Theoretical developments on fast Fourier transform convolution dose calculations in inhomogeneous media

Area of Science:

• Medical Physics
• Radiotherapy Physics
• Computational Dosimetry

Background:

• Accurate dose calculations are crucial for effective radiation therapy.
• Previous fast Fourier transform (FFT) convolution methods had limitations in predicting doses within inhomogeneous media.
• Empirical adjustments were previously made to theoretical models.

Purpose of the Study:

• To extend existing first-order theory for dose calculations in inhomogeneous media.
• To develop a new, theoretically justified correction dose formula.
• To improve the accuracy of three-dimensional (3D) treatment planning for photon beams.

Main Methods:

• Extension of Boyer and Mok's first-order theory to include second-order inhomogeneity effects.
• Derivation of a novel correction dose formula for scattered radiation.
• Theoretical justification of the primary dose formula used in previous empirical models.
• Utilizing fast Fourier transform (FFT) convolution for dose calculations.

Main Results:

• A new correction dose formula was derived, demonstrating improved performance over empirical methods.
• The primary dose calculation formula was theoretically validated.
• The study clarifies assumptions and approximations, defining the limitations of the FFT convolution method.

Conclusions:

• The extended theory provides a more accurate method for dose calculations in inhomogeneous media.
• The new correction dose formula enhances the precision of 3D treatment planning.
• This work contributes to more reliable and effective radiotherapy by refining dose calculation methodologies.