Shear wave speed image obtained with laboratory data obtained for a phantom from Mathias Fink's laboratory. The image was created using the arrival time algorithm.

Elastography
Precise and quick imaging of human tissue is a critical need.

High-quality images targeted to differentiate between benign and cancerous inclusions can offer doctors an improved ability to locate abnormal tissue.

IPRPI researchers use elastography – the process of imagining elastic tissue properties – to create images that display stiffness changes in the body, in order to improve the detection of such abnormalities.

Much can be learned from examining elastic properties of tissues, since they are directly related to the underlying structure of the tissue and are strongly affected by pathological changes.

Tumor inclusions or tissue blocked from its blood nutrients are stiffer than normal tissue; benign and cancerous tumors also have distinguishing elastic properties.

How this project works
This project targets low frequency shear wave propagation, since the shear wave moves forward significantly faster in abnormal tissue.

For abnormalities, the speed can be two to four times that of normal tissue. The speed is then a direct measure of tissue stiffness.

The propagating wave is measured with an ultrasound system (selected for its low cost).

Team members use data from a wave and sound laboratory at the Ecole Superieure de Physique et de Chimie Industrielles (ESPCI) in Paris. This lab is led by ESPCI Professor Mathias Fink, who has developed a high-speed data acquisition system that is able to image a wave propagating in tissue at 5,000 frames per second.

Advantages of this method
The advantage of the combined experiment of a low frequency propagating shear wave measured with a high frequency ultrasound acquisition system is that wave speed changes in abnormal tissue may be detected in images based on ordinary ultrasound.

A further expected advantage is that shear wave propagation in benign tissue will be distinguished from different propagation in cancerous tissue. The resulting image will provide an important diagnostic tool to the medical community.

Four key challenges
Rensselaer's elastography project has four key challenges:

• Finding the best quality data sets
• Creating mathematical models that distinguish abnormalities
• Locating stable image constructions that are not sensitive to noise
• Providing rapid results

Significant Advances
This project, begun in mid-2002, already has made significant advances:

• An arrival time algorithm, which uses level set methods and is based on the positions of the propagating front of the shear wave, has been successfully tested for sensitivities with synthetic data and been applied to experimental data on tissue-mimicking material.
• Finite element models are being tested to determine sources of instability, in order to analyze errors and to investigate modeling accuracy.
• Geometric optics-based algorithms are being tested for accuracy and sensitivity.
• Theoretical results establish the richness of the time and space dependent wave propagation data.
• All of the reconstruction methods address the ill-posedness of the problem: the constructed solution is sensitive to noise, unless "intelligent" algorithms, such as the one mentioned above, are developed.

Funding
Rapid progress for this elastography project has been possible due to funding provided by:

• National Science Foundation
• Department of Mathematical Sciences Focus Group Award (intended for initiating new interdisciplinary projects)
• National Institutes of Health
• Office of Naval Research

Additional graduate student and postdoc support comes from an NSF Vertical Integration of Research and Education (VIGRE) award.

Project members
Under the leadership of Dr. Joyce McLaughlin, Rensselaer professor of mathematical sciences and IPRPI director, this interdisciplinary team includes professors, postdoctoral fellows, and graduate students in Rensselaer's departments of Mathematical Sciences and Mechanical, Aerospace, and Nuclear Engineering.

Rensselaer Faculty
Joyce R. McLaughlin
Antoinette Maniatty

NSF Advance Grant Visitor
Liz Rachele

Research Scientists
Dan Renzi
Jeong-Rock Yoon

Graduate Students
Kui Lin
Ning Zhang

BS/PH.D. Students
Ashley Thomas
Jessica Jones

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Inverse Problems Center at Rensselaer
Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180-3590.
(518) 276-2145• E-mail: mclauj3@rpi.edu