Investigation of the Phase of Nonlinear Echoes From Microbubbles During Amplitude Modulation

Contrast-enhanced ultrasound (CEUS) imaging relies on distinguishing between microbubble and tissue echoes. Amplitude modulation (AM), a nonlinear pulsing scheme, has been developed to take advantage of the amplitude-dependent nonlinearity of microbubble echoes. However, with AM, tissue nonlinear propagation can also degrade the image contrast. Segmentation of CEUS images based on amplitude-dependent phase difference in the echoes, defined in this article as ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ , has been proposed as an additional method of enhancing contrast-to-tissue ratio as tissue is not expected to create the same degree of ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ ; however, this has not been robustly investigated. In this work, we evaluate the source of ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ through simulations of unshelled versus shelled microbubble oscillation and simulations of nonlinear propagation in tissue. We then validate the simulated ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ results with experimental ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ measurements during in vitro scattering and imaging in a flow phantom. We show that shelled and unshelled microbubbles resulted in a ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ with similar overall magnitude with some differences in trends, and that tissue echoes have a small yet detectable degree of ${\sf \varDelta } {\sf \varPhi }_{\textit {AM}}$ due to nonlinear propagation. The results from this work can help inform optimal parameter selection for phase segmentation and implementation on a clinical scanner.