2012 Proceedings - International Tissue Elasticity Conference

045 STRAIN ESTIMATION FOR QUASI–STATIC ELASTOGRAPHY THROUGH ANALYTICAL PHASE
TRACKING.
Lili Yuan 1 , Peder C. Pedersen 1 .
1 Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, USA.
Background: Quasi–static elastography with an externally applied force often involves strain of several
percent. In such cases, cross–correlation (CC) based methods are computationally demanding and prone to
ambiguity, while speckle tracking has resolution limitations and may have decorrelation–induced errors.
Aims: To develop a robust and efficient method for extracting axial displacement (DPM) and strain in
response to the applied forcing function in freehand quasi–static elastography. The method is based on
tracking the analytical phase through a slow time sequence of radio frequency (RF) signals.
Methods: For 1D axial DPM estimation, a sequence of RF signals as a function of slow time (applied
external force function) is recorded. Via the Hilbert transform, amplitude and wrapped phase of the
analytical signal are obtained along fast time. The (fast time wrapped) phase values for all RF signals are
stored in a phase matrix, where rows and columns represent slow and fast time, respectively. Let the
analytical signal phase at a specified time, t0, be φ0. Our method is an efficient way of tracking φ0 across the
phase matrix, while recording the time shift in the fast time location of φ0, proportional to DPM of scatterers
initially at t0. This method is distinctly different from other reported phase–based methods with limited
resolution due to windowing, such as extracting DPM from the complex CC at zero lag [1], or at zero phase
[2] and weighted phase separation [3]. In our current implementation, only phase values near 0 radians are
retained, as illustrated by the phase bands in Figure 1a, which can have bifurcation or other anomalies
when the corresponding amplitude is low. Therefore, an amplitude threshold is applied to the phase matrix,
giving the result in Figure 1b. Finally, discontinuous phase bands are removed, with only connected phase
bands retained, as seen in Figure 1c. Connected component labeling is then used to recognize zero phase
trajectories, and slow time shifts are computed by subtracting row index at pre–compression. The axial
strain is estimated by applying 2D linear least square fitting to DPM maps.The method was first tested with
a simulated tissue–mimicking 30mm×15mm phantom with a 5mm diameter circular inclusion at its
center whose stiffness was 5 and 10 times that of the surrounding tissue. Using finite element analysis
(FEA) method (Comsol), axial compressions of 0.8%, 5% and 10% were applied to the phantom, and the
ultrasound RF signals of the compressed medium were simulated with Field II. The DPM and strain were
computed with the phase tracking method and compared to the results from FEA and standard CC. The
method was then tested experimentally on a tofu phantom, using an Ultrasonix RP 4MHz transducer at a
high frame rate. A time sequence of 2D RF lines for several cycles of the manual forcing function was
acquired and the corresponding DPM along slow time were determined and compared with CC result.
Figure 1: (a) Phase matrix showing wrapped (a) (b) (c)
phase values near 0 radians
(limited in +/-0.2π);
(b) Phase matrix with normalized
amplitude threshold applied;
(c) Phase matrix with amplitude
threshold applied and discontinuous
phase curves removed.
Results: The DPM and strain from Comsol and Field II simulations and experiments confirm the validity
of the phase tracking method. For DPM magnitudes on the order of 0.5 to 1 mm, the error at peak
compression is typically 5%. In comparison to a standard implementation of the conventional CC method,
our analytical–phase method was at least 10 times faster, with a resolution, accuracy, SNRe, and CNRe
comparable to or better than what we obtained with the CC method.
Conclusions: The phase tracking method has been implemented with a fast time sampling rate of 30 times
the center frequency and the slow time sampling rate chosen so that the maximum DPM of scatterers
between consecutive RF lines is λ/10 or less. The method minimizes performance degradation through
region of low RF signal amplitude, generally caused by destructive interference, by tracking only wrapped
fast time phase, which is not affected by phase anomalies common to unwrapped phase.
Acknowledgements: Funding by the Telemedicine and Advanced Technology Research Center is greatly appreciated.
References:
[1] O'Donnell M et al.: IEEE UFFC, 41(3), pp. 314–325, 1994.
[2] Pesavento A et al.: IEEE UFFC, 46(5), pp. 1057–1067, 1999.
[3] Lindop JE et al.: IEEE UFFC, 55(1), pp. 94–111, 2008.
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