Sources of image degradation in fundamental and harmonic ultrasound imaging using nonlinear, full-wave simulations

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). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. 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 beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging.

Fig. 1

A graphical representation of the variation in the speed of sound for a portion of one of the abdominal layers provided by the Diagnostic Ultrasound Research Laboratory [25, 41, 42] (not shown are spatial variations in attenuation, nonlinearity, and density).

Fig. 2

A comparison of the theoretical and simulated power spectrum of the backscatter from a field of randomly distributed scatterers in the Rayleigh regime.

Fig. 3

The acoustic field of a propagating diagnostic pulse at the focus depth (echo dynamic range is compressed by fractional exponentiation to emphasize small amplitudes).

Fig. 4

Control PSFs from an unapodized transducer in a homogeneous medium. The fundamental (left) and harmonic (right) PSFs are shown normalized relative to their peak. Note that the scales for the x- and y-axes are not geometrically proportional. The scale to the right of each image has units of decibels.

Fig. 5

The fundamental (left) and harmonic (right) PSFs showing clutter resulting from the propagation of an ultrasonic pulse through an abdominal wall. The harmonic PSF shows a significant reduction in clutter preceding the ultrasonic pulse, which is associated with reverberation clutter. There is a smaller reduction in clutter in the trailing region, which is associated with pulse lengthening.

Fig. 6

Images of the reverberation clutter from propagation through a representation of the abdominal wall. The fundamental (left) and harmonic (right) images are shown without any signal from a point target.

Fig. 7

Isoimpedance point-spread-functions, obtained by subtracting the reverberation clutter from the PSFs in Fig. 5.

Fig. 8

Point-spread-functions without aberration obtained by propagating the ultrasonic pulse through a medium with no variations in the speed of sound but with an unchanged impedance compared to the abdominal layer.

Fig. 9

Fundamental (left) and harmonic (right) point-spread-functions for a transmit focus at 5 cm and a receive focus at 3 cm after propagation through a representation of the abdomen. The PSFs show increased reverberation clutter due to the proximity of the target to the abdominal layer.

Fig. 10

Simulated fundamental (top) and harmonic (bottom) ultrasound images of 5 mm anechoic lesions at 3 and 5 cm using delay-and-sum beamforming and a transmit focus at 5 cm. Images are shown for a homogeneous medium (left), an abdominal layer (middle-left), an isoimpedance material (middle-right), and an isovelocity material (right). Images are shown with 50 dB of dynamic range.