Ultrasound elastography is an imaging modality to evaluate elastic properties of soft tissue. Recently, 1D quasi-static elastography method has been commercialized by some companies. However, its performance is still limited on high strain level. In order to improve the precision of estimation during high compression, some algorithms have been proposed to expand the 1D window to a 2D window for avoiding the side-slipping. But they are usually more computationally expensive. In this paper, we proposed a modified 2D multiresolution hybrid method for displacement estimation, which can offer an efficient strain imaging with stable and accurate results. A FEM phantom with a stiffer circular inclusion is simulated for testing the algorithm. The elastographic contrast-to-noise rate (CNRe) is calculated for quantitatively comparing the performance of the proposed algorithm with conventional 1D elastography using phase zero estimation and the 1D elastography using downsampled (d-s) baseband signals. Results show that the proposed method is robust and performs similarly as other algorithms in low strain but is superior when high level strain is applied. Particularly, the CNRe of our algorithm is 15 times higher than original method under 4% strain level. Furthermore, the execution time of our algorithm is five times faster than other algorithms.
Mechanical properties of soft tissue have been used as an important indicator of several diseases, such as breast [
Ultrasound elastography has been developing into an effective method in cancer diagnosis due to its capability and simple implementation [
Accurate estimation of tissue displacement is a very important step in ultrasound elastography. Different methods were proposed in the last two decades. Majority of these methods use correlation technique in time domain or the phase domain for displacement estimation [
In this paper, we proposed a modified 2D multiresolution hybrid method for displacement estimation, which can offer an efficient strain imaging with stable and accurate results. To test the algorithm, a heterogeneous computational phantom is simulated using finite element model (FEM), with a rectangle background containing a stiffer circular inclusion. The synthetic RF data are generated from Filed II software [
In order to make a tradeoff between speed and accuracy, we proposed a method using modified 2D multiresolution hybrid elastography. Preprocessing procedure is first applied to the raw RF data to obtain envelopes and baseline signals at different resolutions. Chen et al. proposed a hybrid displacement estimation method, which applied 3-level estimation based on cross-correlation and weighted phase separation (WPS) [
The analytic signals of predeformation and postdeformation radio frequency (RF) signals are obtained by applying Hilbert transformation to the raw RF data. The baseband signals can be calculated by demodulating the analytic signals with a carrier wave
The baseband signals are downsampled at different downsample rates. The downsample rates should satisfy the Nyquist sampling condition. The downsampled baseband signals are then converted into amplitude and phase data using FFT. The amplitude data at different scales are used in corresponding coarse to fine estimation, but the phase data are only used for fine estimation.
Nine evenly distributed windows have been selected in the coarsest scale of the predeformation frame (see Figure
Over of the level 1 search, the calculate windows and search windows are equally distributed.
Level 2 search is performed at a finer scale than level 1 search. Seven by 11 evenly distributed calculate windows are selected on the predeformation frame. The size of the calculate windows is 1/3 of the size at level 1 and the size of the search windows is bigger than that at level 1, which is selected according to the deformation degree. The initial axial and lateral displacement estimates of level 2 are inherited from the output of level 1 and bilinear interpolated to the finer scale. The search windows located at the point according to the output and the center of calculate windows.
The so-called “following tracking” strategy (see Figure
Level 2 search strategy. (a) Set the initial center point of search window to be a reference point and then find the max in its neighbours according to the correlation coefficient. (b) Propagate the reference and its neighbours and then continue to calculate the correlation coefficient.
However, this time the searches are not independent; there is another delivering strategy that is used to deliver displacement estimations from one window to the next window which on the same column. The next window’s initial reference point is no longer the center point of search window, but the position according to the output of the current window.
The advantage of the searching strategy above is that we can find the point which matches the highest correlation coefficient quickly with lower computational complexity. Moreover, the strategy has a good error-correction mechanism to ensure displacement continuity in both axial and lateral direction.
The calculate windows and search windows are the smallest in coarse search and this process should finish the whole frame search. The size of calculate windows should be 1/2 of the size at level 2, and level 3 search stops when the calculate windows cover the whole frame. Similar as in level 2, we also need to interpolate the displacement results in level 2 to level 3 with finer scale. And we use the same search strategy to obtain the axial and lateral displacement in level 3 [
The initial axial and lateral displacement estimation over the whole RF data can be bilinear interpolated from the coarse estimation from level 3 search. A modified phase zero algorithm is proposed for the fine displacement estimation [
Let us denote
Since the maximum of the autocorrelation equals the maximum of the cross-correlation, the conventional cross-correlation determines this maximum to estimate the time shift. When we return the baseband signals to analytic signals, the phase
In original phase zero-crossing estimation, the displacement estimation of the previous window will be used as the initial value for the next window [
We propose a modified algorithm to solve the problems described above. We get the coarse estimation including axial and lateral displacement in the previous coarse calculation, so the iteration between the neighbouring windows can be simplified comparing with 1D elastography method. And the lateral deviation will be applied to the computational process. The calculation is independent of each window, so it makes it easier to take this algorithm to be executed based upon CUDA (Compute Unified Device Architecture)
Strain is defined as the gradient of the displacement. Here we only calculate the axial strain and the least-squares strain estimator (LSQSE) is used, which employs a piecewise linear curve fitting [
A FEM (finite element model) phantom is simulated using Commercial FEM software COMSOL Multiphysics 5.0 (COMSOL USA). FIELD II software is used for ultrasound simulations. The size of rectangle background of the 2D model is 20 mm × 20 mm, with a stiffer circular inclusion in the center. The radius of the inclusion is 3 mm. Triangular mesh was generated and refined automatically by COMSOL (see Figure
Heterogeneous finite element model simulates the stiffer circular inclusion.
A 192-element linear array transducer (64 active elements) with a center frequency of 7.5 Mhz is simulated. The transducer has a pitch of 0.255 mm and an element height of 5 mm. The element width is equal to the wavelength. The number of scan-lines is 128 and the distance between adjacent lines is equal to the pitch. The transmitting focus is at 30 mm and dynamic focusing with focal zones step by 1 mm is used for receiving focus. The image zone has a width of 20 mm and a depth of 20 mm. The speed of sound is assumed to be 1540 m/s and the sampling frequency of the RF signals is 120 Mhz. The original scatters are randomly distributed in the image zone with random scattering amplitude. The predeformation RF signals are simulated with FIELD II using the parameters described above [
Ultrasound RF data was generated using computer simulation. With the synthetic RF data, the displacement and strain distribution were calculated using the modified 2D multiresolution hybrid elastography. Comparison was made between the proposed method, the original 1D elastography and the 1D elastography using downsampled (d-s) baseband signals. Since the modified method has a downsampled step, we make a downsampled version of 1D elastography to compare with the proposed method. To achieve that, we use the same processes as the 1D elastography method to get envelop signals, and the envelop signals will be then downsampled and further 1D elastography calculations will be performed on the downsampled envelop signals.
Figure
Strain map simulated by COMSOL as the ground truth.
Strain maps of three different algorithms. Different strain levels as 1.5%, 2.0%, 3.0%, 3.5%, and 4.0% are applied at each row. The first column ((a)–(e)), the second column ((f)–(j)), and the third column ((k)–(o)) show, respectively, the strain map obtained by original 1D elastography and original 1D elastography with downsampled and modified 2D multiresolution hybrid elastography.
To quantify the performance of different algorithms, CNRe is calculated at each strain level and we use the binary strain image to measure the accuracy of each algorithm [
The extra area of inclusion and background for the calculation of CNRe and the average estimated strain rate.
We have made a record of the average estimated strain rate for both inclusion and background for comparison purpose. The ratio of
The ratio of average estimated strain rates of the inclusion and the background.
We make a complete test with three algorithms under different strain level range 0.2% to 4%. Same as 1D algorithms, the CNRe of our algorithms is too low to distinguish between the lesion and background when strain level is lower than 0.8%, which means the noise on strain estimation will blur the boundary between lesion and background. And the CNRe of the modified 2D multiresolution hybrid elastography algorithm is much higher than the other two algorithms at high strain level (see Figure
The CNRe results of three different algorithms.
The strain binary images (see Figure
Strain binary images of three different algorithms. Different strain levels as 1.5%, 2.0%, 3.0%, 3.5%, and 4.0% are applied at each column. The first column ((a)–(e)), the second column ((f)–(j)), and the third column ((k)–(o)) show, respectively, the strain binary map obtained by the corresponding strain map using 1D elastography, downsampled 1D elastography, and the proposed 2D elastography method.
The inclusion area ratios results of three different algorithms, where the standard denotes the inclusion area ratio in FEA model.
In the algorithm we proposed, the lateral resolution depends on the amount of the windows in level 3 search. The lateral resolution increased with the increasing of the amount until the resolution is equal to the sampling frequency of the RF data. The axial resolution is determined by the physical size of transducer such as the kerf of the array element. The purpose of the consideration of lateral displacement in our algorithm is not to improve the later resolution but to compensate for the interference of lateral offset and get higher accuracy in axial strain image.
All the algorithms were executed with an Intel(R) Core(TM) i7-4790K CPU @2.40 GHz 8.00 GB RAM, and MATLAB 2014b was used for implementing and testing them on Windows operation system. The execution times of the different methods are shown in Table
Execution times of three different algorithms.
Method | 1D | 1D with downsampled | Modified 2D |
Times (s) | 10.2 | 2.3 | 1.8 |
A modified 2D multiresolution hybrid method has been proposed in this paper. Using finite element model phantom under different strain levels, we have shown that the new algorithm can achieve better CNRe comparing with different methods including original 1D elastography method and original 1D elastography method with downsampled (d-s). These results demonstrate that the method we suggested is robust and accurate when high level strain is applied. The result of execution time has shown that the new framework has a higher efficiency that it may well be more suitable for real-time application in clinical practice. The limitation of our algorithm is that, to a great extent, the accuracy of the final result is determined by the output of coarse estimation. The strain image calculated by our algorithm is slightly worse than original 1D elastography under low strain level. In this study, we use simulated data to compare the performance of the proposed method with other methods in different strain level, since ground truth of strain map can be easily obtained. In our next study, we will test our method using phantom and in vivo data.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work is supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant no. 2017YFC0107202), the Funds for Technology of Suzhou, China (Grants nos. SYG201505 and SZS201510), the Funds for Jiangsu Provincial Key Research and Development Plan (Grant no. BE2017601), and International Cooperation Program of Jiangsu Province (Grants nos. BZ2016023 and BK20161235).