Principal component analysis of shear strain effects Hao Chen, Tomy Varghese * Department of Medical Physics, The University of Wisconsin-Madison, 1111 Highland Avenue, Madison, WI-53706, USA Department of Electrical and Computer Engineering, The University of Wisconsin-Madison, Madison, WI-53706, USA article info Article history: Received 16 September 2008 Received in revised form 18 December 2008 Accepted 18 December 2008 Available online 1 January 2009 Keywords: Displacement Elastography Elastogram Elasticity Elasticity imaging Strain Shear strain Principal component analysis Ultrasound abstract Shear stresses are always present during quasi-static strain imaging, since tissue slippage occurs along the lateral and elevational directions during an axial deformation. Shear stress components along the axial deformation axes add to the axial deformation while perpendicular components introduce both lat- eral and elevational rigid motion and deformation artifacts into the estimated axial and lateral strain ten- sor images. A clear understanding of these artifacts introduced into the normal and shear strain tensor images with shear deformations is essential. In addition, signal processing techniques for improved depiction of the strain distribution is required. In this paper, we evaluate the impact of artifacts intro- duced due to lateral shear deformations on the normal strain tensors estimated by varying the lateral shear angle during an axial deformation. Shear strains are quantified using the lateral shear angle during the applied deformation. Simulation and experimental validation using uniformly elastic and single inclusion phantoms were performed. Variations in the elastographic signal-to-noise and contrast-to- noise ratios for axial deformations ranging from 0% to 5%, and for lateral deformations ranging from 0 to 5° were evaluated. Our results demonstrate that the first and second principal component strain images provide higher signal-to-noise ratios of 20 dB with simulations and 10 dB under experimental conditions and contrast-to-noise ratio levels that are at least 20 dB higher when compared to the axial and lateral strain tensor images, when only lateral shear deformations are applied. For small axial defor- mations, the lateral shear deformations significantly reduces strain image quality, however the first prin- cipal component provides about a 1–2 dB improvement over the axial strain tensor image. Lateral shear deformations also significantly increase the noise level in the axial and lateral strain tensor images with larger axial deformations. Improved elastographic signal and contrast-to-noise ratios in the first principal component strain image are always obtained for both simulation and experimental data when compared to the corresponding axial strain tensor images in the presence of both axial and lateral shear deformations. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Techniques that image tissue elasticity or local stiffness proper- ties of tissue are relatively newer methods for the non-invasive investigation of tissue mechanical properties [1–7]. Local tissue displacements along the ultrasound beam propagation direction are estimated using classical time delay estimation techniques [1]. Signal processing techniques for estimating local tissue dis- placements have progressed from the earlier one dimensional (1D) cross-correlation techniques, to two-dimensional (2D) cross- correlation based tracking and processing [8] and to 2D algorithms with three-dimensional (3D) tracking [9,10]. Significant improve- ments in the spatial resolution of the axial strain estimates have also been reported, with axial window dimensions on the order of 1–2 wavelengths [11], 2D kernels with axial dimensions of less than a wavelength along with several A-lines in the lateral direc- tion [7]. However, most of the strain tensor estimation methods dis- cussed in the literature estimate primarily the axial component of the strain, while the lateral (perpendicular to insonification direction and within the scan plane) and elevational (perpendicu- lar to the insonification direction and scan plane) displacements and strain are generally not estimated. Since, the quasi-static tissue deformation introduces motion and displacements in three- dimensions, all strain tensor and displacement vector components are required to completely characterize the applied deformation [6,12]. Several methods have been proposed for the estimation of the displacement vector and the normal and shear strain tensor components [13–16]. Estimation of all the displacement vector and strain tensor components provide a complete depiction of tis- sue deformation in most situations, however, in certain cases such as for cardiac motion, [17,18] tissue deformations encountered are complex and other approaches for quantifying the displacement 0041-624X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2008.12.003 * Corresponding author. Address: Department of Medical Physics, The University of Wisconsin-Madison, 1111 Highland Avenue, Madison, WI-53706, USA. Tel.: +1 608 265 8797; fax: +1 608 262 2413. E-mail address: [email protected] (T. Varghese). Ultrasonics 49 (2009) 472–483 Contents lists available at ScienceDirect Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Principal component analysis of shear strain effects
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