Modelling of nonlinear effects and the response of ultrasound contrast micro bubbles : simulation and experiment.

Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach

A non-linear ultrasound imaging simulation software should be capable of simulating the non-linear fields for any kind of transducer, focusing, apodization, and attenuation At present, a major issue is the overlong simulation time of the non-linear software An Angular Spectrum Approach (ASA) using a quasi-linear approximation for solving the Westervelt equation can simulate the second harmonic pressure at any distance Therefore, it shortens the execution time compared with the operator splitting method The purpose of this paper is to implement the monochromatic solution for the second harmonic component based on ASA and Field II, and to compare with results from the simulation program Abersim A linear array transducer with a center frequency of 4 MHz and 64 active elements is used as the transmitting source The initial plane is 5 mm away from the transducer surface, and the fundamental pressure is calculated by Field II The second harmonic pressure in k-space along the propagating direction is calculated as an auto-convolution of the fundamental pressure multiplied by an exponential propagating coefficient In this case, the second harmonic pressure can be calculated using ASA for any plane parallel to the initial plane In the focal plane (elevation-lateral) at 60 mm from the transducer surface, calculated by ASA, the RMS errors for the fundamental component are 266% referred to Field II and 428% referred to Abersim For the second harmonic component, the RMS error is 091% referred to Abersim

/pdf/simulation-of-second-harmonic-ultrasound-fields-18ms1p8fn2.pdf

Simulation of second harmonic ultrasound fields

In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared
to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the
emitting source. The measured pulses are first compared with the linear simulation program Field II, which will
be used to generate the source for the AS simulation. The generated non-linear ultrasound field is measured
by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with
the AS simulation, which is used to calculate both fundamental and second harmonic fields. The focused piston
transducer with a center frequency of 5 MHz is excited by a waveform generator emitting a 6-cycle sine wave.
The hydrophone is mounted in the focal plane 118 mm from the transducer. The point spread functions at the
focal depth from Field II and measurements are illustrated. The FWHM (full width at half maximum) values are
1.96 mm for the measurement and 1.84 mm for the Field II simulation. The fundamental and second harmonic
components of the experimental results are plotted compared with the AS simulations. The RMS (root mean
square) errors of the AS simulations are 7.19% and 10.3% compared with the fundamental and second harmonic
components of the measurements.

/pdf/comparison-of-simulated-and-measured-non-linear-ultrasound-4y55x8yu0e.pdf

Comparison of Simulated and Measured Non-linear Ultrasound Fields

The theory for modeling non-linear acoustic propagation is addressed in the dissertation. The solutions to both the linear and non-linear wave equations have been found by an angular spectrum approach (ASA), in which an analytical expression can be derived. This makes the calculation complete without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program Abersim, respectively. The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements are performed under water by two geometrical focused piston transducers. It can be seen that the time pulses measured from a 0.5 inch diameter transducer and linearly simulated using the ASA are fairly comparable. The root mean square (RMS) error for the second harmonic field simulated by the ASA is 10.3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS) with a linear array transducer. The second harmonic imaging is obtained by a pulse inversion technique. The received data is beamformed by the SASB using a Beamformation Toolbox. In the measurements the lateral resolution at -6 dB is improved by 66% compared to the conventional imaging algorithm. There is also a 35% improvement for the lateral resolution at -6 dB compared with the sole harmonic imaging and a 46% improvement compared with merely using the SASB. vii

/pdf/non-linear-ultrasound-imaging-2qwi8v537y.pdf

Non-linear Ultrasound Imaging

The pressure field emitted from multi-element medical ultrasound transducers can be simulated with Field II in the linear regime. By expanding this program's application to the nonlinear regime, beamforming schemes can be studied under strong focusing and high pressure levels as well, providing a valuable tool for simulating ultrasound harmonic imaging. An extended version of Field II is obtained by means of operator splitting. The pressure field is calculated by propagation of the field from the transducer through a number of planes. Every plane serves as a virtual aperture for the next plane, and nonlinear distortion is accounted for by the lossless Burgers' Equation. This method has no plane-wave approximation and the full effects of diffraction, attenuation, and nonlinear wave propagation can be observed under electronic focusing of array transducers in medical ultrasound systems. A single example of the approach is demonstrated by comparing results from simulations and measurements from a convex array transducer. The new simulation tool is capable of simulating the formation of higher harmonics in water on the acoustical axis. The generation of nonlinear higher harmonic components can be predicted with an accuracy of 2.6 dB and 2.0 dB for the second and third harmonic, respectively.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Modeling of higher harmonics formation in medical ultrasound systems

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Modeling of higher harmonics formation in medical ultrasound systems