3D Elastography Enabling Technology to Better Segment Isoechoic Lesions Harish Krishnaswamy, Parker

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3D ElastographyEnabling Technology to Better
Segment Isoechoic Lesions Harish Krishnaswamy,
Parker WilsonMentor Emad Boctor, Dr. Russell
Taylor
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Project Goals

• Construction of liver phantom to simulate
  isoechoic lesion.
• Collection of 2D US of liver phantom and
  implementation of Strain Estimation Concept
  algorithm for Ultrasonic Elastography.
• Generating 3D Strain and 3D US at the same rate.

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Paper Selection A Time-Efficient and Accurate
Strain Estimation Concept for Ultrasonic
Elastography Using Iterative Phase Zero Estimation
This paper was chosen to demonstrate our
implementation of the strain algorithm used to
manipulate our RF ultrasound data.
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Imaging of Elastic Properties of Biological Tissue

• Two concepts exist for measuring elastic tissue
  properties sonoelasticity and elastography.
• In elastography, strain within the tissue is
  estimated following external pressure.
• To Improve SNR of strain images a fast algorithm
  for the estimation of temporal displacements
  between two images is necessary.
• Algorithms estimating time shift from phases of
  analytic (complex) RF signals or baseband signals
  are much faster than algorithms determining the
  maximum of the cross correlation function.

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Signals Backround
In Elastography, the postcompression echo signal
is considered to be a compressed and time-shifted
version of the precompression signal
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Signals Backround
For gradient-based strain estimators, the echo
signals are considered to be only time shifted
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Cross Correlation
The cross correlation function has a maximum at
t - tau. The phase of the cross correlation
function phi(t) of the analytic signals has a
root at -tau. To estimate the time shift find the
root of phi(t).
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Determining an Analytic Signal From RF Data

• A complex signal can be calculated from RF data
  by adding the imaginary part to the RF data. The
  imaginary part is equal to the signals Hilbert
  transform.

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Finding the Root of the Correlation Function of
Analytic Signals Newton Iteration
In each iteration the zero phase is calculated by
a linear function with the slope equal to the
tranducers centroid frequency. The intercept of
the linear function with the abscissae is the new
estimate for the time delay.
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Newton Iteration
Note that phi(tn) is the phase of the current
estimate of the time delay and that the
derivative is the slope of the nominal centroid
frequency Wo. Ie. The derivative of a complex
phase is its frequency.
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Base-band Signal Conversion and Interpolation
A baseband signal can be calculated from its
analytic signal as follows
Interpolation is needed to estimate the
correlation function for discrete temporal
positions. The interpolation can be done more
accurately using the base-band signals.
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Relationship between Cross Correlation of
Analytic and Base-band Signals
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Iterative Estimation of Time Shifts from Phases
of the Correlation Function
The time shift must be estimated at discrete
positions. In practice choose Wm Wo . k is the
discrete temporal position and N is the
iteration number
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Logarithmic Compression

• Easily applicable to base band signals
• Reduces amplitude variations that cause the
  estimated time shift to deviate from the center
  of the window.

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Assessment

• This algorithm is a faster equivalent to
  comparable cross-correlation techniques.
• Logarithmic compression can be used to mitigate
  problems with decorrelation noise of time-shift
  estimation.
• 2 6 iterations lead to sufficient accuracy.

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Future Work

• Implementation and comparison of several
  combinations of the algorithms to our RF data
  including the following
• Algorithm 1 (linear interpolation) without
  logarithmic compression
• Algorithm 1 with logarithmic compression
• Algorithm 2 (nearest neighbor interpolation) with
  logarithmic compression