Minisymposia Abstracts

Speaker: Ben Cox
University College, London, UK
Title: Quantitative Photoacoustic Imaging
Abstract: The aim of quantitative photoacoustic imaging is to obtain absolute values of absorption coefficient spectra (or chromophore concentrations, or useful physiological parameters such as blood oxygenation) from photoacoustic images obtained at multiple optical wavelengths. As photoacoustic images are inherently three-dimensional with tens of millions of voxels, recovering absorption spectra for each voxel becomes a large scale parameter estimation problem. The various approaches that have been taken to try and solve this problem will be briefly reviewed, and the remaining difficulties outlined. Possible routes to solving this problem for cases of practical interest will be discussed, and recent results using the radiative transfer equation will be presented.

Speaker: Peter Burgholzer
RECENDT, Linz, Austria
Title: Dissipation limited resolution in photoacoustic imaging
Abstract: In biomedical imaging and in non destructive imaging the information about the interior spatial pattern of a sample has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be detected and the interior structure is reconstructed from the measured signals. The amount of information about the interior of the sample, which can be gained from the detected waves on the sample surface, is essentially influenced by the propagation from its excitation to the surface. Scattering, attenuation, or diffusion causes an entropy production which results in a loss of information of the propagating waves.
This loss of information can be described by stochastic processes: first for the example of thermal diffusion with temperature as a random variable. Thermal waves are a good example because they are "very dispersive" due to thermal diffusion. The amplitude of thermal waves decreases more than 500 times at a distance of just one wavelength. In a second example for photoacoustic imaging taking acoustic attenuation of the generated ultrasound wave into account, the pressure of the acoustic wave is described by a stochastic process. For both examples the connection of entropy production and loss of information results in a theoretical limit for the achievable spatial resolution in the reconstructed image."

Speaker: David Isaacson
RPI, Troy, NY
Title: Problems in Electromagnetic Imaging
Abstract: We describe a variety of problems that arise in constructing electrical impedance imaging systems. We explain how the solutions to these problems have motivated the designs of the Adaptive Current Tomography (ACT) systems that we have built at RPI. We will show images and movies of reconstructions made from the RPI ACT systems.

Speaker: Armando Manduca Mayo Clinic, Rochester, Minnesota
Title: Magnetic Resonance Elastography
Abstract: Magnetic resonance elastography (MRE) is a phase contrast based MRI imaging technique that can directly visualize and quantitatively measure propagating acoustic strain waves in tissue-like materials subjected to harmonic mechanical excitation. The data acquired allows the calculation of local quantitative values of shear modulus and viscosity the generation of images that depict viscoelastic properties of tissue. There is strong precedent in clinical medicine for the concept that tissue viscoelastic properties, assessed by palpation, are markedly affected by a variety of disease processes. MRE thus represents a quantitative, non-invasive technique for "palpation by imaging", which is already finding clinical application in the staging of liver fibrosis. We describe MRE in the context of other recent techniques for imaging elasticity, discuss the processing algorithms for elasticity reconstruction and the issues and assumptions they involve, and present recent results.

Speaker: Guillaume Bal
Columbia University, NY, NY.
Title: Stability and reconstruction results in ultrasound modulated electrical and optical tomography
Abstract: UMEIT and UMOT offer the possibility to combine the high contrast often observed in the the electrical and optical properties of tissues with the high resolution of ultrasound. Mathematically, these problems are formulated as inverse problems with internal information, which are referred to as hybrid inverse problems. We will review recent results of injectivity and stability obtained in the context of redundant measurements of UMEIT and UMOT.

Speaker: Faouzi Triki
Joseph Fourier University, Grenoble, France
Title: Wave imaging with internal perturbation
Abstract: TBA

Speaker: Plamen Stefanov
Purdue University, West Lafayette, IN
Title: Uniqueness and Reconstruction in Thermoacoustic Tomography with a variable speed
Abstract: We will present theoretical and numerical results about recovery of a source in Thermoacoustic Tomography, given a variable speed - continuous or discontinuous. We will also discuss the problem of recovery of the speed, given the source. The talk will be based on results obtained jointly with Gunther Uhlmann.

Speaker: Linh Nguyen
formerly Texas A&M, College Station, TX
Title: Some mathematical problems of thermoacoustic tomography
Abstract: Thermoacoustic tomography (TAT) is an emerging hybrid modality of medical imaging. A very short pulse of electromagnetic (EM) radiation is scanned through the biological tissue to slightly heat it up. The elastic expansion of the tissue leads to some ultrasound (pressure) wave propagation. The pressure is measured by transducers on an observation surface. From this data, one reconstructs the initial pressure distribution, and thus the EM absorption inside the body.
The talk addresses the following two issues of TAT:
1. Instability: we prove that the reconstruction is not Holder stable if a natural visibility condition is violated. This complements the recent results by V. Palamodov (for constant speed) and P. Stefanov and G. Uhlmann (for variable speed), which show that under the visibility condition, the reconstruction is Lipschitz stable.
2. TAT with unknown sound speed: most of the work done in TAT assumes that the ultrasound speed is known. However, it is usually not known in applications. It is natural to ask whether the TAT data could determine both the ultrasound speed and the initial pressure. We will discuss some partial answers to this question (joint work with M. Agranovsky and P. Kuchment).

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