Waves & Inverse Problems group at University of Minnesota

Wave-based Imaging of Solids and Soft Tissues

Problem

Non-invasive sensing of inner heterogeneities in solids and tissues by way of mechanical waves is a long-standing problem in engineering mechanics owing to its roles in seismology, non-destructive testing, and medical diagnosis. In the context of 3D tomography the supporting inverse scattering solutions, derived from a variety of simulation platforms, commonly bear near-prohibitive computational cost that is compounded by the need for prior information. In soft tissues, the problem is somewhat mitigated by the fact that the illuminating mechanical waves may be originated not only on the boundary of an organ, but also in its interior via the use of high-intensity focused ultrasound. In this way the analysis, and thus the computation, can be confined to the immediate neighborhood of a focal point of the ultrasound transducer – de facto amounting to internal palpation. Thus generated body force, termed the acoustic radiation force (ARF), is however scarcely understood in terms of the underpinning nonlinear and thermo-mechanical wave phenomena.

Approach

To mitigate the above impediments to the 3D interrogation of solid bodies, a rapid imaging tool that voids the need for customary non-linear optimization and supporting prior information (e.g. initial "guess") was developed by building upon the concept of topological sensitivity (TS). Physically, TS quantifies the variation of a cost functional when an infinitesimal defect is nucleated at a sampling, i.e. trial point inside the reference solid. For inverse scattering problems involving mechanical waves, this quantity permits explicit bi-linear representation in terms of two elastodynamic states computed for the reference (e.g. defect-free) solid: the so-called free field, and the adjoint field. In this way the inner heterogeneities are exposed non-iteratively from the spatial distribution of TS, via regions were the latter attains pronounced negative values (see Figure). On the forefront of soft-tissue interrogation, the phenomenon of the ARF in tissue-like solids due to modulated ultrasound is investigated via a dual-time-scale approach, which facilitates rigorous thermo-mechanical analysis of the nonlinear ultrasound waves entailing two disparate time scales, namely that affiliated with the MHz-rate ultrasound excitation and its kHz-rate modulation counterpart.

Recent Findings

Ongoing applications of the TS methodology include i) magnetic resonance elastography of breast tissue, and ii) non-contact interrogation of defects in nuclear graphite, expected to make up the core of the next-generation nuclear plants. In the latter application, the triaxial surface motion of a graphite unit is captured by a Laser Doppler Vibrometer (see Figure), and then used as an input for the TS reconstruction of internal defects. Recent results demonstrate that the TS paradigm furnishes a robust imaging tool in experimental settings that are intertwined with measurement and modeling uncertainties. In exposing the mechanics and physics of the acoustic radiation force, it was found that the ARF in soft tissues entails two critical features that have eluded previous studies, namely: i) the scaling with a particular constitutive coefficient of tissue nonlinearity, and ii) the modulation-driven term that is comparable in magnitude to its (previously known) attenuation-driven companion.

Impact

In a philosophical departure from the earlier wave-based imaging methodologies, the TS operator serves as a minimization-free "LED" indicator that "lights up" for trial, i.e. sampling points striking the subsurface heterogeneity. As a result, the TS imaging methodology is ideally suited for non-destructive testing applications and seismic imaging problems where a "real-time" image of the preexisting or created subsurface structure is critical (e.g. hydrofracking). On the other hand, the newly discovered nature of the ARF in soft tissues opens the possibilities for aiding the early diagnosis of a variety of degenerative diseases.

Selected Publications

1. E. Dontsov and B.B. Guzina "Acoustic radiation force in tissue-like solids due to modulated sound field", J. Mech. Phys. Solids, to appear.

2. E. Dontsov and B.B. Guzina "Effect of low-frequency modulation on the acoustic radiation force in Newtonian fluids", SIAM J. Appl. Math. 71, 356-378 (2011).

3. B.B. Guzina, F. Cakoni, and C. Bellis "On the multi-frequency obstacle reconstruction via the linear sampling method", Inverse Problems 26, 125005 (2010).

4. M. Bonnet and B.B. Guzina "Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework", J. Comp. Phys. 228, 294-311 (2009).

5. B.B. Guzina and I. Chikichev "From imaging to material characterization: a generalized concept of topological sensitivity", J. Mech. Phys. Solids 55, 245-279 (2007).