A heterogeneous nonlinear attenuating full- wave model of ultrasound

Abstract

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A −78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.

Ultrasound Simulation on the Cell Broadband Engine Using the Westervelt Equation

“…For comparison with [6], the results reported below are for the simulation of 6000 time steps (the equivalent of one scan line computation) using a grid of size of 2064 × 2064. 4 The sound speeds within the medium were defined using a numerical phantom of a fetus [20]. This contained a small number of large homogeneous regions and other regions consisting of sub-wavelength scatterers.…”

“…For example, the central frequency of a diagnostic ultrasound transducer can range from 2 − 15 MHz, with depth penetrations from cms to tens of cms. To discretize domains of this size, a 2 dimensional finite-difference time-domain (FDTD) simulation can require grid sizes in excess of 1000 × 1000 grid points [4,5]. Similarly, the simulation of a single scan line in which waves propagate from the transducer into the medium and back can require more than 6000 time steps [6].…”

Nonlinear Ultrasound Simulation Based on Full-Wave Model and Comparisons with KZK

“…The full-wave equation describes the propagation of ultrasound through biological tissues with the effect of attenuation, nonlinearity, scattering, reflection and refraction [4], [7]. …”

“…The FDTD method is used to solve the full-wave equation [4]. The idea of the method is to discretize the space into lots of small grids and to calculate the pressure field of the whole simulated space.…”

“…Since the simulation must be truncated into a finite space, some boundary conditions are necessary. Here we use the Perfectly Matched Layers (PML) to truncate the simulation field [4], [12]. PML can absorb the wave arriving at the boundary to avoid unwanted reflection which will bring error into the simulation.…”