Region-Based Endocardium Tracking on Real-Time Three-Dimensional Ultrasound

Abstract

Matrix-phased array transducers for real-time three-dimensional ultrasound enable fast, non-invasive visualization of cardiac ventricles. Typically, 3D ultrasound images are semi-automatically segmented to extract the left ventricular endocardial surface at end-diastole and end-systole. Automatic segmentation and propagation of this surface throughout the entire cardiac cycle is a challenging and cumbersome task. If the position of the endocardial surface is provided at one or two time frames during the cardiac cycle, automated tracking of the surface over the remaining time frames could reduce the workload of cardiologists and optimize analysis of 3D ultrasound data. In this paper, we applied a region-based tracking algorithm to track the endocardial surface between two reference frames that were manually segmented. To evaluate the tracking of the endocardium, the method was applied to 40 open-chest dog data sets with 484 frames in total. Ventricular geometry and volumes derived from region-based endocardial surfaces and manual tracing were quantitatively compared, showing strong correlation between the two approaches. Statistical analysis showed that the errors from tracking were within the range of inter-observer variability of manual tracing. Moreover, our algorithm performed well on ischemia data sets, suggesting that the method is robust to abnormal wall motion. In conclusion, the proposed optical flow-based surface tracking method is very efficient and accurate, providing dynamic “interpolation” of segmented endocardial surfaces.

Introduction

Cardiac screening using ultrasound is beneficial as it provides the highest temporal resolution, but it is limited to two dimensions in most medical centers. Development of 3D echocardiography began in the late 1980s with the introduction of off-line 3D medical ultrasound imaging systems. Many review articles have been published over the past decade, assessing the progress and limitations of 3D ultrasound technology for clinical screening (Belohlavek, Foley 1993, Fenster and Downey 2000, Ofili and Nanda 1994, Rankin, Fenster 1993). These articles reflect the diversity of 3D systems developed for both image acquisition and reconstruction. Although 2D transducers can be configured to assemble a 3D image from a series of planar views, for truly real-time acquisition, only matrix phased array transducers can scan true three-dimensional volumes with stationary transducers (Ramm and Smith 1990). There are few alternative technologies which also enable real-time acquisition based on vibrating or fast rotating transducers (Canals, Lamarque 1999, Voormolen, Krenning 2006). Real-time 3D ultrasound technology is an improvement over former generations of 3D systems because volumetric data can be acquired rapidly (20–25 frames per second), enabling cardiologists to visualize moving cardiac structures from any given plane in real-time. A first generation of real-time three-dimensional ultrasound (RT3D) scanners was introduced in the early 1990s by Volumetrics© (Ramm and Smith 1990) but low spatial resolution over the whole cardiac volume prevented the technology from meeting its initial expectation and reaching its full potential. A new generation of RT3D transducers was introduced by Philips Medical Systems (Best, The Netherlands) in the 2000s with the SONOS 7500, and most recently the iE33 ultrasound system that can acquire a fully sampled cardiac volume in four cardiac cycles. Four sector acquisitions are performed with each scan, acquiring ¼ of the cardiac volume. These sectors are spatially aggregated to generate one ultrasound volume over one cardiac cycle. This technical design enabled dramatically increased spatial resolution and image quality. The latest research upgrade of iE33 also enables a true real-time model which provides 4D ultrasound streaming data without any spatial compounding (Duan, Shechter 2007).

Clinical evaluation of 3D ultrasound data for assessment of cardiac function is performed via visualization using selected 2D projection planes. Inspection of 3D data sets with 2D visualization tools is time demanding, motivating the development of computational tools for quantitative analysis of ventricular function. It has been shown that abnormal ventricular wall motion can be detected accurately on RT3D data with quantitative four-dimensional analysis of the endocardial surface and computation of local fractional shortening (Herz, Ingrassia 2005, Ingrassia, Usyk 2007). Monaghan’s group has also shown that endocardial surface data derived from RT3D ultrasound is valuable in accessing dyssynchrony (Horstman, Monaghan 2007, Kapetanakis, Kearney 2005). These preliminary studies confirmed that RT3D ultrasound provides unique and valuable quantitative information about cardiac motion based on manually or semi-automatically traced endocardial contours. To facilitate the segmentation process over the entire cardiac cycle, we evaluated the use of region-based tracking between segmented frames to alleviate the manual tracing task. In previous research on motion tracking with ultrasound data, intensity-based OF tracking methods described in (Bardinet, Cohen 1996, Boukerroui, Noble 2003, Mikic, Krucinski 1998, Paragios 2003, Tsuruoka, Umehara 1996, Yu, Lin 2003) combined local intensity correlation with specific regularizing constraints (e.g. continuity of the displacements). The presence of speckle noise in ultrasound prevents the use of gradient-based methods, however relatively large region-matching methods are robust to the presence of noise. In this study, we propose a surface tracking application using a 4D correlation-based tracking method on 3D volumetric ultrasound intensity data.

This study aimed to address the following questions, focusing on the left ventricle (LV): Can the proposed method track the endocardial surface between end-diastole (ED) and end-systole (ES) with reliable positioning accuracy? How does dynamic information derived from tracking on RT3D ultrasound compare to information obtained from a single segmentation method? Can the proposed method be used as a dynamic interpolation tool for tracking the endocardial surface?

Methods

Region-Based Tracking Utilizing Correlation Metric

In 1981, when Horn and Schunck (Horn and Schunck 1981) proposed the term “optical flow”, it was defined as “the distribution of apparent velocities of movement of brightness patterns in an image”. In other word, the original optical flow definition was referring to a velocity field or displacement field of the motion of pixel patterns in an image. Optical flow (OF) tracking involves the computation of such fields on deforming objects in an image, based on the assumption that the intensity of the object remains constant over time. In this context, object motion is characterized by a flow of pixels with constant intensity. There are two widely used families of OF computation techniques (Barron, Fleet 1994): (1) Differential techniques (Cremers, Rousson 2007, Frangi, Niessen 2001, Horn and Schunck 1981, Lucas and Kanade 1981, Nagel 1983, Yilmaz, Javed 2006) that compute velocity from spatio-temporal derivatives of pixel intensities based on the “optical flow constraint” equation: $I_x{v}_x+I_y{v}_y+I_z{v}_z+I_t=0$, with spatial-temporal gradients I* of image I and spatial components of optical flow vector v* (Black and Anandan 1996, Horn and Schunck 1981, Lucas and Kanade 1981), and (2) region-based matching techniques (Anandan 1989, Singh 1990), which compute OF by identifying local displacements that correlate best between two consecutive image frames. Since the first two pilot studies on optical flow estimation (Horn and Schunck 1981, Lucas and Kanade 1981) were focused on differential techniques, differential OF accounts for a large portion of OF-based applications (Ledesma-Carbayo, Kybic 2005, Suhling, Arigovindan 2005, Veronesi, Corsi 2006). Compared to differential OF approaches, region-based methods use similarity measures, such as summed-squared differences or cross-correlation coefficients, that are less sensitive to noise, fast motion, and potential occlusions and discontinuities (Anandan 1989, Bleyer, Gelautz 2005, Convertino 1997, Linguraru, Vasilyev 2006, Revell, Mirmehdi 2004, Singh 1990, Wang, Gu 2007, Xiao, Zhang 2005), while assuming that displacements in small neighborhoods are similar. Given the relatively high noise corrupting 3D ultrasound volume series, we adopted a region-based tracking approach to estimate myocardial surface displacements between two consecutive frames. Specifically, we utilized a correlation metric-based tracking method.

Given two data sets from consecutive time frames: (I (x, t ), I (x, t + Δt)), the displacement vector Δx for pixels in a small neighborhood Ω around each pixel x is estimated by maximizing the cross-correlation coefficient as follows::

$$r=\frac{{\displaystyle \sum _{\mathbf{x}\in \mathrm{\Omega }}}(I(\mathbf{x},t)I(\mathbf{x}+\mathrm{\Delta }\mathbf{x},t+\mathrm{\Delta }t))}{\sqrt{{\displaystyle \sum _{\mathbf{x}\in \mathrm{\Omega }}}{I}^2(\mathbf{x},t){\displaystyle \sum _{\mathbf{x}\in \mathrm{\Omega }}}{I}^2(\mathbf{x}+\mathrm{\Delta }\mathbf{x},t+\mathrm{\Delta }t)}}.$$ (1)

In this study, correlation-based tracking was performed in 3D to estimate the displacement of selected voxels between two consecutive ultrasound volumes in the cardiac cycle. The search window Ω was centered around every (5×5×5) pixel volume and was set to size (7×7×7) for a voxel size of 0.6 x 0.6 x 0.6 mm. Regularization of the displacement field was enforced via local averaging of the vector values. A priori information on high contrast between the myocardium and the blood was incorporated in the tracking process to avoid tracking in blood region and minimize erroneous tracking positions, falling away from the endocardial surfaces. Preprocessing of the RT3D data with a speckle-specific anisotropic diffusion filter previously designed by our group (Duan, Angelini 2004) was applied prior to the tracking.

Preprocessing

Since noise in the data will degrade the performance in motion tracking algorithms (Bachner, Adam 2007, Yu, Yan 2006), all data sets were pre-smoothed with edge-preserving anisotropic diffusion as developed in (Duan, Angelini 2004). Anisotropic diffusion methods apply the following heat-diffusion dynamic equation to the gray levels of a given 3D image data set I (x, y, z, t):

$$\frac{\partial I}{\partial t}=\mathit{div}(c(x,y,z,t)\nabla I),$$ (2)

where c (x, y, z, t) is the diffusion parameter, div denotes the divergence operator, and ∇I is the gradient of the image intensity.

In the original work of Perona and Malik (Perona and Malik 1987, Perona and Malik 1990), the concept of anisotropic diffusion was introduced with the selection of a variable diffusion parameter which is a decreasing function g of the gradient of the image data:

$$c(x,y,z,t)=g(\mid \nabla I(x,y,z,t)\mid ).$$ (3)

We used the diffusion function proposed by Weickert (Weickert, Romeny 1998) defined as:

$$g(x,\lambda )=\{\begin{array}{ll}1\hfill & x\le 0\hfill \\ 1-e^{-\frac{3.315}{{(x\mid \lambda )}^4}}\hfill & x>0\hfill \end{array}.$$ (4)

The parameter λ serves as a gradient threshold, defining edge points x_k at locations where |∇I_xk|> λ This bell-shaped diffusion function acts as an edge-enhancing filter, with high diffusion values in smooth areas and low values at edge points. The structure of the diffusion tensor with separate weights for each dimension enables to control the direction of the diffusion process, with flows parallel to edge contours.

In the case of noisy textured data, as ultrasound data with speckle noise, as the diffusion process evolves, the characteristics of the image data change and the gradient threshold parameter value should therefore be modified. It was reported in a paper by Montagnat et al (Montagnat, Sermesant 2003) that values of significant edges decrease as homogeneous regions in the ultrasound data are filtered. Therefore they chose to decrease the threshold gradient over time. Values were selected as a fraction of the cumulative histograms of the data gradients that were recomputed at each iteration of the diffusion process. In the proposed method, a linear model was used to control the gradient weight:

$$\lambda (t)={\lambda }_0+at,$$ (5)

with λ₀ representing an initial gradient value, a the slope parameter and t the time iteration index. Parameters were set empirically for the data sets processed. In our previous algorithm using Volumetrics© data (Duan, Angelini 2004), a linearly increasing scheme was used to suppress the granularity in the acquired images, whereas with the data acquired by the iE33 imaging system, such an aggressive diffusion process was not needed. In this paper, a decreasing scheme was used with λ₀ =20 and a=−1. Sample cross-section views after denoising are shown in Figure 1(d–f).

Figure 1.

Cross-sectional views at ED for one of the data: (a–c) original data, and (d–f) the data after diffusion process. (a, d) axial, (b, e) elevation and (c, f) azimuth views.

Three-Dimensional Ultrasound Data Sets

The OF tracking approach was tested on 40 data sets with 484 frames in total acquired with an iE33 3D ultrasound machine. This data was obtained as part of a separate study under a protocol approved by Columbia University’s Institutional Animal Care and Use Committee. Four coronary artery occlusions were performed on 5 anesthetized, open-chest dogs (20 occlusions total). 3D echocardiograms were acquired at baseline and 60–90 seconds after temporary ligation of the left anterior descending (LAD), and left circumflex (LCx) coronary arteries at the proximal and distal levels. These data sets were obtained by positioning the transducer directly on the apex of the heart, providing high image quality in a small field of view. Spatial resolution of the analyzed data was about (0.6 mm)³ and 10–14 frames were acquired during each cardiac cycle depending on the heart rate, under an acquisition frame rate at 20–25 frames per second. Cross-sectional views from one of the open-chest baseline data sets at end-diastole (ED) are shown in Figure 1(a–c). The data acquisition was gated by ECG and the ED frame was the first frame for all 4D data series.

Segmentation

The endocardial surface of the left ventricle (LV) was semi-automatically segmented using TomTec© software by TomTec Inc (Munich, Germany). Manual editing of the endocardial surface was required. An experienced user performed manual tracing of all time frames on all data sets, on rotating B-scan views (long-axis views rotating around the central axis of the ventricle) and C-scan views (short-axis views at different depths).

Defining a “gold standard” for evaluating the performance of tracking is a challenging task. To evaluate segmentation or boundary extraction methods on clinical data is difficult in general since no ground truth can be perfectly defined. As a result, under such circumstances, segmentations from experienced users are usually used as the “ground truth”. In order to take manual tracing variability into account, discrepancy of segmentation methods are usually compared to inter-observer variability (Brandt, Wigstrm 1999, Heijman, Aben 2008, Juergens, Seifarth 2008, Pednekar, Kakadiaris 2003, van Geuns, Baks 2006), viewing the computer-based method as another “observer”. If the discrepancy is comparable to inter-observer variability, then it is safe to consider that the proposed method is acceptable since the error in the method has fallen within the variance of the ground truth. Following the same rationale, two additional trained cardiologists traced a subset of the data to measure inter-observer variability. We hypothesized that region-based tracking of the endocardial surface from RT3D ultrasound data could achieve comparable accuracy to human observers’ variability. In other words, we expected that surface discrepancy between a tracked surface and the corresponding manual tracing should be similar to the difference between two surfaces traced by two different trained users (or cardiologists), i.e. the inter-observer variability.

Tracking with Region-Based Technique

Tracking of the endocardial surface was applied after initialization with manually traced end-diastolic (ED) data. Starting with a set of endocardial surface data (about 650 data points, roughly 1.5 mm apart) defined at ED, the tracking algorithm was used to track the surface in time throughout the entire cardiac cycle. The proposed method was not being applied as a segmentation tool, but used as a surface tracking tool for a given segmentation method. No additional reinitialization or forward-and-backward tracking as proposed in (Duan, Angelini 2005) was needed, due to high image quality provided by the open-chest acquisition setup.

Evaluation

We evaluated tracking accuracy by quantitatively comparing the dynamic ventricular geometry to the manually segmented surfaces. Segmentation results were typically compared using global measurements such as volume or mean-square errors. In order to provide regional comparisons, we proposed a novel comparison method based on a parameterization of the endocardial surface in prolate spheroidal coordinates (Ingrassia, Herz 2003), which has previously been used for comparison of ventricular geometry from two 3D ultrasound machines in (Angelini, Hamming 2002). The endocardial surfaces were registered through time using three manually selected anatomical landmarks: the center of the mitral orifice, the endocardial apex, and the equatorial mid-septum point. The surface data was fitted in prolate spheroidal coordinates (λ,μ,θ), projecting the radial coordinate λ to a 64-element surface mesh with bicubic Hermite interpolation, yielding a realistic 3D endocardial surface. The fitting process was performed using a custom finite element algorithm.

Fitted nodal values and spatial derivatives of the radial coordinate, λ, were then used to map relative differences between the two compared surfaces (seg from manual tracing and RT from Region-based tracking), ε = (λ_seg − λ_RT) / λ_seg using our custom software. Hammer mapping was used to preserve relative areas of the flattened endocardial surfaces (Hunter and Smaill 1988).

Root mean square errors (RMSE) of the difference in λ, across the entire endocardial surface were computed for every time frame, between algorithm-tracked and the manual segmentation results. Since RMSE is actually the normalized distance between two surfaces, it could provide a fairer comparison than conventional point-to-surface metrics under clinical settings. Furthermore, it can be shown that multiplying the focus length of the model with the RMSE measurements will provide an upper bound of the point-wise errors. In other words, RMSE is a more conservative, efficient, and clinically relevant version of the conventional metrics. Ventricular volumes were also computed for the manually segmented and the automatically tracked endocardial surfaces. Finally, relative λ difference maps were generated at end systole (ES), providing a direct quantitative comparison of ventricular geometry. These maps were visualized with iso-contour lines, representing the fractional difference in λ position between the two surfaces.

Results

Overall Performance

As mentioned in the previous section, the regional-based tracking algorithm was initialized by manual tracing of the first frame (end-diastolic (ED) frame) for each of the 40 data sets. Then the endocardium was automatically tracked throughout the entire cardiac cycle, which provided 444 frames in total where endocardial surface from both manual tracing and automated tracking were available. A sample result from one data set is shown in Figure 2. The time course of RMSE for this data set is graphed in Figure 2a, which shows small absolute errors (below 0.07 ~ 7%) despite error accumulation as previously observed in (Duan, Angelini 2005). Time courses of the LV volumes estimated from manual tracing (solid line) and tracking (dashed line) are shown in Figure 2b. These two measures were very close especially during the systolic phase except for the last 2–3 frames where accumulated errors became larger. Hammer mapping of the percent relative surface discrepancy at end-systole (ES) is shown in Figure 2c. For this data set, 96.7% of the entire endocardial surface generated from algorithm tracking had less than 10% difference when compared to the manually traced surface.

Figure 2.

(a–c) Example results from one data set: (a) root mean squared error (RMSE) of absolute differences in λ over one cardiac cycle; (b) LV volumes from manual tracing (solid line), and OF tracking (dashed line) over one cardiac cycle; and (c) Relative difference maps between OF and manual tracing surfaces at end systole showing most of the surface under 10% (i.e. 0.1) difference.

Across all 444 frames, the mean value of the RMSE was 0.05 with a standard deviation of 0.023540. The maximum RMSE value was 0.14. Regarding volume measurements, the mean difference in estimated volume for all 444 frames was 3.93 ml with a standard deviation of 2.54 ml. The maximum difference in volume estimation was 13.59 ml. There was a strong correlation between volume measurements from region-based tracking and manual tracing with a correlation coefficient r = 0.93 (r² = 0.86) and a slope of 0.79 with a bias of 9.8 ml. The regression plot and corresponding Bland-Altman plot are shown in Figure 3(a, b). Average computational time for tracking each frame was 9 seconds with a standard deviation of 0.12 seconds and a maximum value of 9.2 seconds. All computations were implemented in C programming language and executed on a 2.4GHz 64-bit AMD single processor server, running Red Hat Linux Enterprise AS.

Figure 3.

Volume comparisons between manual tracing and region-based tracking: (a, b) overall performance with regression plot (a) and Bland-Altman statistical analysis (b); (c, d) performance on normal group with regression plot (c) and Bland-Altman statistical analysis (d); (e, f) performance on ischemia group with regression plot (e) and Bland-Altman statistical analysis (f); Each blue circle represents a single data point; the center black line represents the mean value; and the two red dashed lines represent 95% confidence interval.

Comparison to Inter-Observer Variability

Since it is difficult to define an absolute “gold standard” for the position of the endocardium, we used an alternate approach to validate our method. Our hypothesis is that region-based tracking of the endocardium from RT3D ultrasound can achieve comparable accuracy to human observer variability. We tested whether the difference between an algorithm-tracked surface and the corresponding manual tracing was comparable to the difference between two surfaces traced by separate experienced users, i.e. inter-observer variability.

In order to quantify inter-observer variability, 12 data sets were randomly selected from the total 40 data sets. The end-diastolic frame for each data set was traced by two cardiologists using separate customized software. All traced surfaces were reconstructed using the methods described above and differences in surface positions and LV volumes were measured at ED. The reference tracings were similar to those used in the previous section.

On all 12 data sets, the mean value of the RMSE between the two cardiologists was 0.15 with a standard deviation of 0.14. The maximum RMSE value was 0.59. The mean difference in estimated volumes for all frames was 11.83 ml with a standard deviation of 9.64 ml. The maximum difference in volume estimation was 27.84 ml.

Region-based tracking provided smaller mean and standard deviation values for both RMSE and volume differences. Maximum RMSE and volume error values from region-based tracking were comparable to mean inter-observer volume differences. To test the hypothesis that the performance of region-based tracking was comparable to inter-observer errors, RMSE values between region-based tracking and manual tracing were compared to RMSE values between two experienced users’ tracing by a two-sample t-test. Since our hypothesis is that region-based tracking has comparable performance with human expert tracing, in terms of RMSE values, the null hypothesis for the statistical test was that RMSE values from region-based tracking had larger mean value than mean RMSE value from a human expert (a left-tail test), i.e. region-based tracking had worse performance than an expert. Variances for both methods were not assumed equal for the purpose of fairness. The t-test with α=0.05 yielded a result of rejecting the null-hypothesis with a p-value of 0.018, which indicates that statistically, region-based tracking is unlikely to have worse performance than manual tracing by multiple experts.

Performance Comparison on Baseline versus Occlusion

To test the performance of region-based tracking on diseased cases with altered wall motion, we compared the ability of region-based tracking to track the endocardium on baseline data sets and during regional ischemia. It is clinically essential that computer-aided diagnostic tools perform well on abnormal data, which is not often addressed or tested in clinical studies evaluating the performance of such tools.

The recorded 444 data frames were divided into two groups, a normal group (224 frames) and an ischemia group (220 frames). Statistics on surface discrepancies and volume differences for each group are reported in Table 1.

Table 1.

Statistics of surface discrepancies and volume differences for the normal group and the ischemia group

	Normal Group	Ischemia Group
Mean RMSE	0.06	0.05
STD RMSE	0.03	0.02
Max RMSE	0.14	0.10
Mean Volume Difference (ml)	4.24	3.61
STD Volume Difference (ml)	2.65	2.38
Max Volume Difference (ml)	13.59	11.48

To evaluate the difference in mean values of RMSE and volumes for each group, two-sample t-tests with α=0.05 were performed on RMSE values and volume differences. Abnormal data showed significantly lower RMSE and volume differences than normal data (p=5.97e−14 and 0.0085, respectively). An additional statistical power analysis yielded 100% power for RMSE values and 75.22% power for volume differences to detect the difference in the discrepancy measurement between the two groups with a two-sided t-test with type I error level of 0.05. These results suggest that our method may be valuable for clinical applications where abnormal wall motion may be present.

Results of regression plots and Bland-Altman plots for left ventricular volume measures for normal group and ischemia group were plotted in Figure 3(c–f). The 95% confidence interval is defined with a center value equal to the mean error and width equal to two standard deviations of the volume errors. These error intervals were equal to 2.55 ml ± 8.62 ml for normal group and 1.85 ml ± 7.83 ml.

To best summarize the results for the volume comparisons between the overall manual and OF tracings, the inter-observer results and the two comparisons between manual and OF tracings for the normal and ischemia subgroups, five metrics for each study including regression equation, correlation, standard error of the estimate, mean difference, and limit of agreement and P-value of the t-test, were presented in Table 2.

Table 2.

Correlation measures and statistical differences: Volume comparisons between the overall manual tracing and region-based tracking, inter-observer variability and comparisons between manual tracing and region-based tracking for the normal and ischemia subgroups

Study	Regression equation	Correlation	Standard error of the estimate	Mean difference	P-Value
Overall	y =0.79x + 9.81	0.93	3.23	10.88	0.001
Interobserver	y =1.23x − 3.70	0.54	12.96	15.78	0.16
Normal	y=0.75x+10.48	0.91	3.30	10.26	0.005
Ischemia	y=0.78x+10.93	0.92	3.03	9.65	0.034

Discussion

Based on the presented quantitative validation studies, results on comparison between OF tracking and manual tracing were very encouraging. A strong correlation pattern between manual tracing and region-based tracking was found with correlation coefficients as well as the slope and the bias values comparable to findings in the literature (Angelini, Homma 2005, Corsi, Borsari 2001, Sanchez-Ortiz, Wright 2002) on RT3D ultrasound segmentation.

Tracking errors were within the range of inter-observer variability, which were confirmed by statistical tests. Although the mean values of RMSE and volume differences from region-based tracking were smaller than from two experienced users, it cannot be inferred that region-based tracking had better performance. One reason that the errors for the proposed method were lower was that the region-based tracking was initialized by the user whose tracing was compared to. If tracking errors were within the range of inter-observer variability, it is nonetheless safe to conclude that when initialized using manual tracing of the ED frame, region-based tracking is a good alternative to tracing every time frame in a RT3D ultrasound study.

The reason that region-based tracking performed better in the ischemia data compared to the normal data was probably related to the reduced motion due to ischemia, which made tracking easier. However, this is an important feature compared with shape-based segmentation algorithms, for which abnormal wall motion sometimes generates abnormal shapes that would complicate the segmentation process.

Minimal computational time was required for analysis, with region-based tracking requiring less than 2 minutes to track the endocardial surface over the entire cardiac cycle, compared to the time required for manual tracing by a cardiologist (one hour). This computational time is reasonable for processing RT3D ultrasound data sets in a clinical setting. While measurements of fractional shortening or ejection fraction require only ED and ES time frames, region-based tracking may be particularly useful for LV synchrony analysis, which requires the segmentation of the entire cardiac cycle.

Although current RT3D ultrasound can offer 20–25 frames per second, as reported in the acquisition set up of the data used in this paper, the actual number of frames per cardiac cycle is limited by the heart rate as well. In most clinical settings, RT3D ultrasound usually can provide 16–20 frames per cardiac cycle. Under animal experiments, especially during some depressed situations such as open chest experiments, the heart rate increases to 110–130 bpm on average so that actual frames available in one cardiac cycle become limited. Moreover, current 3D technology cannot reach a frame rate above hundred frames per second as in 2D echocardiography. These screening constraints remain limiting factors in the application of RT3D ultrasound for motion analysis. Moreover, this limitation is not an intrinsic limitation for the region-based tracking but rather a limitation of current RT3D ultrasound technology. Region-based tracking can work with higher frame rate as well. As the advances of RT3D ultrasound technology, the performance of the proposed framework will also be expected to improve given the higher temporal resolution of the data.

As pointed out in (Bland and Altman 1986), regression analysis alone is not sufficient to validate the performance of novel clinical measurements such as region-based tracking of the endocardium. For this reason, statistical analyses including t-test and power analysis were also included in the evaluation of our method, which all yielded consistent results.

Lastly, this study was focused on validating the tracking ability of the region-based tracking algorithm. The displacement field, a by-product of the tracking, also provided novel 4D dynamic cardiac information that may be useful for analyzing RT3D ultrasound data. Detailed discussion on this extension of the method can be found in (Duan, Angelini 2007, Duan, Angelini 2006, Duan, Angelini 2005).

Conclusion

A correlation-based tracking method was evaluated for its ability to track the LV endocardial surface over the entire cardiac cycle in RT3D ultrasound after being initialized with manual segmentation of the ED frame. Endocardial surface geometries obtained from manual segmentation and region-based tracking were compared at every time frame in the cardiac cycle. This geometric comparison was mapped and results were promising, showing that region-based tracking closely followed the endocardial surface throughout the entire cardiac cycle on 444 data frames. There was a strong correlation between region-based tracking and manual tracing. Statistical analysis showed that tracking errors were within the range of inter-observer variability with manual tracing by expert cardiologists. Moreover, our algorithm performed well both on normal and ischemia data, suggesting that our method may be valuable for clinical applications where abnormal wall motion may be present. This study showed that region-based tracking can accurately track the LV endocardial surface, yielding dynamic information from RT3D ultrasound data and provides automated dynamic interpolation between segmented endocardial surfaces.