Retrieval of the equivalent acoustic constitutive parameters of an inhomogeneous fluid-like object by nonlinear full waveform inversion

Abstract

This study addresses the problem of the acoustic characterization of an inhomogeneous object such as a soft-tissue organ containing a cyst or tumor whose size and/or composition evolve either negatively due to increased disease or positively due to increased response to treatment. The so-called ‘corrupted’ binary object, probed by a transient, acoustic plane wave, is a tube composed of a homogenous fluid-like (or assumed as such) mantle (medium 1: three acoustic constitutive parameters, one geometric parameter) surrounding a homogeneous fluid-like (or assumed as such) core (medium 2: three acoustic constitutive parameters, one geometric parameter), immersed in a spatially-infinite, homogeneous fluid (host medium 0: two acoustic parameters). The complete inversion of the diffracted acoustic field response of this object involves the retrieval of seven (six acoustic and one geometric) parameters, assuming we know beforehand the outer radius of the tube and acoustic parameters of the host. An alternative to this time-consuming, hazardous (due to the ill-posed nature of the) procedure, is to minimize the discrepancy, between the full waveform response of the binary object to a transient plane wave and the response of a homogeneous cylinder (medium characterized by three acoustic parameters, one geometric parameter) to the same transient plane wave, so as to retrieve the (three so-called equivalent) acoustic parameters of the homogeneous object. Thus, the first inverse problem is replaced by a second one (same assumptions concerning the outer radius of the objects, the host medium, the probe radiation and the sensing configuration as the first one) involving the retrieval of only three (instead of six) acoustic parameters. This procedure is potentially useful if the variation of at least one of the three equivalent parameters is sensitive to the variation of a key parameter of the inhomogeneous body (usually the characteristic dimension or the wavespeed of the core) and this variation can be expressed in a simple algebraic form (such as by a mixing formula). It is shown that this situation can arise if the average frequency of the acoustic probe radiation is sufficiently low. A sidelight of this investigation is the discovery that the equivalent constitutive parameters of the homogeneous cylinder are dispersive even when the component materials of the tube are not dispersive.