Magnetic Resonance in Medicine 49:743–754 (2003)
Unsupervised Reconstruction of a Three-Dimensional Left Ventricular Strain From Parallel Tagged Cardiac Images Thomas S. Denney, Jr.,1* Bernhard L. Gerber,2 and Litao Yan3 A new algorithm, called the Unsupervised Tag ExTraction and Heart strain(E) Reconstruction (UNTETHER) algorithm, is presented for quantifying three-dimensional (3D) myocardial strain in tagged cardiac MR images. Five human volunteers and five postinfarct patients were imaged. 3D strains measured by UNTETHER and a user-supervised technique were compared. Each study was analyzed in 49 ⴞ 8 min with UNTETHER, compared to ⬃4 hr with the user-supervised technique. For pooled human data, the correlation coefficient between the two methods for circumferential shortening (Ecc) was r ⴝ 0.91 at the mid-wall (P < 0.0005). UNTETHER is capable of measuring wall motion abnormalities resulting from coronary artery disease, and has the potential to overcome the main limitations (time and user-supervision requirements) to routine clinical use of tagged cardiac MRI. Magn Reson Med 49:743–754, 2003. © 2003 Wiley-Liss, Inc. Key words: cardiac MRI; left ventricle; myocardium; image processing; tagging
Tagged MRI (1) is a valuable technique for noninvasively assessing the regional mechanical function of the left ventricular (LV) wall. Analysis of wall motion abnormalities with dobutamine stress echocardiography and cine-MRI are established methods of detecting myocardial ischemia, but are either semiquantitative or subjective (2,3). In tagged MR images, the myocardium appears with a spatially encoded pattern that moves with the tissue and can be analyzed to compute quantitative measures of regional myocardial contractile performance, such as three-dimensional (3D) strain. Quantitative 3D analysis of tagged MRI has shown promise for detecting ischemia and differentiating between viable and nonviable myocardium (4,5). Several methods have been developed to quantitatively analyze tagged images (6 –12). Most techniques first use a tag detection algorithm to extract the positions of tag lines in each image in a study. Myocardial motion is then reconstructed by fitting a deformation model to the tag line positions. Regional 3D strain can be computed with these methods, but the process is time-consuming because the user must supervise the extraction of myocardial contours and, in some cases, the tag lines themselves from each image in a study. More recently, a harmonic phase (HARP)
technique (13) was proposed that automatically computes two-dimensional (2D) strain by analyzing the spectral peaks created by the tagging process in the Fourier domain. HARP analysis involves relatively simple and fast computations, but presently can only compute 2D strains. Also, there is no way for the user to alter the analysis to correct for isolated areas of poor image quality. In this work we present and validate a technique called the UNsupervised Tag ExTraction and Heart strain(E) Reconstruction (UNTETHER) algorithm, which automatically computes 3D strain from a tagged imaging study. To our knowledge, the UNTETHER algorithm is the only unsupervised algorithm published to date for reconstructing 3D strain from tagged cardiac MR images. First, tag line features are automatically detected in each image using an improved version of a previously published tag detection algorithm (14). The UNTETHER algorithm then uses a new technique based on level sets (15) to automatically compute an approximate 3D myocardium segmentation from the detected tag line points. Finally, from the tag line features and segmentation, 3D deformation and strain are computed using the discrete model-free (DMF) technique (12), and output on a mesh of 3 radial ⫻ 6 circumferential ⫻ 3 longitudinal LV material points. Because UNTETHER is an automated analysis algorithm, tag detection errors can occur, such as false positives or negatives, and errors in tag location, that are usually corrected in usersupervised processing. The UNTETHER algorithm does not automatically detect or correct for these tag detection errors. Instead, the UNTETHER algorithm relies on the spatial localization properties of the DMF algorithm and averaging of the reconstructed strains to reduce the effect of these errors. We validated the UNTETHER algorithm on both normal human volunteers and patients with myocardial infarction (MI) by comparing strains computed automatically by UNTETHER to those computed with user-supervised processing. METHODS MR Studies
1 Department of Electrical and Computer Engineering, Auburn University, Auburn, Alabama. 2 Cardiology Division, Department of Medicine, Johns Hopkins University, Baltimore, Maryland. 3 Clinical Systems Applications, GE Medical Systems, Milwaukee, Wisconsin. Grant sponsor: NIH/NHLBI; Grant number: R01-HL6134301. *Correspondence to: Thomas S. Denney, Jr., Ph.D., Department of Electrical and Computer Engineering, Auburn University, 200 Broun Hall, Auburn University, Auburn, AL 36849-5201. E-mail:
[email protected] Received 7 November 2001; revised 13 December 2002; accepted 13 December 2002. DOI 10.1002/mrm.10434 Published online in Wiley InterScience (www.interscience.wiley.com).
© 2003 Wiley-Liss, Inc.
The UNTETHER algorithm was developed and optimized on a set of images acquired in 10 subjects (eight normal volunteers and two patients with MI). An additional set of 10 imaging studies (from five volunteers and five patients) were used to assess tag tracking accuracy, tag detection rate, reproducibility, and the differences strains measured with UNTETHER (unsupervised) and supervised quantitative strain measurement techniques. Informed consent for all of the studies was obtained according to the standards of the Joint Committee on Clinical Investigation of the Johns Hopkins Hospital.
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Each image was acquired with the subject in a supine position on a Signa 1.5-T scanner (GE Medical Systems, Milkwaukee, WI), with a flexible surface coil wrapped around the left side of the subject’s chest. A cardiac-gated pulse sequence with parallel plane tagging (16,17) was used during breath-holds in 22 heartbeats at end-expiratory lung volume. Six subjects in the development group and six subjects in the evaluation group were imaged with blood saturation (18) to create black-blood contrast. The remaining studies were acquired with a white-blood protocol (16,17). The tagging sequence consisted of five nonselective radiofrequency (RF) pulses with relative amplitudes of 0.7, 0.9, 1.0, 0.9, and 0.7 separated by spatial modulation of magnetization (SPAMM) (19) encoding gradients to achieve a tag spacing of 5 pixels and a tag full width at half maximum (FWHM) of 2 pixels. The tagging tip angle was tuned to 180°. Five to seven parallel, shortaxis 10-mm-thick slices were acquired with no separation between slices. Six 10-mm-thick long-axis slices were imaged in a radial orientation about the long axis of the LV with an angular spacing of 30°. Six to 12 cardiac phases were imaged starting at 46 ms after detection of the upslope of the electrocardiograph R wave, and spaced 32.5 ms apart through systole. The imaging parameters were as follows: TR ⫽ 6.5 ms, TE ⫽ 2.3 ms (fractional echo), 15° flip angle, 110 phase-encoding steps (matrix ⫽ 256 ⫻ 110), FOV ⫽ 32–36 cm, and one average. Five phase-encoding views were acquired for each movie frame per heartbeat. Sample images from a normal volunteer are shown in Fig. 1. Overview of the UNTETHER Algorithm The UNTETHER algorithm first split the images for a given study into groups (one group for each tag line orientation). For each short-axis group, the user selected a single circular region of interest (ROI) for all images with that group, as well as the center and spacing of the undeformed tag lines. For the long-axis images, an elliptical ROI was selected, and a separate ROI and alignment were specified for each slice. After the initial conditions were set, the tag lines were then tracked and the myocardial contours were estimated for each slice through all time frames. This procedure was repeated for all groups in the study. Once the tag tracking and contour estimation was completed for all groups, the DMF algorithm computed deformation and strain for each time frame. The details for each of these steps are given below. Tag Tracking The tag tracking algorithm was based on the maximum likelihood/maximum a posteriori (ML/MAP) algorithm described in Ref. 14. The imaging protocol described above generated tag lines with an inverted Gaussian profile (20), and the UNTETHER algorithm used this information to distinguish tag lines from the surrounding tissue. First, the positions of a set of candidate tag line centers were estimated in the ROI using an inverted Gaussian tag template embedded in an active contour (14). The value of the template match criterion was then compared to a threshold to determine which of the tag centers were actually part of a tag line.
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FIG. 1. MR images of a normal human volunteer acquired with a black-blood, parallel-tagged imaging protocol. Shown are two cardiac phases: early systole and late systole. For each phase, two short-axis and one long-axis images are shown; each displays tag lines from a different tag plane orientation.
Candidate Tag Center Estimation Each tag line in the ROI was modeled as an active contour composed of a connected set of points that represented the tag line center. For vertically oriented tag lines, there was only one tag line center per image row and the position of the center could only be adjusted horizontally. Other tag line orientations were rotated to the vertical position before processing, and then rotated back to their original orientation after the tags were tracked. The active contour was optimized so that, subject to global smoothness tag separation constraints (14), each point on the contour minimized the squared difference between an ideal tag profile centered at and the local image data given by 1 L T共兩w兲 ⫽ 关t共兲 ⫺ w兴T 关t共兲 ⫺ w兴 2
[1]
where w is a 1 ⫻ (2 Ns ⫹ 1) neighborhood of image pixels [w–Ns w–Ns⫹1 . . . w0 . . . wNs–1 wNs] along a line perpendicular to the undeformed tag line and centered at the pixel nearest . Ns is the next integer larger than the FWHM of the tag line in pixels. The ideal tag line profile centered at was defined as t共兲 ⫽ q.*关t共 ⫺ Ns ⫺ 兲 t共 ⫺ 共Ns ⫺ 1兲 ⫺ 兲 · · · t共 ⫺ 兲 · · · t共Ns ⫺ 兲兴
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each candidate tag center were tested to determine whether the center was actually part of a tag line. If a candidate tag center is part of a tag line, the ideal tag profile (untagged myocardium signal multiplied by the tag profile) is a good match to the image pixels. If a candidate center is not part of a tag line, the untagged myocardium signal alone is a good match to the image pixels. Therefore, a candidate tag center is considered part of a tag line if
冘 NS
FIG. 2. Rough segmentation of myocardial tags needed for tag tracking: (a) tagged image, and (b) result of segmentation.
where .* denotes elementwise multiplication, and the vector q ⫽ [q–Ns q–Ns⫹1 . . . q0 . . . qNs–1 qNs] is an estimate of the untagged myocardium signal (described below) in the same neighborhood as w. The tag line profile t(x) was modeled by the inverted Gaussian function (14) t共x兲 ⫽ 1 ⫺ Aexp{⫺x2 /22 }
[2]
where A is the tag line amplitude and 2 ⫽ (FWHM)2/ (8ln2). The value of A changed with the time frame to approximately model the T1 relaxation of the tag according to the formula A ⫽ exp{– tQRS/T1nom}, where tQRS is the delay time after detection of the QRS complex that the image was acquired and T1nom ⫽ 500 ms is a nominal value of T1 for the myocardium. The local untagged myocardium signal vector q was estimated by removing the tag lines from the ROI with a grayscale morphological closing operation (21). The initial spacing and position of the tag lines is specified by the user with a graphical user interface (GUI) on the first time frame image. Each tag line was then optimized individually using the active contour evolution algorithm in Ref. 14. The evolution algorithm in Ref. 14 requires a rough segmentation of the myocardium to break the smoothness constraints imposed by the active contour at the myocardial boundaries. This rough segmentation was obtained by running the tag detection test described below on each pixel in the ROI (see Fig. 2). Once the tag line positions were optimized for the first time frame image, 1D HARP tracking (13) was used to estimate the position of each tag line in the second time frame. Phase images for the first and second time frames were created by computing the 2D discrete Fourier transform (DFT) of each image, filtering them with a circular filter, and computing the phase of the inverse DFT. The circular filter was centered at the first spectral peak (1/Ts mm–1, where Ts is the tag spacing) with radius 1/(2Ts). The phase of each tag point in the first image was computed by linear interpolation, and the position in the second time frame phase image of the closest point in the same row with the same phase was determined. The active contour evolution algorithm was then run with this position as a starting point. This procedure was repeated for the remaining time frames. Tag Detection Once a set of candidate tag line centers were estimated using the above procedure, the image pixels neighboring
L T共兩w兲 ⬍
关wk ⫺ qk 兴2
[3]
k⫽⫺N S
where LT(|w) is the squared difference between the image pixels and the ideal tag profile, and the right-hand side is proportional to the squared difference between the image pixels, wk, and the untagged myocardium signal estimates, qk. is a parameter that was determined by receiver operating characteristic (ROC) analysis to be 0.35. For each tag center tested, the parameters FWHM and T1nom were optimized over a range of 1–3 pixels and 100 –900 ms, respectively, to minimize LT(|w). This optimization accounted for deformation of the tag profile due to deformation of the underlying myocardium and obliquity of the tag line relative to the image row, as well as to changes in T1 over the myocardium. Finally, for each slice, the tag points for all time frames were run through a pruning algorithm (14) that removed any tag points that were isolated in time or space. Analysis of Tag Tracking and Detection Errors Tag tracking errors were studied by comparing the tag lines identified by the UNTETHER algorithm to tag lines identified by user-supervised processing (21,22). The minimum distance was computed between each tag point identified by UNTETHER and the corresponding user-supervised tag line. An UNTETHER tag line was considered to have lost correspondence with the tag line in the image if the average magnitude distance from the UNTETHER tag line to the user-supervised tag line was ⬎2 mm. These tag lines were excluded from the error analysis but used to compute strain. The tag detection rate was computed by dividing the number of tag points detected by UNTETHER inside a set of LV contours identified by user-supervised analysis (21,22) by the total number of tag points tracked inside the LV contours. The false-positive rate was defined as the number of tag points identified outside the LV contours divided by the total number of tag points tracked outside the LV contours. LV Contour Estimation After the tag lines were tracked for a given slice in both tag line orientations, the endocardial and epicardial boundaries of the LV were estimated from the identified tag line points using a level set algorithm (15). Level set algorithms embed an image contour in a 2D surface, u(x,y,t), and the surface is then evolved so that the contour corresponding to the zero level set of the surface optimizes a cost function. The result is a nonparametric description of the con-
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FIG. 3. a: Image g used for LV contour estimation in a normal human data set overlaid with tag points (white dots) and estimated contours (white lines). b and c: LV contours in image a overlaid on the image data.
tour that is constructed without any prior assumptions as to its structure. The endocardial and epicardial contours were computed separately. The initial level set surface, u(x,y,0), for the endocardium was a cone centered at the center of mass, (mx,my), of the tag point image u共x,y,0兲 ⫽
冑共x
⫺ m x兲 2 ⫹ 共y ⫺ m y兲 2 ⫺ r.
[4]
The cone radius, r, was set to 5 pixels. Note that the zero level set of this surface is a circle of radius 5. A cone was also used as the initial surface for the epicardial contour with r set to the radius of the largest circle centered at (mx,my) that would fit in the bounding box of the tag line points. To control the evolution of the contours, we used a cost function based on a computed image, g, constructed from the identified tag line points that are close to zero inside the myocardium and close to one outside the myocardium. The image g was constructed in two steps. First a binary tag point image, B, was constructed that was one where a tag point was identified and zero elsewhere. Another image, g, was then computed according to the formula g ⫽ exp{–(B *G)}, where *G denotes convolution with a Gaussian kernel with an FWHM equal to the FWHM of the tag line. As shown in Fig. 3, the image g is small where the tag density is high (which is the case inside the myocardium) and large where the tag density is low. Each level set surface was evolved according to the partial differential equation (23) u t ⫽ g共c ⫹ 兲兩ⵜu兩 ⫹ ⵜu.ⵜg
[5]
where ut denotes partial derivative with respect to t, t,ⵜu denotes spatial gradient, c is a constant parameter, and is the curvature of the level sets. Level set algorithms move a contour by moving the surface u up or down. For example, if the cone surface described above moves upward, the zero level set contour gets smaller in radius. Equation [5] moves the surface u locally depending on , ⵜu, g, and c. The and ⵜu terms act to smooth out corners in the contour (creases in u) by moving u faster in regions of high curvature or gradient. The constant parameter c controls the global direction that u moves. If c ⬎ 0, the contour moves inward. If c ⬍ 0, the contour moves outward. The
magnitude of c controls the global speed at which the contour moves. Finally, the g term causes the contour to slow down and eventually stop when g flattens out to zero inside the myocardium. Equation [5] was discretized with a time step of ⌬t ⫽ 0.03 and evolved using the upwind scheme described in Ref. 15. In most level set algorithms, the g(c ⫹ ) and ⵜg terms are only evaluated on the zero level set and are extended to the rest of the domain via a time-consuming interpolation procedure (24). Instead, we evaluated these terms locally at each point in the image domain, which resulted in a level set surface that remained relatively stationary inside the myocardium, where g is close to zero, and moved the contour either inward (c ⬎ 0) or outward (c ⬍ 0) outside the myocardium, where g is close to one. The convergence properties for this level set algorithm are described in Ref. 25. For the epicardial contour, we used c ⫽ 2, so the contour evolved inward from its initial position. The level set surface, u, was initially a cone with negative values inside the zero level set contour and positive values outside. Because the g is close to zero inside the myocardium, u was relatively unchanged inside the myocardium and stayed negative. Outside the myocardium, the level set surface was positive and increased in magnitude, which moved the zero level set contour toward the myocardium. A similar situation occurred with the endocardial surface (c ⫽ –2), with the exception that the contour evolved outward from its initial position. In both cases, the level set surface was evolved until the segmentation defined by the two zero level sets did not change in 1/(c*⌬t) iterations, or 200 iterations were performed. Examples of estimated contours overlaid on the raw image data are shown in Fig. 3. Analysis of Myocardial Contour Estimation Errors The accuracy and precision of myocardial contours estimated by the UNTETHER algorithm were studied by comparing the contours identified by the UNTETHER algorithm to contours identified by user-supervised processing (21,22). For each of 64 equally spaced points on the endocardial and epicardial contours computed by UNTETHER, the signed minimum distance was computed between each point and the corresponding user-supervised contour. A negative sign meant the point on the UNTETHER contour was outside the user-supervised contour.
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FIG. 4. Myocardial deformation is expressed as 3D strains in three orthogonal directions: circumferential shortening (Ecc), radial thickening (Err), and longitudinal shortening (Ell).
Deformation and Strain Reconstruction After all tag lines were tracked in all images in the study and the LV contours were estimated in each short-axis slice, end-systolic material coordinate displacement and Lagrangian strain were reconstructed using the DMF technique (12). This technique uses finite difference analysis to fit a displacement field to the tag line measurements in each imaged cardiac phase, subject to the following soft constraint on the spatial variation of the displacement field:
冕 冘冋 册 ij
2u i x 2j
2
dx
[6]
where ui and xi are the ith components of the spatial coordinate displacement field u and spatial coordinate position vector x, respectively. The DMF technique requires a 3D discrete segmentation of the LV for each imaged cardiac phase to compute the finite differences used in the reconstruction. This segmentation was computed for a given timeframe by interpolating between all the 2D segmentations for the timeframe using shape-based interpolation (26). Segmentation points are equally spaced on a grid with spacing equal to the pixel size in the MR image data (1.25–1.41 mm). An end-systolic, 3D, Lagrangian strain tensor (E) was computed on a 3 radial ⫻ 6 circumferential ⫻ 3 longitudinal mesh of material points equally spaced around the myocardium from the most-basal imaged slice to the most-apical imaged slice. For comparison purposes, we used the mesh constructed during the user-supervised analysis described below. The sectors of the mesh were oriented via a user-specified landmark to correspond to the antero-septal, anterior, lateral, posterior, postero-lateral, and septal walls. While an entire strain tensor was computed at each segmentation point, we only analyzed the normal strains—radial thickening (Err), circumferential shortening (Ecc), and longitudinal shortening (Ell) (see Fig. 4)—and maximal shortening (E3), defined as the minimum eigenvalue of E. Normal LV contraction is characterized by negative strains for shortening (Ecc, Ell, and E3), and a positive sign for thickening (Err). Conversely, abnormal LV
contraction is characterized by positive signs for shortening and negative signs for thickening. To compute the strains we first computed E at each point in the 3D segmentation for each of three imaged time frames that bracket end-systole, using the DMF. Although we could have computed strain at each imaged time frame, we used only three time frames in order to reduce computation time. The strains at each point on the 3 ⫻ 6 ⫻ 3 mesh were then computed for each of the last three each imaged cardiac phases by averaging the strains over the segmentation points nearest the mesh point (⬃1000 segmentation points per average). This averaging increased the robustness of the strains to isolated errors in tag and contour detection. Also, the use of this mesh size kept the number of functional parameters for each study fairly small, so that these parameters could be recorded in a patient’s chart and tracked over a period of time. The end-systolic strain mesh was not computed with a fixed time frame. Instead, for each mesh point the time frame corresponding to minimal Ecc at that mesh point over the three time frames was determined. The strain tensor at that time was used as the end-systolic strain tensor at that mesh point. User-Supervised Analysis of Tagged Images For comparison purposes, we also measured 3D strains in each data set using a user-supervised method (8,21,22). This method required a user-supervised identification of myocardial contours and tag lines in each image in the study. The tag and contour data were then used to fit an LV deformation model based on a series expansion in a prolate spheroidal coordinate system that was carefully constructed to match the morphology of the LV under study. Finally, strains were computed from the deformation model on a 3 radial ⫻ 6 circumferential ⫻ 3 longitudinal mesh of material points. End-systolic strain was computed using the same non-fixed time method described above. Statistical Analysis The mean values are expressed as mean ⫾ SD. The interobserver reproducibility of the end-systolic UNTETHER strain measurements were assessed in 10 human imaging studies by correlation analysis and coefficient of variation between strains measured by two independent users. These 10 studies were not used for algorithm development. Comparisons of end-systolic myocardial strains measured by UNTETHER (unsupervised) and user-supervised methods were assessed on the same 10 human studies by correlation analysis, BlandAltman plots, and coefficient of variation. The hypothesized mean difference for computing the significance of mean differences was the mean average, (X ⫹ Y)/2, for reproducibility and the mean user-supervised strain in the user-supervised comparison. The coefficient of variation was defined as the SD of the strain difference divided by the mean of the two strains for the reproducibility study, and the SD of the strain difference divided by the mean of the user-supervised strain for the comparison study. RESULTS Analysis of Tag Tracking and Contour Estimation Errors In 10 human imaging studies, the root-mean-square (RMS) difference between end-systolic UNTETHER tag lines and
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FIG. 5. Maps of radial thickening (Err), circumferential shortening (Ecc), and longitudinal shortening in a human patient with an antero-septal MI computed using UNTETHER (left column) and user-supervised (right column) methods. The red and green balls are septal and apical landmarks, respectively. Each image is color-coded, with yellow indicating thickening and blue indicating shortening. Normal radial thickening (yellow), and circumferential and longitudinal shortening (blue) occurred in the inferior posterior wall, which was noninfarcted. Conversely, the antero-septal wall (corresponding to the infarction) presented an absence of thickening (red) in the radial direction, and passive stretching (yellow) in the circumferential and longitudinal directions.
user-supervised tag lines was 0.25 mm for short-axis slices, which is within the theoretical precision of the user-supervised tag lines (0.3 mm (20)). The RMS error for long-axis slices was 0.58 mm. In this study, 0.15% of the 20962 tag points identified inside the user-defined LV
contours in the short-axis images, and 2.49% of the 7747 tag points identified inside the contours in the longaxis images were part of tag lines that lost correspondence and were not included in the error analysis. UNTETHER successfully identified 78% of the short-axis and 80% of
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Table 1 Correlation Coefficient (r), Mean Difference, and Coefficient of Variation (cv) Between Strains Measured With UNTETHER by Two Independent Users
Sub-endocardium Err Ecc Ell E3 Mid-wall Err Ecc Ell E3 Sub-epicardium Err Ecc Ell E3 a
r
P
Mean ⫾ SD
P
0.92 0.97 0.84 0.97
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
0.0085 ⫾ 0.0391 0.0021 ⫾ 0.0162 ⫺0.0011 ⫾ 0.0416 0.0015 ⫾ 0.0102
NS ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
741% 7% 30% 4%
0.88 0.96 0.83 0.96
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
0.0099 ⫾ 0.0793 0.0032 ⫾ 0.0168 ⫺0.0021 ⫾ 0.0418 0.0022 ⫾ 0.0121
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
44% 10% 31% 5%
0.92 0.94 0.81 0.88
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
⫺0.0105 ⫾ 0.0908 0.0034 ⫾ 0.0209 ⫺0.0026 ⫾ 0.0388 0.0008 ⫾ 0.0190
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
39% 17% 30% 9%
cv
Samples were obtained in normal volunteers and patients (N ⫽ 10).
the long-axis tag points between user-defined myocardial contours at end-systole. UNTETHER identified 32% of the 43008 tag points tracked outside LV contours identified by user-supervised analysis in short-axis images. In long-axis images, UNTETHER identified 31% of the 28,072 tag points tracked outside the LV contours. The epicardial contours estimated by UNTETHER at end-systole were located on average outside the epicardial contours estimated by user-supervised analysis with a signed distance of – 4.5 ⫾ 5.7 mm over the 10 human studies. The UNTETHER endocardial contours at end-systole were located on average inside the user-supervised contours with a signed distance of 2.3 ⫾ 5.2 mm. Myocardial Strain by UNTETHER and User-Supervised Methods Specifying the ROI and tag line alignment for a given study took ⬃3 min. Once these tasks were completed, the unsupervised UNTETHER analysis required 46 ⫾ 8 min per 3D
study on an Ultra80 workstation (SUN Microsystems, Mountain View, CA). The user-supervised analysis took almost 4 hr per study. Figure 5 shows maps of end-systolic radial thickening (Err), circumferential shortening (Ecc), and longitudinal shortening (Ell) for a patient with an anterior MI computed by UNTETHER and user-supervised methods, with reduced radial thickening and circumferential shortening in the infarcted region. According to pooled data from both normal volunteers and patients, the UNTETHER algorithm resulted in reproducible results between two independent users for Err, Ecc, and E3 in all three layers (Table 1). The reproducibility for longitudinal strains was good, but not as good compared to the other strains. The coefficient of variation for subendocardial Err was large (741% ⫽ .039/.00527 ⫻ 100%) because Err was significantly underestimated by both observers. Pooled data from both normal volunteers and patients indicated that the UNTETHER and the user-supervised
Table 2 Correlation Coefficient (r), Mean Difference, and Coefficient of Variation (cv) Between Strains Measured With UNTETHER (Unsupervised) and User-Supervised Analysis
Sub-endocardium Err Ecc Ell Emin Mid-wall Err Ecc Ell Emin Sub-epicardium Err Ecc Ell Emin a
r
P
Mean ⫾ SD
P
⫺0.05 0.83 0.50 0.80
NS ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
⫺0.3018 ⫾ 0.1939 0.0176 ⫾ 0.0416 ⫺0.0038 ⫾ 0.0644 0.0063 ⫾ 0.0388
0.785 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
63% 17% 48% 14%
0.09 0.91 0.63 0.86
NS ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
⫺0.1498 ⫾ 0.2306 0.0007 ⫾ 0.0288 ⫺0.0017 ⫾ 0.0494 ⫺0.0158 ⫾ 0.0264
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
69% 17% 38% 12%
0.08 0.74 0.58 0.60
NS ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
⫺0.1157 ⫾ 0.2774 0.0018 ⫾ 0.0458 ⫺0.0125 ⫾ 0.0528 ⫺0.0357 ⫾ 0.0419
⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005 ⬍ 0.0005
80% 37% 45% 23%
Samples were obtained in normal volunteers and patients (N ⫽ 10).
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FIG. 6. Bland-Altman (left) and correlation (right) plots for comparing UNTETHER (Y) and user-supervised (X) strain measurements in the (a) subendocardium, (b) midwall, and (c) subepicardium. In the Bland-Altman plots, lines above and below the difference ⫽ 0 line represent ⫾2 SD of the difference. In the correlation plots, the dashed line represents perfect correlation.
methods showed good correlation in Ecc and E3 in the endocardium and mid-wall, but less agreement in the epicardium (Table 2). Err showed poor correlation with the user-supervised method in all layers. Comparisons between the two sets of strains are displayed in Bland-Altman plots in Fig. 6. DISCUSSION We have described and validated a new algorithm, called UNTETHER, that can automatically compute 3D myocardial strain from tagged cardiac images. The UNTETHER algorithm consists of an automated tag tracker followed by an automatic estimation of the endocardial and epicardial contours, and strain reconstruction via the DMF algorithm. We demonstrated on humans that the circumferential shortening (Ecc) and maximal shortening (E3) strains measured by UNTETHER are reproducible and similar to those obtained using a different LV deformation model from tag line data and contours obtained with a user-supervised algorithm in both human volunteers and patients with MI. Our results show that the UNTETHER Ecc and E3 strains are most accurate in the endocardium and mid-wall. Bland-Altman analysis shows that any disagreement be-
tween the two methods in the Ecc and E3 strains is due to outliers and is not systemic. UNTETHER measurements of radial thickening (Err) did not compare well with the measurements obtained with user-supervised analysis; however, these strains tend to be more variable than circumferential strain in tagged images. One factor in Err variability is that tagging with either parallel lines or rectangular grids results in relatively sparse sampling of myocardial motion in the radial direction. For example, a 10-mm-thick myocardium with a tag spacing of 8 mm yields only one or two tag lines in the radial direction, which makes the resulting measurement of Err sensitive to noise in the tag line position measurements and highly influenced by the deformation model. Another source of variability in both Err and Ell is the difficulty of defining the radial and longitudinal directions on the curved LV wall, particularly at the apex. Another automated technique for analyzing tagged cardiac MR images is HARP analysis, which is based on changes in phase associated with spectral peaks in tagged images. HARP analysis has been validated clinically (27), and the UNTETHER algorithm uses HARP tracking to provide a starting point for tracking tags in a given time frame. However, HARP analysis is a 2D technique and does not
Unsupervised Reconstruction of 3D LV Strain
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FIG. 6. Continued.
compensate for the heart’s through-plane motion. UNTETHER computes 3D strains, which have been shown to allow more accurate evaluation of cardiac mechanics (28). Furthermore, since UNTETHER analysis is based on tag line positions, the user can correct errors in tag or contour detection. While user interaction in tag and contour identification runs counter to the idea of automated analysis, and was not used in this study, the option of selectively editing the tag and contour data may allow an imaging study to be analyzed that would otherwise be useless. The tag tracking algorithm used by UNTETHER is similar in spirit to the ML/MAP algorithm (14), but the signal model used in UNTETHER (Eqs. [1] and [2]) does not require an estimate of image intensity statistics for the myocardium and other tissues, which can be difficult to obtain (particularly in white-blood images). The signal model and tag center estimator used in UNTETHER are similar to the template match techniques of Guttman et al. (21,22) and Amini (29). The active contours used in UNTETHER are similar to those used by Guttman et al. (22) and Young (6); however, the algorithms used in Refs. 6 and 22 require user-specified myocardial contours to ensure that only tags within the myocardium are tracked.
An important component of the UNTETHER algorithm is the DMF myocardial deformation reconstruction algorithm. The DMF reconstruction has been validated with both human (30) and canine (12) data, and compared with other deformation reconstruction methods (31). The DMF reconstruction has two important characteristics that are advantageous for automatically estimating strain from the image data. First, the DMF reconstruction is highly localized. If the automated tag tracker makes an error in tracking a tag line, it only affects a localized region around the error, and this can be averaged out. Second, in contrast to finite-element (6,32) and prolate-spheroidal reconstruction methods (8), the DMF does not need a carefully constructed coordinate system for the LV to do the reconstruction. As with any automated image analysis technique, errors in tag detection and ventricular contour estimation are bound to occur, and UNTETHER is no exception. Sources of error in the UNTETHER analysis include failure to detect a tag point when one is present (false negative), detection of a tag point when one is not present (false positive), attraction of a tag point to a non-tag feature in the ROI (such as the pericardial sac), and loss of tag line
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FIG. 6. Continued.
correspondence (positioning a tag point in a part of the image corresponding to another tag line). The sources of interobserver variability in the UNTETHER algorithm are the ROIs and initial tag alignments set by the user at the beginning of the tag tracking process. ROIs drawn by different users can result in a slightly different set of false-positive tag detections sent to the strain reconstruction routine. The effects of false positives are discussed below. The initial alignment specifies the starting position for the active contour used to track tags. Initial alignments specified by different users can result in slightly different final tag line locations, which can cause small changes in the resulting strains. As shown in Table 1, however, these effects are relatively minor. Both short- and long-axis tag lines identified by UNTETHER are close to the user-supervised tag lines. For short-axis tag lines, the difference between the positions of UNTETHER and user-supervised tag lines are within the theoretical precision with which the tag line positions can be determined. For long-axis tag lines, the difference is larger due to greater interaction between tag lines in the myocardium and tag lines in adjacent, nonmyocardial tis-
sues. Also, while the number of tag lines that lose correspondence is small, this is more likely to occur in longaxis tag lines because of rapid contraction during early systole. The UNTETHER algorithm detected 78 – 80% of the tag line points inside the myocardium in 10 human studies. Since the tag line measurements are sparse relative to the volume of the myocardium even in cases of perfect detection, the strain reconstruction is insensitive to a small number of scattered false negatives because of the deformation model. In large regions of false negatives, strain cannot be computed, and the level set algorithm removes these regions from the LV segmentation. UNTETHER detected 31–32% of the tag points tracked outside a set of user-defined LV contours. This false-positive rate includes tag points detected in surrounding tagged tissue, such as the right ventricular wall and liver. False positives affect the strain computation in two ways. First, the segmentation algorithm tends to enclose all tag points in a given slice, so false positives tend to make the LV segmentation bigger than it should be. This is why the myocardium defined by the UNTETHER contours tends to
Unsupervised Reconstruction of 3D LV Strain
enclose the myocardial contours defined by user-supervised analysis. However, a larger myocardium segmentation is only a problem if the segmentation includes both stationary and significantly deforming tissues in close proximity to each other. Second, false positives, tag points attracted to non-tag features in the ROI, and loss of tag line correspondence cause errors in the resulting strain map because the deformation is reconstructed to fit these erroneous points. The DMF reconstruction, however, is highly localized, so the effect of these errors is limited to a small region around the erroneous points. The effect of these errors is further reduced because strains at each mesh point are computed by averaging strains over several segmentation points. The myocardial contours identified by UNTETHER tend to define a larger LV than that defined by user-supervised analysis, and have a wide variation. The primary source of this variation is that the ROI is defined large enough to enclose the LV at the base, and the same ROI is used for all slices. Near the apex, the ROI will enclose more, possibly tagged, tissues other than the LV wall. As a result, there are more false positives in apical slices, leading to a larger epicardial contour. Furthermore, the initial contour endocardial contour radius is 5 pixels, which is too large for some apical slices. Finally, as mentioned above, if there are myocardial regions in which there is no or little tag detection, the level set algorithm will produce a contour that excludes this region from the myocardial segmentation. However, the effect of these contour errors was reduced in the final strain map because the strain was averaged over a several segmentation points. As a result, the UNTETHER algorithm still produced strain maps that correlated well with user-supervised strain maps. We validated the UNTETHER strains by comparing them to strains computed from the same image data with a user-supervised method (8). While the user-supervised strains are not a gold standard, this technique has been extensively validated in mathematical models (8) and moving phantoms (33), and has been used in several studies with in vivo human (34) and canine (4,35–37) data sets. Future Clinical Applications One of the main obstacles to the routine clinical use of tagged MRI is the time and user supervision required to perform quantitative analysis of the image data. Because UNTETHER is an unsupervised algorithm, it may have important clinical applications. UNTETHER analysis of tagged images acquired under dobutamine stress may be useful in detecting myocardial ischemia, and quantifying functional recovery in stunned and hibernating myocardium. UNTETHER quantification of circumferential shortening or maximal shortening at the mid-wall would result in 18 parameters (strain at 6 circumferential ⫻ 3 longitudinal points) that could be recorded on a patient’s chart and, in a series of imaging studies over time, used to track the progress of LV remodeling or the efficacy of treatments. CONCLUSIONS The UNTETHER algorithm provides fast, unsupervised measurements of 3D strain from tagged MR images, and is
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capable of measuring wall motion abnormalities resulting from MI. The UNTETHER algorithm has the potential to overcome the main limitations (time and user-supervision requirements) to routine clinical use of tagged cardiac MRI. ACKNOWLEDGMENTS The authors thank Elliot R. McVeigh, Ph.D., for allowing us access to the human imaging studies. REFERENCES 1. Zerhouni EA, Parish DM, Rogers WJ, Yangand A, Shapiro EP. Human heart: tagging with MR imaging—a method for noninvasive assessment of myocardial motion. Radiology 1988;169:59 – 63. 2. Picano E, Lattanzi F, Orlandini A, Marini C, L’Abbate A. Stress echocardiography and the human factor: the importance of being expert. J Am Coll Cardiol 1991;17:666 – 669. 3. Nagel E, Lehmkuhl HB, Bocksch W, Klein C, Vogel U, Frantz E, Ellmer A, Dreysse S, Fleck E. Noninvasive diagnosis of ischemia-induced wall motion abnormalities with the use of high-dose dobutamine stress MRI: comparison with dobutamine stress echocardiography. Circulation 1999;99:763–770. 4. Croisille P, Moore CC, Judd RM, Lima JA, Arai M, McVeigh ER, Becker LC, Zerhouni EA. Differentiation of viable and nonviable myocardium by the use of three-dimensional tagged MRI in 2-day-old reperfused canine infarcts. Circulation 1999;99:284 –291. 5. Kramer CM, Rogers Jr WJ, Mankad S, Theobald TM, Pakstis DL, Hu YL. Contractile reserve and contrast uptake pattern by magnetic resonance imaging and functional recovery after reperfused myocardial infarction. J Am Coll Cardiol 2000;36:1835–1840. 6. Young AA, Kraitchman DL, Dougherty L, Axel L. Tracking and finite element analysis of stripe deformation in magnetic resonance tagging. IEEE Trans Med Imaging 1995;14:413– 421. 7. Ozturk C, McVeigh ER. Four-dimensional B-spline based motion analysis of tagged MR images: introduction and in vivo validation. Phys Med Biol 2000;45:1683–1702. 8. O’Dell WG, Moore CC, Hunter WC, Zerhouni EA, McVeigh ER. Displacement field fitting for calculating 3D myocardial deformations from parallel-tagged MR images. Radiology 1995;195:829 – 835. 9. Moulton MJ, Creswell LL, Downing SW, Actis RL, Szabo BA, Vannier MW, Pasque MK. Spline surface interpolation for calculating 3-D ventricular strains from MRI tissue tagging. Am J Physiol 1996;270:H281– H297. 10. Kerwin WS, Prince JL. Tracking MR tag surfaces using a spatiotemporal filter and interpolator. Int J Imaging Syst Technol 1999;10:128 –142. 11. Huang J, Abendschein D, Davila-Roman VG, Amini AA. Spatio-temporal tracking of myocardial deformations with a 4-D B-spline model from tagged MRI. IEEE Trans Med Imaging 1999;18:957–972. 12. Denney Jr TS, McVeigh ER. Model-free reconstruction of three-dimensional myocardial strain from planar tagged MR images. J Magn Reson Imaging 1997;7:799 – 810. 13. Osman NF, Kerwin WS, McVeigh ER, Prince JL. Cardiac motion tracking using CINE harmonic phase (HARP) magnetic resonance imaging. Magn Reson Med 1999;42:1048 –1060. 14. Denney Jr TS. Estimation and detection of myocardial tags in MR images without user-defined myocardial contours. IEEE Trans Med Imaging 1999;18:330 –344. 15. Sethian J. Level set methods and fast marching methods, 2nd ed. Cambridge: Cambridge University Press; 1999. 16. McVeigh ER, Atalar E. Cardiac tagging with breath-hold cine MRI. Magn Reson Med 1992;28:318 –327. 17. McVeigh ER. MRI of myocardial function: motion tracking techniques. Magn Reson Imaging 1996;14:137–150. 18. Croisille P, Guttman MA, Atalar E, McVeigh ER, Zerhouni EA. Precision of myocardial contour estimation from tagged MR images with a “black-blood” technique. Acad Radiol 1998;5:93–100. 19. Axel L, Dougherty L. MR imaging of motion with spatial modulation of magnetization. Radiology 1989;171:841– 845. 20. Atalar E, McVeigh ER. Optimization of tag thickness for measuring position with magnetic resonance imaging. IEEE Trans Med Imaging 1994;13:152–160.
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