Dose Course 2018_Flipping book

calculation techniques:

Fast Fourier Transform (FFT) convolution

FFT is a way to compute the same result more quickly: operations proportional to N ln( N ) per dimension instead of N 2  decrease calc burden from N 4 to 2 N 2 ln( N ), a factor proportional to 2ln( N )/ N 2 shorter time, with N x N fluence pixels. Scaling example N factor 10 1 100 0.02 200 0.006

Calculation recipe for the lateral dose distribution at a given depth through FFT convolution.

1. Perform a 2D FFT on the pencil kernel (can be pre-stored!) 2. Perform a 2D FFT on the lateral energy fluence distribution 3. Mulitply the two transformed distributions 4. Perform an inverse 2D FFT (FFT -1 ) on the resulting product 5. Done – for all points in a plane at a certain depth (not a 3D matrix, yet)!

R Mohan and CS Chui (1987) Med Phys 14 , 70-7

Used at some stage in most TPS that use pencil kernels