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Tracking of Left Ventricular Long Axis From Real-Time Three-Dimensional Echocardiography Using Optical Flow Techniques F. Veronesi, C. Corsi, E. G. Caiani, A. Sarti, and C. Lamberti

Abstract—Two-dimensional echocardiography (2DE) is routinely used in clinical practice to measure left ventricular (LV) mass, dimensions, and function. The reliability of these measurements is highly dependent on the ability to obtain nonforeshortened long axis (LA) images of the left ventricle from transthoracic apical acoustic windows. Real time three-dimensional echocardiography (RT3DE) is a novel imaging technique that allows the acquisition of dynamic pyramidal data structures encompassing the entire ventricle and could potentially overcome the effects of LA foreshortening. Accordingly, the aim of this paper was to develop a nearly automated method based on optical flow techniques for the measurement of the left ventricular (LV) LA throughout the cardiac cycle from RT3DE data. The LV LA measurements obtained with the automated technique has been compared with LA measurements derived from manual selection of the LA from a volumetric display of RT3DE data. High correlation (r = .99, SEE = 1.8%, y = .94x + 5.3), no significant bias (−0.18 mm), and narrow limits of agreement (SD: 1.91 mm) were found. The comparison between the LA length derived from 2DE and RT3DE data showed significant underestimation of the 2DE based measurements. In conclusion, this study proves that RT3DE data overcome the effects of foreshortening and indicates that the method we propose allows fast and accurate quantification of LA length throughout the cardiac cycle. Index Terms—Foreshortening, left ventricle (LV), long-axis (LA), optical flow, real time 3-D echocardiography (RT3DE).

I. INTRODUCTION N CLINICAL practice, two-dimensional transthoracic echocardiography (2DE) is considered as the standard screening technique for the evaluation of left ventricular (LV) morphology and function. Quantitative analysis of 2DE images is based on the detection of the LV endocardial and epicardial contours and on the extraction of the LV long axis (LA) length. Then, geometrical models can be applied to derive LV volumes, ejection fraction, and mass [1], [2]. Moreover, LV shortening in the long axis direction, defined as the difference between the LA length at end distole and at any other instant in the cardiac cycle, is considered as an index of LV global and systolic function [3]–[6]. Therefore, an incorrect evaluation of LA length

I

Manuscript received January 31, 2005; revised May 18, 2005. F. Veronesi is with the Bioengineering Department, Polytechnic of Milan, Milan, Italy and with the University of Bologna, Department of Electronics, Computer Science and Systems, Bologna, Italy (e-mail: [email protected] unibo.it). C. Corsi, A. Sarti, and C. Lamberti are with the Department of Electronics, Computers Science and Systems, University of Bologna, Bologna, Italy (e-mail: [email protected]; [email protected]; [email protected]). E. G. Caiani is with the Polytechnic of Milan, Bioengineering Department, Milan, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TITB.2005.855535

can affect the estimates of clinical parameters derived from its measurement. The measurement of the LA from 2DE is highly dependent on the ability to obtain nonforeshortened long-axis images from apical acoustic windows, which in many patients is compromised by limited access to the LV apex through the intercostal spaces. Moreover, this measurement is subjective and time consuming. Recently, transthoracic real time three-dimensional echocardiographic (RT3DE) imaging [7], [8] has been developed. This system allows fast acquisition of 3-D high quality datasets from a single acoustic window, thus potentially avoiding apical foreshortening. Nevertheless, in clinical practice, the available analysis techniques of RT3DE data are still based on 2-D manual tracings of LV contours on manually selected slices [9]–[11]. In a recent paper [11], the importance of the selection of the most anatomically correct nonforeshortened apical view from the RT3DE data to obtain a correct estimate of LV mass has been stressed, and the major cause of underestimation of LV mass by 2DE has been proved to be apical foreshortening. Actually, the offline selection of the nonforeshortened apical view is performed manually, by interactively adjusting the projections along three orthogonal planes [11]. Even if this procedure resulted in high accuracy of the extracted measurements, it is still manual and consequently time consuming, and thus its application is limited to the analysis of end-diastolic (ED) and end-systolic (ES) frames only for the computation of LV volumes and mass. We hypothesized that a nearly automated identification of the LV long axis from RT3DE data along the cardiac cycle could provide the basis for an automated quantification of LV shortening, thus reducing manual interaction in the selection of anatomically correct, nonforeshortened apical views. Accordingly, the aim of this study was to develop a nearly automated method, based on optical flow techniques [12], [13], to detect frame-by-frame the LV LA. To validate our technique, automated LA measurements were compared to the corresponding measurements derived from manual selection of the LA from a volumetric display of RT3DE data and, to demonstrate the improvements achieved analyzing RT3DE data, our results were compared with those manually obtained from 2DE and from the 2-D analysis of RT3DE data. II. METHODS The proposed procedure requires two steps: 1) for one frame in the cardiac cycle, the operator manually selects five points

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VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

Fig. 1. Detection of the center of the mitral valve: the operator selects the long-axis plane in which the mitral annulus is best visualized (left) and selects two points (A and B) where the anterior and posterior mitral leaflets are attached to the annulus. On the orthogonal plane (center) passing through the center of the segment AB (M), two additional mitral annulus points (C and D) are chosen. The center of the mitral annulus is computed as the center of the segment CD.

from which the LV LA position in the 3-D space is automatically derived; 2) the optical flow approach [12], [13] is applied to automatically follow the LA position throughout the cardiac cycle. A. Manual Initialization In order to evaluate the LV LA position, the coordinates of the points representing the center of the mitral annulus and the apex of the LV chamber need to be determined on one frame. Twelve cross sectional long axis views (15◦ apart) are displayed to allow the operator to select the projection in which the mitral annulus was best visualized. Then, on the selected plane, the operator manually selects two points A and B, where the anterior and posterior mitral leaflets are attached to the annulus; two additional points, C and D, are then selected in correspondence to the mitral annulus, on a second plane perpendicular to the first one and passing through the center M of the line connecting A and B. Finally, the center of the mitral annulus is calculated as the center of the line connecting the points C and D (see Fig. 1). Theoretically, more than four points could be chosen by the operator in order to find the mitral valve center, but this would be time consuming with likely no appreciable improvements in the center computation. From a volumetric visualization of the LV chamber, the lower tip of the LV is chosen as the apex. The straight line connecting these two points is considered as the initial LV long axis position for this particular time frame (Fig. 2, panel A).

Fig. 2. Examples of the long axis rendered from volumetric display of RT3DE (panel A) and from manual analysis of RT3DE (panel B) and 2DE data (panel C).

algorithm in the 3-D space and the region matching techniques [12], [13]; this allows independent calculation of the long axis of the ventricle for each consecutive frame. Differential optical flow techniques are based on the gradient constraint equation proposed by Horn and Shunck [14] ∇I(x, t) · v + It (x, t) = 0

x∈Ω

where Ω is the domain containing the neighborhood of x and W (x) is a three-dimensional window that gives more relevance to central terms rather than the ones in the periphery. At the time t the window W (x) contains λ points xi ∈ Ω and it has the size L × L × L voxels. In matrix form, the solution of the minimization (2.2) is given by AT W2 Av = AT W2 b

(2.3)

where A = [∇I(x1 ), . . . , ∇I(xλ )] , W = diag [∇W (x1 ), . . . , ∇W (xλ )], b = −(It (x1 ), . . . , ∇It (xλ ))T . The solution of (2.3) is obtained by isolating v T

v = [AT W 2 A]−1 AT W 2 b

(2.1)

where I(x, t) represents the brightness of the point x at the time t, It (x, t) is its partial time derivative and v = (u, v, w)T is the unknown velocity to be determined. In order to solve this equation, the brightness conservation assumption dI(x, t)/dt = 0 is considered fulfilled. To evaluate the velocity v, Lucas and Kanade [13] proposed using a weighted least-square implementation that has the computational advantage of considering a small window instead of the whole image. Following this suggestion, (2.1) is minimized using (2.2) W 2 (x)[∇I(x, t) · v + It (x, t)]2 (2.2)

B. Point Tracking The two mitral points, C and D, whose middle point is the center of the mitral valve, and the apex are subsequently tracked for each frame in the cardiac cycle applying the Lucas–Kanade

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(2.4)

and solved in closed form if AT W 2 A is nonsingular; in the three-dimensional case this matrix can be written as shown in (2.5) at the bottom of the page.

2 2 W (x)Ix2 (x) W (x)Ix (x)Iy (x) AT W 2 A = W 2 (x)Iy (x)Ix (x) W 2 (x)Iy2 (x) W 2 (x)Iz (x)Iy (x) W 2 (x)Iz (x)Ix (x)

2 W 2 (x)Ix (x)Iz (x) W (x)Iy (x)Iz (x) W 2 (x)Iz2 (x)

(2.5)

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Once the velocity is known, it is possible to determine the position of the starting point xt , into the next frame xLK = xt + [dLK ]

(2.6)

where dLK = v∆t is the displacement and [·] represents the rounding operator applied to obtain integer values for the components dx, dy, and dz in case of noninteger coordinates. Since echocardiographic images are characterized by a high level of noise, differential techniques, such as the one previously described, may be inappropriate if used alone and may lead to an inaccurate point detection. Therefore, we additionally implemented the region based matching technique. A threedimensional window V(xLK ) of dimensions N × N × N voxels, whose center is the point xLK found by applying the Lucas– Kanade optical flow, is considered. For each point inside this window, another window F(x) of dimensions M × M × M voxels is defined and compared to the window of the same size around the point, xt , F(xt ) by means of the sum of the squared difference (SSD) φ(xt+1 ) =

m m m

F (i, j, k)

i=−m j =−m k =−m

C. Population and Data Acquisition Patients were included in the study if they had adequate transthoracic acoustic window that allowed adequate endocardial visualization without contrast enhancement: following this criterion, ten patients were enrolled. Transthoracic RT3DE imaging was performed from the apical window, with the patient in the left lateral decubitus position, using a commercial ultrasound scanner (SONOS 7500, Philips Medical Systems, Andover, MA) equipped with a fully sampled matrix array transducer (X4, 2–4 MHz) working in the harmonic mode. RT3DE datasets were acquired using the wide-angled acquisition mode, wherein four wedge-shaped subvolumes (93◦ × 21◦ ) were acquired over four cardiac cycles during a breath-hold with ECG gating. Acquisition of each subvolume was triggered to the R-wave of every other heartbeat in order to allow sufficient time for the probe to be recalibrated and each subvolume stored. Care was taken to include the entire LV cavity within the pyramidal 3-D scan volume. RT3DE datasets were stored digitally for offline analysis. In addition to RT3DE acquisition, 2-D images were acquired at held respiration from apical 2- and 4-chamber views while care was taken to avoid foreshortening, and stored digitally.

× [It (xt + (i, j, k)) − It+1 (xt+1 + (i, j, k))]2 . (2.7) For each point inside V(xLK ), the function ϕ(xt+1 ) is evaluated and the point corresponding to the minimum value of ϕ(xt+1 ) is the one that best fitted the window around the starting point, and thus it was considered as the resulting point of the algorithm i for xiLK ∈ V(xLK ). xﬁnal t+1 = arg min φ xLK The final location of the starting point xt is xﬁnal t+1 = xLK + dM = xt + [dLK ] + dM

(2.8)

where dM is the displacement evaluated using the region-based matching. These procedures were applied to the points manually selected in the first frame to estimate their coordinates throughout the cardiac cycle. Each frame was analyzed starting from the points obtained in the previous frame. Importantly, since in the detection of the points, increasing distance involves increasing error, the a priori knowledge that the cardiac sequences were loops was considered: the manually initialized frame was used as the starting frame for half of the frames in the cardiac cycle, going forward and backward in the temporal sequence. In this way, the analysis was performed throughout half of the frames in the cine-loop, resulting in a more accurate tracking. For each frame, from the tracked points the center of the mitral valve was computed as described in Fig. 1, and connected to the point corresponding to the LV apex, thus defining the LA. Then, the LA length was calculated as the geometrical distance between its extremities.

D. Data Analysis Manual Analysis: The RT3DE datasets were analyzed with commercial software (3DQ-QLab, Philips). The pyramidal volume data were displayed in 3 different cross sections; the anatomically correct 2- and 4-chamber views with the largest long-axis dimensions were selected as described in [11]. For each view, the points of insertion of the mitral leaflets into the annulus were connected by a straight line, and the LV long-axis dimension was measured as the distance between the center of this line and the most distal point at the apical endocardium. Then, the LV LA measurement was obtained as the average of the two measurements, relevant to apical 2- and 4- chamber views. This procedure was applied to the ED frame (Fig. 2, panel B). Moreover, from a volumetric visualization of the RT3DE data, the operator manually selected the LA for each frame throughout the cardiac cycle. This resulted in LA length-time curve. 2DE images were also analyzed. For both apical 2- and 4-chamber views, the ED frame was selected as the image with the largest LV cavity, and the LA was calculated as the distance between the LV apex and LV base as defined by the manually traced endocardial contours (EnConcert, Philips) (Fig. 2, panel C). Automated Analysis: The RT3DE datasets were analyzed using the proposed procedure for point tracking based on optical flow and the region based matching. One frame was used to manually initialize the position of the points to be tracked along the cardiac cycle. For each frame, the position of the initialized points was determined as a result of the optical flow algorithm and used to compute the LV LA length throughout the cardiac cycle.

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E. Statistical Analysis To evaluate the performance of the automated technique compared to the manual analysis of RT3DE, linear regression and Bland-Altman analyses were computed. Moreover, a paired ttest (p < 0.05) was applied to verify the presence of no differences, discrepancies, or suspiciously outlying results due to random and not systematic errors. In addition, for each subject, percent discordance between the manually obtained and the automatically computed LA length was calculated throughout the cardiac cycle for each pair of LA measurements as their point-by-point sum of absolute differences, normalized by the point-by-point sum of manual values. Accumulated position error of points tracking throughout a complete cardiac cycle was computed for the apex and the center of the mitral valve. The locations of the apex and of the center of the mitral valve at initial and final frames were also compared. To evaluate the effects of foreshortening as the possible source of error by the conventional 2DE analysis, in a subset of five patients, a comparison between the ED LA measurements derived from manual 2DE and RT3DE analysis, separately for both apical 2- and 4-chamber views, was carried out. Twofactor ANOVA with repeated measures (p < 0.05) was applied to test the significance of the differences between the groups of measurements; in addition, the average values of the two measurements derived from the two standard views at ED from 2DE and RT3DE were compared with the results of both volumetric manual tracing and our method performed on RT3DE data at ED, applying the one-way ANOVA test for correlated samples (p < 0.05). Mean percentage errors between the estimates and the manual values were calculated as the difference between the estimate and the manual value, divided by the manual value *100. III. EXPERIMENTAL RESULTS All the experiments were performed using MatLab 6.1 Release 12, using the following parameters settings: the 3-D window in which the Lucas-Kanade optical flow was evaluated (L) is of 9 voxels side; the best fit research was done inside a cubic window (M) of 9 voxels side; the SSD was evaluated in a cubic volume of 5 voxels side for each point belonging to previous window M. These windows were big enough to grant low noise sensitivity and small enough not to include structures different from the mitral valve that could have introduced false positive detections. The subjects had a mean frame rate of 19 frames per s (range: 14 ÷ 22 frames per second). For each subject, the RT3DE analysis with the proposed automated technique, including data retrieval, points selection in one frame only, computation of the center of the mitral valve, and dynamic tracking of the LV LA throughout the cardiac cycle, required between 1 and 2 min., depending on the number of frames in the cardiac cycle, using a personal computer (Pentium IV, 2.6 GHz, 1 Gb RAM). Conversely, the manual analysis of the 2DE and RT3DE datasets using the commercial software required about 10 min., while the LA selection from a volumetric visualization required between 4 and 6 min.

Fig. 3. Example of the results of the application of the proposed procedure based on optical flow techniques for the tracking of the center of the mitral valve throughout the cardiac cycle. Panel A: 3-D perspective of the initial frame (mitral valve closed) with the manually selected starting points and the computed center of the valve; panels B1 ÷ B6: 2-D perspectives of the tracked mitral annulus points in the cardiac cycle visualized in different long axis planes for each frame, as they correspond to the plane passing through the three aligned points and orthogonal to the transducer face.

In Fig. 3, an example of the results of the tracking of the points of insertion of the mitral leaflets along the cardiac cycle using the proposed technique is reported. Fig. 4 shows the results of the linear regression (top) and Bland–Altman analyses (bottom) between the results obtained frame-by-frame in 10 patients by volumetric RT3DE manual tracing and by the proposed automated procedure. A high correlation coefficient (r = 0.99, p < 0.05) was found, with a regression line equal to y = 0.94x + 5.3. The standard error of estimate was 1.8%. No significant bias (−0.18 mm, corresponding to −0.2% of the mean value) between the two techniques was found with narrow 95% limits of agreement (3.82 mm). The calculated percentage of discordance was 1.73% ± 0.57% (range: 0.60% ÷ 2.38%), confirming the excellent rate of agreement between the two techniques. Moreover, the paired t-test evidenced no significant differences between the two groups of measurements. In Fig. 5, an example of the LA length (black lines) over time in percentage of the heart cycle duration obtained from a RT3DE

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Fig. 5. Example of the LA length (black lines) over time in percentage of the heart cycle duration (%RR) curves obtained from a RT3DE dataset by automated analysis (with symbols, initialized frame marked with a circle) and by manual tracing (without symbols), together with the corresponding LV shortening (secondary y-axis, gray lines, with and without symbols, respectively). TABLE I LONG AXIS MEASUREMENTS DERIVED FROM 2DE AND RT3DE DATA

Fig. 4. Results of the linear regression (top) and Bland Altman (bottom) analyses of the frame-by-frame measurements of the LV LA obtained by RT3DE manual tracing versus the proposed automated procedure in the analyzed population (N = 10).

dataset by automated analysis (with symbols) and by manual tracing (without symbols) is shown, together with the corresponding LV shortening (secondary axis, gray lines). In this way, it is possible to appreciate in detail the frame-by-frame agreement of the measurements obtained with the two technique. In all analyzed subjects, mean accumulated position error computed by tracking the apex and the center of the mitral valve throughout a complete cardiac cycle resulted in 0.6 mm and 0.8 mm, respectively. The differences in the locations of the apex and of the center of the mitral valve as computed by the optical flow tracking between the initial and final frames resulted in a mean error of 0.7 mm and 2.1 mm, respectively. Table I reports the LA measurements for the ED frame, analyzing RT3DE and 2DE data for five patients. For all the measurements derived from 2DE and RT3DE obtained analyzing the 2- and 4-chamber acquisitions using the commercial software, two-factor ANOVA with repeated measures evidenced a significant underestimation of the LA derived from 2DE with respect to RT3DE measurements (p = 0.005). No significant differences between the two different views were found (p = 0.10) while a significant difference was detected considering the combination between the different type of data acquisition and the distinct views (p = 0.025). A t-test performed on the

same group of data showed significant differences (p < 0.01) between: 1) 2- and 4-chamber 2DE derived LA measurements; 2) 2-chamber 2DE and RT3DE derived LA measurements; 3) 4-chamber 2DE and RT3DE derived LA measurements. No significant differences were observed between 2- and 4-chamber RT3DE derived LA measurements (p = 0.24). LA derived from 2DE data showed a significant underestimation versus RT3DE for both the standard views (2-chamber: p = 0.008, 4-chamber: p = 0.002), with a mean percentage error of 5.5% for the 2-chamber view and of 10.3% for the 4-chamber view. In the comparison between the mean LA length values at ED derived from 2DE and RT3DE using the commercial software and the LA length values obtained by volumetric manual tracing and our method applied to RT3DE data, 2DE derived results showed significant underestimation with respect to all the RT3DE derived measurements with a mean percentage error of 7.9% (p = 0.002), 6.2% (p = 0.002), and 6.0% (p = 0.0002), respectively. The mean error between LA length obtained applying our method and by volumetric manual tracing was −0.2% (p = 0.34).

VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

IV. DISCUSSION AND CONCLUSION Although 2DE has been traditionally used for the quantification of LV morphology and function, the inadvertent imaging of foreshortened apical views could potentially result in inaccurate estimates of LV volumes and mass [11], [15], [16]. RT3DE offers the opportunity to overcome this limitation by acquiring a pyramidal dataset that can be analyzed offline to select anatomically correct, nonforeshortened apical views. As for the extraction of other cardiac parameters (LV volume, stoke volume, cardiac output, mass, wall motion) [7]–[11], the RT3DE analysis for LA measurements is performed offline after downloading the data on a dedicated PC. However, in the new ultrasound equipment recently delivered to the market (iE33), the RT3DE manual analysis software has been incorporated into the system, allowing the user to perform the quantitative analysis without the need to download the data. From this perspective, our method could be incorporated in the existing software on the system, thus avoiding the time-consuming downloading process and allowing a more straightforward, nearly automated analysis of the LV LA length and LV shortening throughout the cardiac cycle. The choice of 2DE as reference technique for LA length evaluation is due to the clinically widespread use of this technique to quantify this parameter. Other imaging techniques, such as cardiac magnetic resonance that is the reference technique for LV function evaluation, would be inappropriate because standard cardiac acquisitions are performed in the short axis view, to be able to obtain LV volumes and mass measurements by modified Simpson’s rule. In this way, only a discrete number of slices with a fixed slice thickness is acquired. Each slice contains information derived from the anatomical volume inside that thickness. Therefore, the left ventricular long axis measurement could be affected by an error up to the slice thickness. Moreover, the sequences used for cardiac studies do not allow optimal mitral annulus and leaflets visualization. The availability of tools which require minimal user interaction for RT3DE data analysis is becoming a common need from the scientific community, due to the growing diffusion of this new ultrasound equipment and its huge potential in both the research and in the clinical fields. However, currently available tools are based on a manual cross-section of the 3-D dataset, and measurements based on the 2-D approach. In particular, the computation of LV shortening in the long-axis direction over time, which is considered an important index of systolic and diastolic function [3]–[6], requires the analysis of all frames in the cardiac cycle, resulting in a tedious and cumbersome procedure. To overcome this limitation, we developed a technique for automated detection of the LV LA and the evaluation of the LV shortening throughout the cardiac cycle. The method we developed is based on optical flow techniques, that have been previously applied to calculate 2-D and 3-D cardiac motion field from a large variety of medical images [17]–[23]. However, in this study we applied the optical flow techniques from a different point of view, not to extract global motion information but to perform local analysis of the LV LA position throughout the cardiac cycle. The method we applied in this

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study combines the advantages of two distinct optical flow techniques: 1) a differential technique based on the assumption that the brightness of a pattern in the image is invariant over time, and 2) a region-based matching algorithm, that yields the best fit between image regions at different time, computed minimizing the sum of their squared differences. The application of the Lucas-Kanade algorithm in the 3-D space results in the estimate of the velocity vector that gives information about the area where the feature to be identified in the next frame belongs to. However, this estimate could be inaccurate because differential methods are based on the intensity conservation assumption and they are sensitive to noise, which is not negligible on echocardiographic data [24]. Moreover, the velocities of the tracked points are usually not integers, thus requiring a mathematical approximation of the points coordinates in the next frame. The application of the region-based matching in cascade to the differential technique allows the position of the points to be accurately estimated, thus avoiding approximations. In order to evaluate the points displacement, the application of the region-based matching algorithm without the first step would require the use of bigger windows, thus increasing the chance to find the best fit in correspondence to a point far from the desired one. The comparison among the performance of different optical flow techniques applied to RT3DE data is beyond the scope of this study; however, our simulations performed applying the two techniques separately resulted in an unsatisfactory tracking. This novel combination of two existing techniques resulted in an effective and fast points tracking that could be applied to any type of 3-D data. Our results showed that the extraction of the LA length throughout the cardiac cycle applying the proposed technique is feasible and requires minimal user interaction, by selecting few anatomical points in one frame only. Direct point-by-point comparison of automatically extracted LA measurements with those obtained by manual analysis, considered as the reference technique for comparison, showed excellent agreement, minimal bias, and very low percent discordance. The integration of the 3-D application of optical flow techniques to volumetric data acquired in real time allowed us to overcome foreshortening. As previous studies show, tangential scan plane cannot be avoided [25] [26]: despite the care taken to avoid foreshortening during the acquisition, in all the patients for which 2DE data were available, the LA evaluation at ED using commercial software resulted in a significant underestimation of LA length compared to RT3DE and obviously in an incorrect evaluation of derived parameters. The two different LA length values obtained manually analyzing RT3DE data can be explained considering that the selection of the 2- and 4-chamber views is performed without exploiting the additional volumetric information available in the RT3DE data. However, the possibility to select nonforeshortened orthogonal 2-D apical views in the 3-D data potentially improves the LA measurements even if this procedure does not take into account the real complex shape of the mitral annulus. The result of the two-factor ANOVA with repeated measures for these data showed that this underestimation is due to the different type of data, and there is no dependence on the different views.

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But the combination between the different type of data and the distinct views showed a significance that could be explained by the results of the t-test performed on the 2DE data considering the two views that evidenced a significant difference between the LA measurements. The additional results obtained considering the volumetric measurements confirmed the significance of differences between 2DE and RT3DE derived results. As RT3DE data analysis has been shown to provide better correlation with magnetic resonance imaging compared to 2DE analysis for LV morphology and function quantification [11], our results show the potential utility of our algorithm for the quantification of LV LA shortening. In fact, both the reduction in user interaction and the time required for the analysis could allow this quantification to be conducted in clinical settings. Moreover, this tracking procedure could represents the basis for the development of more complex analysis tools applied to RT3DE data, such as the tracking of the valvular annulus for quantification of shape changes due to pre- and post-surgical intervention, or a 3-D analysis of the kinesis of the ventricular base.

[11]

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[16]

[17] [18]

ACKNOWLEDGMENT The authors would like to thank R. M. Lang, M. D., V. Mor-Avi, Ph.D., and L. Weinert, of the Noninvasive Cardiac Imaging Laboratories, University of Chicago Medical Center, for their invaluable contributions.

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of cardiac volumes and function using semi-automatic border detection and comparison with cardiac magnetic resonance imaging,” J. Am. Coll. Cardiol, vol. 43, no. 11, pp. 2083–2090, Jun. 2004. V. Mor-Avi, L. Sugeng, L. Weinert, P. MacEneaney, E. G. Caiani, R. Koch, I. S. Salgo, and R. M. Lang, “Fast measurement of left ventricular mass with real-time three-dimensional echocardiography: Comparison with magnetic resonance imaging,” Circulation, vol. 110, no. 13, pp. 1814– 1818, Sep. 2004. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vision, vol. 12, pp. 43–77, 1994. B. D. Lucas and T. Kanade, “An interative image registration technique with an application to stereo vision,” in Proc. 7th Int. Joint Conf. Artificial Intelligence,Vancouver, BC, Canada, pp. 674–679. B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell., vol. 17, pp. 185–203, 1981. M. L. Chuang, R. A. Beaudin, M. F. Riley, M. G. Mooney, W. J. Mannin, P. S. Douglas, and M. G. Hibberd, “Three-dimensional echocardiographic measurement of left ventricular mass: Comparison with magnetic resonance imaging and two-dimensional echocardiographic determinations in man,” Int. J. Card. Imaging, vol. 16, no. 5, pp. 347–357, Oct. 2000. S. G. Myerson, H. E. Montgomery, M. J. World, S. E. Humphries, and D. J. Pennell, “Left ventricular mass reliability of M mode and 2-dimensional echocardiographic formulas,” Hypertension, vol. 40, pp. 673–678, 2002. S. C. Amartur and H. J. Vesselle, “A new approach to study cardiac motion: The optical flow of cine MR images,” Magn. Reson. Med., vol. 29, no. 1, pp. 59–67, Feb. 1993. V. Behar, D. Adam, P. Lysyansky, and Z. Friedman, “Improving motion estimation by accounting for local image distortion,” Ultrasonics, vol. 43, no. 1, pp. 57–65, Nov. 2004. L. Dougherty, J. C. Asmuth, A. S. Blom, L. Axel, and R. Kumar, “Validation of an optical flow method for tag displacement estimation,” IEEE Trans. Med. Imag., vol. 18, no. 4, pp. 359–363, May 1999. J. M. Gorce, D. Friboulet, and I. E. Magnin, “Estimation of threedimensional cardiac velocity fields: Assessment of a differential method and application to three-dimensional CT data,” Med. Image Anal., vol. 1, no. 3, pp. 245–261, May 1997. G. J. Klein and R. H. Huesman, “Four-dimensional processing of deformable cardiac PET data,” Med. Image Anal., vol. 6, no. 1, pp. 29–46, Apr. 2002. R. Noumeir, G. E. Mailloux, and R. Lemieux, “Detection of motion during tomographic acquisition by an optical flow algorithm,” Comput. Biomed. Res., vol. 29, no. 1, pp. 1–15, Mar. 1996. J. L. Prince, S. N. Gupta, and N. F. Osman, “Bandpass optical flow for tagged MRI,” Med. Phys., vol. 27, no. 1, pp. 108–118, Feb. 2000. P. Baraldi, A. Sarti, C. Lamberti, A. Prandini, and F. Sgallari, “Evaluation of differential optical flow techniques on synthesized echo images,” IEEE Trans. Biomed. Eng., vol. 43, no. 3, pp. 259–272, Mar. 1996. R. Erbel, P. Schweizer, H. Lambertz, G. Henn, J. Meyer, W. Krebs, and S. Effert, “Echoventriculography—A simultaneous analysis of twodimensional echocardiography and cineventriculography,” Circulation, vol. 67, no. 1, pp. 205–215, Jan. 1983. S. Muller, T. Bartel, M. A. Katz, O. Pachinger, and R. Erbel, “Partial cutoff of the left ventricle: Determinants and effects on volume parameters assessed by real-time 3-D echocardiography,” Ultrasound Med. Biol., vol. 29, no. 1, pp. 25–30, Jan. 2003.

F. Veronesi received the Doctoral degree in electronic engineering from the University of Bologna, Bologna, Italy, in 2004. He is currently working towards the Ph.D. degree at the Bioengineering Department, Polytechnic of Milan, Milan, Italy. His research activity, now at the Department of Electronics Informatics and Statistics (DEIS) of Bologna, is focused on biomedical image processing, with particular interest on parameters extraction from 3D cardiac imaging data.

VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

C. Corsi received the M.S. degree in electronic engineering from the University of Bologna, Bologna, Italy, in 1997 and the Ph.D. degree in bioengineering from the Department of Electronics, Computer Science and Systems, University of Bologna, in 2001. She spent six months visiting the Mathematics Department, University of California, Berkeley, and the Math Department at the Lawrence Berkeley National Laboratory, Berkeley, working on level set methods applied to medical data processing. Since 2004, she has been collaborating with the Noninvasive Cardiac Imaging Laboratories, University of Chicago as a Research Associate. Actually, she holds a Postdoctoral Research Grant at University of Bologna. Her research interests include new expertized and advanced technologies and methods, applied to medical data processing, in particular, echocardiographic and magnetic resonance data.

E. G. Caiani was born in Monza in 1970. He received the M.S. degree in electronic engineering and the Ph.D. degree in biomedical engineering from the Politenico di Milano, Milan, Italy, in 1996 and 2000, respectively. Since 2000, he has been collaborating with the Noninvasive Cardiac Imaging Laboratories, University of Chicago, where he worked as a Research Associate in 2000 and 2003, respectively. He is with the Department of Biomedical Engineering, Politecnico di Milano, as a Researcher. His interest consists in the development of processing techniques to quantify indices of cardiac function and perfusion from cardiac imaging data, and in space-related applications. Dr. Caiani received the "Rosanna Degani Young Investigator Award" from the IEEE Computers in Cardiology.

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A. Sarti was born in Modena, in 1964. He received the Laurea degree (cum laude) in electronic engineering from the University of Bologna, Bologna, Italy, in 1992, and the Ph.D. degree in bioengineering from the University of Bologna, in 1996. From 1997 to 2000, he was appointed with a Postdoc position at the Mathematics Department, University of California, Berkeley and the Math Department of the Lawrence Berkeley National Laboratory, Berkeley, working in the group of J. Sethian and A. Chorin. Since 2001, he has been with the University of Bologna, where he teaches classes in bioimaging. In 2003, he was also appointed as Maitre de Recherche at CREA, Ecole Polytechnique, Paris. He wrote more then 80 pubblications in the field of computer vision, medical imaging, and biologically based models of visual perception. With G. Citti, he is responsible for the Gruppo Interdipartimentale di Visione, an interdisciplinary group comprehending the Dipartmento di Elettronica, Informatica e Sistemistica and the Dipartimento di Matematica at the Bologna University. In the last three years, he gave lectures at Yale University, UC Los Angeles, UC Berkeley, Freie Universitat Berlin, Ecole Normale Superieure Cachan, Palazzone di Cortona Scuola Normale Superiore di Pisa.

C. Lamberti received the Doctoral degree in mechanical engineering from the University of Bologna, Bologna, Italy, in 1974 and the Postgraduate degree in biomedical technology from the University of Bologna School of Medicine, in 1978. He is currently an Associate Professor at the Department of Electronics, Computer Science and Systems, University of Bologna. Since 1991, he is in charge at University of Bologna of the course Computer and Systems Science in Health Care. His research activity is focused on biomedical signal and image processing and biomedical technology assessment. He has served on the Board of the Centro Ricerche e Studi Tecnologie Biomediche e Sanitarie (CRSTBS) at Scientific Park of Trieste (Italy) during 1989– 1998. He has also served on the Board of the Associazione Italiana degli Ingegneri Clinici (AIIC) since 1993. He has published several papers on arrythmias recognition, left ventricular wall motion, echocardiography image processing, estimation of motion in 3-D echocardiography, computeraided virtual surgery, and computer systems for management of biomedical technology.

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IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 10, NO. 1, JANUARY 2006

Tracking of Left Ventricular Long Axis From Real-Time Three-Dimensional Echocardiography Using Optical Flow Techniques F. Veronesi, C. Corsi, E. G. Caiani, A. Sarti, and C. Lamberti

Abstract—Two-dimensional echocardiography (2DE) is routinely used in clinical practice to measure left ventricular (LV) mass, dimensions, and function. The reliability of these measurements is highly dependent on the ability to obtain nonforeshortened long axis (LA) images of the left ventricle from transthoracic apical acoustic windows. Real time three-dimensional echocardiography (RT3DE) is a novel imaging technique that allows the acquisition of dynamic pyramidal data structures encompassing the entire ventricle and could potentially overcome the effects of LA foreshortening. Accordingly, the aim of this paper was to develop a nearly automated method based on optical flow techniques for the measurement of the left ventricular (LV) LA throughout the cardiac cycle from RT3DE data. The LV LA measurements obtained with the automated technique has been compared with LA measurements derived from manual selection of the LA from a volumetric display of RT3DE data. High correlation (r = .99, SEE = 1.8%, y = .94x + 5.3), no significant bias (−0.18 mm), and narrow limits of agreement (SD: 1.91 mm) were found. The comparison between the LA length derived from 2DE and RT3DE data showed significant underestimation of the 2DE based measurements. In conclusion, this study proves that RT3DE data overcome the effects of foreshortening and indicates that the method we propose allows fast and accurate quantification of LA length throughout the cardiac cycle. Index Terms—Foreshortening, left ventricle (LV), long-axis (LA), optical flow, real time 3-D echocardiography (RT3DE).

I. INTRODUCTION N CLINICAL practice, two-dimensional transthoracic echocardiography (2DE) is considered as the standard screening technique for the evaluation of left ventricular (LV) morphology and function. Quantitative analysis of 2DE images is based on the detection of the LV endocardial and epicardial contours and on the extraction of the LV long axis (LA) length. Then, geometrical models can be applied to derive LV volumes, ejection fraction, and mass [1], [2]. Moreover, LV shortening in the long axis direction, defined as the difference between the LA length at end distole and at any other instant in the cardiac cycle, is considered as an index of LV global and systolic function [3]–[6]. Therefore, an incorrect evaluation of LA length

I

Manuscript received January 31, 2005; revised May 18, 2005. F. Veronesi is with the Bioengineering Department, Polytechnic of Milan, Milan, Italy and with the University of Bologna, Department of Electronics, Computer Science and Systems, Bologna, Italy (e-mail: [email protected] unibo.it). C. Corsi, A. Sarti, and C. Lamberti are with the Department of Electronics, Computers Science and Systems, University of Bologna, Bologna, Italy (e-mail: [email protected]; [email protected]; [email protected]). E. G. Caiani is with the Polytechnic of Milan, Bioengineering Department, Milan, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TITB.2005.855535

can affect the estimates of clinical parameters derived from its measurement. The measurement of the LA from 2DE is highly dependent on the ability to obtain nonforeshortened long-axis images from apical acoustic windows, which in many patients is compromised by limited access to the LV apex through the intercostal spaces. Moreover, this measurement is subjective and time consuming. Recently, transthoracic real time three-dimensional echocardiographic (RT3DE) imaging [7], [8] has been developed. This system allows fast acquisition of 3-D high quality datasets from a single acoustic window, thus potentially avoiding apical foreshortening. Nevertheless, in clinical practice, the available analysis techniques of RT3DE data are still based on 2-D manual tracings of LV contours on manually selected slices [9]–[11]. In a recent paper [11], the importance of the selection of the most anatomically correct nonforeshortened apical view from the RT3DE data to obtain a correct estimate of LV mass has been stressed, and the major cause of underestimation of LV mass by 2DE has been proved to be apical foreshortening. Actually, the offline selection of the nonforeshortened apical view is performed manually, by interactively adjusting the projections along three orthogonal planes [11]. Even if this procedure resulted in high accuracy of the extracted measurements, it is still manual and consequently time consuming, and thus its application is limited to the analysis of end-diastolic (ED) and end-systolic (ES) frames only for the computation of LV volumes and mass. We hypothesized that a nearly automated identification of the LV long axis from RT3DE data along the cardiac cycle could provide the basis for an automated quantification of LV shortening, thus reducing manual interaction in the selection of anatomically correct, nonforeshortened apical views. Accordingly, the aim of this study was to develop a nearly automated method, based on optical flow techniques [12], [13], to detect frame-by-frame the LV LA. To validate our technique, automated LA measurements were compared to the corresponding measurements derived from manual selection of the LA from a volumetric display of RT3DE data and, to demonstrate the improvements achieved analyzing RT3DE data, our results were compared with those manually obtained from 2DE and from the 2-D analysis of RT3DE data. II. METHODS The proposed procedure requires two steps: 1) for one frame in the cardiac cycle, the operator manually selects five points

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VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

Fig. 1. Detection of the center of the mitral valve: the operator selects the long-axis plane in which the mitral annulus is best visualized (left) and selects two points (A and B) where the anterior and posterior mitral leaflets are attached to the annulus. On the orthogonal plane (center) passing through the center of the segment AB (M), two additional mitral annulus points (C and D) are chosen. The center of the mitral annulus is computed as the center of the segment CD.

from which the LV LA position in the 3-D space is automatically derived; 2) the optical flow approach [12], [13] is applied to automatically follow the LA position throughout the cardiac cycle. A. Manual Initialization In order to evaluate the LV LA position, the coordinates of the points representing the center of the mitral annulus and the apex of the LV chamber need to be determined on one frame. Twelve cross sectional long axis views (15◦ apart) are displayed to allow the operator to select the projection in which the mitral annulus was best visualized. Then, on the selected plane, the operator manually selects two points A and B, where the anterior and posterior mitral leaflets are attached to the annulus; two additional points, C and D, are then selected in correspondence to the mitral annulus, on a second plane perpendicular to the first one and passing through the center M of the line connecting A and B. Finally, the center of the mitral annulus is calculated as the center of the line connecting the points C and D (see Fig. 1). Theoretically, more than four points could be chosen by the operator in order to find the mitral valve center, but this would be time consuming with likely no appreciable improvements in the center computation. From a volumetric visualization of the LV chamber, the lower tip of the LV is chosen as the apex. The straight line connecting these two points is considered as the initial LV long axis position for this particular time frame (Fig. 2, panel A).

Fig. 2. Examples of the long axis rendered from volumetric display of RT3DE (panel A) and from manual analysis of RT3DE (panel B) and 2DE data (panel C).

algorithm in the 3-D space and the region matching techniques [12], [13]; this allows independent calculation of the long axis of the ventricle for each consecutive frame. Differential optical flow techniques are based on the gradient constraint equation proposed by Horn and Shunck [14] ∇I(x, t) · v + It (x, t) = 0

x∈Ω

where Ω is the domain containing the neighborhood of x and W (x) is a three-dimensional window that gives more relevance to central terms rather than the ones in the periphery. At the time t the window W (x) contains λ points xi ∈ Ω and it has the size L × L × L voxels. In matrix form, the solution of the minimization (2.2) is given by AT W2 Av = AT W2 b

(2.3)

where A = [∇I(x1 ), . . . , ∇I(xλ )] , W = diag [∇W (x1 ), . . . , ∇W (xλ )], b = −(It (x1 ), . . . , ∇It (xλ ))T . The solution of (2.3) is obtained by isolating v T

v = [AT W 2 A]−1 AT W 2 b

(2.1)

where I(x, t) represents the brightness of the point x at the time t, It (x, t) is its partial time derivative and v = (u, v, w)T is the unknown velocity to be determined. In order to solve this equation, the brightness conservation assumption dI(x, t)/dt = 0 is considered fulfilled. To evaluate the velocity v, Lucas and Kanade [13] proposed using a weighted least-square implementation that has the computational advantage of considering a small window instead of the whole image. Following this suggestion, (2.1) is minimized using (2.2) W 2 (x)[∇I(x, t) · v + It (x, t)]2 (2.2)

B. Point Tracking The two mitral points, C and D, whose middle point is the center of the mitral valve, and the apex are subsequently tracked for each frame in the cardiac cycle applying the Lucas–Kanade

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(2.4)

and solved in closed form if AT W 2 A is nonsingular; in the three-dimensional case this matrix can be written as shown in (2.5) at the bottom of the page.

2 2 W (x)Ix2 (x) W (x)Ix (x)Iy (x) AT W 2 A = W 2 (x)Iy (x)Ix (x) W 2 (x)Iy2 (x) W 2 (x)Iz (x)Iy (x) W 2 (x)Iz (x)Ix (x)

2 W 2 (x)Ix (x)Iz (x) W (x)Iy (x)Iz (x) W 2 (x)Iz2 (x)

(2.5)

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Once the velocity is known, it is possible to determine the position of the starting point xt , into the next frame xLK = xt + [dLK ]

(2.6)

where dLK = v∆t is the displacement and [·] represents the rounding operator applied to obtain integer values for the components dx, dy, and dz in case of noninteger coordinates. Since echocardiographic images are characterized by a high level of noise, differential techniques, such as the one previously described, may be inappropriate if used alone and may lead to an inaccurate point detection. Therefore, we additionally implemented the region based matching technique. A threedimensional window V(xLK ) of dimensions N × N × N voxels, whose center is the point xLK found by applying the Lucas– Kanade optical flow, is considered. For each point inside this window, another window F(x) of dimensions M × M × M voxels is defined and compared to the window of the same size around the point, xt , F(xt ) by means of the sum of the squared difference (SSD) φ(xt+1 ) =

m m m

F (i, j, k)

i=−m j =−m k =−m

C. Population and Data Acquisition Patients were included in the study if they had adequate transthoracic acoustic window that allowed adequate endocardial visualization without contrast enhancement: following this criterion, ten patients were enrolled. Transthoracic RT3DE imaging was performed from the apical window, with the patient in the left lateral decubitus position, using a commercial ultrasound scanner (SONOS 7500, Philips Medical Systems, Andover, MA) equipped with a fully sampled matrix array transducer (X4, 2–4 MHz) working in the harmonic mode. RT3DE datasets were acquired using the wide-angled acquisition mode, wherein four wedge-shaped subvolumes (93◦ × 21◦ ) were acquired over four cardiac cycles during a breath-hold with ECG gating. Acquisition of each subvolume was triggered to the R-wave of every other heartbeat in order to allow sufficient time for the probe to be recalibrated and each subvolume stored. Care was taken to include the entire LV cavity within the pyramidal 3-D scan volume. RT3DE datasets were stored digitally for offline analysis. In addition to RT3DE acquisition, 2-D images were acquired at held respiration from apical 2- and 4-chamber views while care was taken to avoid foreshortening, and stored digitally.

× [It (xt + (i, j, k)) − It+1 (xt+1 + (i, j, k))]2 . (2.7) For each point inside V(xLK ), the function ϕ(xt+1 ) is evaluated and the point corresponding to the minimum value of ϕ(xt+1 ) is the one that best fitted the window around the starting point, and thus it was considered as the resulting point of the algorithm i for xiLK ∈ V(xLK ). xﬁnal t+1 = arg min φ xLK The final location of the starting point xt is xﬁnal t+1 = xLK + dM = xt + [dLK ] + dM

(2.8)

where dM is the displacement evaluated using the region-based matching. These procedures were applied to the points manually selected in the first frame to estimate their coordinates throughout the cardiac cycle. Each frame was analyzed starting from the points obtained in the previous frame. Importantly, since in the detection of the points, increasing distance involves increasing error, the a priori knowledge that the cardiac sequences were loops was considered: the manually initialized frame was used as the starting frame for half of the frames in the cardiac cycle, going forward and backward in the temporal sequence. In this way, the analysis was performed throughout half of the frames in the cine-loop, resulting in a more accurate tracking. For each frame, from the tracked points the center of the mitral valve was computed as described in Fig. 1, and connected to the point corresponding to the LV apex, thus defining the LA. Then, the LA length was calculated as the geometrical distance between its extremities.

D. Data Analysis Manual Analysis: The RT3DE datasets were analyzed with commercial software (3DQ-QLab, Philips). The pyramidal volume data were displayed in 3 different cross sections; the anatomically correct 2- and 4-chamber views with the largest long-axis dimensions were selected as described in [11]. For each view, the points of insertion of the mitral leaflets into the annulus were connected by a straight line, and the LV long-axis dimension was measured as the distance between the center of this line and the most distal point at the apical endocardium. Then, the LV LA measurement was obtained as the average of the two measurements, relevant to apical 2- and 4- chamber views. This procedure was applied to the ED frame (Fig. 2, panel B). Moreover, from a volumetric visualization of the RT3DE data, the operator manually selected the LA for each frame throughout the cardiac cycle. This resulted in LA length-time curve. 2DE images were also analyzed. For both apical 2- and 4-chamber views, the ED frame was selected as the image with the largest LV cavity, and the LA was calculated as the distance between the LV apex and LV base as defined by the manually traced endocardial contours (EnConcert, Philips) (Fig. 2, panel C). Automated Analysis: The RT3DE datasets were analyzed using the proposed procedure for point tracking based on optical flow and the region based matching. One frame was used to manually initialize the position of the points to be tracked along the cardiac cycle. For each frame, the position of the initialized points was determined as a result of the optical flow algorithm and used to compute the LV LA length throughout the cardiac cycle.

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E. Statistical Analysis To evaluate the performance of the automated technique compared to the manual analysis of RT3DE, linear regression and Bland-Altman analyses were computed. Moreover, a paired ttest (p < 0.05) was applied to verify the presence of no differences, discrepancies, or suspiciously outlying results due to random and not systematic errors. In addition, for each subject, percent discordance between the manually obtained and the automatically computed LA length was calculated throughout the cardiac cycle for each pair of LA measurements as their point-by-point sum of absolute differences, normalized by the point-by-point sum of manual values. Accumulated position error of points tracking throughout a complete cardiac cycle was computed for the apex and the center of the mitral valve. The locations of the apex and of the center of the mitral valve at initial and final frames were also compared. To evaluate the effects of foreshortening as the possible source of error by the conventional 2DE analysis, in a subset of five patients, a comparison between the ED LA measurements derived from manual 2DE and RT3DE analysis, separately for both apical 2- and 4-chamber views, was carried out. Twofactor ANOVA with repeated measures (p < 0.05) was applied to test the significance of the differences between the groups of measurements; in addition, the average values of the two measurements derived from the two standard views at ED from 2DE and RT3DE were compared with the results of both volumetric manual tracing and our method performed on RT3DE data at ED, applying the one-way ANOVA test for correlated samples (p < 0.05). Mean percentage errors between the estimates and the manual values were calculated as the difference between the estimate and the manual value, divided by the manual value *100. III. EXPERIMENTAL RESULTS All the experiments were performed using MatLab 6.1 Release 12, using the following parameters settings: the 3-D window in which the Lucas-Kanade optical flow was evaluated (L) is of 9 voxels side; the best fit research was done inside a cubic window (M) of 9 voxels side; the SSD was evaluated in a cubic volume of 5 voxels side for each point belonging to previous window M. These windows were big enough to grant low noise sensitivity and small enough not to include structures different from the mitral valve that could have introduced false positive detections. The subjects had a mean frame rate of 19 frames per s (range: 14 ÷ 22 frames per second). For each subject, the RT3DE analysis with the proposed automated technique, including data retrieval, points selection in one frame only, computation of the center of the mitral valve, and dynamic tracking of the LV LA throughout the cardiac cycle, required between 1 and 2 min., depending on the number of frames in the cardiac cycle, using a personal computer (Pentium IV, 2.6 GHz, 1 Gb RAM). Conversely, the manual analysis of the 2DE and RT3DE datasets using the commercial software required about 10 min., while the LA selection from a volumetric visualization required between 4 and 6 min.

Fig. 3. Example of the results of the application of the proposed procedure based on optical flow techniques for the tracking of the center of the mitral valve throughout the cardiac cycle. Panel A: 3-D perspective of the initial frame (mitral valve closed) with the manually selected starting points and the computed center of the valve; panels B1 ÷ B6: 2-D perspectives of the tracked mitral annulus points in the cardiac cycle visualized in different long axis planes for each frame, as they correspond to the plane passing through the three aligned points and orthogonal to the transducer face.

In Fig. 3, an example of the results of the tracking of the points of insertion of the mitral leaflets along the cardiac cycle using the proposed technique is reported. Fig. 4 shows the results of the linear regression (top) and Bland–Altman analyses (bottom) between the results obtained frame-by-frame in 10 patients by volumetric RT3DE manual tracing and by the proposed automated procedure. A high correlation coefficient (r = 0.99, p < 0.05) was found, with a regression line equal to y = 0.94x + 5.3. The standard error of estimate was 1.8%. No significant bias (−0.18 mm, corresponding to −0.2% of the mean value) between the two techniques was found with narrow 95% limits of agreement (3.82 mm). The calculated percentage of discordance was 1.73% ± 0.57% (range: 0.60% ÷ 2.38%), confirming the excellent rate of agreement between the two techniques. Moreover, the paired t-test evidenced no significant differences between the two groups of measurements. In Fig. 5, an example of the LA length (black lines) over time in percentage of the heart cycle duration obtained from a RT3DE

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Fig. 5. Example of the LA length (black lines) over time in percentage of the heart cycle duration (%RR) curves obtained from a RT3DE dataset by automated analysis (with symbols, initialized frame marked with a circle) and by manual tracing (without symbols), together with the corresponding LV shortening (secondary y-axis, gray lines, with and without symbols, respectively). TABLE I LONG AXIS MEASUREMENTS DERIVED FROM 2DE AND RT3DE DATA

Fig. 4. Results of the linear regression (top) and Bland Altman (bottom) analyses of the frame-by-frame measurements of the LV LA obtained by RT3DE manual tracing versus the proposed automated procedure in the analyzed population (N = 10).

dataset by automated analysis (with symbols) and by manual tracing (without symbols) is shown, together with the corresponding LV shortening (secondary axis, gray lines). In this way, it is possible to appreciate in detail the frame-by-frame agreement of the measurements obtained with the two technique. In all analyzed subjects, mean accumulated position error computed by tracking the apex and the center of the mitral valve throughout a complete cardiac cycle resulted in 0.6 mm and 0.8 mm, respectively. The differences in the locations of the apex and of the center of the mitral valve as computed by the optical flow tracking between the initial and final frames resulted in a mean error of 0.7 mm and 2.1 mm, respectively. Table I reports the LA measurements for the ED frame, analyzing RT3DE and 2DE data for five patients. For all the measurements derived from 2DE and RT3DE obtained analyzing the 2- and 4-chamber acquisitions using the commercial software, two-factor ANOVA with repeated measures evidenced a significant underestimation of the LA derived from 2DE with respect to RT3DE measurements (p = 0.005). No significant differences between the two different views were found (p = 0.10) while a significant difference was detected considering the combination between the different type of data acquisition and the distinct views (p = 0.025). A t-test performed on the

same group of data showed significant differences (p < 0.01) between: 1) 2- and 4-chamber 2DE derived LA measurements; 2) 2-chamber 2DE and RT3DE derived LA measurements; 3) 4-chamber 2DE and RT3DE derived LA measurements. No significant differences were observed between 2- and 4-chamber RT3DE derived LA measurements (p = 0.24). LA derived from 2DE data showed a significant underestimation versus RT3DE for both the standard views (2-chamber: p = 0.008, 4-chamber: p = 0.002), with a mean percentage error of 5.5% for the 2-chamber view and of 10.3% for the 4-chamber view. In the comparison between the mean LA length values at ED derived from 2DE and RT3DE using the commercial software and the LA length values obtained by volumetric manual tracing and our method applied to RT3DE data, 2DE derived results showed significant underestimation with respect to all the RT3DE derived measurements with a mean percentage error of 7.9% (p = 0.002), 6.2% (p = 0.002), and 6.0% (p = 0.0002), respectively. The mean error between LA length obtained applying our method and by volumetric manual tracing was −0.2% (p = 0.34).

VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

IV. DISCUSSION AND CONCLUSION Although 2DE has been traditionally used for the quantification of LV morphology and function, the inadvertent imaging of foreshortened apical views could potentially result in inaccurate estimates of LV volumes and mass [11], [15], [16]. RT3DE offers the opportunity to overcome this limitation by acquiring a pyramidal dataset that can be analyzed offline to select anatomically correct, nonforeshortened apical views. As for the extraction of other cardiac parameters (LV volume, stoke volume, cardiac output, mass, wall motion) [7]–[11], the RT3DE analysis for LA measurements is performed offline after downloading the data on a dedicated PC. However, in the new ultrasound equipment recently delivered to the market (iE33), the RT3DE manual analysis software has been incorporated into the system, allowing the user to perform the quantitative analysis without the need to download the data. From this perspective, our method could be incorporated in the existing software on the system, thus avoiding the time-consuming downloading process and allowing a more straightforward, nearly automated analysis of the LV LA length and LV shortening throughout the cardiac cycle. The choice of 2DE as reference technique for LA length evaluation is due to the clinically widespread use of this technique to quantify this parameter. Other imaging techniques, such as cardiac magnetic resonance that is the reference technique for LV function evaluation, would be inappropriate because standard cardiac acquisitions are performed in the short axis view, to be able to obtain LV volumes and mass measurements by modified Simpson’s rule. In this way, only a discrete number of slices with a fixed slice thickness is acquired. Each slice contains information derived from the anatomical volume inside that thickness. Therefore, the left ventricular long axis measurement could be affected by an error up to the slice thickness. Moreover, the sequences used for cardiac studies do not allow optimal mitral annulus and leaflets visualization. The availability of tools which require minimal user interaction for RT3DE data analysis is becoming a common need from the scientific community, due to the growing diffusion of this new ultrasound equipment and its huge potential in both the research and in the clinical fields. However, currently available tools are based on a manual cross-section of the 3-D dataset, and measurements based on the 2-D approach. In particular, the computation of LV shortening in the long-axis direction over time, which is considered an important index of systolic and diastolic function [3]–[6], requires the analysis of all frames in the cardiac cycle, resulting in a tedious and cumbersome procedure. To overcome this limitation, we developed a technique for automated detection of the LV LA and the evaluation of the LV shortening throughout the cardiac cycle. The method we developed is based on optical flow techniques, that have been previously applied to calculate 2-D and 3-D cardiac motion field from a large variety of medical images [17]–[23]. However, in this study we applied the optical flow techniques from a different point of view, not to extract global motion information but to perform local analysis of the LV LA position throughout the cardiac cycle. The method we applied in this

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study combines the advantages of two distinct optical flow techniques: 1) a differential technique based on the assumption that the brightness of a pattern in the image is invariant over time, and 2) a region-based matching algorithm, that yields the best fit between image regions at different time, computed minimizing the sum of their squared differences. The application of the Lucas-Kanade algorithm in the 3-D space results in the estimate of the velocity vector that gives information about the area where the feature to be identified in the next frame belongs to. However, this estimate could be inaccurate because differential methods are based on the intensity conservation assumption and they are sensitive to noise, which is not negligible on echocardiographic data [24]. Moreover, the velocities of the tracked points are usually not integers, thus requiring a mathematical approximation of the points coordinates in the next frame. The application of the region-based matching in cascade to the differential technique allows the position of the points to be accurately estimated, thus avoiding approximations. In order to evaluate the points displacement, the application of the region-based matching algorithm without the first step would require the use of bigger windows, thus increasing the chance to find the best fit in correspondence to a point far from the desired one. The comparison among the performance of different optical flow techniques applied to RT3DE data is beyond the scope of this study; however, our simulations performed applying the two techniques separately resulted in an unsatisfactory tracking. This novel combination of two existing techniques resulted in an effective and fast points tracking that could be applied to any type of 3-D data. Our results showed that the extraction of the LA length throughout the cardiac cycle applying the proposed technique is feasible and requires minimal user interaction, by selecting few anatomical points in one frame only. Direct point-by-point comparison of automatically extracted LA measurements with those obtained by manual analysis, considered as the reference technique for comparison, showed excellent agreement, minimal bias, and very low percent discordance. The integration of the 3-D application of optical flow techniques to volumetric data acquired in real time allowed us to overcome foreshortening. As previous studies show, tangential scan plane cannot be avoided [25] [26]: despite the care taken to avoid foreshortening during the acquisition, in all the patients for which 2DE data were available, the LA evaluation at ED using commercial software resulted in a significant underestimation of LA length compared to RT3DE and obviously in an incorrect evaluation of derived parameters. The two different LA length values obtained manually analyzing RT3DE data can be explained considering that the selection of the 2- and 4-chamber views is performed without exploiting the additional volumetric information available in the RT3DE data. However, the possibility to select nonforeshortened orthogonal 2-D apical views in the 3-D data potentially improves the LA measurements even if this procedure does not take into account the real complex shape of the mitral annulus. The result of the two-factor ANOVA with repeated measures for these data showed that this underestimation is due to the different type of data, and there is no dependence on the different views.

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But the combination between the different type of data and the distinct views showed a significance that could be explained by the results of the t-test performed on the 2DE data considering the two views that evidenced a significant difference between the LA measurements. The additional results obtained considering the volumetric measurements confirmed the significance of differences between 2DE and RT3DE derived results. As RT3DE data analysis has been shown to provide better correlation with magnetic resonance imaging compared to 2DE analysis for LV morphology and function quantification [11], our results show the potential utility of our algorithm for the quantification of LV LA shortening. In fact, both the reduction in user interaction and the time required for the analysis could allow this quantification to be conducted in clinical settings. Moreover, this tracking procedure could represents the basis for the development of more complex analysis tools applied to RT3DE data, such as the tracking of the valvular annulus for quantification of shape changes due to pre- and post-surgical intervention, or a 3-D analysis of the kinesis of the ventricular base.

[11]

[12] [13] [14] [15]

[16]

[17] [18]

ACKNOWLEDGMENT The authors would like to thank R. M. Lang, M. D., V. Mor-Avi, Ph.D., and L. Weinert, of the Noninvasive Cardiac Imaging Laboratories, University of Chicago Medical Center, for their invaluable contributions.

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of cardiac volumes and function using semi-automatic border detection and comparison with cardiac magnetic resonance imaging,” J. Am. Coll. Cardiol, vol. 43, no. 11, pp. 2083–2090, Jun. 2004. V. Mor-Avi, L. Sugeng, L. Weinert, P. MacEneaney, E. G. Caiani, R. Koch, I. S. Salgo, and R. M. Lang, “Fast measurement of left ventricular mass with real-time three-dimensional echocardiography: Comparison with magnetic resonance imaging,” Circulation, vol. 110, no. 13, pp. 1814– 1818, Sep. 2004. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vision, vol. 12, pp. 43–77, 1994. B. D. Lucas and T. Kanade, “An interative image registration technique with an application to stereo vision,” in Proc. 7th Int. Joint Conf. Artificial Intelligence,Vancouver, BC, Canada, pp. 674–679. B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell., vol. 17, pp. 185–203, 1981. M. L. Chuang, R. A. Beaudin, M. F. Riley, M. G. Mooney, W. J. Mannin, P. S. Douglas, and M. G. Hibberd, “Three-dimensional echocardiographic measurement of left ventricular mass: Comparison with magnetic resonance imaging and two-dimensional echocardiographic determinations in man,” Int. J. Card. Imaging, vol. 16, no. 5, pp. 347–357, Oct. 2000. S. G. Myerson, H. E. Montgomery, M. J. World, S. E. Humphries, and D. J. Pennell, “Left ventricular mass reliability of M mode and 2-dimensional echocardiographic formulas,” Hypertension, vol. 40, pp. 673–678, 2002. S. C. Amartur and H. J. Vesselle, “A new approach to study cardiac motion: The optical flow of cine MR images,” Magn. Reson. Med., vol. 29, no. 1, pp. 59–67, Feb. 1993. V. Behar, D. Adam, P. Lysyansky, and Z. Friedman, “Improving motion estimation by accounting for local image distortion,” Ultrasonics, vol. 43, no. 1, pp. 57–65, Nov. 2004. L. Dougherty, J. C. Asmuth, A. S. Blom, L. Axel, and R. Kumar, “Validation of an optical flow method for tag displacement estimation,” IEEE Trans. Med. Imag., vol. 18, no. 4, pp. 359–363, May 1999. J. M. Gorce, D. Friboulet, and I. E. Magnin, “Estimation of threedimensional cardiac velocity fields: Assessment of a differential method and application to three-dimensional CT data,” Med. Image Anal., vol. 1, no. 3, pp. 245–261, May 1997. G. J. Klein and R. H. Huesman, “Four-dimensional processing of deformable cardiac PET data,” Med. Image Anal., vol. 6, no. 1, pp. 29–46, Apr. 2002. R. Noumeir, G. E. Mailloux, and R. Lemieux, “Detection of motion during tomographic acquisition by an optical flow algorithm,” Comput. Biomed. Res., vol. 29, no. 1, pp. 1–15, Mar. 1996. J. L. Prince, S. N. Gupta, and N. F. Osman, “Bandpass optical flow for tagged MRI,” Med. Phys., vol. 27, no. 1, pp. 108–118, Feb. 2000. P. Baraldi, A. Sarti, C. Lamberti, A. Prandini, and F. Sgallari, “Evaluation of differential optical flow techniques on synthesized echo images,” IEEE Trans. Biomed. Eng., vol. 43, no. 3, pp. 259–272, Mar. 1996. R. Erbel, P. Schweizer, H. Lambertz, G. Henn, J. Meyer, W. Krebs, and S. Effert, “Echoventriculography—A simultaneous analysis of twodimensional echocardiography and cineventriculography,” Circulation, vol. 67, no. 1, pp. 205–215, Jan. 1983. S. Muller, T. Bartel, M. A. Katz, O. Pachinger, and R. Erbel, “Partial cutoff of the left ventricle: Determinants and effects on volume parameters assessed by real-time 3-D echocardiography,” Ultrasound Med. Biol., vol. 29, no. 1, pp. 25–30, Jan. 2003.

F. Veronesi received the Doctoral degree in electronic engineering from the University of Bologna, Bologna, Italy, in 2004. He is currently working towards the Ph.D. degree at the Bioengineering Department, Polytechnic of Milan, Milan, Italy. His research activity, now at the Department of Electronics Informatics and Statistics (DEIS) of Bologna, is focused on biomedical image processing, with particular interest on parameters extraction from 3D cardiac imaging data.

VERONESI et al.: TRACKING OF LEFT VENTRICULAR LONG AXIS FROM REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY

C. Corsi received the M.S. degree in electronic engineering from the University of Bologna, Bologna, Italy, in 1997 and the Ph.D. degree in bioengineering from the Department of Electronics, Computer Science and Systems, University of Bologna, in 2001. She spent six months visiting the Mathematics Department, University of California, Berkeley, and the Math Department at the Lawrence Berkeley National Laboratory, Berkeley, working on level set methods applied to medical data processing. Since 2004, she has been collaborating with the Noninvasive Cardiac Imaging Laboratories, University of Chicago as a Research Associate. Actually, she holds a Postdoctoral Research Grant at University of Bologna. Her research interests include new expertized and advanced technologies and methods, applied to medical data processing, in particular, echocardiographic and magnetic resonance data.

E. G. Caiani was born in Monza in 1970. He received the M.S. degree in electronic engineering and the Ph.D. degree in biomedical engineering from the Politenico di Milano, Milan, Italy, in 1996 and 2000, respectively. Since 2000, he has been collaborating with the Noninvasive Cardiac Imaging Laboratories, University of Chicago, where he worked as a Research Associate in 2000 and 2003, respectively. He is with the Department of Biomedical Engineering, Politecnico di Milano, as a Researcher. His interest consists in the development of processing techniques to quantify indices of cardiac function and perfusion from cardiac imaging data, and in space-related applications. Dr. Caiani received the "Rosanna Degani Young Investigator Award" from the IEEE Computers in Cardiology.

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A. Sarti was born in Modena, in 1964. He received the Laurea degree (cum laude) in electronic engineering from the University of Bologna, Bologna, Italy, in 1992, and the Ph.D. degree in bioengineering from the University of Bologna, in 1996. From 1997 to 2000, he was appointed with a Postdoc position at the Mathematics Department, University of California, Berkeley and the Math Department of the Lawrence Berkeley National Laboratory, Berkeley, working in the group of J. Sethian and A. Chorin. Since 2001, he has been with the University of Bologna, where he teaches classes in bioimaging. In 2003, he was also appointed as Maitre de Recherche at CREA, Ecole Polytechnique, Paris. He wrote more then 80 pubblications in the field of computer vision, medical imaging, and biologically based models of visual perception. With G. Citti, he is responsible for the Gruppo Interdipartimentale di Visione, an interdisciplinary group comprehending the Dipartmento di Elettronica, Informatica e Sistemistica and the Dipartimento di Matematica at the Bologna University. In the last three years, he gave lectures at Yale University, UC Los Angeles, UC Berkeley, Freie Universitat Berlin, Ecole Normale Superieure Cachan, Palazzone di Cortona Scuola Normale Superiore di Pisa.

C. Lamberti received the Doctoral degree in mechanical engineering from the University of Bologna, Bologna, Italy, in 1974 and the Postgraduate degree in biomedical technology from the University of Bologna School of Medicine, in 1978. He is currently an Associate Professor at the Department of Electronics, Computer Science and Systems, University of Bologna. Since 1991, he is in charge at University of Bologna of the course Computer and Systems Science in Health Care. His research activity is focused on biomedical signal and image processing and biomedical technology assessment. He has served on the Board of the Centro Ricerche e Studi Tecnologie Biomediche e Sanitarie (CRSTBS) at Scientific Park of Trieste (Italy) during 1989– 1998. He has also served on the Board of the Associazione Italiana degli Ingegneri Clinici (AIIC) since 1993. He has published several papers on arrythmias recognition, left ventricular wall motion, echocardiography image processing, estimation of motion in 3-D echocardiography, computeraided virtual surgery, and computer systems for management of biomedical technology.

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