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. 2012 Nov 21;57(22):7329-53.
doi: 10.1088/0031-9155/57/22/7329. Epub 2012 Oct 18.

Methods for robust in vivo strain estimation in the carotid artery

M McCormick  1 , T Varghese, X Wang, C Mitchell, M A Kliewer, R J Dempsey
Affiliations

Methods for robust in vivo strain estimation in the carotid artery

M McCormick et al. Phys Med Biol. .

Abstract

A hierarchical block-matching motion tracking algorithm for strain imaging is presented. Displacements are estimated with improved robustness and precision by utilizing a Bayesian regularization algorithm and an unbiased subsample interpolation technique. A modified least-squares strain estimator is proposed to estimate strain images from a noisy displacement input while addressing the motion discontinuity at the wall-lumen boundary. Methods to track deformation over the cardiac cycle incorporate a dynamic frame skip criterion to process data frames with sufficient deformation to produce high signal-to-noise displacement and strain images. Algorithms to accumulate displacement and/or strain on particles in a region of interest over the cardiac cycle are described. New methods to visualize and characterize the deformation measured with the full 2D strain tensor are presented. Initial results from patients imaged prior to carotid endarterectomy suggest that strain imaging detects conditions that are traditionally considered high risk including soft plaque composition, unstable morphology, abnormal hemodynamics and shear of plaque against tethering tissue can be exacerbated by neoangiogenesis. For example, a maximum absolute principal strain exceeding 0.2 is observed near calcified regions adjacent to turbulent flow, protrusion of the plaque into the arterial lumen and regions of low echogenicity associated with soft plaques. Non-invasive carotid strain imaging is therefore a potentially useful tool for detecting unstable carotid plaque.

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Figures

Figure 1
Figure 1
Axial strain SNRe versus strain magnitude when scaling the matching-block according to the strain obtained in the previous level and without scaling. Values are the SNRe calculated over a 31 × 12 mm area surrounding the focal zone in a uniform phantom. Error bars are a single standard error computed for five measurements of the SNRe for each value.
Figure 2
Figure 2
Frame skip for tracking of subject 157’s left carotid over the period of a single cardiac cycle. A small frame skip is used during systole when the strain rate is high, and a larger frame skip is used during diastole when the strain rate is small. The maximum frame skip was limited to six frames.
Figure 3
Figure 3
Subject 157 ROIs, where the particle strains explored in figures 4–7, are tracked over the cardiac cycle.
Figure 4
Figure 4
Axial strain over the cardiac cycle for 20 randomly selected particles from the anterior ROI highlighted in figure 3.
Figure 5
Figure 5
Shear strain over the cardiac cycle for 20 randomly selected particles from the anterior ROI highlighted in figure 3.
Figure 6
Figure 6
Lateral strain over the cardiac cycle for 20 randomly selected particles from the anterior ROI highlighted in figure 3.
Figure 7
Figure 7
Strain metrics over the cardiac cycle for 20 randomly selected particles from the anterior ROI highlighted in figure 3. (a) Maximum principal strain, (b) maximum shear strain, (c) total strain energy and (d) distortional energy.
Figure 8
Figure 8
A hypoechoic atherosclerotic mass, often classified as ‘soft’ plaque, that exhibit high strain throughout the plaque. (a) Accumulated displacement vectors (movement is primarily in superior direction), (b) strain tensor ellipses, (c) maximum absolute principal strain, (d) maximum shear strain, (e) total strain energy, (f) distortional energy. The displacement vector glyphs are scaled by four times their true value.
Figure 9
Figure 9
Strain pattern in an echogenically homogeneous plaque that varies depending on the geometry of the plaque and its position relative to blood flow. (a) Displacement vectors, (b) strain tensor ellipses, (c) distortional energy, (d) maximum shear strain. The displacement vector glyphs are scaled by four times their true value.
Figure 10
Figure 10
High strain near the interface of the plaque with the surrounding tissue that occurs with lateral motion of the plaque. (a) Strain tensor ellipses, (b) maximum absolute principal strain, (c) maximum shear strain, (d) axial strain, (e) shear strain and (f) lateral strain.
Figure 11
Figure 11
Low strain in a calcified plaque, but high strain in other areas. (a) Displacement vectors, (b) strain tensor ellipses, (c) maximum absolute principal strain, (d) maximum shear strain, (e) total strain energy, (f) distortional energy. The displacement vector glyphs are scaled by four times their true value.
Figure A.1
Figure A.1
Visualization of the strain tensor field for a cylindrical inclusion undergoing uniaxial compression. The ellipses are colored on a scale according to the magnitude of their major principal axis; the color is not related to the sign of tensor eigenvalues and does not reflect the compressive on tensile status.
See this image and copyright information in PMC

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