Am J Physiol Heart Circ Physiol 289: H1218-H1225, 2005.
First published April 29, 2005; doi:10.1152/ajpheart.00169.2005
0363-6135/05 $8.00
Mitral tetrahedron as a geometrical surrogate for chronic ischemic mitral regurgitation
Hsi-Yu Yu,1,3
Mao-Yuan Su,2
Yih-Sharng Chen,1
Fang-Yue Lin,1 and
Wen-Yih Isaac Tseng2,4
Departments of 1Surgery and 2Medical Imaging, National Taiwan University Hospital, and 3Institute of Biomedical Engineering and 4Center for Optoelectronic Biomedicine, National Taiwan University Medical College, Taipei, Taiwan, Republic of China
Submitted 18 February 2005
; accepted in final form 25 April 2005
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ABSTRACT
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The present study tests the hypothesis that a mitral tetrahedron (MT) is a useful geometrical surrogate for assessment of chronic ischemic mitral regurgitation (CIMR). Fifty-eight subjects were divided into three groups on the basis of left ventricular ejection fraction (LVEF) and the presence or absence of CIMR: LVEF 
0.5 and negative CIMR (group 1, n = 28), LVEF <0.5 and negative CIMR (group 2, n = 12), and LVEF <0.5 and positive CIMR (group 3, n = 18). MT was defined by its four vertices at the anterior annulus, posterior annulus, and medial and lateral papillary muscle roots, determined by MRI at peak systole. The results showed no clear cutoff values of MT parameters between groups 2 and 1. In contrast, all MT indexes were significantly different between groups 3 and 2 (P < 0.05), and significant cutoff values differentiated the two groups. A scoring system employing parameters of the whole MT confirmed the absence of CIMR with total edge length index <268 mm/BSA1/3, total surface area index <2,528 mm2/BSA2/3, and volume index <5,089 mm3/BSA (where BSA is body surface area). The sensitivity, specificity, and positive and negative predictive values were 1.00. This preliminary study demonstrates that MT might serve as a good geometrical surrogate for assessing CIMR. The derived geometrical criteria of MT may be useful in surgical correction of CIMR.
coronary disease; mitral valve; magnetic resonance imaging
CHRONIC ISCHEMIC MITRAL REGURGITATION (CIMR) is caused by geometrical derangement of the mitral complex owing to local or global chronic ischemia of the myocardium (5, 12). Ring annuloplasty, in addition to revascularization of the myocardium, is the standard treatment for CIMR. The recurrence rate after the surgical procedure, however, is high, even in medical institutions where many of these procedures are performed (10). Development of a more effective treatment requires comprehensive understanding of the relations between the structure of the mitral complex and CIMR. Although geometry of the mitral complex in CIMR can be quantified, data are still lacking. Yu et al. (17) demonstrated the feasibility of relating a mitral tetrahedron (MT) obtained from MRI to CIMR. In the present study, a more comprehensive analysis of geometrical indexes of MT was performed, and these indexes were compared in patients with and without CIMR. We aimed to test the hypothesis that geometrical analysis of MT could serve as a useful surrogate for assessment of CIMR.
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MATERIALS AND METHODS
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Study population.
Fifty-eight subjects, including 40 patients with chronic ischemic heart disease and 18 age-matched healthy volunteers, comprised the study population (Fig. 1). They were divided into three groups according to left ventricular (LV) ejection fraction (LVEF) and the presence or absence of CIMR: LVEF 0.5 and negative CIMR (group 1, n = 28, 10 patients and 18 healthy volunteers), LVEF <0.5 and negative CIMR (group 2, n = 12), and LVEF <0.5 and positive CIMR (group 3, n = 18). In all subjects, LV function and MT geometry were analyzed by MRI. Chronic ischemic heart disease was diagnosed on the basis of positive findings on coronary angiogram showing significant narrowing (>90% stenosis) of coronary arteries and the absence of acute coronary syndrome within 1 mo before MRI study. Old infarct was defined by a Q wave with conventional ECG. Mitral regurgitation was diagnosed with Doppler echocardiography by a semiquantitative method in several views for the maximal color jets. CIMR was diagnosed after exclusion of obvious anatomic abnormalities of chordae or leaflets by two-dimensional echocardiographic examination. Subjects recruited into the study gave informed consent, and the study was approved by the Institutional Review Board of the National Taiwan University Hospital.
Image acquisition and analysis.
Image acquisition and analysis were described in detail previously (17). Briefly, the study was performed with a 1.5-T MRI system (Siemens Sonata, Erlangen, Germany). Cine MRI was acquired with prospective ECG R-wave trigger mode and a two-dimensional balanced steady-state free precession sequence (TrueFISP; TR/TE = 30/1.5 ms, flip angle = 60°, slice thickness/gap = 7/3 mm, field of view = 37 x 30 cm, matrix = 256 x 208). The slices were in short-axis view encompassing the LV from base to apex. Cine images at one slice location were obtained in one breath hold, 
12 s. Approximately 12 intermittent breath holds at consistent condition were required to complete the image acquisition. The total scan time was 10 min. LV end-diastolic volume (LVEDV), LV end-systolic volume (LVESV), and LVEF were derived from cine MRI with an in-house semiautomatic algorithm reported previously (15).
Vertices of MT.
For analysis of MT, the end-systolic phase was identified as the time when the LV showed maximal contraction. Multiple short-axis images from the base to the apex at this time point were interpolated to reconstruct the three-dimensional geometry of the LV, from which position coordinates of the anterior annulus (A), posterior annulus (P), medial papillary muscle root (M), and lateral papillary muscle root (L) were determined (Fig. 2). These four points defined the four vertices of MT and represented the geometry of the mitral apparatus.
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Fig. 2. Selection of vertices of the mitral tetrahedron (MT) from reconstructed MRI images in end-systolic phase. Anterior annulus (A, black arrow) and posterior annulus (P, white arrow) were selected on an imaginary plane in the middle and perpendicular to a line connecting medial and lateral trigones. Medial (M) and lateral (L) papillary muscles were located at the junction of the papillary muscle base and the LV wall on an imaginary plane perpendicular to the long axis of the LV cavity.
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Indexes of edge lengths and mitral area.
After determination of the vertices of the MT, the length indexes of six edges of the MT (DIAP,DIML, DIAL, DIAM, DIPL, and DIPM) were computed (Fig. 3 ). Additionally, the mitral area index (MAI) was determined from the area enclosed by the contour manually traced along the mitral annulus shown on the reconstructed images.
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Fig. 3. One-dimensional parameters of the MT: edge length indexes (DI) of MT and mitral annular area index (MAI). Cutoff values between groups 2 and 3 are indicated by horizontal dotted lines. Sens, sensitivity; Spec, specificity; BSA, body surface area.
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Indexes of surface triangles and whole tetrahedron.
In addition to six edges, each MT consisted of four surface triangles: 1) the anterior triangle, defined by vertices A, M, and L, 2) the posterior triangle, defined by P, M, and L, 3) the medial triangle, defined by A, P, and M, and 4) the lateral triangle, defined by A, P, and L. Four boundary length indexes, TIM, TIP, TIM, and TIL, and four area indexes, AIA, AIP, AIM, and AIL, were then determined for anterior, posterior, medial, and lateral triangles, respectively. These eight indexes were categorized as the indexes of the surface triangles. For the whole tetrahedron, we computed the total edge length index (6-DI), total surface area index (4-AI), and volume index (VI). These three indexes were categorized as the indexes of the whole tetrahedron. Image analysis and data processing were performed with Matlab (MathWorks, Natick, MA).
Data normalization.
For consistency of the indexes in different dimensions, volume data, including LVESV, LVEDV, and volume of the MT, were divided by body surface area (BSA), edge lengths of MT by BSA1/3, and area data, including the area of the mitral annulus and areas of surface triangles of MT, by BSA2/3. This procedure was different from that described in a previous study (9), in which volume and length data were normalized by BSA.
Statistics.
Dichotomous data were compared by 
2 test. Numeric data were compared with unpaired Student's t-test between every two groups. Cutoff values of respective parameters for CIMR were selected using receiver operating characteristics (ROC) analysis with a tangent line with slope of 1.0 to the ROC curve. P < 0.05 was considered statistically significant. All statistical work was performed with SPSS for Windows (SPSS, Chicago, IL).
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RESULTS
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Demography of study population.
Gender, age, and BSA were comparable between the three groups (Table 1). From group 1 to group 3, a significant decrease in LVEF and a significant increase in LVEDV and LVESV indexes (LVEDVI and LVESVI) were found (Table 1, Fig. 1). The percentages of coronary lesions involving the left anterior descending artery, right coronary artery, and left circumflex artery showed no significant difference between groups 2 and 3: 56.3 vs. 50.0% for the left anterior descending artery (P = 1.000), 50.0 vs. 50.0% for the right coronary artery (P = 1.000), and 56.3 vs. 20.0% for the left circumflex artery (P = 0.109). No significant difference was found in the percentages of old anterior infarct and old inferior infarct: 45.5 vs. 31.3% for old anterior infarct (P = 0.687) and 27.3 vs. 37.5% for old inferior infarct (P = 0.692).
Indexes of edge lengths and mitral area.
All six edge length indexes and MAI differed significantly between groups 2 and 3, whereas only DIAM and DIPM differed significantly between groups 1 and 2 (Fig. 3). Moreover, cutoff values with sensitivity and specificity >0.80 distinguished group 2 from group 3 in five edge length indexes (except DIAP) and MAI. Marked distinction was noted in DIAM and DIML: for DIAM, a cutoff value of 56.9 mm/BSA1/3 had sensitivity of 0.89 and specificity of 1.00; for DIML, a cutoff value of 27.0 mm/BSA1/3 had sensitivity of 0.94 and specificity of 1.00.
Boundary length indexes of surface triangles.
Although there were differences in TIL, TIM, TIA, and TIP between groups 1 and 2, no clear cutoff values could be found (Fig. 4). In contrast, TIL, TIM, TIA, and TIP were significantly greater in group 3 than in group 2: 149.6 ± 18.1 vs. 114.3 ± 14.2 mm/BSA1/3 for TIL, 151.4 ± 12.9 vs. 120.4 ± 10.4 mm/BSA1/3 for TIM, 154.2 ± 14.7 vs. 117.5 ± 12.6 mm/BSA1/3 for TIA, and 141.1 ± 11.8 vs. 108.6 ± 10.3 mm/BSA1/3 for TIP (all P < 0.001). Clear cutoff values differentiated group 2 from group 3 in these four indexes: 130.8 mm/BSA1/3 for TIL (sensitivity = 0.83 and specificity = 0.92), 134.1 mm/BSA1/3 for TIM (sensitivity = 0.89 and specificity = 0.92), 133.2 mm/BSA1/3 for TIA (sensitivity = 0.94 and specificity = 0.92), and 117.6 mm/BSA1/3 for TIP (sensitivity = 1.00 and specificity = 0.92).
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Fig. 4. Two-dimensional parameters of the MT: boundary length indexes (TI) of medial, lateral, anterior, and posterior triangles.
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Area indexes of surface triangles.
Area indexes of surface triangles showed results similar to those for boundary length indexes (Fig. 5). No clear cutoff values for AIL, AIM, AIA, and AIP could be found between groups 1 and 2. However, clear cutoff values distinguished group 2 from group 3 in all area indexes: 702.7 mm2/BSA2/3 for AIL (sensitivity = 0.83 and specificity = 1.00), 641.0 mm2/BSA2/3 for AIM (sensitivity = 1.00 and specificity = 0.83), 592.4 mm2/BSA2/3 for AIA (sensitivity = 1.00 and specificity = 0.83), and 580.1 mm2/BSA2/3 for AIP (sensitivity = 0.94 and specificity = 1.00).
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Fig. 5. Two-dimensional parameters of the MT: surface area indexes (AI) of medial, lateral, anterior, and posterior triangles.
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Indexes of the whole tetrahedron.
Total edge length index (6-DI) was higher in group 2 than in group 1 (230.4 ± 21.1 vs. 206.0 ± 29.3 mm/BSA1/3, P = 0.013), but the two groups could not be distinguished clearly with a cutoff value (Fig. 6). In contrast, 6-DI was significantly higher in group 3 than in group 2 (298.1 ± 26.1 vs. 230.4 ± 21.1 mm/BSA1/3, P < 0.001), and a cutoff value with good sensitivity and specificity could be found (cutoff value of 268.1 mm/BSA1/3 with sensitivity = 0.89 and specificity = 1.00). Total surface area index (4-AI) was higher in group 2 than in group 1, but no clear cutoff could be found (Fig. 6). In contrast, 4-AI was significantly higher in group 3 than in group 2 (3,513 ± 708 vs. 3, 1,996 ± 385 mm2/BSA2/3, P < 0.001), and the two groups could be distinguished clearly by a cutoff value of 2,528 mm2/BSA2/3 (sensitivity = 1.00 and specificity = 1.00). Despite a 2.8-fold difference in LVESVI between groups 1 and 2 (18.4 ± 8.2 vs. 50.9 ± 26.0; Table 1), the difference in VI was only 1.4-fold: 3,351 ± 1,069 vs. 2,360 ± 1,058 mm3/BSA (P = 0.010; Fig. 6). On the other hand, despite a 1.7-fold difference in LVESVI between groups 3 and 2 (87.3 ± 33.8 vs. 50.9 ± 26.0; Table 1), VI was 2.4 times greater in group 3 than in group 2: 8,141 ± 3,334 vs. 3,351 ± 1,069 mm3/BSA (P < 0.001). A cutoff value of 5,089 mm3/BSA distinguished group 2 from group 3 (sensitivity = 0.94 and specificity = 1.00).
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Fig. 6. Three-dimensional parameters of the MT: total edge length index (6-DI), total surface area index (4-AI), and volume index (VI).
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Scoring system for CIMR.
Three scoring systems for CIMR were developed on the basis of parameters related to individual edges: 1) six edge length indexes and MAI, 2) parameters related to individual surface triangles, i.e., four boundary length indexes and four area indexes, and 3) parameters related to the whole tetrahedron, i.e., 6-DI, 4-AI, and VI. The thresholds of each index used the cutoff values determined from the ROC analysis (Figs. 3–6). Among the three scoring systems (Fig. 7), the system employing parameters related to the whole tetrahedron could readily confirm the presence or absence of CIMR with the combination of the following thresholds: 6-DI = 268 mm/BSA1/3, 4-AI = 2,528 mm2/BSA2/3, and VI = 5,089 mm3/BSA. The sensitivity, specificity, positive predictive rate, and negative predictive rate were 1.0.
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Fig. 7. Three scoring systems for CIMR based on 1-dimensional (6 edge length indexes and MAI), 2-dimensional (boundary length indexes and area indexes of surface triangles), and 3-dimensional (6-DI, 4-AI, and VI) parameters. Cutoff values of respective parameters were selected by receiver operating characteristics analysis (see Figs. 3–6.)
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DISCUSSION
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In the present preliminary study, we identified an analytic approach to quantitatively evaluate the geometrical alteration of LV in CIMR that is promising and merits further prospective evaluation in a larger sample of normal and abnormal subjects.
Geometrical alteration of the mitral complex in functional mitral regurgitation has been studied extensively. Several plausible mechanisms have been proposed, including dilation of the mitral annulus (1, 2, 14), a tethering effect on mitral leaflets by posterior displacement of the papillary muscles (2, 3, 12, 16, 17), sphericalization of the LV (13), and widening of the interpapillary distance (17) (Table 2). Owing to the multifactorial nature of CIMR, a comprehensive assessment of the geometry of the MT was performed and the relation of each geometrical index with CIMR was investigated in the presentstudy. We found that the MT was an effective geometrical surrogate for CIMR. Specifically, a combination of 4-AI, 6-DI, and VI below their respective cutoff values could reliably indicate the absence of CIMR.
Although geometrical alteration of the MT leads to CIMR, it should be noted that volume overload induced by mitral regurgitation can cause secondary remodeling of the LV. Therefore, in the present study, geometrical alteration of the MT in group 3 should be considered a cause and a consequence of CIMR. Nonetheless, it is reasonable to conclude that an MT with all indexes below their respective cutoff values guarantees a normal structure without CIMR.
Complete ring annuloplasty is the most popular surgical procedure for repair of CIMR (2, 4, 10). Although the procedure is relatively simple and effective, a failure rate of 30% has been reported at 6 mo (10). The findings in the present study provide an explanation for the moderate success rate of ring annuloplasty. In fact, this procedure corrects for only two of the MT indexes, namely, DIAP and MAI, and may not be adequate to restore a sound structure of MT to eliminate CIMR. In light of our results, several additional procedures may be considered to tailor the correction of MT geometry. For example, an interpapillary sling (6) and intraventricular papillary imbrication (11) are comparable to decreasing DIML. A myosplint, a transcavitary tensioning device designed to change (LV) shape, is comparable to decreasing DIAM and DIAL. Our results from Figs. 3–6 can serve as a guide for deciding an effective correction procedure. Moreover, a successful outcome can be predicted if the procedure decreases the abnormal indexes so that 4-AI, 6-DI, and VI are below their respective cutoff values.
The present study showed a 1.4-fold difference in VI (3,351 ± 1,069 vs. 2,360 ± 1,058 mm3/BSA) and a 2.8-fold difference in LVESVI (50.9 ± 26.0 vs. 18.4 ± 8.2 mm3/BSA) between groups 1 and 2 and a 2.4-fold difference in VI (8,141 ± 3,334 vs. 3,351 ± 1,069 mm3/BSA) and a 1.7-fold difference in LVESVI (87.3 ± 33.8 vs. 50.9 ± 26.0 mm3/BSA) between groups 2 and 3. This peculiar finding might be explained by a functional division of the LV into anterior and posterior halves on the basis of their location with respect to the MT. The LV can be divided by an imaginary plane passing through the anterior mitral annulus, the medial papillary muscle root, and the lateral papillary muscle root (Fig. 8). It is clear that the MT is located in the posterior half of the LV. Although the anterior and posterior halves determine LVEF, only the posterior half is relevant to functional mitral regurgitation. Our finding suggests that corrective procedures for CIMR should focus on the posterior half of the LV.
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Fig. 8. A proposed model of functional division of the LV by an imaginary plane determined by the anterior mitral annulus and roots of the medial and lateral papillary muscles. Although anterior and posterior halves of the LV determine LVEF, only the posterior half determines CIMR.
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Some experimental procedures used in the present study were different from those used previously. 1) Papillary muscle roots, rather than tips (9, 12), were used as one end of the annular-papillary distance, because papillary muscle tips usually branch. Therefore, error in length measurement can be reduced if papillary muscle roots are used. 2) A point on the mitral annulus between the medial and lateral trigones was chosen as the anterior annulus point. This is different from previous studies in which the medial trigone was used as the reference point (8, 9, 12, 16). 3) Instead of normalizing all parameters by BSA (1, 9), we normalized the length parameters by BSA1/3 and the area parameters by BSA2/3. In this way, parameters in different dimensions could be weighted appropriately.
To serve as a control group with LVEF >0.5, we included 18 healthy volunteers and 10 patients in group 1. All the study parameters regarding LV volume and MT geometry were comparable between the healthy volunteers and the patients: 51.5 ± 14.5 vs. 54.6 ± 15.6 mm3/BSA (P = 0.614) for LVEDVI, 16.8 ± 7.3 vs. 21.1 ± 9.3 mm3/BSA (P = 0.186) for LVESVI, 0.67 ± 0.08 vs. 0.62 ± 0.10 (P = 0.202) for LVEF, 15.3 ± 5.8 vs. 16.8 ± 3.9 mm/BSA1/3 (P = 0.494) for DIML, 204.1 ± 19.6 vs. 209.4 ± 42.7 mm/BSA1/3 (P = 0.660) for 6-DI, 1,553 ± 347 vs. 1,660 ± 557 mm2/BSA2/3 (P = 0.533) for 4-AI, and 2,279 ± 1,016 vs. 2,509 ± 1,170 mm3/BSA (P = 0.590) for VI. Therefore, the parameters of the MT were averaged over these 28 subjects and used as normal control values.
Study limitation.
The concept of an MT presented in this study does not take into consideration that the mitral leaflet might stretch to accommodate dilation of the mitral complex, as proposed in a previous study (1).
Because the original spatial resolution in the longitudinal direction was 10 mm in the present study, the leaflet structure and the coapting point between leaflets cannot be located precisely. Therefore, the tethering effect on the anterior leaflet and the corresponding downward displacement of the coapting point away from the mitral annular plane (8, 9) cannot be evaluated.
The effect of local ventricular perfusion status and viability on annular contraction and geometrical change of the MT was not investigated in the present study.
Conclusion.
We have demonstrated that the MT is an effective quantitative geometrical surrogate for assessment of structural derangement of the mitral complex in CIMR. Thresholds of the MT parameters reported in the present study may serve as a guideline for presurgical planning and individualized correction.
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GRANTS
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This work was in part supported by National Science Council (Taiwan) Grants NSC91-2314-B-002-217-M08 and NSC93-2314-B-002-245.
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FOOTNOTES
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Address for reprint requests and other correspondence: W.-Y. I. Tseng, No. 1, Jen-Ai Rd., Sec. 1, Center for Optoelectronic Biomedicine, National Taiwan Univ. Medical College, Taipei, Taiwan, ROC (E-mail: wytseng{at}ha.mc.ntu.edu.tw)
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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Copyright © 2005 by the American Physiological Society.
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ABSTRACT
MATERIALS AND METHODS
, n = 28), LVEF <0.5 and no significant MR (group 2, 
, n = 12), and depressed LVEF and significant MR (group 3, 
, n = 18). In all patients with chronic ischemic MR (CIMR), LVEF was <0.5. LV end-systolic volume index (LVESVI) was inversely correlated with LVEF.