Fast ultrasound beam prediction for linear and regular two-dimensional arrays

Abstract

Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the long-standing issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 × 109 field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 2563 field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 202 pistons, respectively, thus facilitating future real-time thermal dose predictions.

Full-wave acoustic and thermal modeling of transcranial ultrasound propagation and investigation of skull-induced aberration correction techniques: a feasibility study

“…Numerical validation of the lossless and lossy LAPWE solvers was performed in simplified setups against the freely available software FOCUS [ 47 – 49 ]. FOCUS employs an entirely different model of acoustic wave propagation, namely the fast near-field method (FNM) [ 49 – 52 ], which is based on numerical approximations of analytical solutions and which has been extensively validated by its authors against the well-established software Field II [ 48 ].…”

Simulation techniques in hyperthermia treatment planning

“…Alternatively, high performance computing (HPC) techniques for the acceleration of computations, e.g. the use of computer clusters and graphical processing units (GPU), may gradually make full-wave 3D US-HTP more applicable (69). However, to date, US-HTP has been used most frequently to optimize or adapt the aperture of US phased-arrays to the tumor location and/or shape (70-72).…”

Huygens on speed: Interactive simulation of ultrasound pressure fields

“…The only inputs needed are the field point and source point properties. Examples of other simulators implemented using GPU computing includes [6] and [7]. The first simulates 3D pressure fields at high speeds using a fast near field method, and the latter is capable of simulating ultrasound images in real time using convolution and an assumption of a shift-invariant imaging system.…”