Strain Imaging

III. METHODOLOGY

III.3 Tracked Ultrasound

III.3.6 Strain Imaging

 

frame was entered into the buffer, it was matched to the tracking matrix from 11 ms prior in the tracking buffer. This simple approach was sufficient to address the issue of temporal synchronization of the two data streams.

 

for breast imaging with the VFX13‐5 transducer, which has a frequency bandwidth of 5 to 13 MHz.

Although it was intended for breast imaging, it was easily translatable to other anatomy like the brain, so long as the objects to be imaged were no deeper than the transducer’s display depth of 6 cm and the large probe could be placed on the tissue of interest. The strain images produced by this software were displayed as real‐time video in the same manner as conventional B‐mode images and thus were captured and synchronized to the tracking data in exactly the same manner described previously. An example strain image acquired from a gel phantom containing a stiff inclusion is shown in Figure 9 along with the corresponding B‐mode image.

Figure 9. Siemens commercial elastography software. A gel phantom containing a hard inclusion was  imaged using B‐mode (left) and strain imaging (right). 

The Siemens elastography software had the advantage of providing real time strain images, but had the disadvantage of not allowing access to the raw data used to generate the images, and did not provide any quantitative measurement of calculated tissue displacements or relative strain values. These values would be useful in validation of the commercial strain images, as well as additional analysis of the underlying tissue behavior. The Acuson Antares ultrasound machine did,

 

however, also have a separate ultrasound research interface URI called Axius Direct which provided access to raw beamformed radiofrequency RF data. The unprocessed RF data could be collected during a normal imaging procedure by manually triggering the URI software on the ultrasound machine, which then saved RF data files to the hard drive. The files were then transferrable to a PC to be processed by the user. In this framework, it was extremely difficult to synchronize the raw RF data files with the external tracking system. Therefore there was a need for both the commercial strain imaging package and the URI, in order to get the benefits of tracking data and quantitative strain imaging, respectively. Although the raw RF data was not ultimately used in this dissertation due to the synchronization issue, an overview of strain image creation from RF signals will now be described to provide a general understanding of the process.

The raw RF data can be converted to strain images using a variety of algorithms 133, 134 . An ultrasound elastography algorithm used by Solbekk

et al

. was been implemented in Matlab Mathworks Inc., Natick, MA due to its simplicity and demonstrated efficacy in brain tumor imaging 135, 136 . This method was used for generating only axial strain images, as the axial resolution is greater than the lateral resolution in ultrasound images. The general procedure for generating a strain image begins with the acquisition of at least two frames of RF data while dynamically compressing the tissue of interest. The RF data is recorded as an array of voltage values generated by the piezoelectric elements in the transducer as the acoustic waves reflected by the tissue are recorded over time. A non‐uniform distribution of scatters in the interrogated medium gives unique RF signatures throughout an image. An example of an RF frame and its equivalent processed B‐mode image is shown in Figure 10 acquired from a linear array transducer .

 

Figure 10. Example of unprocessed RF data (left) and processed B‐mode image (right) from a gel  phantom containing hard inclusion. 

Assuming that the deformation applied to the tissue was very small, the basic shape of the post‐compression echo, for a given window at a specific depth, will not have changed significantly in shape when compared with the pre‐compression echo. However, there will be a phase difference between the two echo signals due to the difference in acoustic travel time arising from the change in distance to the probe brought about by compression. An illustration of this phase shift is shown for a single axial trace in Figure 11.

 

Figure 11. Pre‐compression (solid line) and post‐compression (dashed line) axial RF signals from two  frames in a single window. These curves represent approximately the same signal separated by a phase  difference. 

Local tissue displacements may be estimated by exploiting the phase shifted signal described above. A computational framework for matching the two signals based on cross‐

correlation CC can calculate the lag between them, and thus the displacement which would have resulted in the phase difference. For an RF signal

r m,n,k

at sample

m

of trace

n

in frame

k,

the cross‐correlation at lag

q

between frames

k

and

k

1 is found from:

, ; , 0 , , ∙ , , 1 7

In the algorithm used here, the cross‐correlation function is only calculated along the axial traces, with zero lag in the lateral n direction. The correlation function needs a certain window size in order to generate accurate results. A window that is too large, however, will reduce the ability to detect smaller local displacements. The applied window size was generally selected based on visual

 

inspection of the resulting strain image. Given a sufficiently high frame rate, the tissue movement between consecutive RF frames was small enough that the maximum value of the cross‐correlation function in each window occured within a few samples of zero lag. An example of the cross‐

correlation function for one window is shown in Figure 12.

Figure 12. Cross correlation function for one window of RF data matched in the axial direction. Here, the  maximum discrete value occurs at a lag of 2 samples. 

In Figure 12, the maximum CC value appears at a time lag of 2 samples, which would suggest that the tissue displaced a distance of 2 samples. However, the CC equation only computes values discretely located at sample intervals and does not provide subsample estimates of the CC function. Further processing must be done in order to determine the true maximum value of the underlying function. One method of achieving this is to exploit a characteristic of the Hilbert transform, which is defined as:

1 8

The Hilbert transform is used to create the analytic form of the CC function:

, , , , ∙ , , ∗ 9

 

where

*

is the convolution operator. The analytic form of a signal created in this fashion is known to have some useful properties. The most relevant is that the phase of the analytic signal crosses zero at maximum values of the original signal 137 . The significance of this is that the true maximum value of the CC function may be estimated at subsample resolution via simple linear interpolation of the analytic phase values:

, 2 ∙ ∠ , ; , 0

∠ , ; 1,0 ∠ , ; 1,0 10

where

dt

is the estimated lag between the two RF signals, ∠ is the phase operator,

q

max is the discrete maximum lag of the CC function, and

T

sampis the sampling time of the RF data. The equation above is derived from a simple line equation using a center‐difference approach for the slope. At each zero crossing the phase angle function becomes approximately linear, and so the angles corresponding to

q

max,

q

max 1, and

q

max‐ 1 can be used to determine the subsample lag estimation.

This interpolation procedure is illustrated in Figure 13.

Figure 13. Phase angle of the analytic CC function at each lag value. Each zero crossing corresponds to a  maximum CC value. The exact zero crossing may be estimated by approximating the phase angle  function as a line using three points (shown above). 

 

The CC window slides in the axial direction down each RF trace and produces a field of time lag values using the procedure described above. Utilizing the assumption that the shift in signal is the direct result of tissue displacement, these lag values are converted to axial strain by differentiation:

, 1, ,

11 An example of a completed strain image using this method is shown in Figure 14. A gel phantom containing a hard inclusion was sampled with the URI and RF data was collected to reconstruct both a B‐mode image and strain image.

Figure 14. B‐mode image (left) and strain image overlay (right). Both images were computed from raw  RF data acquired from the research interface on the Acuson Antares machine.