Imaging of Nonlinear Scattering using Dual-frequency Band Ultrasound

Abstract

The work presented in this thesis is focused on developing a method for imaging of nonlinear scattering from stiff particles using dual-frequency band pulses. The pulse complexes are comprised of a low-frequency manipulation pulse and a high-frequency imaging pulse where the the two pulses overlap in time and there is a frequency relationship of 1:8-10. It may be shown that the polarity of the nonlinear scattering follows the polarity of the low-frequency pulse, while linear scattering does not. By transmitting two such dual-frequency band pulses in each beam direction where the polarity of the low-frequency pulse is inverted from the first to the second, nonlinear scattering may be detected. The low-frequency pulse not only manipulates the scattering but also the propagation of the high-frequency imaging pulse. These nonlinear propagation effects will mask the nonlinear scattering and must be corrected for in order to suppress the linear scattering and detect the nonlinear scattering.In the first paper of this thesis, the nonlinear propagation effects using confocal low-frequency and high-frequency beams are investigated in a water tank setup. A dual-frequency band annular array, where the low-frequency element is place behind the high-frequency element, to form a stack, was used. When the high-frequency pulse is short compared to the low-frequency pulse period, the nonlinear propagation effects can be approximated by a nonlinear propagation delay and frequency shift. It is shown how the delay and frequency shift increases close to linearly with increasing manipulation pressure and how axis the profiles of the high-frequency beam are affected. On transmit, the size relationship between the low and high-frequency apertures can be varied, and it is shown how the nonlinear propagation effects is dependent on the array setup.By transmitting an unfocused low-frequency beam together with a focused high-frequency beam, the position of the high-frequency pulse relative to the low-frequency pulse can be kept close to constant over the whole imaging region. By placing the imaging pulse at the peak of the manipulation pulse, the frequency shift due to nonlinear propagation can be minimized. In the second paper, the suppression of linear scattering using such a beam setup and only correcting for the propagation delay is investigated. Applying a low-frequency pressure of 85 to 500 kPa, the linear scattering could be suppressed 35 to 17 dB. It is shown that there is an amplitude difference between the first and second received pulse which is due to diffraction differences of the first and second beam. Since the low-frequency beam is unfocused, the manipulation pressure will vary over the focused high-frequency beam and distort the spherical focusing. This distortion will be different for the first and second beam and produce different diffraction of the two beams, which will yield an amplitude difference. Frequency shift due to nonlinear propagation will also affect the diffraction but it is indicated that the nonlinear aberration is the dominating factor.In the third paper three different beamforming strategies for dual-frequency band imaging is investigated; 1. Focused low freq. + Focused high freq., 2. Unfocused low freq. + Focused high freq. and 1. Unfocused low freq. + Unfocused high freq. The nonlinear propagation delay and frequency shift are estimated and predicted based on the estimated low-frequency manipulation pressure experienced by the high-frequency pulse. There is good accordance between the estimated and predicted values until diffraction becomes significant. When diffraction becomes significant, differences in diffraction between the first and second pulse will also introduce a frequency shift and delay other than that generated by the nonlinear manipulation pressure. Differences in the pulse form of the first and second pulse is thus not only due to manipulation of the propagation of the high-frequency pulse by the low-frequency, but also by differences in diffraction.The nonlinear propagation and scattering are generated by equal processes but are different in the way that nonlinear propagation is an accumulative effect while scattering is a local effect. In the last part of the thesis the difference between nonlinear propagation and scattering is investigated using simulations, where the bandwidth of the high-frequency pulse relative to the center frequency of the manipulation pulse is varied. It is shown that when the high-frequency pulse is shorter in time than one period of the low-frequency pulse, the nonlinear propagation and scattering becomes different and the nonlinear scattering can be detected if the nonlinear propagation is corrected for.The correction of nonlinear propagation can be in the form of a filter, and a method for estimating this filter is also presented in the last part. Based on statistical analysis of the filter, it is shown that the average suppression of linear scattering using the proposed correction filter, is dependent on the homogeneity of the relation between the first and second pulse over the receive beam. Said in another way; if this relation is not constant over the receive beam, the optimal correction for a given signal segment is dependent on the unknown distribution of scatterers within the beam.The level of suppression of linear scattering using the proposed filter method will be dependent on the transmit beam setup. A simulation study where the effect of aperture size relationship between the low- and high-frequency beams and f-number of the high-frequency beam on the level of suppression of linear scattering is presented. In order to achieve a high degree of homogeneity, the diffraction of the HF and LF beams should be equal, which is not trivial to achieve in a medium with attenuation. Choosing the aperture sizes in order for the fresnel numbers to be equal for the two beams was thought to yield the optimal setup, but as attenuation affects the low and high-frequency pulses differently, this is not necessarily  true. The level of suppression of linear scattering increases when the the high-frequency aperture is increased, making the beam narrower, but the low-frequency aperture must also be increased accordingly.