Relative stiffness imaging of soft tissue is an important technique for the diagnosis of injury and disease, such as finding tumor inclusions in soft tissue and inelastic regions of the heart due to heart attack.
We present and test an algorithm to create a stiffness image based on changes in shear wave speed. This algorithm is based on transient elastography experiments performed by Sandrin et al. [1]. These experiments are of particular interest because they obtain accurate time dependent displacement fields in the interior of the body resulting from a short duration impulse. During the experiments, a shear wave propagates through the medium. With interior displacements one can find the arrival times of this wave. These arrival times form a surface in the displacement data. We regard this surface as an object to be detected in the data, and use an object detection scheme based on active contours. This approach flows a starting surface into the arrival time surface with a velocity synthesized from the displacement gradient. The partial differential equation describing this surface evolution is solved using the level set method. When sufficiently smooth, the arrival time surface satisfies the eikonel equation, which relates the arrival times to the shear wave speed.
In our initial investigation of the problem, we assume the density is
constant and displacements satisfy the acoustic wave equation. We generate
synthetic data of a propagating shear wave, find the arrival time surface for this wave, and determine the shear wave speed.
References
[1] Sandrin L, Tanter M, Catheline S, Fink M. Shear modulus imaging with 2-D transient elastography. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency control, 2002:49(4):426-35
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