- Email: [email protected]
Monitoring change in the three-dimensional shape of the human left ventricle
Monitoring Change in the Three-dimensional Shape of the Human Left Ventricle Michal Hubka, John A. McDonald, PhD, Selwyn Wong, MD, Edward L. Bolson, MS, and Florence H. Sheehan, MD, Seattle, Washington, and Auckland, New Zealand
Background: Characterizing left ventricular (LV) remodeling after myocardial infarction or LV shape change resulting from LV shape-restoration operation can yield valuable prognostic information. However, current methods measure only global parameters of LV shape. Methods: We developed and validated a method for measuring change in regional LV shape by aligning a patient’s follow-up 3-dimensional LV surface reconstruction to baseline surface. We tested the diagnostic power of 6 distance functions to detect a known shape deformation. To create the test data, the LV endocardial surface of a control subject was reconstructed using 3-dimensional echocardiographic techniques. The surface was deformed 9 different ways to model LV dilation (3 different locations and severities). Normal shape variability was defined from 18 serial studies of 6 control subjects. The severity of regional dilation was computed as the orthogonal distance between the aligned baseline and deformed LV surfaces. Deformation was quantified according to regional location using the 16-segment map of the LV.
Characterizing left ventricular (LV) remodeling af-
ter a pathologic process or LV shape change resulting from LV shape-restoration operation can yield valuable prognostic information.1 LV shape changes include alteration to a spherical LV because of chronic volume overload,2 and asymmetric aneurysmal dilation of necrotic tissue after a regional ischemic event. Current developments in the field of shape-restoration operation aim at improving LV function, but no 3-dimensional (3D) method for evaluating, quantifying, and correlating postoperative shape changes to clinical outcomes exists.3 From the Cardiovascular Research and Training Center, University of Washington; and Green Lane Hospital, Auckland, New Zealand (S.W.). Supported in part by a grant from the John L. Locke, Jr. Charitable Trust (Seattle, Wash). Reprint requests: Florence H. Sheehan, MD, University of Washington, Box 356422, Seattle, WA 98195-6422. (E-mail: [email protected]). 0894-7317/$30.00 Copyright 2004 by the American Society of Echocardiography. doi:10.1016/j.echo.2004.02.005
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Results: Normal LV shape variability was 3.38 mm. The LV deformations ranged from 2.95 to 8.02 mm. Gaussian distance function produced the highest accuracy for measuring deformation distances (P < .005 by analysis of variance). In addition, the gaussian function correctly identified the location of the maximum deformation in 6 of the 9 distorted surfaces. In the 3 remaining surfaces, the gaussian alignment selected an adjacent basal segment with a similar deformation distance (mean error: 0.2 ⴞ 0.17 mm). The gaussian function’s accuracy in pinpointing the deformation equaled or exceeded the performance of the other 5 functions tested. Conclusion: This new method of aligning 3-dimensional LV surfaces in space facilitates detecting, measuring, and localizing regional shape change in the human LV independent of anatomic landmarks or geometric references. Potential applications include quantitative monitoring of change in regional LV shape after a pathologic process and/or surgical procedure to document efficacy of treatment and to assess prognosis. (J Am Soc Echocardiogr 2004;17: 404-10.)
LV shape predicts exercise capacity,4 is a primary determinant of functional mitral regurgitation,5 and has prognostic information independent of clinical variables, LV function, and coronary anatomy after myocardial infarction (MI) and in dilated cardiomyopathies.6,7 Most studies of LV morphology after MI have measured volume rather than shape. These studies have clearly demonstrated an association between LV dilation, risk for complications, and the development of heart failure.8-12 However, characterizing remodeling in terms of volume change uses its least sensitive metric. Volume lacks specificity as an infinite number of LV shapes can contain the same volume, and volume provides minimal information concerning regional processes by which the LV modifies its structure in response to disease. Global shape parameters such as sphericity are not more informative.12 In contrast, more focused information is obtained from regional analysis– echocardiographic measurement of myocardial bulging in the infarct region predicts risk for infarct expansion and septal rupture,6,13 and regional LV shape abnormalities predicts risk for functional mitral regurgita-
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tion in patients with dilated cardiomyopathy.14 Thus, regional shape analysis can elucidate the mechanisms of complications, and may prove useful in research intended to better understand the mechanism of dilation, guide the search for more effective therapy, and evaluate the effectiveness of both medical and surgical therapies by monitoring and quantifying LV shape in patients. Currently available shape-analysis methods apply only to 2-dimensional LV contours, or have geometric assumptions or other limitations. We developed and validated a method of detecting and quantifying regional changes in 3D LV shape without geometric references.
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Figure 1 Normal left ventricle was deformed to produce 3 severities of dilation in anterior wall.
METHODS Three-dimensional Echocardiography Image acquisition. We imaged a control subject by freehand scanning using a 3-MHz phased-array scanhead and a commercial ultrasound machine (Philips, Bothell, Wash). We acquired an image set of 6 6-second periods at held end-expiration using a magnetic field system to track the ultrasound scanhead (Flock of Birds model 6D-FOB, Ascension Technology Corp, Burlington, Vt).15 Images were registered with position data, and scanning parameters using custom software.16 To avoid ferromagnetic interference from the hospital bed, a custom wooden bed was used. The magnetic field system had a precision of 0.74 mm and an accuracy of ⫺0.12 ⫾ 0.76 mm.17 The study was approved by the human subjects review committee at the University of Washington, Seattle, Wash. Image analysis. We manually selected the image frames corresponding to end-diastole and end-systole and applied the most common systolic interval to all imaging planes. We then manually traced the borders of the LV and its anatomic features. As each border is traced it is reviewed in 3D with previously traced borders using a software interface (Advanced Visual Systems, Waltham, Mass) to verify image plane registration and border tracing consistency.18 All images are traced using the leading-edge technique with the border passing through the middle of the bright part of the lateral echoes. Three-dimensional reconstruction of the LV endocardium and epicardium. The traced borders were aug-
mented with curves defining the valve annuli. To define the aortic annulus, a circle is fit to the traced points of its perimeter. To reconstruct the mitral valve annulus, its traced points are ordered and then connected to form a polygon. A smooth curve is constructed using Fourier series approximations in x, y, and z relative to path length along the polygon.19 Surface reconstruction was performed using piecewise smooth subdivision surfaces, fitting a triangular mesh to the traced borders and reconstructed annuli. The fitting process minimizes a penalized least squares criterion by trading off fidelity to the borders against surface smoothness.17 The control mesh is recur-
sively subdivided to produce a mesh of approximately 800 faces. The piecewise smooth subdivision surface method has been shown to accurately measure volume17 and is the only method shown to reproduce LV shape with anatomic accuracy.19,20 This is of crucial importance for analysis of regional LV shape. Preparation of LV models for testing. We manually retraced the outlines of the control subject’s LV creating 9 separate deformations of the normal LV shape (3 severities of local dilatation in the anterior, inferior, and lateral regions) (Figure 1). The retraced LV surfaces were reconstructed in 3D, and the deformation distances between the normal baseline and each model were computed using the center-surface method (Figure 2).21 This method generates a medial surface (center surface) midway between the 2 input surfaces and constructs chords orthogonal to the center surface extending to both surfaces. The length of each chord is the local distance enabling quantification of the deformation. We projected the standard 16-segment map22 of the LV onto the normal surface and each of the distorted surfaces to permit measurement of the mean intersurface distance in each segment. This enabled identification of the segment with the maximum distance for each baseline-model pair. Method for LV Shape Analysis The approach that we selected was to align the patient’s LV surface from the follow-up study to the same patient’s baseline LV, then measure the distance between them to characterize the change in regional LV shape. The crux of the problem in this approach is the alignment. We sought a method that would align surfaces so that the similar parts match, while ignoring the mismatch of dissimilar parts. We theorized that identifying the parts on a follow-up LV surface that resembled corresponding regions on the baseline study would enable aligning the 2 LV surfaces along these similar parts. This would allow us to measure the magnitude of their shape changes using the local distance between the 2 aligned surfaces. The distances between aligned surfaces were computed using the center-surface method.21
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Figure 2 Center-surface method for measuring local distance between 2 surfaces. Input surfaces are left ventricular endocardium (gold) and epicardium (blue). Center surface (green) is shown midway between input surfaces. Local distance between input surfaces is measured as length of chords drawn orthogonal to center surface.
Alignment is the repositioning of 2 LV surfaces in space to approximate the regions of unchanged shape, which are recognized by their shape similarity. To distinguish normal variability from significant shape change, we used a distance function to guide the alignment. The usual distance function used in alignment is the method of least squares. In the least squares method the distance between surfaces is squared. The squaring assigns a heavy penalty to large intersurface distances during the alignment. This forces the shape alignment to reposition the 2 surfaces in a way that minimizes large intersurface distances. Consequently, abnormal deformations are averaged over the entire LV surface (Figure 3). We, therefore, tested 5 other distance functions corresponding to standard influence functions from robust statistics (Figure 4).23-25 Each of these distance functions differs from least squares by allowing a lower penalty for intersurface distances greater than normal variability. The distance between corresponding regions for which shifts are within the normal variability range are minimized; the distance between corresponding regions having a greater change are retained, allowing their detection as significant shape changes. All of the functions are monotone transforms of euclidean distance. Four of the functions are identical to euclidean distance for distances less than normal variability and then are proportional to mathematic functions that grow more slowly than euclidean distance for distances greater than normal variability. One of these is the standard M-estimate distance function. A final distance function is proportional to an inverted
Figure 3 Top, Method of least squares tends to average out local shape abnormalities so that large deformation may be redistributed. Pull-out from sphere was redistributed to right. Bottom, We sought distance function that permits alignment of 2 surfaces along regions of similar shape, so that deformation can be identified and measured.
Figure 4 Schematic displaying distance functions for alignment that we tested. All functions followed method of least squares for distances less than normal variability. They differed in handling of larger deformation distances.
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Table 1 Accuracy of distance functions in measuring segmental left ventricular shape Distance function
Mean absolute error, mm
Least squares Flat Gaussian Linear Log Square root P*
0.44 ⫾ 0.39 0.35 ⫾ 0.35 0.27 ⫾ 0.28 0.39 ⫾ 0.37 0.36 ⫾ 0.36 0.37 ⫾ 0.36 .0017
*P ⫽ .0002 for comparison of gaussian versus other 5 functions by analysis of variance with a priori contrast.
Figure 5 Six distance functions differed significantly in accuracy of distance measurement (horizontal bars indicate means; N ⫽ 144 [16 segments by 9 deformations]; P ⬍ .02). Gaussian function (3) had lower error than other 5 functions combined (P ⬍ .005). 1, Least squares; 2, flat; 4, linear; 5, log; 6, square root.
gaussian density function, where the scale parameter is the SD of the gaussian density. To assist the alignment we used regional feature labeling to restrict the distance calculation. Specifically we sampled points for each feature (eg, apex, base, aortic valve annulus), then computed distances to the closest points on the second surface with the same label. Minimum distance alignment with regional feature labels constrains the result so that, for example, the general regions labeled “apex” and “base” are aligned together. It does not require that any individual points be aligned, so it can be used when there are no precisely identifiable corresponding points. It also does not have correspondence errors that hinder the use of various pseudolandmark methods, such as aligning using corresponding mesh vertices. We measured normal variability from serial studies of 8 control subjects. LV reconstructions of 2 to 4 serial studies of each subject (18 surface pairings) were aligned using the least squares method. We computed their intersurface distances postalignment using the center-surface method. We defined normal variability to be the 90th percentile of the mean intersurface distance between serial studies. Distance function testing. We randomly repositioned each of the model surfaces away from the baseline LV surface in 3D space using custom software. We then performed alignments of each model to the baseline surface using each of the 6 distance functions. After alignment we computed the mean absolute distance in each of the 16 LV segments using the center-surface method.21 In addition, we identified the segment that was most displaced for each function-aligned baseline-model pair.
Statistical Analysis The true value for deformation distance in each model was defined as the distance between the baseline LV surface and its deformed self. The alignment value for deformation distance was the distance between the baseline LV and its deformed self after the latter was randomly repositioned away from and then aligned back to the baseline LV using one of the distance functions. Distances were averaged in each of the 16 segments of the LV. Mean absolute error in deformation distance by each distance function was computed as the absolute value of the difference from the true value. The performance of the distance functions was compared using analysis of variance. The accuracy of the best-performing distance function was compared with that of the other 5 functions using analysis of variance with a priori contrast.
RESULTS Normal LV shape variability was 3.38 mm. The true deformation distances ranged from 2.95 to 8.02 mm. Gaussian alignment produced the smallest mean absolute error in measuring deformation distance (Figure 5,Table) over the 16 segments. This indicated that the gaussian distance function performed best at matching the original relative positions of the baseline and deformed 2 surfaces (Figure 6). That is, this alignment achieved our goal by superimposing the unchanged regions of the LV. The gaussian function correctly computed the location of the maximum deformation in 6 of the 9 distorted surfaces. In the remaining 3 surfaces the gaussian alignment detected the maximum deformation in the adjacent basal segment. The average error in deformation distance between the segment of maximum deformation and the detected segment was only 0.2 ⫾ 0.17 mm, indicating that the 2 segments were dilated to nearly the same degree. The gaussian function’s accuracy in pinpointing the deformation equaled or exceeded the performance of the other 5 functions tested.
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Figure 6 Gaussian distance function accurately aligned deformed displaced left ventricular (LV) surface back to its original position relative to baseline normal LV, as indicated by close agreement between true versus measured deformation distances.
DISCUSSION The results of this study indicate that 3D echocardiography can be used to accurately detect and measure regional shape changes and to facilitate localizing a regional shape change in the human LV independent of anatomic landmarks and geometric references. Most previous methods for analysis of LV shape only measured global parameters and provided little or no information about 3D regional shape. The most common method of describing LV shape is geometric, eg, by computing the ratio of the major to minor axis length.7,26 This type of analysis is subject to variability in the border tracing and axis placement. Because it examines only a few points on the LV and lacks any regional information about the LV, an unlimited number of shapes can present with the same axis ratio. Methods that relate volume or a surrogate of volume, such as cavity area, to an idealized LV shape measure only global shape and provide little mechanistic information.27,28 Of the methods for regional analysis of 2-dimensional contours, curvature analysis is free of geometric assumptions, provides some regional shape information, and can compare shape with a populationderived normal value.29 However, curvature is sensitive to noise in border tracing unless averaged over a longer portion of the contour, in which case this parameter becomes relatively insensitive to local shape.30 Because regional shape abnormalities
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affect curvature not in the region itself but at its limits, interpretation of this parameter is less than intuitive. Furthermore, the method assumes an anatomic correspondence between each point on the patient’s LV and the same numbered point in the normal reference LVs. Another approach to LV shape analysis is to represent the contour as the weighted sum of geometric shape terms.31 Eigenshape or principal component analysis derives its shape terms from analysis of a population of LVs; therefore, each term has a ventricular shape.32 Neither Fourier nor eigenshape analysis provide an easy format for measuring the depth of an aneurysm because these methods express abnormality by the magnitudes of coefficients for multiple global terms in which shapes are increasingly complex. Both Fourier and eigenshape approaches have been applied to 3D LV reconstructions. However, the authors found these derived basis geometries so “difficult to comprehend intuitively” that they modified the approach to relate the LV to simple geometric shapes such as a cone or cylinder.33 The new approach is invariant to aspect ratio, however, so cannot distinguish a sphere from an ellipse. We previously reported the center-axis method for 3D regional LV shape analysis.20 It has proven useful in studies of idiopathic dilated cardiomyopathy.14 However, the assumption that the point most distant from the mitral centroid is an anatomically stable anchor for defining the center (long) axis makes this shape analysis method unsuitable for coronary artery disease, which may be expected to produce varying shape abnormalities in the apical region. Our method of shape analysis permits visual appreciation of shape changes of patient’s LV over time and measurement of their magnitude and location by aligning 2 LV surfaces from serial studies. Alignment is most easily performed when the target possesses landmarks that are plentiful and evenly distributed over its surface. The landmarks of the LV endocardium are unfortunately quite limited. There are 2 valves, papillary muscle insertions, and the interventricular septum. The LV apex, although frequently cited as a landmark, is not an anatomic structure and is difficult to identify for patients with aneurysms.34 The usual approach for handling a structure possessing so few landmarks is to evenly divide the surface and assume a correspondence between same-numbered subdivisions. This is the approach used by virtually all methods of measuring regional wall motion. We initially attempted alignment using corresponding vertices in the subdivision mesh as landmarks. However, the vertex-based approach produced inappropriate alignments, probably because we needed more landmarks to preserve vertex
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correspondence. Therefore, in this study we performed landmark-free alignment by choosing the alignment transform that minimized distance between the 2 LV surfaces. For landmark-free alignment, we needed a landmark-free measure of distance. Landmark-free measures of distance are usually on the basis of projection or closest points, as in the widely used iterated closest point method.35 The crux of the matter was selecting the method for measuring distance. To achieve an alignment that matches similar parts of the diseased and normal LV surfaces while ignoring the dissimilar parts, we compared the performance of several distance functions. The most commonly used alignment approach, the method of least squares with landmarks, minimizes the sum of the squared distances between 2 LV surfaces. The problem with this approach is that the squared penalty term tends to force an alignment that reduces the deviation of a localized deformation and instead diffuses the abnormality over the rest of the surface. However, the method of least squares is useful for defining normal variability because by definition it minimizes the SD around the mean. In contrast, the gaussian function succeeded in aligning the LV surfaces so that the similar regions matched while ignoring the mismatch of dissimilar regions. Thus, our method is robust, ie, the alignment proceeded along those similar regions while displaying resistance to changes in the dissimilar regions. By aligning a patient’s baseline and follow-up LV along regions of similar shape, our approach mimics a physician’s approach to visual assessment of shape, with the added benefit of being able to quantify the change in shape. Our implicit assumption is that regions less severely altered by disease will remain within normal variability of intersurface distances. This assumption is supported by cardiac anatomy. The base of the heart tends to retain a normal size and shape because of its cartilaginous skeleton and its attachments to the great vessels and atria. Even in acute transmural MI we observed only a small change in the angle between the mitral and aortic valve planes.36 In comparison, the lateral wall and apex are freer to be deformed by a disease process. Of the 6 distance functions tested, the gaussian alignment provided the greatest diagnostic accuracy. Furthermore, the alignment approach enabled not only direct visual comparison of the LV surface before and after deformation, but also quantitative analysis in terms of the distance between the LV’s normal state and after dilation. Analysis of shape change using a simple distance measurement is considerably more interpretable than previously described metrics.
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Study Limitations We have, thus far, only tested the gaussian alignment method on synthetic deformations. Further testing is indicated to clinically validate this shape analysis method. We did not apply normal study-to-study variability thresholds to individual triangles in the LV surface mesh. Instead, we simply used the 90th percentile value for the entire LV. However, further study is warranted to determine whether local application of the variability threshold improves diagnostic accuracy in shape analysis. Our shape method is intended for, and validated for, analysis of regional change in LV shape. The performance of this method in global ventricular dilation is currently under evaluation. Clinical Applications Potential clinical applications of this method are in both cardiology and cardiac operation. The alignment method’s ability to detect shape changes in serial studies of the same patient would allow the cardiologist to assess the degree of remodeling of a diseased LV, and could assist in predicting those most likely to have LV rupture after acute MI, decompensate into heart failure, or have complications develop related to LV geometry such as functional mitral regurgitation. The sensitivity of the gaussian alignment allows detection of slight LV remodeling and may yield a better-tailored therapy. LV shape-restoration operation may be facilitated by careful 3D evaluation and quantification of shape changes achieved, and correlation to clinical outcomes. Our method for monitoring changes in regional LV shape provides, for the first time, a way of describing and characterizing shape changes in specific regions of the LV in terms that are easily understandable, unlike curvature and eigenshape analysis. By permitting direct comparison between 2 LV surfaces, regional description of shape can be correlated directly with coronary anatomy and with LV perfusion, metabolism, and function. This will facilitate a more focused analysis of pathology of LV shape, and allow further investigation of the interrelationship between shape and function. Additional studies are indicated to demonstrate that this method provides a comprehensive and accurate analysis of shape changes for clinical patient evaluation.
REFERENCES 1. Di Donato M, Sabatier M, Dor V, Gensini GF, Toso A, Maioli M, et al. Effects of the Dor procedure on left ventricular dimension and shape and geometric correlates of mitral regurgitation one year after surgery. J Thorac Cardiovasc Surg 2001;121:91-6.
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2. Dodge HT, Frimer M, Stewart DK. Functional evaluation of the hypertrophied heart in man. Circ Res 1974;35(Suppl 2):122-7. 3. Dor V. Left ventricular reconstruction for ischemic cardiomyopathy. J Card Surg 2002;17:180-7. 4. Lamas GA, Vaughan DE, Parisi AF, Pfeffer MA. Effects of left ventricular shape and captopril therapy on exercise capacity after anterior wall acute myocardial infarction. Am J Cardiol 1989;63:1167-73. 5. Kono T, Sabbah HN, Rosman H, Alam M, Jafri S, Goldstein S. Left ventricular shape is the primary determinant of functional mitral regurgitation in heart failure. J Am Coll Cardiol 1992;20:1594-8. 6. Jugdutt BI. Identification of patients prone to infarct expansion by the degree of regional shape distortion on an early two-dimensional echocardiogram after myocardial infarction. Clin Cardiol 1990;13:28-40. 7. Douglas PS, Morrow R, Ioli A, Reichek N. Left ventricular shape, afterload and survival in idiopathic dilated cardiomyopathy. J Am Coll Cardiol 1989;13:311-5. 8. Gaudron P, Eilles C, Kugler I, Ertl G. Progressive left ventricular dysfunction and remodeling after myocardial infarction: potential mechanisms and early predictors. Circulation 1993; 87:755-63. 9. White HD, Norris RM, Brown MA, Brandt PWT, Whitlock RML, Wild CJ. Left ventricular end-systolic volume as the major determinant of survival after recovery from myocardial infarction. Circulation 1987;76:44-51. 10. Warren SE, Royal HD, Markis JE, Grossman W, McKay RG. Time course of left ventricular dilation after myocardial infarction: influence of infarct-related artery and success of coronary thrombolysis. J Am Coll Cardiol 1988;11:12-9. 11. Jeremy RW, Allman KC, Bautovitch G, Harris PJ. Patterns of left ventricular dilation during the six months after myocardial infarction. J Am Coll Cardiol 1989;13:304-10. 12. St John Sutton M, Pfeffer MA, Moye L, Plappert T, Rouleau JL, Lamas G, et al. Cardiovascular death and left ventricular remodeling two years after myocardial infarction: baseline predictors and impact of long-term use of captopril-information from the survival and ventricular enlargement (SAVE) trial. Circulation 1997;96:3294-9. 13. Jugdutt BI, Michorowski BL. Role of infarct expansion in rupture of the ventrical septum after acute myocardial infarction: a two-dimensional echocardiographic study. Clin Cardiol 1987;10:641-52. 14. Aikawa K, Sheehan FH, Otto CM, Coady K, Bashein G, Bolson EL. The severity of functional mitral regurgitation depends on the shape of the mitral apparatus: a three dimensional echo analysis. J Heart Valve Dis 2002;11:627-36. 15. Detmer PR, Bashein G, Hodges T, Beach KW, Filer EP, Burns DH, et al. 3D ultrasonic image feature localization based on magnetic scanhead tracking: in vitro calibration and validation. Ultrasound Med Biol 1994;20:923-36. 16. Filer EP. A data acquisition and image capture system for three-dimensional transesophageal echocardiography [master’s thesis]. Seattle: University of Washington; 1994. 17. Legget ME, Leotta DF, Bolson EL, McDonald JA, Martin RW, Li XN, et al. System for quantitative three-dimensional echocardiography of the left ventricle based on a magnetic field position and orientation sensing system. IEEE Trans Biomed Eng 1998;45:494-504.
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18. Sheehan FH, Bolson EL, McDonald JA, Bashein G, Zeppa ML, Martin RW. Three dimensional echocardiography system for quantitative analysis of the left ventricle. IEEE Comput Cardiol 1998;25:649-52. 19. Legget ME, Bashein G, McDonald JA, Munt BI, Martin RW, Otto CM, et al. Three-dimensional measurement of the mitral annulus by multiplane transesophageal echocardiography: in vitro validation and in vivo demonstration. J Am Soc Echocardiogr 1998;11:188-200. 20. Munt BI, Leotta DF, Martin RW, Otto CM, Bolson EL, Sheehan FH. Left ventricular shape analysis from three-dimensional echocardiograms. J Am Soc Echocardiogr 1998; 11:761-9. 21. Hubka M, Lipiecki J, Bolson EL, Martin RW, Munt B, Maza SR, et al. Three-dimensional echocardiographic measurement of left ventricular wall thickness: in vitro and in vivo validation. J Am Soc Echocardiogr 2002;15:129-35. 22. Schiller NB, Shah PM, Crawford M, DeMaria A, Devereux R, Feigenbaum H, et al. Recommendations for quantitation of the left ventricle by two-dimensional echocardiography. J Am Soc Echocardiogr 1989;2:358-67. 23. Hampel FR. Robust statistics: the approach based on influence functions. New York: Wiley; 1986. 24. Huber PJ. Robust statistics. New York: Wiley; 1981. 25. Huber PJ. Robust statistical procedures. 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics; 1996. 26. D’Cruz IA, Aboulatta H, Killam H, Bradley A, Hand RC. Quantitative two-dimensional echocardiographic assessment of left ventricular shape in ischemic heart disease. J Clin Ultrasound 1989;17:569-72. 27. Gibson DG, Brown DJ. Continuous assessment of left ventricular shape in man. Br Heart J 1975;37:904-10. 28. Tomlinson CW. Left ventricular geometry and function in experimental heart failure. Can J Cardiol 1987;3:305-10. 29. Mancini GBJ, McGillem MJ. Quantitative regional curvature analysis: validation in animals of a method for assessing regional ventricular remodeling in ischemic heart disease. Int J Card Imaging 1991;7:73-8. 30. Van Eyll C, Pouleur H, Raigoso J, Gurne O, Charlier AA, Rousseau MF. Curvature analysis of ventriculograms: how useful is it to assess progression of left ventricular remodeling and dysfunction? Comput Cardiol Chicago: IEEE Computer Society Press, 1991. p. 577-580. 31. Kass DA, Traill TA, Keating M, Altieri PI, Maughan WL. Abnormalities of dynamic ventricular shape change in patients with aortic and mitral valvular regurgitation: assessment by Fourier shape analysis and global geometric indexes. Circ Res 1988;62:127-38. 32. Sampson PD, Bookstein FL, Sheehan FH, Bolson EL. Eigenshape analysis of left ventricular outlines from contrast ventriculograms: advances in morphometrics. New York: Plenum Press; 1996. 33. Azhari H, Beyar R, Sideman S. On the human left ventricular shape. Comput Biomed Res 1999;32:264-82. 34. Brower RW. Evaluation of pattern recognition rules for the apex of the heart. Catheter Cardiovasc Diagn 1980;6:145-57. 35. Besl PJ, McKay HD. A method for registration of 3-D shapes. IEEE Trans Pattern Anal Machine Intell 1992;14:239-56. 36. Harmon KE, Sheehan FH, Hosokawa H. Effect of acute myocardial infarction on the angle between the mitral and aortic valve plane. Am J Cardiol 1999;84:342-4.
Background: Characterizing left ventricular (LV) remodeling after myocardial infarction or LV shape change resulting from LV shape-restoration operation can yield valuable prognostic information. However, current methods measure only global parameters of LV shape. Methods: We developed and validated a method for measuring change in regional LV shape by aligning a patient’s follow-up 3-dimensional LV surface reconstruction to baseline surface. We tested the diagnostic power of 6 distance functions to detect a known shape deformation. To create the test data, the LV endocardial surface of a control subject was reconstructed using 3-dimensional echocardiographic techniques. The surface was deformed 9 different ways to model LV dilation (3 different locations and severities). Normal shape variability was defined from 18 serial studies of 6 control subjects. The severity of regional dilation was computed as the orthogonal distance between the aligned baseline and deformed LV surfaces. Deformation was quantified according to regional location using the 16-segment map of the LV.
Characterizing left ventricular (LV) remodeling af-
ter a pathologic process or LV shape change resulting from LV shape-restoration operation can yield valuable prognostic information.1 LV shape changes include alteration to a spherical LV because of chronic volume overload,2 and asymmetric aneurysmal dilation of necrotic tissue after a regional ischemic event. Current developments in the field of shape-restoration operation aim at improving LV function, but no 3-dimensional (3D) method for evaluating, quantifying, and correlating postoperative shape changes to clinical outcomes exists.3 From the Cardiovascular Research and Training Center, University of Washington; and Green Lane Hospital, Auckland, New Zealand (S.W.). Supported in part by a grant from the John L. Locke, Jr. Charitable Trust (Seattle, Wash). Reprint requests: Florence H. Sheehan, MD, University of Washington, Box 356422, Seattle, WA 98195-6422. (E-mail: [email protected]). 0894-7317/$30.00 Copyright 2004 by the American Society of Echocardiography. doi:10.1016/j.echo.2004.02.005
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Results: Normal LV shape variability was 3.38 mm. The LV deformations ranged from 2.95 to 8.02 mm. Gaussian distance function produced the highest accuracy for measuring deformation distances (P < .005 by analysis of variance). In addition, the gaussian function correctly identified the location of the maximum deformation in 6 of the 9 distorted surfaces. In the 3 remaining surfaces, the gaussian alignment selected an adjacent basal segment with a similar deformation distance (mean error: 0.2 ⴞ 0.17 mm). The gaussian function’s accuracy in pinpointing the deformation equaled or exceeded the performance of the other 5 functions tested. Conclusion: This new method of aligning 3-dimensional LV surfaces in space facilitates detecting, measuring, and localizing regional shape change in the human LV independent of anatomic landmarks or geometric references. Potential applications include quantitative monitoring of change in regional LV shape after a pathologic process and/or surgical procedure to document efficacy of treatment and to assess prognosis. (J Am Soc Echocardiogr 2004;17: 404-10.)
LV shape predicts exercise capacity,4 is a primary determinant of functional mitral regurgitation,5 and has prognostic information independent of clinical variables, LV function, and coronary anatomy after myocardial infarction (MI) and in dilated cardiomyopathies.6,7 Most studies of LV morphology after MI have measured volume rather than shape. These studies have clearly demonstrated an association between LV dilation, risk for complications, and the development of heart failure.8-12 However, characterizing remodeling in terms of volume change uses its least sensitive metric. Volume lacks specificity as an infinite number of LV shapes can contain the same volume, and volume provides minimal information concerning regional processes by which the LV modifies its structure in response to disease. Global shape parameters such as sphericity are not more informative.12 In contrast, more focused information is obtained from regional analysis– echocardiographic measurement of myocardial bulging in the infarct region predicts risk for infarct expansion and septal rupture,6,13 and regional LV shape abnormalities predicts risk for functional mitral regurgita-
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tion in patients with dilated cardiomyopathy.14 Thus, regional shape analysis can elucidate the mechanisms of complications, and may prove useful in research intended to better understand the mechanism of dilation, guide the search for more effective therapy, and evaluate the effectiveness of both medical and surgical therapies by monitoring and quantifying LV shape in patients. Currently available shape-analysis methods apply only to 2-dimensional LV contours, or have geometric assumptions or other limitations. We developed and validated a method of detecting and quantifying regional changes in 3D LV shape without geometric references.
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Figure 1 Normal left ventricle was deformed to produce 3 severities of dilation in anterior wall.
METHODS Three-dimensional Echocardiography Image acquisition. We imaged a control subject by freehand scanning using a 3-MHz phased-array scanhead and a commercial ultrasound machine (Philips, Bothell, Wash). We acquired an image set of 6 6-second periods at held end-expiration using a magnetic field system to track the ultrasound scanhead (Flock of Birds model 6D-FOB, Ascension Technology Corp, Burlington, Vt).15 Images were registered with position data, and scanning parameters using custom software.16 To avoid ferromagnetic interference from the hospital bed, a custom wooden bed was used. The magnetic field system had a precision of 0.74 mm and an accuracy of ⫺0.12 ⫾ 0.76 mm.17 The study was approved by the human subjects review committee at the University of Washington, Seattle, Wash. Image analysis. We manually selected the image frames corresponding to end-diastole and end-systole and applied the most common systolic interval to all imaging planes. We then manually traced the borders of the LV and its anatomic features. As each border is traced it is reviewed in 3D with previously traced borders using a software interface (Advanced Visual Systems, Waltham, Mass) to verify image plane registration and border tracing consistency.18 All images are traced using the leading-edge technique with the border passing through the middle of the bright part of the lateral echoes. Three-dimensional reconstruction of the LV endocardium and epicardium. The traced borders were aug-
mented with curves defining the valve annuli. To define the aortic annulus, a circle is fit to the traced points of its perimeter. To reconstruct the mitral valve annulus, its traced points are ordered and then connected to form a polygon. A smooth curve is constructed using Fourier series approximations in x, y, and z relative to path length along the polygon.19 Surface reconstruction was performed using piecewise smooth subdivision surfaces, fitting a triangular mesh to the traced borders and reconstructed annuli. The fitting process minimizes a penalized least squares criterion by trading off fidelity to the borders against surface smoothness.17 The control mesh is recur-
sively subdivided to produce a mesh of approximately 800 faces. The piecewise smooth subdivision surface method has been shown to accurately measure volume17 and is the only method shown to reproduce LV shape with anatomic accuracy.19,20 This is of crucial importance for analysis of regional LV shape. Preparation of LV models for testing. We manually retraced the outlines of the control subject’s LV creating 9 separate deformations of the normal LV shape (3 severities of local dilatation in the anterior, inferior, and lateral regions) (Figure 1). The retraced LV surfaces were reconstructed in 3D, and the deformation distances between the normal baseline and each model were computed using the center-surface method (Figure 2).21 This method generates a medial surface (center surface) midway between the 2 input surfaces and constructs chords orthogonal to the center surface extending to both surfaces. The length of each chord is the local distance enabling quantification of the deformation. We projected the standard 16-segment map22 of the LV onto the normal surface and each of the distorted surfaces to permit measurement of the mean intersurface distance in each segment. This enabled identification of the segment with the maximum distance for each baseline-model pair. Method for LV Shape Analysis The approach that we selected was to align the patient’s LV surface from the follow-up study to the same patient’s baseline LV, then measure the distance between them to characterize the change in regional LV shape. The crux of the problem in this approach is the alignment. We sought a method that would align surfaces so that the similar parts match, while ignoring the mismatch of dissimilar parts. We theorized that identifying the parts on a follow-up LV surface that resembled corresponding regions on the baseline study would enable aligning the 2 LV surfaces along these similar parts. This would allow us to measure the magnitude of their shape changes using the local distance between the 2 aligned surfaces. The distances between aligned surfaces were computed using the center-surface method.21
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Figure 2 Center-surface method for measuring local distance between 2 surfaces. Input surfaces are left ventricular endocardium (gold) and epicardium (blue). Center surface (green) is shown midway between input surfaces. Local distance between input surfaces is measured as length of chords drawn orthogonal to center surface.
Alignment is the repositioning of 2 LV surfaces in space to approximate the regions of unchanged shape, which are recognized by their shape similarity. To distinguish normal variability from significant shape change, we used a distance function to guide the alignment. The usual distance function used in alignment is the method of least squares. In the least squares method the distance between surfaces is squared. The squaring assigns a heavy penalty to large intersurface distances during the alignment. This forces the shape alignment to reposition the 2 surfaces in a way that minimizes large intersurface distances. Consequently, abnormal deformations are averaged over the entire LV surface (Figure 3). We, therefore, tested 5 other distance functions corresponding to standard influence functions from robust statistics (Figure 4).23-25 Each of these distance functions differs from least squares by allowing a lower penalty for intersurface distances greater than normal variability. The distance between corresponding regions for which shifts are within the normal variability range are minimized; the distance between corresponding regions having a greater change are retained, allowing their detection as significant shape changes. All of the functions are monotone transforms of euclidean distance. Four of the functions are identical to euclidean distance for distances less than normal variability and then are proportional to mathematic functions that grow more slowly than euclidean distance for distances greater than normal variability. One of these is the standard M-estimate distance function. A final distance function is proportional to an inverted
Figure 3 Top, Method of least squares tends to average out local shape abnormalities so that large deformation may be redistributed. Pull-out from sphere was redistributed to right. Bottom, We sought distance function that permits alignment of 2 surfaces along regions of similar shape, so that deformation can be identified and measured.
Figure 4 Schematic displaying distance functions for alignment that we tested. All functions followed method of least squares for distances less than normal variability. They differed in handling of larger deformation distances.
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Table 1 Accuracy of distance functions in measuring segmental left ventricular shape Distance function
Mean absolute error, mm
Least squares Flat Gaussian Linear Log Square root P*
0.44 ⫾ 0.39 0.35 ⫾ 0.35 0.27 ⫾ 0.28 0.39 ⫾ 0.37 0.36 ⫾ 0.36 0.37 ⫾ 0.36 .0017
*P ⫽ .0002 for comparison of gaussian versus other 5 functions by analysis of variance with a priori contrast.
Figure 5 Six distance functions differed significantly in accuracy of distance measurement (horizontal bars indicate means; N ⫽ 144 [16 segments by 9 deformations]; P ⬍ .02). Gaussian function (3) had lower error than other 5 functions combined (P ⬍ .005). 1, Least squares; 2, flat; 4, linear; 5, log; 6, square root.
gaussian density function, where the scale parameter is the SD of the gaussian density. To assist the alignment we used regional feature labeling to restrict the distance calculation. Specifically we sampled points for each feature (eg, apex, base, aortic valve annulus), then computed distances to the closest points on the second surface with the same label. Minimum distance alignment with regional feature labels constrains the result so that, for example, the general regions labeled “apex” and “base” are aligned together. It does not require that any individual points be aligned, so it can be used when there are no precisely identifiable corresponding points. It also does not have correspondence errors that hinder the use of various pseudolandmark methods, such as aligning using corresponding mesh vertices. We measured normal variability from serial studies of 8 control subjects. LV reconstructions of 2 to 4 serial studies of each subject (18 surface pairings) were aligned using the least squares method. We computed their intersurface distances postalignment using the center-surface method. We defined normal variability to be the 90th percentile of the mean intersurface distance between serial studies. Distance function testing. We randomly repositioned each of the model surfaces away from the baseline LV surface in 3D space using custom software. We then performed alignments of each model to the baseline surface using each of the 6 distance functions. After alignment we computed the mean absolute distance in each of the 16 LV segments using the center-surface method.21 In addition, we identified the segment that was most displaced for each function-aligned baseline-model pair.
Statistical Analysis The true value for deformation distance in each model was defined as the distance between the baseline LV surface and its deformed self. The alignment value for deformation distance was the distance between the baseline LV and its deformed self after the latter was randomly repositioned away from and then aligned back to the baseline LV using one of the distance functions. Distances were averaged in each of the 16 segments of the LV. Mean absolute error in deformation distance by each distance function was computed as the absolute value of the difference from the true value. The performance of the distance functions was compared using analysis of variance. The accuracy of the best-performing distance function was compared with that of the other 5 functions using analysis of variance with a priori contrast.
RESULTS Normal LV shape variability was 3.38 mm. The true deformation distances ranged from 2.95 to 8.02 mm. Gaussian alignment produced the smallest mean absolute error in measuring deformation distance (Figure 5,Table) over the 16 segments. This indicated that the gaussian distance function performed best at matching the original relative positions of the baseline and deformed 2 surfaces (Figure 6). That is, this alignment achieved our goal by superimposing the unchanged regions of the LV. The gaussian function correctly computed the location of the maximum deformation in 6 of the 9 distorted surfaces. In the remaining 3 surfaces the gaussian alignment detected the maximum deformation in the adjacent basal segment. The average error in deformation distance between the segment of maximum deformation and the detected segment was only 0.2 ⫾ 0.17 mm, indicating that the 2 segments were dilated to nearly the same degree. The gaussian function’s accuracy in pinpointing the deformation equaled or exceeded the performance of the other 5 functions tested.
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Figure 6 Gaussian distance function accurately aligned deformed displaced left ventricular (LV) surface back to its original position relative to baseline normal LV, as indicated by close agreement between true versus measured deformation distances.
DISCUSSION The results of this study indicate that 3D echocardiography can be used to accurately detect and measure regional shape changes and to facilitate localizing a regional shape change in the human LV independent of anatomic landmarks and geometric references. Most previous methods for analysis of LV shape only measured global parameters and provided little or no information about 3D regional shape. The most common method of describing LV shape is geometric, eg, by computing the ratio of the major to minor axis length.7,26 This type of analysis is subject to variability in the border tracing and axis placement. Because it examines only a few points on the LV and lacks any regional information about the LV, an unlimited number of shapes can present with the same axis ratio. Methods that relate volume or a surrogate of volume, such as cavity area, to an idealized LV shape measure only global shape and provide little mechanistic information.27,28 Of the methods for regional analysis of 2-dimensional contours, curvature analysis is free of geometric assumptions, provides some regional shape information, and can compare shape with a populationderived normal value.29 However, curvature is sensitive to noise in border tracing unless averaged over a longer portion of the contour, in which case this parameter becomes relatively insensitive to local shape.30 Because regional shape abnormalities
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affect curvature not in the region itself but at its limits, interpretation of this parameter is less than intuitive. Furthermore, the method assumes an anatomic correspondence between each point on the patient’s LV and the same numbered point in the normal reference LVs. Another approach to LV shape analysis is to represent the contour as the weighted sum of geometric shape terms.31 Eigenshape or principal component analysis derives its shape terms from analysis of a population of LVs; therefore, each term has a ventricular shape.32 Neither Fourier nor eigenshape analysis provide an easy format for measuring the depth of an aneurysm because these methods express abnormality by the magnitudes of coefficients for multiple global terms in which shapes are increasingly complex. Both Fourier and eigenshape approaches have been applied to 3D LV reconstructions. However, the authors found these derived basis geometries so “difficult to comprehend intuitively” that they modified the approach to relate the LV to simple geometric shapes such as a cone or cylinder.33 The new approach is invariant to aspect ratio, however, so cannot distinguish a sphere from an ellipse. We previously reported the center-axis method for 3D regional LV shape analysis.20 It has proven useful in studies of idiopathic dilated cardiomyopathy.14 However, the assumption that the point most distant from the mitral centroid is an anatomically stable anchor for defining the center (long) axis makes this shape analysis method unsuitable for coronary artery disease, which may be expected to produce varying shape abnormalities in the apical region. Our method of shape analysis permits visual appreciation of shape changes of patient’s LV over time and measurement of their magnitude and location by aligning 2 LV surfaces from serial studies. Alignment is most easily performed when the target possesses landmarks that are plentiful and evenly distributed over its surface. The landmarks of the LV endocardium are unfortunately quite limited. There are 2 valves, papillary muscle insertions, and the interventricular septum. The LV apex, although frequently cited as a landmark, is not an anatomic structure and is difficult to identify for patients with aneurysms.34 The usual approach for handling a structure possessing so few landmarks is to evenly divide the surface and assume a correspondence between same-numbered subdivisions. This is the approach used by virtually all methods of measuring regional wall motion. We initially attempted alignment using corresponding vertices in the subdivision mesh as landmarks. However, the vertex-based approach produced inappropriate alignments, probably because we needed more landmarks to preserve vertex
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correspondence. Therefore, in this study we performed landmark-free alignment by choosing the alignment transform that minimized distance between the 2 LV surfaces. For landmark-free alignment, we needed a landmark-free measure of distance. Landmark-free measures of distance are usually on the basis of projection or closest points, as in the widely used iterated closest point method.35 The crux of the matter was selecting the method for measuring distance. To achieve an alignment that matches similar parts of the diseased and normal LV surfaces while ignoring the dissimilar parts, we compared the performance of several distance functions. The most commonly used alignment approach, the method of least squares with landmarks, minimizes the sum of the squared distances between 2 LV surfaces. The problem with this approach is that the squared penalty term tends to force an alignment that reduces the deviation of a localized deformation and instead diffuses the abnormality over the rest of the surface. However, the method of least squares is useful for defining normal variability because by definition it minimizes the SD around the mean. In contrast, the gaussian function succeeded in aligning the LV surfaces so that the similar regions matched while ignoring the mismatch of dissimilar regions. Thus, our method is robust, ie, the alignment proceeded along those similar regions while displaying resistance to changes in the dissimilar regions. By aligning a patient’s baseline and follow-up LV along regions of similar shape, our approach mimics a physician’s approach to visual assessment of shape, with the added benefit of being able to quantify the change in shape. Our implicit assumption is that regions less severely altered by disease will remain within normal variability of intersurface distances. This assumption is supported by cardiac anatomy. The base of the heart tends to retain a normal size and shape because of its cartilaginous skeleton and its attachments to the great vessels and atria. Even in acute transmural MI we observed only a small change in the angle between the mitral and aortic valve planes.36 In comparison, the lateral wall and apex are freer to be deformed by a disease process. Of the 6 distance functions tested, the gaussian alignment provided the greatest diagnostic accuracy. Furthermore, the alignment approach enabled not only direct visual comparison of the LV surface before and after deformation, but also quantitative analysis in terms of the distance between the LV’s normal state and after dilation. Analysis of shape change using a simple distance measurement is considerably more interpretable than previously described metrics.
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Study Limitations We have, thus far, only tested the gaussian alignment method on synthetic deformations. Further testing is indicated to clinically validate this shape analysis method. We did not apply normal study-to-study variability thresholds to individual triangles in the LV surface mesh. Instead, we simply used the 90th percentile value for the entire LV. However, further study is warranted to determine whether local application of the variability threshold improves diagnostic accuracy in shape analysis. Our shape method is intended for, and validated for, analysis of regional change in LV shape. The performance of this method in global ventricular dilation is currently under evaluation. Clinical Applications Potential clinical applications of this method are in both cardiology and cardiac operation. The alignment method’s ability to detect shape changes in serial studies of the same patient would allow the cardiologist to assess the degree of remodeling of a diseased LV, and could assist in predicting those most likely to have LV rupture after acute MI, decompensate into heart failure, or have complications develop related to LV geometry such as functional mitral regurgitation. The sensitivity of the gaussian alignment allows detection of slight LV remodeling and may yield a better-tailored therapy. LV shape-restoration operation may be facilitated by careful 3D evaluation and quantification of shape changes achieved, and correlation to clinical outcomes. Our method for monitoring changes in regional LV shape provides, for the first time, a way of describing and characterizing shape changes in specific regions of the LV in terms that are easily understandable, unlike curvature and eigenshape analysis. By permitting direct comparison between 2 LV surfaces, regional description of shape can be correlated directly with coronary anatomy and with LV perfusion, metabolism, and function. This will facilitate a more focused analysis of pathology of LV shape, and allow further investigation of the interrelationship between shape and function. Additional studies are indicated to demonstrate that this method provides a comprehensive and accurate analysis of shape changes for clinical patient evaluation.
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