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(Circulation. 1997;95:924-931.)
© 1997 American Heart Association, Inc.

Articles

Detection and Quantification of Dysfunctional Myocardium by Magnetic Resonance Imaging

A New Three-dimensional Method for Quantitative Wall-Thickening Analysis

Eduard R. Holman, MA; Vincent G.M. Buller, MSc; Albert de Roos, MD; Rob J. van der Geest, MSc; Leo H.B. Baur, MD; Arnoud van der Laarse, PhD; Albert V.G. Bruschke, MD; Johan H.C. Reiber, PhD; Ernst E. van der Wall, MD

the Departments of Cardiology (E.R.H., L.H.B.B., A. van der L., A.V.G.B., J.H.C.R., E.E. van der W.) and Diagnostic Radiology and Nuclear Medicine (V.G.M.B., A. de R., R.J. van der G., J.H.C.R.), University Hospital, Leiden, Netherlands, and Interuniversity Cardiology Institute of the Netherlands (E.R.H., A. de R., A. van der L., A.V.G.B., J.H.C.R., E.E. van der W.), Utrecht, Netherlands.

Correspondence to Ernst E. van der Wall, MD, Department of Cardiology, Bldg 1, C5-P25, University Hospital, Albinusdreef 2, 2333 AA Leiden, Netherlands. E-mail vanderwall@cardio.azl.nl.

	Abstract

Top Abstract Introduction Methods Results Discussion Appendix References

 
Background Regional left ventricular dysfunction is a major consequence of myocardial ischemia, and its extent determines long-term prognosis. Accurate and reproducible analysis of left ventricular dysfunction is therefore useful for risk stratification and patient management.

Methods and Results Short-axis cardiac cine magnetic resonance (MR) imaging was performed in 25 patients after anterior myocardial infarction at 21±2.1 days after the acute onset. The MR images were analyzed with the use of a dedicated analytical software package (MASS version 1.0), which includes a modified centerline method and a new three-dimensional analysis approach. A database of 48 healthy volunteers was constructed to objectively depict myocardial dysfunction in the patients; this database was compared with enzymatically determined infarct size. The mean (±SEM) quantity of dysfunctional myocardium and enzymatically calculated infarct size equaled 24.0±3.0 and 22.3±2.9 g, respectively (P=.69). Enzymatically determined infarct size correlated strongly with left ventricular dysfunction determined by cine MR imaging (y=0.90x+3.7; r=.92, P<.0001). Segments related to the distribution of the left anterior descending coronary artery showed a significantly lower percentage wall thickening in patients than did corresponding segments of 48 normal subjects (46.0±8.22% versus 87.1±3.45%, mean±SEM, respectively; P<.001). The mean (±SEM) end-diastolic wall thickness of the infarcted segment did not differ from that of corresponding normal segments (7.4±0.33 versus 7.5±0.15 mm; P=.75).

Conclusions We conclude that the use of three-dimensional quantitative analysis of cine MR images accurately quantifies the extent of regional left ventricular dysfunction in the infarcted heart. This method of analysis may be useful in assessing the effect of interventional therapies.

Key Words: imaging • myocardial infarction • myocardial contraction

	Introduction

Top Abstract Introduction Methods Results Discussion Appendix References

 
Prognosis after myocardial infarction is closely related to the extent of myocardial necrosis¹ and the degree of contractile dysfunction of the left ventricle.^{2 3 4} Impairment of systolic wall thickening has been shown to be a reliable indicator of segmental contractile dysfunction after myocardial infarction.⁵ Accordingly, the development of reliable noninvasive and easily reproducible imaging modalities to evaluate regional LV wall thickening after myocardial infarction is useful for risk stratification and for monitoring of therapies. During the last decade, MR imaging has emerged as a noninvasive modality that permits acquisition of high-resolution images in virtually any tomographic plane. In particular, the gradient-echo (cine) MR imaging technique has been used widely to evaluate global and regional LV function by analysis of wall motion and wall thickening.^{6 7} However, most previous studies relied on visual assessment of wall motion and wall thickening,^{6 8 9 10} which precludes the measurement of a large number of data points. Accurate analysis of LV wall thickening to assess the quantity of dysfunctional myocardium is currently cumbersome owing to the unavailability of commercial image-analysis software and time-consuming analytical procedures. Recently, a dedicated analytical software package for short-axis MR images (MASS version 1.0) was developed at our institution that allows accurate measurement of regional LV function. A 3D approach has been implemented to calculate wall thickness at different cardiac phases perpendicular to the LV myocardial wall.¹¹ This system incorporates an improved centerline method to quantify wall motion and wall thickening.¹² The two-dimensional centerline method has proved its accuracy for the quantification of regional LV dysfunction in pigs in relation to myocardial infarction.¹³ In the latter study, data obtained from the same animals before induction of myocardial infarction served as a reference standard to assess the quantity of dysfunctional myocardium after induction of myocardial infarction. To apply the centerline method to infarcted human hearts, we set up a database of normal regional LV function for reference purposes. Therefore, 48 healthy individuals were studied for analysis of LV function.

The purpose of the present study was to quantify the extent of LV dysfunction in patients 3 weeks after myocardial infarction, relative to a database of normal values. Results were correlated to coronary x-ray arteriography, ECG, and enzymatic indexes of myocardial infarct size.

	Methods

Top Abstract Introduction Methods Results Discussion Appendix References

 
Patient Selection
To evaluate a homogeneous patient group, only patients with an anterior myocardial wall infarction were included. Twenty-five patients (mean age, 54.6±12.4 years; range, 30 to 73 years) fulfilled the following study entrance criteria: first anterior myocardial infarction diagnosed by clinical history, ECG, and increased plasma enzyme levels. The percentage of patients in each age decade is presented in Table 1. The location of the infarct was assessed by ECG. In all patients, the left descending coronary artery was identified as the infarct-related artery by coronary arteriography. All patients underwent PTCA because this procedure is the current therapy for patients with anterior wall infarction in our hospital. All subjects gave informed consent. The study protocol was approved by the Medical Ethical Committee of the Leiden University Hospital.

View this table: [in this window] [in a new window]   Table 1. Percentage of Healthy Volunteers and Patients in Each Age Decade

Volunteers
Forty-eight healthy volunteers (mean age, 37.0±15.5 years; range, 21 to 89 years) were selected to contribute to a database of reference values. The percentage of normal subjects in each age decade is presented in Table 1. By means of clinical history, ECG, and echocardiography, cardiac disease was excluded.

MR Imaging
MR examinations were performed at 0.5 T (T5-II, Philips Gyroscan, Philips Medical Systems) at 21±2.1 days (range, 17 to 24 days) after the onset of the myocardial infarction. Short-axis cine MR imaging with a field of view of 300x300 mm and an acquisition matrix of 256x256 pixels was performed by use of a flow-compensated gradient-echo sequence (repetition time within one RR interval, 30 ms; echo time, 13 ms; excitation angle, 50°; slice thickness, 10 mm; and slice gap, 2 mm). Two signals were averaged to improve the signal-to-noise ratio. Ten slices were acquired to encompass the entire heart. The number of sequential frames per cardiac cycle corresponded to the number of 50° pulses delivered within 1 RR interval (9 to 25 frames). The same imaging parameters were used for the 48 healthy volunteers.

Enzyme Analysis
A two-compartment model to account for the kinetics of myocardial proteins between the intravascular and extravascular spaces was used to calculate the quantity of enzyme released per liter of plasma in the first 72 hours after onset of acute myocardial infarction.^{14 15} Plasma HBDH activity was measured every 12 hours after admission for the first 48 hours and at 24-hour intervals until 4 days after admission. HBDH activity was determined by an automated analyzer (DuPont ACA) with -ketobutyrate used as a substrate. The cumulative HBDH activity released in the first 72 hours per liter of plasma (Q₇₂, expressed in units per liter) was used as a measure of infarct size. Multiplication of Q₇₂ by the patient's plasma volume (estimated as 0.041 per kilogram of body weight) and subsequent division by the HBDH activity per gram of normal myocardium (152 U HBDH per gram by use of the assay method mentioned above) yielded the enzymatic infarct size, expressed in grams of myocardium.

MR Image Analysis
End diastole was defined as the image obtained 8 ms after the onset of the R wave of the ECG, corresponding to the largest LV cavity area. End systole was defined as the image with the smallest LV cavity area. MR images were transferred to a UNIX workstation (SUN Microsystems Inc). Image data were analyzed by use of MASS version 1.0. MASS was developed in our image-processing laboratory for the purpose of quantitative analysis of MR images.¹⁶ This software package includes a modified centerline method to quantify regional wall motion and regional wall thickness by use of a 3D approach (see "Appendix" and References 11 and 12). The endocardial and epicardial borders of the end-diastolic and end-systolic frames were manually traced with the use of an optical mouse. Papillary muscles, trabeculae, and epicardial fat were carefully excluded when these measurements were performed. After the endocardial and epicardial borders had been traced, the centerline method was used at the end-diastolic and end-systolic contours to calculate wall thickness at both times in the cardiac cycle (Fig 1). Analysis was performed starting from base to apex. The 10 slices encompassed the entire heart from outflow tract to apex. Slices covering the atria were rejected. Because of the through-plane motion, the lowest apical slices showing no blood volume at systole and slices at the valvular level were also rejected. Therefore, only 5 of 10 slice levels, including the LV myocardium only, were quantitatively analyzed. Slices were numbered from 1 to 5 (base to apex, respectively) and matched accordingly for the different studies.

View larger version (162K): [in this window] [in a new window]   Figure 1. Photographic illustration of the application of the centerline method for assessment of wall thickening. MR image of a healthy volunteer at end diastole (A) and end systole (B) with manually drawn endocardial and epicardial contours. The starting points (white dots) on the end-diastolic and end-systolic images were used to correct for rotational motion. Perpendicular to the centerline drawn midway between the endocardial and epicardial contours, 100 equidistant chords were constructed, each representing the wall thickness at that point. Note the end-diastolic wall thinning (C) and lack of wall thickening (D) (see arrow) in a patient with anterior myocardial infarction.

For 100 centerline points, wall thickening was expressed as the percent systolic wall thickening (%WTh) according to the formula

(E1)

where WThES is the wall thickness at end systole and WThED is the wall thickness at end diastole.

Quantitative data obtained from all images (5 slicesx100 chords per subject) acquired from 48 healthy volunteers were used as a database of reference values of normal wall thickening. To minimize the effect of coincidental abnormalities, LV wall thickening of patients with myocardial infarction was considered abnormal when 4 consecutive chords fell below the range of mean±2 SDs of reference values of corresponding chords. This number of consecutive chords was previously determined by analysis of receiver operator characteristics. From the database of normal values, the relative contribution of each chord at each slice level to the LV mass was calculated by dividing its length by the total length of all chords in this slice at end diastole and was expressed as a factor. When multiplied by the volume of the slice, this factor yields the volume contributed to the slice by each chord. The extent of dysfunctional LV myocardium in each patient was quantified in gram equivalents according to the following formula:

(E2)

in which QWTh is the extent of dysfunctional myocardium (g), _slices is the summation over all slices, _chords is the summation of all chords at a particular slice level, Ch AWTh_{chord, slice} represents a chord with abnormal wall thickening, F_{chord, slice} is the factor representing the relative contribution of the chord to the slice volume, V_slice is the myocardial volume at a particular slice level, and 1.05 represents the specific gravity of myocardial tissue (g/cm³).

To compare wall-thickening values and end-diastolic wall thickness of patients to corresponding values of healthy volunteers, the short-axis images were divided according to the vascular distribution of the coronary arteries.¹⁷ At slice levels 1 and 2 (basal and high papillary levels), chords 11 through 50 were considered to be related to the LAD, chords 51 through 70 to the LCx, and chords 71 through 10 to the RCA. At slice levels 3, 4, and 5, chords 1 through 50, 51 through 70, and 71 through 100 were considered to be related to the LAD, the LCx, and the RCA, respectively (Fig 2).

View larger version (72K): [in this window] [in a new window]   Figure 2. Division of a short-axis MR image according to the vascular distribution of the coronary arteries at the basal and high papillary muscle levels (A) and at the mid and low papillary muscle levels and apical level (B).17

Statistical Analysis
A 95% CI of normal systolic wall thickening was calculated from the data obtained from 48 healthy volunteers. Linear regression analysis was used to compare the quantity of dysfunctional myocardium estimated by cine MR imaging with enzymatic indexes of myocardial necrosis. A paired t test was performed to test for differences between the two modalities. The unpaired t test was used to test for segmental differences and for differences between patients and normal subjects. A value of P<.05 was considered significant. In 10 patients (randomly chosen), MR image analysis was performed by a second independent observer (V.G.M.B.) to obtain a measure of interobserver variability. In addition, one observer (E.R.H.) repeated these measurements 3 months later to determine the intraobserver variability. Variability was expressed as the mean difference between paired measurements ±SD. Data are presented as mean±SEM, with the exception of time and age values, which are presented as mean±SD.

	Results

Top Abstract Introduction Methods Results Discussion Appendix References

 
Qualitative Analysis
One patient did not show wall-thickening abnormalities at visual inspection. However, quantitative analysis showed 8.9 g of dysfunctional myocardium corresponding to 8.0 g of enzymatically determined infarct size. Two patients showed poor image quality and were excluded from quantitative analysis, leaving 23 patients for further evaluation.

Quantitative Analysis
Dysfunctional Myocardium
Table 2 lists the patient data. Linear regression analysis showed a good correlation between the quantity of dysfunctional myocardium determined by cine MR imaging and enzymatically determined infarct size (y=0.90x+3.7; r=.92, P<.0001) (Fig 3).

View this table: [in this window] [in a new window]   Table 2. Infarct Localization Determined by ECG, Visual Inspection of Cine MR Images, Quantity of LV Dysfunction Determined by Cine MR Imaging, and Enzymatic Indexes of Infarct Size (HBDH) in 23 Patients With a First Anterior Wall Infarction

View larger version (25K): [in this window] [in a new window]   Figure 3. Correlation between dysfunctional myocardium determined with cine MR imaging and enzymatically determined infarct size calculated from cumulative release of HBDH activity in plasma. Indicated are regression line and 95% CI. Note that the line of identity (dashed line) is within the 95% CI.

Segmental Analysis
Table 3 summarizes end-diastolic wall thickness and percentage LV systolic wall thickening summed over all slices analyzed (5 of 10) and subdivided by coronary artery distribution. Although segments with wall thickening below reference values were detected in all patients, mean end-diastolic wall thickness in the area perfused by the LAD over all slices did not differ significantly between patients and control subjects. At the basal and high papillary levels, the territory of the LCx showed a slight but significantly higher end-diastolic wall thickness in comparison to the reference values (Fig 4A and 4B). At the other three levels (mid papillary, low papillary, and apical), no significant differences in end-diastolic wall thickness were found between patients and control subjects. Segments related to the LAD and the LCx showed significantly lower systolic LV wall thickening in comparison to reference values (see Table 3 and Fig 5). Moreover, segments related to the LAD showed significantly lower systolic LV wall thickening than did other segments in the same patients.

View this table: [in this window] [in a new window]   Table 3. Mean±SEM Systolic Wall Thickening and End-Diastolic Wall Thickness

View larger version (92K): [in this window] [in a new window]   Figure 4. End-diastolic LV wall thickness measured with the centerline method by use of a 3D approach at the basal (A), high papillary (B), mid papillary (C), low papillary (D), and apical levels (E). Note the significant difference between the segments supplied by LAD and the RCA in healthy volunteers at the low papillary level. Furthermore, note the significant difference of the end-diastolic LV wall thickness at segments supplied by the LCx between patients and normal subjects.

View larger version (88K): [in this window] [in a new window]   Figure 5. LV wall thickening measured with the centerline method by use of a 3D approach at the basal (A), high papillary (B), mid papillary (C), low papillary (D), and apical levels (E). Note the significantly lower systolic wall thickening between patients and normal subjects of the segments supplied by the LAD and the RCA at all slice levels. Also, note the significant difference of systolic wall thickening of the segments supplied by the LAD in patients at all slice levels. Furthermore, note the significant difference between segments supplied by the LAD and LCx in normal subjects (B, C, and D).

Interobserver and Intraobserver Variabilities
The mean difference between paired measurements of the quantity of dysfunctional LV wall thickening performed by two observers (E.R.H. and V.G.M.B.) was 3.8±3.7 g (P=NS). The mean difference between paired measurements of the quantity of dysfunctional LV wall thickening performed by the same observer (E.R.H.) was 2.2±3.1 g (P=NS).

	Discussion

Top Abstract Introduction Methods Results Discussion Appendix References

 
Impairment of systolic wall thickening is known to be a sensitive marker of myocardial ischemia and has been shown to be a reliable indicator of segmental contractile dysfunction after myocardial infarction.^{5 18} The clinical and prognostic evaluation of regional LV contractile function is well established.^{3 5 6 19 20 21 22 23 24 25 26 27 28} Many studies on regional LV function relied on qualitative visual wall-motion analysis, which precludes the measurement of a large number of data points. However, accurate calculation of the quantity of abnormally contracting LV myocardium in patients after myocardial infarction is potentially useful for risk stratification and for the evaluation of interventional therapies. Therefore, we developed a method to accurately determine the quantity of LV dysfunction in patients suffering from myocardial infarction and related these measurements with enzymatic indexes of infarct size.

The centerline method has been accepted as an accurate method to quantify LV (dys)function.^{29 30} Sheehan et al²⁹ successfully applied the centerline method to contrast ventriculographic images to quantify regional wall motion. However, Lieberman et al³¹ showed that analysis of wall thickening approaches true contractile dysfunction more accurately than analysis of wall motion. Therefore, McGillem et al³⁰ used a modified centerline method for the measurement of wall thickening on echocardiographic images. However, difficulties with border definition and registration of images with respect to the external reference frame limits the use of echocardiography in a large number of patients.³² High-resolution images with clearly detectable endocardial and epicardial contours are essential for accurate analysis of wall thickening with high spatial resolution. To assess LV dysfunction in a large number of patients, a computer-assisted analysis system is desired. To this purpose, a dedicated software package (MASS) was developed in our image-processing laboratory, which includes an improved centerline analysis method.¹² With this software package, we are able to analyze wall motion, wall thickness, and wall thickening at 100 points around the LV wall using a 3D approach (see "Appendix" and References 11 and 12). Furthermore, this software package has been applied successfully in experimentally induced myocardial infarction for the quantification of myocardial infarction size in pigs.¹³

Observations in the Present Study
This study describes a method to accurately assess the quantity of LV dysfunction on short-axis cine MR images in patients 3 weeks after anterior myocardial infarction. The quantity of dysfunctional myocardium correlated strongly with enzymatically assessed infarct size. The images were acquired at a mean of 3 weeks after myocardial infarction, at which time the function of infarcted segments has been shown to improve from the ischemic insult.^{33 34 35 36 37} Therefore, the good agreement between the extent of dysfunctional LV myocardium and enzymatic indexes of necrosis is explained by hardly any variability due to the delay between the onset of myocardial infarction and MR image acquisition, at which time myocardial recovery should be complete.^{33 38} Moreover, none of the patients showed clinical signs of ischemia during the interval between admission and the time of cine MR image acquisition. In addition, all patients had undergone primary PTCA, which may have accentuated the recovery of function after the acute event.^{39 40}

Clinical Implications
When the centerline method was applied to analyze regional LV function in the pig heart model, we were able to distinguish dysfunctional from normal segments.¹³ Likewise, in the current study, we were able to accurately determine the quantity of LV dysfunction after myocardial infarction in reference to normal values. When patients are examined shortly after the onset of myocardial infarction, reduction of wall thickening after myocardial infarction will result from the interplay of completed infarction (necrosis) and viable but severely ischemic myocardium. The described method would therefore be suitable to quantify dysfunctional but viable myocardium within the area at risk in patients with myocardial infarction by use of inotropic stimulation.^{41 42} The quantity of recoverable LV myocardium after inotropic stimulation can be calculated accurately. Subsequently, patient management regarding revascularization therapy can be optimized by a priori knowledge of the extent of potentially reversible LV dysfunction.

Study Limitations
Manual contours were reconstructed three-dimensionally to estimate wall thickness at end diastole and end systole. However, no correction was made for through-plane motion, which occurs during systole and may have influenced the measurement of wall thickness. Myocardial tagging or quantification of wall thickening by a 3D volume element approach might overcome this problem.¹⁹ Currently, a correction algorithm for long-axis shortening is being implemented in MASS.

It should be recognized that data acquisition and manual contour tracing are still time consuming (30 minutes' acquisition time per patient and 30 minutes' analysis time per patient) and prone to observer bias. Improvement in terms of faster imaging sequences and algorithms for automatic border recognition may obviate these limitations.^{16 43} However, in the present study, manual contour tracing proved not to be a serious limitation, because interobserver and intraobserver variabilities for wall-thickening data were quite small (3.8±3.7 and 2.2±3.1 g, respectively).

Finally, the selection criteria for inclusion may have been too tight. These criteria were chosen to validate our method in a small group of patients. However, to further validate our method, it will be necessary to include patients with other infarct locations as well as to include patients at other time intervals after onset of myocardial infarction.

Conclusions
We conclude that the use of 3D quantitative analysis of cine MR images accurately quantifies the extent of regional LV dysfunction in the infarcted heart in patients after myocardial infarction. This method is potentially useful for risk stratification, monitoring of therapies, and quantification of viable myocardium by use of inotropic agents.

	Selected Abbreviations and Acronyms

 

3D = three-dimensional HBDH = -hydroxybutyrate dehydrogenase LAD = left anterior descending coronary artery LCx = left circumflex coronary artery LV = left ventricular MASS = MR Analytical Software System MR = magnetic resonance RCA = right coronary artery

View larger version (210K): [in this window] [in a new window]   Figure 6. Schematic presentation of the short-axis image planes (A) and the 3D approach for correction for 3D wall thickness (WT3D) measured perpendicular to the myocardium (B). The angle () between the normal vector of the image plane (Nip) and the normal vector of the myocardium (Nmc) was measured and used for the calculation of WT3D from two-dimensional wall thickness (WT2D): WT3D=WT2Dxsin () (see "Appendix"). CS indicates center surface.

	Appendix

Top Abstract Introduction Methods Results Discussion Appendix References

 
Centerline Method
The applied centerline method offers several advantages for analyzing regional LV function. Wall thickness is measured along 100 equidistant chords, providing a high accuracy to detect subtle abnormalities. Moreover, wall motion is assumed to proceed in a multicentric manner rather than toward a single point. This multicentric movement has potential advantages over other reference-dependent methods that assume that LV contractile motion proceeds toward a single point or centroid, an assumption that has generally been regarded as invalid.⁴⁴ The centerline method does not require a centroid to correct for in-plane translational motion and avoids dependence on reference figures or coordinate systems.²⁹ However, the centerline method needs a reference marker to correct for rotational transformation during systole for accurate determination of systolic thickening. For that purpose, we used a fixed anatomic landmark (chord 1): the internal posterior junction of the right ventricular wall with the interventricular septum.

Implementation of the 3D Wall-Thickness Calculation
Two-dimensional Improved Centerline Method
The 3D wall-thickness calculation starts with the application of the two-dimensional improved centerline algorithm on the endocardial and epicardial boundaries of the left ventricle.^{12 29} This algorithm calculates 100 thickness measurements along the circumference of the myocardium using an iterative method. Because true wall thickness can only be acquired by measuring perpendicular to the myocardium, the main goal of the algorithm is to achieve perpendicularity within the image. Achievement of perpendicularity is the main advantage of this algorithm over procedures that use a single cardiac midpoint.

The algorithm consists of the following steps:

1. Midway between the endocardial and epicardial contours, a centerline is defined: a closed curve with equal distance to the endocardium and epicardium.

2. Perpendicular to this centerline, 100 chords are equally distributed along its circumference.

3. If a chord defined in step 2 does not intersect with either the endocardial or epicardial boundary, it is marked invalid. If two chords intersect, they are also marked invalid.

4. If two or more successive chords are invalid, they are redefined by equally distributing their endpoints on the endocardial and epicardial contours in the area between their closest valid chord crossings. A new centerline is defined through all the chord midpoints.

5. Steps 2 through 4 are repeated until the chords no longer change between subsequent iterations or a maximum number of 30 iterations has been performed.

3D Wall-Thickness Calculation
The improved centerline wall-thickness method was designed to achieve optimal perpendicularity to the myocardium. However, this method is confined to measurement within the imaging plane, which is seldom perpendicular to the strongly curved myocardium. As a result, planar wall-thickness measurements will be performed oblique to the myocardium and thus overestimate true wall thickness with an error that increases toward the apex.

The 3D wall-thickness calculation method¹¹ is based on the dependency of this error of the local angle between the myocardial wall and the imaging plane (Fig 6):

1. The planar improved centerline method is used to calculate centerlines in all stacked multislice, short-axis, LV MR images at a given cardiac phase.

2. Through this stack of curves, a center surface is constructed that is equally spaced between the endocardial and epicardial surfaces.

3. At each of the midpoints of all two-dimensionally calculated centerline chords, a plane tangent to the center surface is defined by horizontal and vertical direction vectors. The horizontal vector is calculated from the planar centerline curve, and the vertical vector is an average of the direction vectors toward upper and lower adjacent slices. At the basal and apical slices, when only one neighboring slice is present, only this slice is used to calculate the vertical direction vector.

4. Normal vectors are calculated to the local direction plane from step 3 and to the imaging plane. Between these normal vectors, the angle µ is calculated.

5. Local 3D wall thickness (WT3D) was then calculated with the formula

(E3)

where WT2D is the two-dimensional centerline algorithm.

Received February 29, 1996; revision received October 7, 1996; accepted October 17, 1996.

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