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Journal of Biomechanical Engineering | Volume 124 | Issue 5 | TECHNICAL PAPERS
TECHNICAL PAPERS

Mechanism of Incomplete Mitral Leaflet Coaptation—Interaction of Chordal Restraint and Changes in Mitral Leaflet Coaptation Geometry: Insight from In Vitro Validation of the Premise of Force Equilibrium

[+] Author and Article Information
Sten Lyager Nielsen

Department of Cardiothoracic and Vascular Surgery and Institute of Experimental Clinical Research, Skejby Sygehus, Aarhus University Hospital, Aarhus, Denmark

Hans Nygaard

Department of Cardiothoracic and Vascular Surgery and Institute of Experimental Clinical Research, Skejby Sygehus, Aarhus University Hospital, and Engineering College of Aarhus, Aarhus, Denmark

Lars Mandrup

Engineering College of Aarhus, Aarhus, Denmark

Arnold A. Fontaine

Applied Research Laboratory, Penn State University, State College, PA

J. Michael Hasenkam

Department of Cardiothoracic and Vascular Surgery and Institute of Experimental Clinical Research, Skijby Sygehus, Aarhus University Hospital, Aarhus, Denmark

Shengqui He, Ajit P. Yoganathan

Institute for Bioscience and Bioengineering, Chemical Engineering Department, Georgia Institute of Technology, Atlanta, GA

J Biomech Eng 124(5), 596-608 (Sep 30, 2002) (13 pages) doi:10.1115/1.1500741 History: Received March 01, 1999; Revised April 01, 2002; Online September 30, 2002
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Copyright © 2002 by ASME
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References

1
Godley,  R. W., Wann,  L. S., Rogers,  E. W., Feigenbaum,  H., and Weyman,  A. E., 1981, “Incomplete Mitral Leaflet Closure in Patients with Papillary Muscle Dysfunction,” Circulation, 63, pp. 565–571.
2
Boltwood,  C. M., Tei,  C., Wong,  M., and Shah,  P. M., 1983, “Quantitative Echocardiography of the Mitral Complex in Dilated Cardiomyopathy: the Mechanism of Functional Mitral Regurgitation,” Circulation, 68, pp. 498–508.
3
Burch,  G. E., DePasquale,  N. P., and Phillips,  J. H., 1968, “The Syndrome of Papillary Muscle Dysfunction,” Am. Heart J., 75, pp. 399–415.
4
Kaul,  S., Spotnitz,  W. D., Glasheen,  W. P., and Touchstone,  D. A., 1991, “Mechanism of Ischemic Mitral Regurgitation. An Experimental Evaluation,” Circulation, 84, pp. 2167–2180.
5
Kono,  T., Sabbah,  H. N., Rosman,  H., Alam,  M., Jafri,  S., Stein,  P. D., and Goldstein,  S., 1992, “Mechanism of Functional Mitral Regurgitation during Acute Myocardial Ischemia,” J. Am. Coll. Cardiol., 19, pp. 1101–1105.
6
Kono,  T., Sabbah,  H. N., Stein,  P. D., Brymer,  J. F., and Khaja,  F., 1991, “Left Ventricular Shape as a Determinant of Functional Mitral Regurgitation in Patients with Severe Heart Failure Secondary to either Coronary Artery Disease or Idiopathic Dilated Cardiomyopathy,” Am. J. Cardiol., 68, pp. 355–359.
7
Sabbah,  H. N., Kono,  T., Rosman,  H., Jafri,  S., Stein,  P. D., and Goldstein,  S., 1992, “Left Ventricular Shape: a Factor in the Etiology of Functional Mitral Regurgitation in Heart Failure,” Am. Heart J., 123, pp. 961–966.
8
Kono,  T., Sabbah,  H. N., Rosman,  H., Alam,  M., Jafri,  S., and Goldstein,  S., 1992, “Left Ventricular Shape is the Primary Determinant of Functional Mitral Regurgitation in Heart Failure,” J. Am. Coll. Cardiol., 20, pp. 1594–1598.
9
Cohen,  G. I., Davison,  M. B., Klein,  A. L., Salcedo,  E. E., and Stewart,  W. J., 1992, “A Comparison of Flow Convergence with other Transthoracic Echocardiographic Indexes of Prosthetic Mitral Regurgitation,” J. Am. Soc. Echocardiogr, 5, pp. 620–627.
10
Otsuji,  Y., Handschumacher,  M. D., Schwammenthal,  E., Jiang,  L., Song,  J. K., Guerrero,  J. L., Vlahakes,  G. J., and Levine,  R. A., 1997, “Insights from Three-dimensional Echocardiography into the Mechanism of Functional Mitral Regurgitation: Direct In Vivo Demonstration of Altered Leaflet Tethering Geometry,” Circulation, 96, pp. 1999–2008.
11
Tsakiris,  A. G., Gordon,  D. A., Padiyar,  R., and Frechette,  D., 1978, “Relation of Mitral Valve Opening and Closure to Left Atrial and Ventricular Pressures in the Intact Dog,” Am. J. Physiol., 234, pp. H146–H151.
12
He,  S., Fontaine,  A. A., Schwammenthal,  E., Yoganathan,  A. P., and Levine,  R. A., 1997, “Integrated Mechanism for Functional Mitral Regurgitation. Leaflet Restriction vs Coapting Force: In Vitro Studies,” Circulation, 96, pp. 1826–1834.
13
Nielsen,  S. L., Nygaard,  H., Fontaine,  A. A., Hasenkam,  J. M., He,  S., Andersen,  N. T., and Yoganathan,  A. P., 1999, “Chordal Force Distribution Determines Systolic Mitral Leaflet Configuration and Severity of Functional Mitral Regurgitation,” J. Am. Coll. Cardiol., 33, pp. 843–853.
14
Yacoub, M., 1976, “Anatomy af the Mitral Valve Chordae and Cusps,” The Mitral Valve. A Pluridisciplinary Approach. D. Kalmonson, ed., Edward Arnold, London, pp. 15–20.
15
Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D., 1996, “SAS© System for Mixed Models,” SAS Institute Inc., Cary, NC, pp. 491.
16
Kunzelman,  K. S., and Cochran,  R. P., 1990, “Mechanical Properties of Basal and Marginal Mitral Valve Chordae Tendineae,” ASAIO Trans., 36, pp. M405–M408.
17
Kunzelman,  K. S., and Cochran,  R. P., 1992, “Stress/Strain Characteristics of Porcine Mitral Valve Tissue: Parallel versus Perpendicular Collagen Orientation,” J. Card. Surg., 7, pp. 71–78.
18
May-Newman,  K., and Yin,  F. C. P., 1998, “A Constitutive Law for Mitral Valve Tissue,” J. Biomech., 120, pp. 38–47.
19
Izumi,  S., Miyatake,  K., Beppu,  S., Park,  Y. D., Nagata,  S., Morioka,  S., Sakakibara,  H., Moriyama,  K., and Nimura,  Y., 1992, “The Gap between Mitral Leaflets as a Cause of Mitral Regurgitation: Relationship to Mitral Valve Prolapse,” Intern Med., 31, pp. 28–32.
20
Izumi,  S., Miyatake,  K., Beppu,  S., Park,  Y. D., Nagata,  S., Kinoshita,  N., Sakakibara,  H., and Nimura,  Y., 1987, “Mechanism of Mitral Regurgitation in Patients with Myocardial Infarction: A Study using Real-time Two-dimensional Doppler Flow Imaging and Echocardiography,” Circulation, 76, pp. 777–785.
21
Arts,  T., Meerbaum,  S., Reneman,  R., and Corday,  E., 1983, “Stresses in the Closed Mitral Valve: A Model Study,” J. Biomech., 16, pp. 539–547.
22
Reimink,  M. S., Kunzelman,  K. S., Verrier,  E. D., and Cochran,  R. P., 1995, “The Effect of Anterior Chordal Replacement on Mitral Valve Function. A Finite Element Study,” ASAIO J., 41, pp. M754–M762.

Figures

Grahic Jump Location
Graphical representation of the left ventricle in a long-axis projection. The impact of papillary muscle (PM) displacement on mitral leaflet coaptation geometry and chordal insertion geometry is schematized (A), and supported by force diagrams for the closed mitral valve condition with normal papillary muscle alignment (B) and following papillary muscle displacement (C). For the closed mitral valve in equilibrium in systole, the pressure forces (FΔP) resulting from the transmitral pressure acting to close the leaflets (coapting forces) are counterbalanced by tethering forces from the annular (FA) and papillary muscle attachments. These force components have different origin and direction, however, their projections along the individual chordae as the chordal coapting (FC) and chordal tethering forces (FT) are also in equilibrium. This force balance of the individual chordae is based on a counterbalance between the coapting forces projected along the chordae (FC) and the projected tethering forces (FT) from the papillary muscle and annular attachment. Since the transmitral pressure force, FΔP, acts perpendicular to the surface area of the anterior and posterior leaflet, the magnitude of the (projected) chordal coapting force component depends on the transmitral pressure difference, the surface area of the anterior and posterior mitral leaflets and the chordal insertion angle (θ) onto the mitral leaflets (see text for details).
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Grahic Jump Location
Overview of methods, measurements and data analysis in the in vitro protocol. The chart illustrates how key para-meters implicated in the theoretical analysis of the chordal force balance (indicated by arrows below) were derived from the in vitro measurements. AAL and APL, occlusional leaflet areas of the anterior and posterior leaflet; FC, chordal coapting force component; FT, chordal tethering force component; ΔP, transmitral pressure difference; ΔLPM: change in papillary muscle tethering length; θAA,θPA,θAP and θPP, chordal inserting angles.
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Grahic Jump Location
The chordal force measure of each chordae tendineae consisted of the chordal tethering force component (FT) and the chordal coapting force component (FC). The difference of the force components, (FC−FT), defined the resulting (valvular directed) force of the chordae tendinea acting on the leaflets at the point of insertion.
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Grahic Jump Location
Diagram of a midsystolic tented mitral leaflet geometry (left) with a typical leaflet contour imaged by 2D echo from apical view (right). Left ventricular side in z-direction. The occlusional leaflet areas of the anterior and posterior leaflet (AAL and APL) were calculated as the sum of fractions of a cone produced from four apical scanning planes rotated around an axis through the mid point of the annulus (right; one fraction of a cone is marked). Notice leaflet edge separation due to leaflet asynergy creating a regurgitant orifice. Variables to describe leaflet configuration are illustrated (r and h). The intersection of the anterior leaflet extension on the posterior leaflet gives the horizontal length r4 and perpendicular distance h4 of the posterior leaflet involved in mitral orifice occlusion. αAL and αPL: Systolic leaflet coaptation angle of the anterior and posterior leaflet.
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Grahic Jump Location
Linear correlations were demonstrated between the orthogonal projections of the chordal coapting force components to the leaflets, ∑([FC,i sin θi]AL and ∑([FC,i sin θi]PL (dependent variables) and the anterior and posterior leaflet occlusional leaflet areas, AAL and APL. Data represents one valve at all test conditions. Trends are representative of all valves (see text).
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Grahic Jump Location
Free body diagram of the force equilibrium of the anterior mitral valve leaflet, showing the force components acting on the anterior mitral leaflet and along the chordae tendineae. In equilibrium the chordal tethering force (FT) is counterbalanced by the chordal coapting force component (FC). The moment due to the force FΔP applied by ΔP on the leaflet is balanced by the moment due to −FC, which is equal to FT. The papillary muscle is deviating into the plane (x-direction). α, leaflet coaptation angle in the plane of chordal insertion; ϕ, angle of incidence of the chordae with respect to the annular plane. θ, chordal insertion angle with the leaflet (=α+ϕ);LAL, length of the anterior leaflet. AAL, occlusional leaflet area of the anterior leaflet. P0, the centerpoint of the moment of the annular hinge (τA,int=0).
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Grahic Jump Location
Schematic illustration of the distribution of the chordal force transducers and the papillary muscle adjustments in normal (N), apical (A), posterolateral (PL) and apical posterolateral (APL) direction. Eight papillary muscle settings were tested. Scaled photograph of the transducer: 1 unit=1 mm.CTAA: Chordae from the anterolateral papillary muscle (APM) to anterior leaflet; CTAP: Chordae from APM to posterior leaflet; CTPA: Chordae from the posteromedial papillary muscle (PPM) to anterior leaflet; CTPP: Chordae from PPM to posterior leaflet; AL: Anterior leaflet.
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Grahic Jump Location
Schematic representation of the three-dimensional reconstruction of the mitral leaflet geometry, using one short axis view of the annulus plane and two parasternal long axis views at the midpoint of the half mitral coaptation line. The primary chordae connected the tip the papillary muscles and the corresponding midpoint of the half mitral coaptation line (* ). The central papillary muscle lines (LAPM and LPPM) are illustrated as double arrows from the papillary muscle tips through the chordae attachment (* ) to the annular plane.
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Grahic Jump Location
Linear correlations were demonstrated between the chordal tethering force components, [FT]AA,[FT]AP [FT]PA [FT]PP (dependent variables) and the change of the respective papillary muscle tethering lengths from normal papillary muscle setting (ΔLAPM and ΔLPPM) (independent variable). Data represents one valve at all test conditions. Trends are representative of all valves (see text).
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Grahic Jump Location
Left panel. 3D diagram showing the changes of the mitral leaflet coaptation geometry (thin arrows) caused by apical (A:A) and posterolateral (PL:PL) papillary muscle (PM) displacement compared to normal (N:N) papillary muscle position. Cross-sectional view of the mitral leaflet contour (y,z-plane). Apical papillary muscle displacement resulted in an apical shift of the leaflet coaptation line. Posterolateral papillary muscle displacement caused a posterior shift of the leaflet coaptation line. Bold arrows indicate direction and magnitude of the chordal tethering (in black) and chordal coapting (in gray) force component. Right panel. Mitral leaflet coaptation geometry was altered through changes of the leaflet coaptation angles, αAL,i and αPL,i, the angles of incidence of the chordae with respect to the annular plane (ϕAA,ϕPA,ϕAP and ϕPP) and the chordal insertion angles (θAA,θPA,θAP and θPP).
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Grahic Jump Location
(A) Diagram illustrating the effect of the initial papillary muscle displacement (ΔLPM) on the anterior mitral valve leaflet closing position. Displacement of the papillary muscle (PM) pulls the leaflets away from closure, which increases the leaflet coaptation angle (α) and tends to straighten out the chordal inserting angle, θi.A0, Annular hinge point; LAL, length of the anterior leaflet; LCT, length of the chordae tendineae; LPM, papillary muscle tehering length; β, angle formed by LPM and the anterior leaflet. Subscript 0 annotates normal papillary muscle position; (B) Increasing papillary muscle displacement, ΔLPM, straightened out the chordal insertion angle, θ. Further papillary muscle displacement, provided by stretching of the chordae (ΔLCT) and the mitral leaflet (ΔLAL), produces a restoring force, that in equilibrium is equal and oppositely directed to the chordal tethering force, FT.
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