The bandwidth of short-pulse to low frequency response and subharmonic response of micro-bubbles—using two-frequency approximation
Date Issued
2004
Date
2004
Author(s)
Liu, Heng-Bin
DOI
zh-TW
Abstract
The subharmonic response due to the nonlinear behavior of microbubble can be used to provide good discrimination between microbubble and surrounding tissue, especially in deep region. However, there is no proper analysis about the subharmonic response under short-pulse insonification. In this work, we extend the two-frequency approximated analytic solution of Newhouse et al. to derive the subharmonic response of microbubble under band-limited insonification. [2]. Based on Fourier theory, a band-limited signal can be synthesized by multiple sinusoids, with a two-frequency approximation being the simplest case. In this work, for a given bubble whose resonance frequency denoted as , the transmission is modeled as the composition of two-frequency (f1,f2,f1>2f0>f2 ) under the constraint condition at which the transmission has spectral continuity. Therefore, the bandwidth of the transmission can be approximated as the width of the spectral region spanned by theses two frequencies. Based on Eller’s analytic solution of the amplitude of the subharmonics, we found that if and are away from (i.e. the bandwidth of the transmission is increased), the amplitude of the subharmonics will decrease rapidly. Our theoretical analysis illustrates that the amplitude of the subharmonics decrease with the transmitted fractional bandwidth. Moreover, under an applied pressure of 0.1 MPa, it approaches zero when the fractional bandwidth is increased to 8 %. In other words, this proves theoretically that only narrowband transmission can excite the microbubble to generate the subharmonics.
Based on the nonlinear behavior of microbubble, in addition to the generation of subharmonics, we also derived that the resulting echo also contains difference response under two-frequency insonification. It is named as low-frequency response at the frequency, fL= f1- f2, in this work. It will reside nearby DC in spectrum if these two frequencies are close. Furthermore, the amplitude of low-frequency response can be derived to increase with the fractional bandwidth, which is different from that of subharmonics. It can be shown that the amplitude of the subharmonics decrease with the transmitted fractional bandwidth ranging from 1 % to 40 % when the emitted frequency is 5 MHz and the acoustic pressure is 0.1 MPa. On the contrary, the low-frequency response increases with the transmitted bandwidth. Consequently, both of range resolution and contrast to surrounding tissues can be achieved by using low-frequency response and subharmonics alternatively in imaging.
Subjects
次諧振
subharmonic
Type
thesis
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