FOCUS

Fast Object-oriented C++ Ultrasound Simulator

About FOCUS

FOCUS simulates the propagation of a continuous ultrasound wave through various media. There are two unique components, the Fast Nearfield Method (FNM) and the Angular Spectrum Approach (ASA). The FNM is used to calculate in initial pressure field from the face of the transducer. Although the FNM can be used to calculate the whole pressure field, the ASA is much faster when used to propagate the wave through the coordinate grid.

Why use FOCUS?

Accuracy

FOCUS calculates pressure fields more accurately and much faster than competing methods based on the Rayleigh-Sommerfeld integral or the impulse response. The FNM algorithm in FOCUS rapidly converges in the nearfield by subtracting a singularity, whereas the Rayleigh-Sommerfeld integral and the impulse response converge much slower in the nearfield due to the singularities that are inherent to these methods. As a result, the nearfield errors are consistently larger with the Rayleigh-Sommerfeld integral and the impulse response than with FOCUS.

Speed

FOCUS is also much faster than methods based on the Rayleigh-Sommerfeld integral and the impulse response. FOCUS achieves substantial reductions in computation time in two ways. First, the FNM algorithm in FOCUS is O(n), whereas methods that subdivide the radiating aperture are inherently O(n²). This means that the time required for calculations with FOCUS increases slowly (linearly) as the number of abscissas increases and that the time for calculations that evaluate 2D integrals (such as the Rayleigh Sommerfeld integral and Field II) increases rapidly (quadratically) as the number of subdivisions increases. Second, for transient calculations, FOCUS only needs to sample the pressure waveform at a rate high enough to capture the relevant frequency components in the excitation signal. In FOCUS, there is no need to sample a pulse with a center frequency of 3.5 MHz at 100 MHz or higher because the impulse response is not used in FOCUS, so no issues with aliasing the impulse response arise in FOCUS. This allows for much lower temporal sampling rates in FOCUS, where these reduced sampling rates facilitate much shorter computation times for transient calculations and imaging simulations without sacrificing accuracy (in general, FOCUS achieves equal or greater accuracy than these competing methods, even when FOCUS simulations are performed at a much lower sampling rate).

Efficiency

FOCUS is also inherently more memory-efficient than methods based on the impulse response. By calculating time-harmonic and transient pressure fields with the fast and efficient FNM algorithm, FOCUS can solve larger problems with a storage scheme that only needs to save as many time samples as needed to represent the transient response with very little additional overhead.

Applications

FOCUS was originally designed for some of the most common applications of therapeutic and diagnostic ultrasound. We are presently using FOCUS to model ultrasound phased arrays for hyperthermia and ablative therapy (HIFU), for diagnostic imaging with phased arrays and linear arrays, and for synthetic aperture imaging. More recently, we have created MATLAB scripts that 1) use FOCUS to calculate the pressure squared for radiation force calculations and 2) use FOCUS in simulations of photoacoustic imaging. The radiation force simulations show that FOCUS calculates the pressure squared more accurately and in less time (~3 minutes) than Field II (4 hours). In these simulations, the errors throughout the 3D volume are equal or better with FOCUS, and the errors are significantly smaller with FOCUS in the focal zone and in the nearfield region.