2020/04/16 by Alexander Dabrowski, Dabrowski, Alexander, Ahcene Ghandriche +3 · 5 citations
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Photoacoustic and Ultrasonic Imaging #Ultrasonics and Acoustic Wave Propagation #Ultrasound and Hyperthermia Applications
paper · pdf · doi:10.48550/arxiv.2004.07808
openalex publication_date 2020/04/16 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We analyze mathematically the acoustic imaging modality using bubbles as\ncontrast agents. These bubbles are modeled by mass densities and bulk moduli\nenjoying contrasting scales. These contrasting scales allow them to resonate at\ncertain incident frequencies. We consider two types of such contrasts. In the\nfirst one, the bubbles are light with small bulk modulus, as compared to the\nones of the background, so that they generate the Minnaert resonance\n(corresponding to a local surface wave). In the second one, the bubbles have\nmoderate mass density but still with small bulk modulus so that they generate a\nsequence of resonances (corresponding to local body waves).\n We propose to use as measurements the far-fields collected before and after\ninjecting a bubble, set at a given location point in the target domain,\ngenerated at a band of incident frequencies and at a fixed single\nbackscattering direction. Then, we scan the target domain with such bubbles and\ncollect the corresponding far-fields. The goal is to reconstruct both the,\nvariable, mass density and bulk modulus of the background in the target region.\n 1. We show that, for each fixed used bubble, the contrasted far-fields reach\ntheir maximum value at, incident, frequencies close to the Minneart resonance\n(or the body-wave resonances depending on the types of bubbles we use). Hence,\nwe can reconstruct this resonance from our data. The explicit dependence of the\nMinnaert resonance in terms of the background mass density of the background\nallows us to recover it, i.e. the mass density, in a straightforward way.\n 2. In addition, this measured contrasted far-fields allow us to recover the\ntotal field at the location points of the bubbles (i.e. the total field in the\nabsence of the bubbles). A numerical differentiation argument, for instance,\nallows us to recover the bulk modulus of the targeted region as well.\n