A comparison of the speeds of three convolution algorithms

Area of Science:

• Medical Physics
• Computational Biology
• Radiotherapy Technology

Background:

• Accurate and efficient dose calculation is critical for effective three-dimensional radiotherapy planning.
• Existing computational methods for dose calculation present challenges in terms of speed and accuracy.
• Novel algorithms are needed to optimize the computational performance of radiotherapy planning systems.

Purpose of the Study:

• To compare the computational speeds of three distinct algorithms for three-dimensional radiotherapy dose calculations.
• To identify the most efficient algorithm for practical implementation in radiotherapy planning software.
• To evaluate the performance of ray-tracing and convolution-based methods.

Main Methods:

• Developed benchmark programs to assess the fundamental running speeds of three algorithms.
• Algorithms evaluated included direct fast ray-tracing, table lookup ray-tracing, and convolution using the fast Fourier transform (FFT).
• Algorithms were tested on three-dimensional arrays of varying sizes using a VAX/750 computer.

Main Results:

• The convolution procedure utilizing the three-dimensional fast Fourier transform demonstrated the shortest execution times.
• Ray-tracing methods, both direct and table lookup, exhibited longer running times compared to the FFT convolution.
• Performance was evaluated across different data sizes, highlighting the scalability of the FFT approach.

Conclusions:

• The convolution algorithm with the three-dimensional fast Fourier transform is computationally superior for radiotherapy dose calculations.
• This algorithm presents significant potential for enhancing the speed and practicality of three-dimensional dose computations in clinical settings.
• The findings suggest a shift towards FFT-based methods for future radiotherapy planning systems.