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 threedimensional 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
tissuelike 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, noninvasive
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). 
Please address administrative questions to aipc@math.tamu.edu. Scientific questions should be addressed to the chair of the Scientific Program Committee: rundell AT math.tamu.edu