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Fast Dose Kernel Interpolation Using Fourier Transform with Application to Permanent Prostate Brachytherapy

D Liu

D Liu*, R Sloboda, University of Alberta, Edmonton, AB

SU-E-T-565 Sunday 3:00PM - 6:00PM Room: Exhibit Hall

Purpose: The Fourier transform (FT) method by Boyer for seed implant dose calculation (Med Phys 1986; 13:525-29) requires that seeds be placed at calculation grid points. This abstract proposes an additional interpolation step enabling arbitrary seed placement while preserving the computational efficiency of the original method.

Methods: The TG-43 dose kernel for an Iodine-125 seed was sampled on a 3-D grid with 1 mm spacing. For each seed, the kernel was shifted to the nearest grid point via a unit impulse convolution. For the remaining fractional shift, the proposed method added a piece-wise 3rd order Lagrange interpolating filter. An additional least-square filter optimized interpolation accuracy for the clinically relevant dose range below 300 Gy at the expense of higher doses. The convolution operations were implemented in the Fourier domain. Results for the proposed interpolating FT method were compared to the original FT method and to TG-43 calculations. Interpolation accuracy for a single seed was evaluated by up-sampling and interpolating the dose kernel. Pre- and post- treatment plans were calculated for 10 patients.

Results: The interpolation error for the single seed kernel was 1 % at 5 mm distance (original method error was 20 %). Treatment plan point dose error was within 2 % for doses under 300 Gy. The dose-volume histogram error was negligible. Computation times for the original and interpolating FT methods were independent of the number of seeds. The addition of the interpolation step did not affect the computation time.

Conclusion: The FT method of Boyer was expanded to include an interpolation step, thereby relaxing the original restriction that seeds be placed at calculation grid points. The proposed interpolating method calculated treatment plans within 2 % accuracy for a clinically relevant dose range. The computational efficiency of the original method was preserved with negligible increase in computation time.

Funding Support, Disclosures, and Conflict of Interest: This work was supported by a Canada Graduate Scholarships doctoral award provided by the Canadian Institutes of Health Research (#226291)

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