapy dose calculation.
• The method's accuracy is suitable for routine treatment planning, despite minor distortions in larger fields.
• This technique offers a viable solution to the computational burden of superposition algorithms.