Abstract
Previous publications have reported on the use of one-dimensional cross-correlation analysis with beam-steered echo signals. However, this approach fails to accurately track displacements at larger depths (>4.5 cm) due to lower signal-to-noise. In this paper, the authors present the use of adaptive parallelogram shaped two-dimensional processing blocks for deformation tracking.
Beam-steered datasets were acquired using a VFX 9L4 linear array transducer operated at a 6 MHz center frequency for steered angles from −15 to 15° in increments of 1°, on both uniformly elastic and single-inclusion tissue-mimicking phantoms. Echo signals were acquired to a depth of 65 mm with the focus set at 40 mm corresponding to the center of phantom. Estimated angular displacements along and perpendicular to the beam direction are used to compute axial and lateral displacement vectors using a least-squares approach. Normal and shear strain tensor component are then estimated based on these displacement vectors.
Their results demonstrate that parallelogram shaped two-dimensional deformation tracking significantly improves spatial resolution (factor of 7.79 along the beam direction), signal-to-noise (5 dB improvement), and contrast-to-noise (8–14 dB improvement) associated with strain imaging using beam steering on linear array transducers.
Parallelogram shaped two-dimensional deformation tracking is demonstrated in beam-steered radiofrequency data, enabling its use in the estimation of normal and shear strain components.
This work was supported by Komen Grant No. BCTR0601153 and National Institutes of Health (NIH)-Cancer Institute (NCI) Grant Nos. 5R21CA140939-02, R01CA112192-S103, and R01CA112192-05.
I. INTRODUCTION
II. MATERIALS AND METHODS
II.A. TM phantoms
II.B. Angular and displacement vector estimation
II.C. Estimation of SNR_{ e }, CNR_{ e }, and strain stiffness contrast (SSC)
III. RESULTS
IV. DISCUSSION AND CONCLUSIONS
Key Topics
- Tensor methods
- 27.0
- Medical image noise
- 25.0
- Spatial dimensions
- 16.0
- Medical imaging
- 15.0
- Shear deformation
- 8.0
Figures
Shear transformation for the spatial grid (top), along with the angular displacement vector. The left column shows the spatial grid and angular displacements obtained using a 8° beam-steered angle, respectively. The right column shows the spatial grid and angular displacement on a 0° spatial grid.
Shear transformation for the spatial grid (top), along with the angular displacement vector. The left column shows the spatial grid and angular displacements obtained using a 8° beam-steered angle, respectively. The right column shows the spatial grid and angular displacement on a 0° spatial grid.
Projection of the actual displacement vector at point O, onto unit vectors along and perpendicular to beam steered direction.
Projection of the actual displacement vector at point O, onto unit vectors along and perpendicular to beam steered direction.
Axial strain images obtained using 2D beam steered datasets for the uniformly elastic TM phantom (a) and an ellipsoidal inclusion phantom (b). The 0.02 value on the color bar represents a 2% strain. The ROIs shown on the images were used to estimate the SNR_{ e } and CNR_{ e }, respectively. The solid line represents the maximum beam steered angle used for angular compounding.
Axial strain images obtained using 2D beam steered datasets for the uniformly elastic TM phantom (a) and an ellipsoidal inclusion phantom (b). The 0.02 value on the color bar represents a 2% strain. The ROIs shown on the images were used to estimate the SNR_{ e } and CNR_{ e }, respectively. The solid line represents the maximum beam steered angle used for angular compounding.
Plots of the mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on a uniformly elastic TM phantom demonstrating the impact of beam steered angular increment for 1D vs 2D deformation tracking.
Plots of the mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on a uniformly elastic TM phantom demonstrating the impact of beam steered angular increment for 1D vs 2D deformation tracking.
Plots of mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on a uniform TM phantom demonstrating the impact of the maximum beam-steered angle on compounded strain images for 1D vs 2D deformation tracking.
Plots of mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on a uniform TM phantom demonstrating the impact of the maximum beam-steered angle on compounded strain images for 1D vs 2D deformation tracking.
Axial displacement (a) and (b) and lateral displacement (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) unbound ellipsoid TM phantom. The units in the color bar for the displacement is in millimeters.
Axial displacement (a) and (b) and lateral displacement (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) unbound ellipsoid TM phantom. The units in the color bar for the displacement is in millimeters.
Axial strain (a) and (b) and lateral strain (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) bound ellipsoid TM phantom. The 0.008 value on the color bar represents a 0.8% strain. The ROIs shown were used to estimate CNR_{ e } and strain stiffness contrast. The solid line represents the maximum beam steered angle used for angular compounding.
Axial strain (a) and (b) and lateral strain (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) bound ellipsoid TM phantom. The 0.008 value on the color bar represents a 0.8% strain. The ROIs shown were used to estimate CNR_{ e } and strain stiffness contrast. The solid line represents the maximum beam steered angle used for angular compounding.
Axial-shear strain (a) and (b) and full-shear strain (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) bound ellipsoid TM phantom. The 0.006 value on the color bar represents a 0.6% strain. The ROIs shown were used to estimate CNR_{ e } and strain stiffness contrast.
Axial-shear strain (a) and (b) and full-shear strain (c) and (d) images obtained using 1D (a) and (c) and 2D (b) and (d), beam steered data for the asymmetric (30°) bound ellipsoid TM phantom. The 0.006 value on the color bar represents a 0.6% strain. The ROIs shown were used to estimate CNR_{ e } and strain stiffness contrast.
Plots of mean CNR_{ e } and standard deviation (error bars) over ten independent beam-steered RF datasets acquired on the four ellipsoid TM phantoms demonstrating the impact of the beam steered angular increment for 1D vs 2D processing. The subplots represent results for (a) symmetric unbound, (b) asymmetric unbound, (c) symmetric bound, and (d) asymmetric bound phantoms, respectively.
Plots of mean CNR_{ e } and standard deviation (error bars) over ten independent beam-steered RF datasets acquired on the four ellipsoid TM phantoms demonstrating the impact of the beam steered angular increment for 1D vs 2D processing. The subplots represent results for (a) symmetric unbound, (b) asymmetric unbound, (c) symmetric bound, and (d) asymmetric bound phantoms, respectively.
Plots of mean CNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on the four ellipsoid TM phantoms demonstrating the impact of the maximum beam-steered angle for 1D vs 2D processing. The subplots represent results for the (a) symmetric unbound, (b) asymmetric unbound, (c) symmetric bound, and (d) asymmetric bound phantom, respectively.
Plots of mean CNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on the four ellipsoid TM phantoms demonstrating the impact of the maximum beam-steered angle for 1D vs 2D processing. The subplots represent results for the (a) symmetric unbound, (b) asymmetric unbound, (c) symmetric bound, and (d) asymmetric bound phantom, respectively.
Plots of mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on an uniformly elastic TM phantom demonstrating the impact of different maximum angles on similar number of compounded strain images. Results are shown for 3 beam steered angles (a), 5 beam-steered angles (b), 7 beam-steered angles (c), and 11 beam-steered angles (d), respectively.
Plots of mean SNR_{ e } and standard deviation (error bars) over ten independent RF datasets acquired on an uniformly elastic TM phantom demonstrating the impact of different maximum angles on similar number of compounded strain images. Results are shown for 3 beam steered angles (a), 5 beam-steered angles (b), 7 beam-steered angles (c), and 11 beam-steered angles (d), respectively.
Tables
Mean and standard deviation of the strain stiffness contrast for the ellipsoidal inclusion TM phantoms for different angular increments for the 1D and 2D deformation tracking approaches.
Mean and standard deviation of the strain stiffness contrast for the ellipsoidal inclusion TM phantoms for different angular increments for the 1D and 2D deformation tracking approaches.
Mean and standard deviation of the strain stiffness contrast for the ellipsoidal inclusion TM phantoms for different maximum beam steered angles for the 1D and 2D deformation tracking approaches.
Mean and standard deviation of the strain stiffness contrast for the ellipsoidal inclusion TM phantoms for different maximum beam steered angles for the 1D and 2D deformation tracking approaches.
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