Investigating the Possibility of Using Pruned FFT in Ultrasound Wave Propagation Simulations

Ultrasound is becoming increasingly popular in non-invasive medical
treatments. These procedures often rely on complex ultrasound
simulations, which are computationally intensive and time-consuming. The
simulations use the pseudo-spectral method with Fourier basis functions
to solve differential equations, resulting in a significant portion of
the simulation time being dedicated to Fast Fourier Transform (FFT)
calculations. This work presents an approach that has the potential to
reduce computation time and, consequently, the calculation costs of
ultrasound wave propagation simulations used in the pre-planning phase
of non-invasive treatments by employing the Pruned Fast Fourier Transform
algorithm (Pruned FFT). To evaluate this approach, the existing
simulation was modified to employ spectrum filtration applied to
acoustic pressure and velocity using a binary map to emulate the
behaviour of the pruned FFT. This allows the evaluation of the impact of
the Pruned FFT on the number of computed elements in the spectral domain
and the accuracy of the simulation. Results on real data have shown
that it is possible to replace the Fast Fourier Transform (FFT) with the
pruned version of the algorithm while getting results that are suitable
for pre-planning purposes. In some cases, we were able to reduce the
number of computed coefficients by more than 80% with an error in the
focal point of around 1.5% in 2D simulation.