Comparison of Displacement Tracking Algorithms for in vivo Electrode Displacement Elastography

Abstract

Hepatocellular carcinoma and liver metastases are common hepatic malignancies presenting with high mortality rates. Minimally invasive microwave ablation (MWA) yields high success rates similar to surgical resection. However, MWA procedures require accurate image guidance during the procedure and for post-procedure assessments. Ultrasound electrode displacement elastography (EDE) has demonstrated utility for non-ionizing imaging of regions of thermal necrosis created with MWA in the ablation suite. Three strategies for displacement vector tracking and strain tensor estimation, namely Coupled Subsample Displacement Estimation (CSDE), a multilevel 2-D normalized cross-correlation method, and quality-guided displacement tracking (QGDT) have previously shown accurate estimations for EDE. This paper reports on a qualitative and quantitative comparison of these three algorithms over 79 patients after an MWA procedure. Qualitatively, CSDE presents sharply delineated, clean ablated regions with low noise except for the distal boundary of the ablated region. Multilevel and QGDT contain more visible noise artifacts, but delineation is seen over the entire ablated region. Quantitative comparison indicates CSDE with more consistent mean and standard deviations of region of interest within the mass of strain tensor magnitudes and higher contrast, while Multilevel and QGDT provide higher CNR. This fact along with highest success rates of 89% and 79% on axial and lateral strain tensor images for visualization of thermal necrosis using the Multilevel approach leads to it being the best choice in a clinical setting. All methods, however, provide consistent and reproducible delineation for EDE in the ablation suite.

Introduction

Hepatocellular carcinoma (HCC), the most prevalent primary hepatic malignancy, is the 6^th most common cancer worldwide with the 3^rd highest mortality rate (Avey et al. 2009; Lencioni and Crocetti 2012). Although mortality with all other cancers have declined over the last decade, the age-adjusted death-rate for liver cancer in the United States surged between 2000–2016 by 43% in men and 40% in women (Xu 2018). Current treatment methods for HCC and liver metastasis include liver transplantation, liver resection, chemotherapy, and minimally invasive ablative therapies. Of these treatment methods, liver transplantation is the most effective when liver cirrhosis is present and liver function is significantly impaired (Maluccio and Covey 2012). However, less than 33% of patients receive a transplant due to the paucity of liver supply and donors (Bruix et al. 2014). Another well-established curative procedure to increase the survival rate for patients is surgical resection. Unfortunately, surgical resection is not feasible in many patients as less than 25% of patients with HCC or liver metastases are suitable candidates due to other medical co-morbidities (Avey et al. 2009; Liu et al. 2009). Minimally invasive methods, such as percutaneous thermal ablation, have therefore become an alternative to surgical resection and have gained popularity for local and minimally invasive treatment of hepatic malignancies (Lencioni and Crocetti 2007; Ganguli and Goldberg 2009).

Percutaneous thermal ablation methods such as radiofrequency ablation (RFA) and microwave ablation (MWA) seek to eradicate tumor tissue with minimal injury to neighboring structures (Goldberg et al. 2000; Dodd et al. 2001). A main advantage of RFA or MWA as compared to surgical resection is the potential for minimal normal tissue loss and fewer procedural complications, while sustaining a comparable success rate for tumors less than 3 cm (Ganguli and Goldberg 2009; Liu et al. 2009; Palmer and Johnson 2009; Bruix et al. 2014). Unfortunately, a major limitation with RFA is the ability to obtain uniform, complete thermal necrosis in tumors larger than 3–4 cm along the major axis (Lencioni et al. 2009). MWA is able to combat this limitation, with the ability to produce significantly larger ablation regions than RFA with improved efficacy in terms of complete uniform ablation (Qian et al. 2012). Several studies have validated the advantages of MWA over RFA in clinical settings (Lu et al. 2005; Liu et al. 2009; Swan et al. 2013; Baker et al. 2017).

One of the problems associated with treatment of HCC is due to metastasis from the original tumor caused by new tumor formation in cirrhotic livers, advanced liver disease, or incomplete ablations contributing to higher risk for recurrence. To properly plan treatment for long-term disease-free survival, accurate imaging of tumor dimensions and location is needed (Palmer and Johnson 2009; Bruix et al. 2014). Contrast- enhanced computed tomography (CECT) is commonly used since it provides accurate tumor portrayal including its spread and mapping of liver vascular anatomy (Liu et al. 2009). In the ablation suite, CT without contrast is generally used to ensure accurate MWA antenna placement. Unfortunately, CT imaging alone without contrast does not demonstrate sufficient distinction between residual tumor tissue and ablation zones due to poor soft-tissue contrast (Liu et al. 2009). CT is also typically time-consuming, ionizing, and expensive. CECT is therefore needed for assessment of the treatment’s efficacy (Lencioni et al. 2009). In search for a higher contrast imaging modality, ultrasound elastography was evaluated.

Elastography was introduced for imaging tissue stiffness by Ophir et al. (1991). Elastography utilizes a mechanical perturbation with subsequent measurement of displacement and strain from this applied force (Ophir et al. 1991), which can be quasi-static, dynamic, or impulse deformations (Ophir et al. 1999; Varghese 2009; Parker et al. 2011; Doherty et al. 2013; Barr et al. 2015). The mechanical force needed to provide deformation for measurement can be applied externally or internally to the liver (Rivaz et al. 2008). A noninvasive approach for elasticity imaging utilizes acoustic radiation force impulse (ARFI), which applies deformation using focused ultrasound pulses, alleviating the need for manual compression by the operator (Nightingale 2011). Good contrast for pre-ablation and post-ablation malignant tumors has been shown, claiming that ARFI provides superior boundary delineation as compared to conventional B-mode (Fahey et al. 2008). Shear wave elasticity imaging (SWE imilar approach that also utilizes acoustic radiation force but uses several pulse bursts at different focal depths to induce a planar shear wave (Pernot et al. 2011; Hollender et al. 2015). Propagation velocities of shear waves are measured to characterize the elasticity or shear modulus of tissue (Sarvazyan et al. 1998). Shear wave speed estimation in the liver has been used to monitor RFA showing comparable results to MRI (Shi et al. 2015). In addition, focused ultrasound (FUS) beams have also been used to induce oscillatory deformations for harmonic motion imaging (HMI). HMI has shown good results for tumor detection and ablation monitoring (E Konofagou et al. 2012; Chen et al. 2015). However when staging liver fibrosis, all approaches using radiation force may fail for individuals with high liver fibrosis/cirrhosis or those with high body mass index (BMI) (Deng et al. 2015), and for depths greater than 8 cm (Yang et al. 2017).

Another approach that has been applied for treatment monitoring, specifically during and after RFA or MWA procedures, is electrode displacement elastography (EDE) (Varghese et al. 2002). It was shown via simulation that using the electrode to induce quasi-static deformations provided a theoretically higher imaged contrast than external compression (Bharat and Varghese 2006). Phantom studies confirmed these simulation findings with contrast-to-noise ratio (CNR)and strain contrast obtained being significantly higher for EDE due to the local nature of the deformation applied (Jiang et al. 2007; Bharat et al. 2008b; Bharat and Varghese 2010). To further validate EDE efficacy, in vivo animal models were utilized showing a high correlation between EDE strain and pathologic areas of ablated regions (Fernandez et al. 2008; Rubert et al. 2010). EDE was then performed on human patients scheduled for percutaneous minimally invasive ablation procedures to further verify its ability to delineate ablated regions (Yang et al. 2016; Yang et al. 2017). Yang et al. has shown that image contrast, CNR, and delineation are significantly higher for strain images obtained using EDE than B-mode (Yang et al. 2016) or ARFI (Yang et al. 2017) imaging.

EDE requires use of a displacement estimation algorithm to estimate electrode induced quasi-static deformations. Many of these algorithms employ time-delay estimation (TDE), and have been implemented using one-dimensional (1-D) or two-dimensional (2-D) algorithms utilizing sum squared differences (SSD), sum absolute differences (SAD), and normalized cross correlation (NCC) based methods (Viola and Walker 2003; Zahiri-Azar and Salcudean 2006). Most of these approaches estimate only the axial component of the displacement vector and strain tensor, while both axial and lateral displacement vectors and strain tensor estimations are essential for EDE due to angle of ablation needle insertion. Many algorithms have incorporated 2-D tracking kernels for axial and lateral estimations (Langeland et al. 2003; McCormick et al. 2012), however lateral estimation accuracy and resolution is low due to conventional ultrasound imaging constraints (Liu et al. 2017). 2-D algorithms have incorporated interpolation (Azar et al. 2010; Liu et al. 2017), scaling factors (Brusseau et al. 2008), pitch and beamwidth parameters (Luo and Konofagou 2009), lateral phase (Chen et al. 2004; Ebbini 2006), regularization (Rivaz et al. 2011), and beam steering/ compounding (Techavipoo et al. 2004; Rao et al. 2007; He et al. 2017) to increase lateral displacement accuracy and resolution. In previous work, three NCC- based algorithms have shown accurate axial and lateral displacement and strain tensor estimations for EDE, namely, quality-guided displacement tracking (QGDT) (Chen et al. 2009), coupled subsample displacement estimation (CSDE) (Jiang and Hall 2015), and a Multilevel 2-D NCC method (Shi and Varghese 2007). Now that EDE based strain imaging has been shown to be feasible for imaging thermally coagulated regions within the liver in a clinic, this paper seeks to compare the performance of these three algorithms.

Materials and Methods

Radiofrequency (RF) data was collected using a Siemens S2000 (Siemens, Mountain View, CA) system with a 6C1 HD curvilinear transducer during MWA procedures at the University of Wisconsin-Madison Hospital and clinics. The study protocol was approved by the health sciences institutional review board (HS-IRB) at UW-Madison. All patients in the study provided informed consent before the procedure. The procedure is initiated with insertion of the MWA antenna through a small incision utilizing B-mode ultrasound for guidance. Antenna placement in the tumor is then verified using CT imaging without contrast. Approximately 80 frames of RF data were collected pre-ablation, and immediately post-ablation. During data collection, manual perturbation of the antenna was performed by the physician. During these perturbations, the antenna was displaced by approximately ±1mm. All signal processing to obtain the displacement vectors and strain tensors was completed off-line using corresponding software packages for each algorithm in MATLAB. RF data acquired from 79 patients were analyzed in this paper. Patient demographics are described in Table 1.

Table 1.

Patient Demographics. Values represent the mean (standard deviation)

Variable	Hepatocellular	Metastasis	Benign	Total
	Carcinoma		Masses
	(n = 51)	(n = 21)	(n = 7)	(n = 79)
Weight (lbs)	191(56)	185(32)	182(107)	191(41)
Age(years)	64(8.7)	63(14)	36(6.0)	61(13)
Depth:
	14%	5%	0%	11%
<5cm
5cm< & <
	51%	52%	43%	52%
8cm
8cm<	35%	43%	57%	39%
Diameter:
	37%	30%	29%	35%
< 2cm
2cm< & <3cm	43%	43%	14%	40%
3cm<	20%	27%	57%	25%

Quality-Guided Search Strategy

The first method evaluated was a quality guided search strategy (QGDT) described by Chen et al. (Chen et al. 2009). This displacement tracking algorithm utilizes a seed-based search strategy quantified by a data quality metric, i.e. correlation coefficient, phase gradient variance, or other user defined metric. A grid of N seeds is created, and the seed with the highest quality is processed to the displacement and correlation, along with its nearest neighbors. If the displacement quality of the neighbors is higher than the current seed, it is discarded, and the new seed is processed. This is continued until all pixels in the RF frame are processed. QGDT had been previously applied to EDE with a kernel size of 3.5 wavelengths x 7 A-lines using normalized correlation coefficient values greater than 0.75 as the quality metric (Yang et al. 2016; Yang et al. 2017).

Fast Hybrid Algorithm with Coupled Subsample Displacement Estimation

The second method used is a fast hybrid algorithm (Jiang and Hall 2011) with Coupled Subsample Displacement Estimation (CSDE) (Jiang and Hall 2015), which also incorporates regularized motion tracking and a predictive search approach, similar to QGDT. The method begins by estimating integer local displacements with a regularized search strategy using large 2 D kernels. A variant of the classic, block matching algorithm is then used to compute displacements on a 6-point diamond stencil grid with a cost associated with each possible solution. The Viterbi algorithm is used to identify trusted displacement seeds and its path. If the first and last displacement vectors of the diamond stencil are different and the correlation value of the displacement vector at the center of the stencil is 0.75 or higher, then that center of the stencil is marked as a trusted seed. These seeds are then used in a modified predictive search strategy described in (Peng et al. 2016). Initialized seeds from the regularized search and all displacements estimated with correlation coefficients less than 0.4 are then discarded. Any holes that the latter produces are interpolated or extrapolated from immediate neighbors.

Once the process of obtaining integer displacements is completed, the search kernel on the post-deformation RF frame is shifted by these integer displacements. Next correlation functions around the vicinity of each correlation peak from the integer displacements are solved to obtain subsample displacement estimates. All 2-D subsample displacement vectors then found by fitting the coordinates of a selected iso-contour of the correlation function to an ellipse. The final displacement vector is the sum of the integer and subsample displacements. CSDE was utilized to process EDE data sets on human subjects reported in (Pohlman et al. 2017). An initial kernel size of 7.5 wavelengths x 29 A-lines was used, with a final kernel of 1 wavelength x 3 A lines, also used for CSDE in this paper.

Multilevel Method

The third algorithm evaluated in this paper is a 2-D Multilevel algorithm (Shi and Varghese 2007). Multilevel operates as a pyramid, where initial displacements are computed starting on a coarse grid using large kernels, followed by computations on finer and finer spatial grids to obtain high SNR estimates with high spatial resolution. This method first transforms RF data into envelope signals for fast and coarse displacement estimation. 2-D normalized crosscorrelation is then used on down-sampled envelope data to track displacements using a large 2-D kernel. Displacements below a correlation coefficient threshold of 0.75 were either replaced with nearest neighbors or interpolated. This coarse displacement map is then used as an initial displacement estimate for the next level of displacement calculations. The next level displacements are calculated on envelope data with more samples, with 2-D cross correlation, and correlation coefficient thresholding repeated using a smaller kernel size and a higher correlation coefficient threshold. This is repeated for all levels until the final level is reached. Here 2-D normalized cross correlation is used on RF data to achieve the highest spatial resolution displacement estimates using the smallest kernel size (Shi and Varghese 2007). For this paper, 4 levels of the 2-D multilevel algorithm were used, utilizing kernel sizes of [8, 4, 2, 1] wavelengths x [7, 5, 3, 3] A-lines.

A normalized correlation coefficient metric of 0.75 was maintained for all methods in this paper. In addition, the final kernel size was reduced to 1 wavelength x 3 A-lines to be consistent across all displacement estimation methods allowing for a fair comparison. Although, the estimation performance of each of the methods compared may not be optimized in this paper, we compare the performance of these methods using the exact same processing parameters.

Data Gridding

In addition to displacement vector tracking and estimation, an important step for all these methods is the approach used to transform displacement data from a sector format to a rectilinear grid. Trigonometric identities using both x and y displacement vectors were used (Peng et al. 2016) to generate axial and lateral displacement vectors for the sector array data. An additional post-displacement task was to localize a rectangular region of interest containing the ablated tumor region and regions of normal liver surrounding it from all the displacement tracking methods for comparison. Because the displacement tracking methods described above provide different displacement mapping spatial resolutions, all data sets were up-sampled to a grid size of 0.1 mm x 0.1 mm. This is done to ensure that all filtering and additional processing done to displacement data is consistent among the three methods. Once all data from the methods are on consistent data maps, further filtering can be done to remove any displacement errors. The first filtering stage applied a 2 mm x 2 mm median filter to data sets to remove false-peak displacement errors, while retaining edge information related to ablated regions. The final filtering stage used 1-D cubic spline smoothing to produce a smoother displacement map by minimization of the expression in Eqn. (1).

$${\displaystyle \sum _{i=1}^n\{Y_i-\widehat{f}{\left(x_i\right)\}}^2}+\lambda {\displaystyle \int {\widehat{f}}^{\prime \prime }}{(x)}^{2}dx$$

where $Y_i=f\left(x_i\right)$ for$\left\{x_i:i=1,\dots ,n\right\}$, $\widehat{f}\left(x_i\right)$ is the cubic spline estimate, and λ is the smoothing factor. Spline smoothing used a smoothing factor of 1,000 in the axial direction and 10,000 in the lateral direction. After filtering of displacement data, a 9-point least squares method for strain calculation was performed on all data sets (Kallel and Ophir 1997).

Region-of-Interest (ROI) Placement

To quantitatively compare all three methods, a rectangular ROI was used with an example shown in Fig. 1. ROI locations were maintained the same for all three displacement estimation methods and strain tensors computed. Measurements taken were the mean, standard deviation of estimates in the inner ROI, the contrast between the inner ROI against the outer ROI, and the CNR of the inner ROI compared to the outer ROI.

Figure 1.

An example of the region-of-interest (ROIs) selected for comparison on axial strain tensor image produced using CSDE. The solid blue ROI denotes the ROI inside the ablation zone and the dotted red ROIs are the halo regions outside the ablation zone at the same depth as the blue ROI. The area enclosed within the blue ROI and both red ROIs combined were equal.

Once all masses were processed using CSDE, Multilevel, and QGDT displacement tracking strategies, axial and lateral strain tensors obtained were compared to each other. Displacement tracking and strain tensor estimation was performed on the exact same RF frame pairs to ensure accurate comparisons of results. The frame pair was selected based on whether an ablation zone was visualized for at least 2 of the displacement tracking strategies. If a RF frame pair exists where all three methods provided delineation of the ablated region, that frame pair was preferred.

Contrast and Contrast-to-Noise Ratio Comparison

The ratio of mean strain outside to inside of the ROEs placed ir ablated region and background, where both are at the same depth, is computed to obtain the contrast using Eqn. (2). Contrast obtained using EDE utilizes the halo region as the outside ROI for comparison (Bharat et al. 2008a; Jiang et al. 2009). Contrast-to-noise ratio (CNR) is calculated using Eqn. (3), as shown in (Varghese and Ophir 1998).

$$\mathrm{Contrast}=\frac{{\mu }_{s_1}}{{\mu }_{s_2}}$$

$$\mathrm{CNR}=\frac{2{\left({\mu }_{s_1}-{\mu }_{s_2}\right)}^2}{\left({\sigma }_{s_1}^2+{\sigma }_{s_2}^2\right)}$$

where μ and σ are the mean and standard deviation, and subscripts s₁ and s₂ strain magnitudes inside and outside the ablation zone, respectively.

Results

Displacement and strain results were computed for all 79 patients in this study using all three methods. Displacement vector estimates were median filtered and smoothened using spline interpolation, with strain tensor images constructed at all stages: with no filtering, median filtering, and median filtering combined with spline interpolation. An example of axial and lateral strain tensor images that incorporate median filtering and spline interpolation for all displacement tracking methods are illustrated in Fig. 2. Note that consistent delineations of ablated regions with axial and lateral strain imaging are observed for all methods in Fig. 2. Over the 79 data sets investigated, computation with CSDE tends to estimate larger ablated regions containing less noise artifacts in both axial and lateral strain tensor images as compared to both Multilevel and QGDT approaches. Since lesion size is not a focus of this study, it is a subjective measure noted by the authors. On the other hand, visualized noise artifacts are quantified by the standard deviation metric on strain tensor images.

Figure 2.

Illustration of axial and lateral strain tensor images produced using CSDE, Multilevel, and QGDT approaches for a patient with colon metastasis at a depth of 6 cm. (a) B-mode image with ROI, (b) CSDE axial strain tensor image, (c) CSDE lateral strain tensor image, (d) Multilevel axial strain tensor image, (e) Multilevel lateral strain tensor image, (f) QGDT axial strain tensor image, and (g) QGDT lateral strain tensor image.

Quantitative comparison results over the 79 patients in our study were grouped based on the type of liver mass diagnosed: HCC (n=51), metastases (n=21), and all masses (n=79) which also includes benign masses (n=7). Distributions of mean, standard deviation, contrast, and CNR across all patients and all three displacement estimation methods are shown in Fig. 3-Fig. 6.

Figure 3.

Mean strain magnitude distributions inside the ablation zone. Distributions are shown for (a) all masses, (b) HCC masses, and (c) metastatic masses using CSDE, Multilevel, and QGDT displacement estimation methods.

Mean

Figure 3 displays mean strain distributions across all masses (a), HCC (b), and metastatic masses (c), respectively. For both CSDE and Multilevel methods, lateral strains have wider distributions than axial strains which are reversed for QGDT as shown in Fig. 3 (a). In most in- vivo human ablations the antenna is inserted at a 30° - 45° angle with respect to the transducer, therefore strain distribution incurred in the localized region around the antenna is expected in both axial and lateral directions. In addition in Fig. 3 (a), CSDE appears to estimate lower values of axial and lateral strains with very narrow upper and lower quartiles meaning very low variation between patients.

Axial and lateral strain estimation with all three approaches shows similar distributions near the median strain for all masses in Fig 3 (a) and HCC masses in (b), with the exception of tighter distribution with axial QGDT. Of all three estimation approaches, QGDT shows the highest variation in the axial strain distribution and appears skewed toward larger strain magnitudes shown in Figs. 3 (a) and (c). Metastatic masses in Fig. 3 (c) have similar distributions, except for the wider axial QGDT distribution. Another important aspect is that all distributions are strongly skewed toward larger magnitude strains for metastatic masses.

Standard Deviation

Standard deviation distributions of strain magnitudes illustrated in Fig. 4 represent all masses (a), HCC (b), and metastatic masses (c). Standard deviation values relate to the amount of variability and noise seen within ablated zones. For all masses represented by Fig. 4 (a), CSDE has the lowest standard deviation median and range. Multilevel shows low median standard deviation and tight quartiles, but a larger range than CSDE. QGDT on the other hand has the largest median standard deviation and largest range. Both QGDT distributions are skewed toward larger standard deviations. Similar results are seen for HCC masses in Fig. 4 (b). Note that the metastatic masses in Fig. 4 (c), show similar standard deviation medians as the masses in Fig 4. (a) and (b), but CSDE and Multilevel present with tighter quartiles and ranges. QGDT shows large standard deviation values inside ablated zones of metastatic masses.

Figure 4.

Standard deviation distributions of the strain magnitudes inside the ablation zone. Distributions are shown for (a) all masses, (b) HCC masses, and (c) metastatic masses using CSDE, Multilevel, and QGDT displacement tracking methods.

Contrast

Strain magnitude contrast for each mass was calculated using Eqn. (2), and the distribution shown in Fig. 5. Contrast is indicated as negative since ablated regions present with low strain due to their increased stiffness, while the halo around ablated regions have relatively high strain values. Therefore, lower contrast values; i.e. large negative numbers, indicate increased contrast between ablated region and surrounding tissue. When all masses are considered in Fig. 5 (a), axial strain estimated with CSDE shows the largest contrast (median value), and other methods show relatively similar median contrast CSDE also indicates larger quartile ranges than the Multilevel and QGDT methods and is skewed toward lower contrasts. Main differences between the strain contrast metric for HCC masses shown in Fig. 5 (b), versus that for metastases in Fig. 5 (c), is the smaller contrast range for metastatic masses when compared to HCC. Axial strain tensors estimated with the Multilevel method provides a consistent contrast range visualized by the tightest distribution for all methods and masses. In general, we anticipate that the stiffness of the ablated region should only vary in a small range when the thermal dose distribution utilized is similar (Bharat et al. 2005; Kiss et al. 2009).

Figure 5.

Contrast distributions of the strain magnitudes inside and outside the ablation zone. Distributions are shown for (a) all masses, (b) HCC and (c) metastatic masses using CSDE, Multilevel, and QGDT displacement tracking methods.

Contrast to Noise Ratio

CNR values are calculated using Eqn. (3), and distributions obtained across patients are shown in Fig. 6. Higher CNR values indicate improved mass detectability (Varghese and Ophir 1998; Pohlman et al. 2017). In Fig. 6 (a), Multilevel and QGDT methods both show the highest median CNR values with tight, similar quartile ranges for all masses. Axial strain estimated with CSDE shows the lowest CNR. In addition, both axial and lateral strains estimated with CSDE have the largest ranges. The CNR for HCC masses in Fig. 6 (b) do not vary when compared to the distribution for all masses in Fig. 6 (a). On the other hand, metastatic masses in Fig. 6 (c) present with very tight distributions for CNR estimated using QGDT and Multilevel, respectively. Both strain tensors estimated using Multilevel present with positive CNRs for metastatic masses. Axial and lateral strain tensors estimated using CSDE show the largest ranges in CNR, with CSDE axial strain tensors having the lowest CNR.

Figure 6.

Contrast-to-noise ratio distributions of the strain magnitudes inside and outside the ablation zone. Distributions are shown for (a) all masses, (b) HCC and (c) metastatic masses using CSDE, Multilevel, and QGDT displacement tracking methods.

Success Rates

A final important aspect to consider with these displacements tracking methods is how successful and consistent these methods are in visualizing ablation regions. Success rates were calculated using the same frame pairs that were used in the distributions previously reported in the paper by a single observer. The same strain dynamic range (0–1%) was used for all the strain tensor images computed from the three methods. Examples of successful and unsuccessful results are shown in Fig. 7. Success rates for the three methods are reported in Table 2, and noted as a qualitative assessment of the strain tensor images.

Figure 7.

An example of axial strain tensor images of the same frame pair across the three methods. (a) B-mode image with ROI, (b) CSDE axial strain tensor, (c) Multilevel axial strain tensor, and (d) QGDT axial strain tensor. In this example, Multilevel and QGDT axial strain tensors would be deemed successful since ablation region can be visualized, while CSDE is unsuccessful.

Table 2.

Success rates for visualizing the ablation region with CSDE, Multilevel, and QGDT for all masses.

	CSDE	Multilevel	QGDT
Axial	63%	89%	83%
Lateral	69%	79%	68%

Discussion

Patient demographics in Table 1 are also correlated to the distributions plotted in Figs. 3-6, specifically for differences seen relative to mass type. For distributions of the mean strain metric computed in an ROI within the ablated region of each mass type, the distribution for all masses shown in Fig. 3 (a), closely match that shown for HCC (n = 51) alone in Fig 3 (b). This is true for all methods other than for the axial strain tensors generated using QGDT. A similar trend is seen in the distributions of the standard deviation metric in Fig. 4. These results demonstrate that metastatic masses (n = 21) (see Fig. 3 (c) and Fig. 4 (c)), do not contribute significantly to the distributions plotted for all masses for the CSDE and Multilevel methods. Furthermore, the tighter distribution also implies that these methods provide lower noise artifacts for metastatic masses when compared to HCC.

On the other hand, the distribution obtained for the contrast metric estimated from the the strain tensor images in Fig. 5, differ from the distributions seen for the other metrics. Here, the distributions obtained with all three methods do not significantly differ for HCC (Fig. 5 (b)), versus metastatic masses (Fig. 5 (c)). On the other hand, CNR distributions in Fig. 6 show significant differences among mass type. Similar to Figs. 3 and 4, metastatic masses in Fig. 6 (c) are represented by tight distributions for the Multilevel and QGDT methods. These results indicate that the local EDE deformations for metastatic masses are tracked with lower standard deviations when compared to HCC masses. These increased standard deviations are also reflected in the CNR distributions.

Based on the distributions of the mean, standard deviation, contrast and CNR metrics shown in Figs. 3–6, we evaluated the statistical significance of the results for the different metrics and methods. We found that the estimated mean, standard deviation, and CNR metrics computed from the strain tensors demonstrate statistically significant differences between estimation methods with p <<< 0.001, while the contrast metric was not significantly different. Therefore, mean, standard deviation, and CNR are valid metrics for the comparison of estimation methods against each another. In addition, within each estimation method, we did not obtain any statistical significant differences between mass types, indicating that each estimation method produces consistent results regardless of mass type.

A comparison of contrast and CNR in axial and lateral strain tensor images for all patients is presented in Table 3. CSDE presents with the largest contrast in the axial direction, while the lateral direction for CSDE and both directions for other methods show similar contrasts. Note that the Multilevel method has the highest CNR in the axial direction along with QGDT in the lateral direction. CSDE shows the lowest CNR for both axial and lateral strain tensor images. To demonstrate the need for filtering on displacement estimates, a comparison of CNR obtained with and without median filtering of displacement estimates are shown in Fig. 8.

Table 3.

Mean and standard deviation (std) of the contrast and CNR metric for the three methods.

Method		Contrast (dB)	CNR (dB)
		mean (std)	mean (std)
	Axial	−15.1 (13.9)	−0.571 (1.98)
CSDE
	Lateral	−8.94 (12.4)	0.215 (1.59)
	Axial	−8.42 (4.61)	1.06 (0.633)
Multilevel
	Lateral	−8.93 (6.96)	0.953 (0.918)
	Axial	−8.87 (6.44)	0.924 (0.790)
QGDT
	Lateral	−9.12 (7.31)	1.13 (0.998)

Figure 8.

Comparison of CNR distributions after filtering stages for all masses. Distributions are shown for (a) no filtering, (b) median filtering, and (c) median filtering with spline smoothing of displacements before strain estimation.

Observe that with median filtering and spline smoothing, the CNR increases among all displacement tracking strategies, except for axial strain tensors estimated with Multilevel processing where quartile ranges remain similar when compared to median filtered results, but with a larger range after spline filtering. The increase in CNR can be attributed to the reduction of noise artifacts with both filtering approaches. Another example of axial and lateral strain tensor images obtained from the same frame pair for the three different strategies are shown in Fig. 9. Note that additional filtering within the ablation region after strain tensor estimation was performed to improve visualization of the ablation region. Analogous to results presented in Fig. 2, CSDE seems to trend toward larger ablation region dimensions when compared to either Multilevel or QGDT. Although the size differentiation among the methods is not quantified in this paper, it is an interesting trend to note and is an important factor for validating tumor ablation margins.

Figure 9.

Improved visualization of strain tensor images for a patient with HCC at a depth of 5 cm generated using CSDE, Multilevel, and QGDT respectively. Additional noise reduction is performed within the ablated region using morphological operators to improve visualization of the ablated region. (a) B-mode image with ROI, (b) CSDE axial strain tensor image, (c) CSDE lateral strain tensor image, (d) Multilevel axial strain tensor image, (e) Multilevel lateral strain tensor image, (f) QGDT a rain tensor image, and (g) QGDT lateral strain tensor image.

Axial strain tensor images obtained with CSDE show the sharpest delineation with the cleanest looking interiors, but often fail to show delineation at the distal part of the mass. Lateral strain estimated with CSDE does not provide a sharp delineation with clean interiors seen with axial strain but provides better delineation of the distal mass. Axial strain images obtained using Multilevel processing typically provide good delineation for masses over the entire circumference of the mass, however it does not match the sharpness obtained with axial strain tensor images obtained with CSDE. Lateral strain tensor images computed using Multilevel analysis show similar results as the lateral CSDE with improved mass delineation and contrast. Axial strain tensor images estimated with QGDT show good delineation, but also contain the most noise artifacts visualized inside and outside the ablated regions. These increased artifacts quantified by the standard deviation distributions shown in Fig. 4. Lateral QGDT provides improved delineation of ablated regions among lateral strain tensor images. An interesting aspect in tensor images generated with Multilevel and QGDT is that ablated region are always smaller than ablated regions delineated by CSDE, which is clearly demonstrated in both Fig. 2 and Fig. 9.

The success rates shown in Table 2 show that CSDE provides the lowest image success rate of the three methods, while Multilevel presents the highest success rate for both axial and lateral strain tensors. Interestingly, lateral strain tensor imaging with CSDE has a higher success rate than that obtained with axial strain tensor imaging. Table 3 displays the mean and standard deviation for contrast and CNR of CSDE, Multilevel and QGDT. Similar to the results shown in Fig. 5, axial strain tensor images obtained with CSDE shows the highest contrast with values approximately 6 dB lower than the other methods. It is also seen that Multilevel and QGDT strain tensor images offer higher CNR than depicted with CSDE.

There are two important points regarding the work presented in this paper. First, we present a brief discussion on the need for comparison between mass sizes estimated on strain tensor images and CECT imaging. Unfortunately, obtaining ‘true’ mass size and areas in-vivo in human subjects is difficult, as the ablations are not excised for histopathological analysis. CECT imaging, as the current “gold standard” for post-ablation assessments, offers a means of comparison of ablated lesion dimensions, areas and volumes. Since current B-mode imaging and RF data collection utilize a curvilinear array, with a single 2D imaging plane, we are limited to displacement tracking and strain images to the 3D CECT data sets is essential for accurate comparison of lesion dimensions and areas. A second aspect to be discussed is regularization of strain tensor images, if any, that is incorporated in these methods. CSDE integrates a Viterbi based regularization scheme, while Multilevel and QGDT presented in the paper do not incorporate regularization. Regularization in CSDE may explain the more consistent mean and lower standard deviations of strain estimates within ablated regions due to the additional smoothening that regularization offers. This regularization-based smoothening may also contribute to the differences of visualized lesion size produced by CSDE when compared to the other methods presented.

Conclusion

CSDE provides the most consistent mean and standard deviation for strain magnitudes within ablation regions as compared to Multilevel and QGDT. Axial strain tensors using CSDE also provide the highest contrast between ablation zones and surrounding liver tissue. However CSDE only has a 63% success rate when compared to the other methods with higher success rates as shown in Table 2. These results indicate that axial strain tensor images with CSDE may provide better delineation of ablated regions from surrounding tissue than the other methods. Note that the CNR, lies in a similar range (with higher CNR values) for both Multilevel and QGDT, when compared to CSDE. The CNR metric quantifies both the contrast and noise properties of the strain tensor image and is a measure of the detectability of the ablated region in the strain tensor images. Since the emphasis in this paper is on the depiction and delineation of the ablated region we utilize the CNR metric. In addition, since the Multilevel method has the highest success of 89% and 79% for axial and lateral strain tensor images, respectively, along with the highest axial CNR and the tightest CNR distributions for axial and lateral strain tensors; it may be the best approach in a clinical setting as it enables more consistent delineation of ablated regions in the clinic. Future work will correlate strain tensor mass sizes with registered CECT mass sizes and will explore regularization methods to improve means and standard deviations of ablated regions estimated with the Multilevel method.