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Papillary muscle and annulus size effect on anterior and posterior annulus tension of the mitral valve: An insight into annulus dilatation
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Journal of Biomechanics 41 (2008) 2524–2532 www.elsevier.com/locate/jbiomech www.JBiomech.com
Papillary muscle and annulus size effect on anterior and posterior annulus tension of the mitral valve: An insight into annulus dilatation Zhaoming He, Shamik Bhattacharya Department of Mechanical Engineering, Texas Tech University, 7th and Boston, PO Box 41021, Lubbock, TX 79409-1021, USA Accepted 6 May 2008
Abstract Mitral valve (MV) annulus mechanics and its effect on annulus dilatation are not well understood. The objective of the current study was to understand annulus tension (AT) during valve closure. A porcine MV rested on top of annulus rings with papillary muscles (PMs) held at slack, normal and taut conditions. The annulus was held by strings in the periphery during valve closure under static trans-mitral pressures. String tensions were measured and further used to calculate the anterior and posterior ATs. Three rings of different sizes were used to simulate normal and dilatated annuli. Fourteen MVs were tested. The anterior ATs were 37.21711.03, 53.86714.98 and 58.87715.72 N/m, respectively, at the slack, normal and taut PM positions in the normal annulus at the trans-mitral pressure of 16.3 kPa (122 mmHg). The posterior ATs were 24.5275.68, 36.2978.89 and 42.32711.82 N/m, respectively, at the slack, normal and taut PM positions in the normal annulus at the trans-mitral pressure of 16.3 kPa (122 mmHg). AT increased as the PM changed from slack to normal, then to taut PM positions. The AT increases with the increase of annulus area and linearly with the increase of trans-mitral pressure. The AT increases with the increases of apical PM displacement and dilatated annulus area, and reduces the potential of annulus dilatation. Low trans-mitral pressure due to existent mitral regurgitation, and MV prolapse increase the potential of annulus dilatation. Published by Elsevier Ltd. Keywords: Annulus tension; Annulus dilatation; Tissue mechanics; Left ventricle
1. Introduction The mitral valve (MV) annulus is an anatomical structure joining the leaflets and left ventricle wall. The MV annulus is a dynamic structure that varies in size and shape during a cardiac cycle. It has a ‘‘sphincteric’’ function when the MV closes, thus helping leaflet coaptation by reducing the annulus orifice area (Ormiston et al., 1981). It also changes saddle height due to contraction or relaxation of the left ventricle (Levine et al., 1989; Gorman et al., 1996; Flachskampf et al., 2000; Timek et al., 2005). The MV leaflets are supported by the annulus and chordae at MV closure. The annulus pulls the MV leaflets and prevents them from shrinking towards center of the MV orifice during systole. Trans-mitral pressure acts on the leaflets and induces leaflet tension, which is transferred to the annulus and chordae (Arts et al., 1983). The leaflet Corresponding author. Tel.: +806 742 3563x225; fax: +806 742 3540.
E-mail address: [email protected] (Z. He). 0021-9290/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jbiomech.2008.05.006
tension at the annulus per unit length is defined as annulus tension (AT). Chordae pull MV leaflets apically and prevent them from prolapsing, and further transfer chordal tensions to papillary muscles (PMs) (He et al., 2000). Even when the MV is fully open during diastole, inflow drag force and chordae tension on the leaflets pulls the leaflets and hence the annulus (Kheradvar and Gharib, 2007). The AT is an interaction force in the equilibrium state between the leaflets and the myocardium. Alteration in either one due to pathologies will break the equilibrium and change the AT, which ultimately results in annulus geometry change such as annulus dilatation. Ischemic heart disease is a disease in which the coronary arteries are blocked partially or completely. This disease leads to left ventricular dilation, which tethers PMs away from the MV annulus. This PM tethering alters MV mechanics and sometimes causes a tented MV, in which MV leaflets look like a tent during closure and do not coaptate, and causes ischemic mitral regurgitation. The peak stresses in the anterior leaflet increase with PM
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displacement (Kunzelman et al., 1998; He et al., 2005). On the other hand, a minimum annulo-papillary length is also required to allow proper MV closure (Espino et al., 2007). PM position influences MV function in a complicated way. Annulus dilatation is a consequence caused by left ventricle remodeling and worsens the MV function. Annulus dilatation occurs primarily in the myocardium annulus and secondarily in the fibrous annulus (Tibayan et al., 2003). This asymmetrical dilatation in the annulus increases specifically septal–lateral annulus diameter, which may be a plausible reason for functional mitral regurgitation (Qin et al., 2002). Annulus dilatation is related to AT and its interaction with the myocardium. AT is on the annulus plane and restricts MV annulus size, while out-ofplane AT components determine MV annulus shape (Jimenez et al., 2003). Annulus dilatation increases leaflet stresses and thus AT (Kunzelman et al., 1993; Quick et al., 1997). The effect of PM displacement and/or annulus dilatation on MV mechanics and function is not well understood. We aim to understand PM position effect on annulus dilatation from the viewpoint of mechanics. It is hypothesized that the AT is one of the important
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mechanisms that control annulus size under different PM positions. This hypothesis can be tested by AT analysis in the PM displacement and annulus dilatation conditions. The objective of the present study was to quantify the MV AT in the annulus dilatation and PM displacement conditions and to understand how the AT interacts with MV annulus dilatation and PM positions in MV coaptation. 2. Methods 2.1. Left heart simulator A left heart simulator, as shown in Fig. 1, was designed to simulate the coaptating MV in systole at a static trans-mitral pressure. It was made up of a annulus-mounting plate, two PM holders and a vacuum pump. The annulus-mounting plate was made of plexiglas and had a plastic ring glued on it. The ring was made to be the same size as the annulus of selected MVs. A porcine MV annulus was placed on the plastic ring. The atrium chamber below the MV was connected to the vacuum pump. The MV and chordae were open to the air. A humidifier was used to spray cold wet air on the MV continuously during the experiment to prevent the MVs from drying. The PMs were sutured to two PM holders. The vacuum pump created a trans-mitral pressure that forced the valve to close. Atrial
Annulus tissue suture
Anterior leaflet ө
ө
Posterior leaflet
ө * * * * ө
ө
* : post with force transducer
* * * ө
θ : post without force transducer
Porcine annulus resting on a ring ө
ө
Cylinder support for force transducers
Papillary muscle holder
Papillary muscle
Annulus-mounting plate
Chordae Leaflet Suture at the annulus edge
Suture at the transducer
Annulus ring
Force transducer
To the valve Pressure transducer Air is drawn from vacuum pump
Tuning valve
Fig. 1. (a) Front (top) and lateral (bottom) pictures of the MV with strings in the annulus; (b) schematic of the left heart simulator and AT measurement system. The left heart simulator consisted of an annulus-mounting plate, two PM holders and a vacuum pump. The annulus-mounting plate had a ring to support the MV annulus, which was also held by multiple strings in the periphery. Two PM holders secured PMs in the slack, normal and taut positions. String tensions were measured and used to calculate the ATs.
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pressure was monitored by a pressure transducer (25KPGAV, Fujikura Amrican Inc. Houston, TX).
2.2. AT measurement A porcine MV was mounted on the left heart simulator. The MV annulus perimeter was connected through thin strings to posts installed at the periphery of the MV in a circular way. The strings were approximately perpendicular to the ring perimeter. The plane formed by all the strings was approximately parallel to the MV annulus plane. The MV annulus tissue could slide freely on the plastic ring. When the MV closed under trans-mitral pressure, all the strings in the MV annulus were in tension, preventing the MV annulus from shrinking towards the MV orifice center. The strings that connected the anterior and posterior annulus were attached to force transducers (Load Cell Central, Monroeton, PA) that were used to measure string tensions. The capacity of the load cell was 5.89 N (600 g). Combined error was 0.02%. A data acquisition (DAQ) board & Labview 8.0 software (National Instruments Corporation, Austin, TX) was used to record the tensions. Force transducers were placed inline with the strings attached to the annulus. Four transducers were placed at the anterior, while three were placed at the posterior. Spacing between strings was approximately 5 mm. The string tensions were divided by the distance between stitches in the annulus to obtain the AT. The friction between the MV annulus and the ring was eliminated by averaging string tensions during the loading and unloading processes. Average tension per unit length of the annulus was calculated and averaged along the anterior and posterior annulus sections in the unit of N/m, referred to as the AT (He and Bhattacharya, 2008). The ATs are presented as mean7standard deviation.
2.3. Experiment preparation and data analysis Fresh porcine hearts were obtained from local slaughterhouses and were stored in a freezer for less than a week before the MVs were harvested. The MVs of annulus size M36 measured by a ring sizer (Edwards Lifescience, Irvine, CA) were selected. Only the MV with a normal geometry of chord and leaflet structure was used in the
Normal annulus size
1.25 times dilatation
1.5 times dilatation
Fig. 2. A picture of the three rings used to support the MV annulus: one normal and two dilatated sizes. The ring was identical to the MV annulus. A normal ring was made according to M36 in an Edwards ring sizer with 7.63 cm2 in area. Two dilatated rings were 1.25 and 1.5 times the normal annulus area. The dilatated rings were similar to pathologies with enlarged septal–lateral diameters and the same commissure-to-commissure diameter.
experiment. PMs were set up in the normal state controlled by PM holders which could be adjusted three-dimensionally. Normal PM position was achieved when the chordae were approximately perpendicular to the annulus plane with neither tension nor slackness in the chordae (He et al., 2003). Slack and taut PM positions were set up with 5 mm displacement to and from the annulus, respectively. Trans-mitral pressures of 11.1, 13.6, 16.3 and 19.6 kPa (83, 102, 122 and 147 mmHg, respectively) were used in the experiment. Three rings were used in the experiment as shown in Fig. 2: one normal and two dilatated sizes. A ring of normal size was made according to M36 on the Edwards ring sizer. The normal annulus area was 7.63 cm2. Two dilatated ring sizes were 1.25 and 1.5 times the normal annulus area. The dilatated rings were similar to pathologies with enlarged septal–lateral diameters and the same commissure-to-commissure diameter. The MV annuli themselves were enlarged to match the enlarged rings during the experiment. A total of 14 MVs were tested. Statistical analysis assumed the observations of the ATs followed a normal distribution. For the comparison of anterior and posterior ATs in the different PM positions, a paired two-sample t-test for means was used. The p-value is based on two-tail distribution, with po0.05 used as the accepted value for significance.
3. Results Most of MVs coaptated normally and built up transmitral pressure in the experiment. One of the 14 MVs did not coaptate normally in the 1.25 times dilatated annulus. Four of 14 MVs did not coaptate normally in the 1.5 times dilatated annulus. The data from these regurgitant MVs were excluded because of low trans-mitral pressures. Fig. 3 is the averaged anterior and posterior ATs under a series of trans-mitral pressures in the 3 PM positions and normal annulus. The error bars are in the format of 71/2 standard deviation centered on the averaged values. It can be seen that the anterior and posterior ATs increased approximately linearly with the increase of trans-mitral pressures for all 3 PM positions in the normal annulus. Linear regression of the anterior and posterior ATs vs. trans-mitral pressure data in the normal annulus all demonstrated R240.98 for the slack, normal and taut PM positions. Both the anterior and posterior ATs increased with apical PM displacement, i.e., from slack to normal to taut PM positions. The taut and slack PM positions demonstrated the highest and lowest anterior ATs in any annulus size. The differences in the anterior and posterior ATs between the slack and normal, and normal and taut PM positions were significant, and all p-values were less than 0.0003. The difference in the anterior and posterior ATs between the normal and taut PM positions was less than that between the normal and slack PM positions in 3 annuli. Fig. 4(a) is the anterior ATs in 3 PM positions and 3 annuli at the trans-mitral pressure of 16.3 kPa (122 mmHg). The anterior ATs were 37.21711.03, 53.86714.98 and 58.87715.72 N/m in the slack, normal and taut PM positions, respectively, in the normal annulus. The slack and taut PM positions demonstrated a 30.9% decrease and a 9.3% increase, respectively, in anterior ATs if compared with the anterior AT in the normal PM position for the normal annulus. The anterior ATs also increased with the increase of annulus area in all the 3 PM positions.
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ATs in 3 PM positions in the normal annulus Anterior AT in the normal PM position Anterior AT in the slack PM position Posterior AT in the taut PM position
Anterior AT in the taut PM position Posterior AT in the normal PM position Posterior AT in the slack PM position
Annulus tension (N/m)
70
50
30
10
90
80
100 110 120 130 Trans-mitral pressure (mmHg or 0.133 kPa)
140
150
Fig. 3. Averaged anterior and posterior ATs in three PM positions under a series of trans-mitral pressures and the normal annulus. The error bars are in the format of 71/2 standard deviation centered on the averaged values. The anterior and posterior ATs increased linearly with the increase of trans-mitral pressures in three PM positions. The anterior and posterior ATs also increased when PM positions changed from the slack to normal, then to taut positions.
Anterior ATs in 3 PM positiions at the trans-mitral pressure of 16.3 kPa (122 mmHg) Slack P<0.00001
Annulus tension (N/m)
80.00 70.00
P<0.00001 53.86
60.00 50.00 40.00
Normal
P<0.00001
Taut
P=0.0065
P=0.0016
63.67
61.52
58.87
67.28
58.15 41.84
40.27
37.2
P<0.00001
30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 16.3 kPa (122 mmHg) Slack
Normal
Taut
80.00 P<0.00001 P<0.00001
Annulus tension (N/m)
70.00 60.00
P<0.00001
P<0.00001
P<0.00001
50.00
42.32
39.66
36.29
40.00 30.00
P<0.00001
24.52
51.47 46.48
45.69
28.18
31.15
20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 4. The anterior and posterior ATs in the three PM positions at the trans-mitral pressure of 16.3 kPa (122 mmHg) in the normal annulus. In all three PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
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Anterior ATs in 3 PM positiions at the trans-mitral pressure of 19.6 kPa (147 mmHg) Slack
Annulus tension (N/m)
80.00
P<0.00001
70.00
60.06
60.00 50.00
P<0.00001
Taut
P<0.00001 P<0.00001
65.51
42.11
Normal
63.93
P<0.00001
P=0.01463
69.83
67.79
73.09
45.90
44.27
40.00 30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 19.6 kPa (147 mmHg) Slack 80.00 Annulus tension (N/m)
70.00
P<0.00049
P=0.00002
P<0.00001
P=0.02791
46.80
43.23 29.23
56.62 53.23
52.09
48.54
50.00
Taut
P<0.00001
P<0.00001
60.00
40.00
Normal
35.30
32.09
30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 5. The anterior and posterior ATs in the 3 PM positions and the normal annulus at the trans-mitral pressure of 19.6 kPa (147 mmHg). In all 3 PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
Regarding the anterior AT change with PM position and annulus size, the anterior AT in the 1.5 times dilatated annulus was 63.67712.04 N/m in the normal PM position and greater than the anterior AT of 58.87715.72 N/m in the normal annulus in the taut PM position. Fig. 4(b) shows the posterior ATs in 3 PM positions and 3 annuli at the trans-mitral pressure of 16.3 kPa (122 mmHg). The posterior ATs were similar to the anterior ATs. The posterior ATs were 24.5275.68, 36.2978.89 and 42.32711.82 N/m in the slack, normal and taut PM positions, respectively, in the normal annulus. The slack and taut PM positions demonstrated a 32.4% decrease and a 16.6% increase, respectively, in the posterior ATs if compared with the posterior AT in the normal PM position for the normal annulus. The posterior AT also increased with the increase of annulus area in all 3 PM positions. Regarding the posterior AT change with PM position and annulus size, the posterior ATs in the 1.5 times dilatated annulus was 46.48710.73 N/m in the normal annulus and the normal PM position and greater than the posterior AT of 42.32711.82 N/m in the normal annulus in the taut PM position.
Figs. 5 and 6 show the anterior and posterior ATs for all 3 PM positions and all 3 annuli at the trans-mitral pressures 13.6 and 19.6 kPa (102 and 147 mmHg). The results were similar to those at the trans-mitral pressure of 16.3 kPa (122 mmHg). The anterior and posterior ATs at the trans-mitral pressure of 19.6 kPa (147 mmHg) were 60.06716.26 and 43.23711.09 N/m, respectively, in the normal annulus and normal PM position. Generally, both anterior and posterior AT increased with the PM change from the slack to normal, and then to taut position, and increased with the increase of the annulus area. Effects of annulus size, trans-mitral pressure and PM position on the anterior and posterior ATs followed the pattern in the ATs: 1.5 times dilatated annulus4trans-mitral pressure of 19.6 kPa (147 mmHg)4taut PM position (5 mm away from the normal PM position).
4. Discussion In the current study, we presented the detailed study of the MV ATs in the anterior and posterior annulus sections
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Anterior ATs in 3 PM positiions at the trans-mitral pressure of 13.6 kPa (102 mmHg) Slack
Normal
Taut
Annulus tension (N/m)
80.00 70.00
P<0.00001 P<0.00001
60.00 46.22
50.00 40.00
P=0.00003
P<0.00001
P=0.02081
50.59
32.14
P=0.00003
49.93
55.56
52.38
60.15
33.89
30.00
21.49
20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 13.6 kPa (102 mmHg) Slack
Normal
Taut
80.00 Annulus tension (N/m)
70.00 60.00 50.00
P<0.00001
P=0.00004
40.00
P=0.00016
P=0.00001 44.31
40.15 34.04
32.16
29.00
30.00 20.00
P=0.00267
P=0.00002
19.65
35.32 24.11
21.41
10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 6. The anterior and posterior ATs in the 3 PM positions and the normal annulus at the trans-mitral pressure of 13.6 kPa (102 mmHg). In all 3 PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
in the 3 PM positions. We summarize our key findings as follows: 1. The AT increases with the increase of annulus area and linearly with increase of trans-mitral pressure in the 3 PM positions. 2. The AT increases with apical PM displacement, i.e., from slack to normal to taut PM positions. 3. The AT increases with change from a normal state (normal annulus, normal PM position, normal transmitral pressure 122 mmHg) to any one of three extreme conditions alone (1.5 times dilatated annulus, taut PM position or 147 mmHg trans-mitral pressure). So far as any one of the three extreme conditions is concerned with other two conditions in the normal state, the AT is greatest in the 1.5 times dilatated annulus while the AT is lowest in the taut PM position. AT can be understood by MV spatial configuration, pressure on the MV and chordal tension in the coaptation. The AT addressed in the current paper is leaflet tension at the anterior and posterior annulus sections. In order to
obtain a clear concept of MV mechanics, we analyze a control volume of the MV, the region outlined by dashed lines in Fig. 7. The ATs, chordal tensions and air pressures are on the control surfaces. The AT has two components: one in the annulus plane and the other normal to the annulus plane. The AT angle is leaflet angle with respect to the annulus plane. The AT components in annulus and in out-of-annulus planes can be calculated with the AT angle. The AT angle changes with PM positions. Leaflet positions in the slack and taut PM positions are shown in the figure by the dotted lines. The AT angle is negative, approximately zero and positive in the slack, normal and taut PM positions, respectively. The AT component in the annulus plane is balanced by chordal tension component and transmitral pressure force on the leaflet in the annulus plane. The leaflet coaptation force is defined as a force in the lateral direction to push the leaflets close together. It is balanced primarily by the AT component in the annulus plane as well as secondarily by chordal tension components in the annulus plane because the chordae are approximately perpendicular to the annulus plane. The leaflet coaptation force is determined primarily by the product of
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Papillary muscle Chordae
Control volume Anterior leaflet in the taut, normal and slack PM positions
Posterior leaflet in the taut, normal and slack PM positions String
String tension String tension AT angle
Annulus-mounting plate
Annulus ring Fig. 7. MV control volume. The ATs, chordal tensions and air pressures act on the control surfaces. The ATs are primarily within the annulus plane in the normal valve configuration. The chordae and their tensions are approximately perpendicular to the annulus plane. Apical force components on the MV are generated by trans-mitral pressure and are balanced primarily by chordal tensions. The leaflet coaptation force, which pushes the leaflets close together in the lateral direction is balanced primarily by the ATs as well as secondarily by chordal tension components in the annulus plane.
the MV leaflet profile area and trans-mitral pressure. The MV leaflet profile area is defined as a projection of the leaflet surface area on a cylinder surface in annulus diameter. The leaflet height and thus MV leaflet profile area is greatest and smallest in the taut and slack PM positions, respectively. Therefore, the AT component in the annulus plane is greatest and smallest in the taut and slack PM positions, respectively. Our results demonstrated agreement with the mechanics analysis based on the control volume. But the AT change did not change linearly with PM position. This fact might be due to differences in chordal structure, AT angle or leaflet coaptation depth in 3 PM positions. The results demonstrated that the anterior AT was consistently higher than the posterior AT in the 3 PM positions and 3 annuli. The difference between the anterior and posterior ATs was caused by the difference in area between (the larger) anterior and (the smaller) posterior leaflets covering the annulus orifice, as well as by the chord structure. For the same reason, the AT increased with the increase of the annulus area, which is supported by the numerical study that the leaflet stresses increased with the annular dilatation for both the anterior and posterior leaflets (Quick et al., 1997). Annulus configuration is determined by two mechanical contributions: leaflet restriction and myocardium force in the annulus. The myocardium force is a force on MV annulus by the left ventricle tissue around annulus, and forms a balance with the AT in the annulus. Our results showed the extent to which the MV leaflets restrict the annulus although the myocardium contribution is unknown. The AT is a force pulling the anterior and posterior annulus sections to each other and balanced by the myocardium in the septal–lateral direction. The force helps prevent the annulus from expanding in the septal–lateral
direction. It is proposed that annulus dilatation is a consequence of imbalance between the AT and myocardium force. This force increases as the left ventricle pressure increases. The low trans-mitral pressure reduces the leaflet restriction force. Less restriction on the annulus from the MV leaflets will possibly cause greater potential for annulus dilatation. This mechanism is supported by the animal experiment in which lower trans-mitral pressure from mitral regurgitation caused mitral annulus area increase (Messas et al., 2001, 2003). This process is described as a cycle: annulus dilatation–regurgitation–low trans-mitral pressure–less restriction force on the annulus–further annulus dilatation. Therefore, the annulus dilatation process is a vicious cycle, which, once it has started, accelerates in the point of view of annulus mechanics. Clinically, the slack PM position was to simulate a prolapsed MV, while the taut PM position was to simulate a dilated left ventricle disease such as ischemic MV disease. AT decreased in the slack PM position, which means less restriction on the annulus. If the AT component in the annulus plane was considered, this restriction force was even smaller. Hence, the prolapsed MV had more potential of annulus dilatation than the normal MV. On the other hand, the AT increased in the taut PM position, and the AT component in the annulus plane probably increased when the AT angle was considered. The taut PM position had a stronger septal–lateral restriction force than the normal PM position. Therefore, taut PM position reduced the potential of annulus dilatation due to the greater AT restricting the annulus expansion. As far as PM displacement, annulus dilatation and transmitral pressure are concerned, their effects on AT are different. The annulus dilatation reduced the leaflet
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coaptation depth and inclined the chordae relative to the annulus plane, and therefore increased coaptation force in the lateral direction and the chordal tension component in the annulus plane, and thus the AT. The leaflet coaptation in annulus dilatation is helped by leaflet redundancy to some extent (He et al., 1999). The taut PM position also reduced leaflet coaptation depth and increased MV lateral profile area, thus coaptation force. However, large apical PM displacement caused by ischemic heart disease can lead to a tented MV and ischemic mitral regurgitation (Messas et al., 2001; Miller, 2001). The taut PM position might not change the chord angle relative to the annulus plane, but changed leaflet profile and thus AT angle. The AT increased with apical PM displacement due to higher leaflet profile; the AT increased with the increase of annulus area (due to increase of chordae tension component in annulus plane), and of the large lateral leaflet profile area (due to the increase of annulus diameter and reduction of leaflet coaptation depth). Trans-mitral pressure increases global forces on the MV and therefore the AT increases linearly with trans-mitral pressure. 5. Limitations The differences in the left ventricle and MV geometry between a porcine heart and a human heart may cause discrepancy in the results. The ATs were measured only in the anterior and posterior annulus regions and do not describe the annulus force conditions in the other region. The chordal tensions may affect the ATs by variations in their structural configuration. Static experiment only provided peak AT without duration in a whole cardiac cycle. This setting limited the explanation of AT in a whole cardiac cycle. The AT angle relative to the annulus plane was not quantified. The lack of angle could cause error in the AT component in the annulus plane. The leakage through the gap between the annulus and the supporting ring might exist. This leaking flow shear stress might cause error in AT measurement. However, the MV tissue is compliant and easily pushed to contact the ring well when the vacuum pump started and trans-mitral pressure was built up. Leakage between the MV and the ring should be very limited. The effect of leaking on the AT would be minor for small air density. The MV geometry and mechanical properties might change due to dehydration even if a humidifier was used to spray wet air to the MV. The change might cause error in the AT measurement. 6. Summary The current study reveals the ATs in the 3 PM positions and their interaction with annulus dilatation and transmitral pressures and provides insight into annulus dilatation. The AT increases with the increase of annulus area and linearly with the increase of trans-mitral pressure in the 3 PM positions. The AT increases from the slack to normal, then to taut PM positions. The AT is greater in the
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taut PM position than that in the normal and slack PM positions. The greatest AT is in a condition of taut PM in the 1.5 times dilatated annulus at the high trans-mitral pressure. The AT increases with change from a normal state (normal annulus, normal PM position, normal transmitral pressure 122 mmHg) to any one of three extreme conditions alone (1.5 times dilatated annulus, taut PM position or 147 mmHg trans-mitral pressure). So far as any one of the three extreme conditions is concerned with other two conditions in the normal state, the AT is greatest in the 1.5 times dilatated annulus while the AT is lowest in the taut PM position. Therefore, annulus configuration is a comprehensive outcome from the trans-mitral pressure, annulus size, PM position and the left ventricular myocardium configuration. The AT increases in apical PM displacement and dilatated annuli, reducing annulus dilatation potential under normal trans-mitral pressure. Low trans-mitral pressure due to existent mitral regurgitation will increase annulus dilatation potential. Mitral regurgitation due to MV prolapse will have a great potential of annulus dilatation. Conflict of interest Dr. Zhaoming He and Shamik Bhattacharya have no potential conflict of interest. Acknowledgments The study was supported by the American Heart Association, Southcentral Affiliate (Beginning-Grant-InAid #0665055Y). The pig hearts were donated to the lab by the Department of Animal & Food Science at Texas Tech University, and Klemke Sausage Haus in Slaton, Texas. References Arts, T., Meerbaum, S., et al., 1983. Stresses in the closed mitral valve: a model study. Journal of Biomechanics 16, 539–547. Espino, D.M., Shepherd, D.E., et al., 2007. Effect of mitral valve geometry on valve competence. Heart Vessels 22, 109–115. Flachskampf, F.A., Chandra, S., et al., 2000. Analysis of shape and motion of the mitral annulus in subjects with and without cardiomyopathy by echocardiographic 3-dimensional reconstruction. Journal of the American Society of Echocardiography 13, 277–287. Gorman III, J.H., Gupta, K.B., et al., 1996. Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization. Journal of Thoracic and Cardiovascular Surgery 112, 712–726. He, Z., Bhattacharya, S., 2008. Mitral valve annulus tension in the anterior and posterior annulus: an in-vitro study. Annals of Biomedical Engineering, submitted for publication. He, S., Lemmon Jr., J.D., et al., 1999. Mitral valve compensation for annular dilatation: in vitro study into the mechanisms of functional mitral regurgitation with an adjustable annulus model. Journal of Heart Valve Disease 8, 294–302. He, S., Weston, M.W., et al., 2000. Geometric distribution of chordae tendineae: an important anatomic feature in mitral valve function. Journal of Heart Valve Disease 9, 495–501 (discussion 502–503).
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He, Z., Sacks, M.S., et al., 2003. Effects of papillary muscle position on invitro dynamic strain on the porcine mitral valve. Journal of Heart Valve Disease 12, 488–494. He, Z., Ritchie, J., et al., 2005. In vitro dynamic strain behavior of the mitral valve posterior leaflet. Journal of Biomechanical Engineering 127, 504–511. Jimenez, J.H., Soerensen, D.D., et al., 2003. Effects of a saddle shaped annulus on mitral valve function and chordal force distribution: an in vitro study. Annals of Biomedical Engineering 31, 1171–1181. Kheradvar, A., Gharib, M., 2007. Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Annals of Biomedical Engineering 35, 2050–2064. Kunzelman, K.S., Cochran, R.P., et al., 1993. Finite element analysis of the mitral valve. Journal of Heart Valve Disease 2, 326–340. Kunzelman, K.S., Quick, D.W., et al., 1998. Altered collagen concentration in mitral valve leaflets: biochemical and finite element analysis. Annals of Thoracic Surgery 66, S198–S205. Levine, R.A., Handschumacher, M.D., et al., 1989. Three-dimensional echocardiographic reconstruction of the mitral valve, with implications for the diagnosis of mitral valve prolapse. Circulation 80, 589–598. Messas, E., Guerrero, J.L., et al., 2001. Chordal cutting: a new therapeutic approach for ischemic mitral regurgitation. Circulation 104, 1958–1963.
Messas, E., Pouzet, B., et al., 2003. Efficacy of chordal cutting to relieve chronic persistent ischemic mitral regurgitation. Circulation 108 (Suppl. 1), II111–II115. Miller, D.C., 2001. Ischemic mitral regurgitation redux-to repair or to replace? Journal of Thoracic and Cardiovascular Surgery 122, 1059–1062. Ormiston, J.A., Shah, P.M., et al., 1981. Size and motion of the mitral valve annulus in man. I. A two-dimensional echocardiographic method and findings in normal subjects. Circulation 64, 113–120. Qin, J.X., Shiota, T., et al., 2002. Impact of left ventricular outflow tract area on systolic outflow velocity in hypertrophic cardiomyopathy: a real-time three-dimensional echocardiographic study. Journal of the American College of Cardiology 39, 308–314. Quick, D.W., Kunzelman, K.S., et al., 1997. Collagen synthesis is upregulated in mitral valves subjected to altered stress. American Society for Artificial Internal Organs Journal 43, 181–186. Tibayan, F.A., Rodriguez, F., et al., 2003. Annular remodeling in chronic ischemic mitral regurgitation: ring selection implications. Annals of Thoracic Surgery 76, 1549–1554 (discussion 1554–1555). Timek, T.A., Glasson, J.R., et al., 2005. Annular height-to-commissural width ratio of annulolasty rings in vivo. Circulation 112, I423–I428.
Journal of Biomechanics 41 (2008) 2524–2532 www.elsevier.com/locate/jbiomech www.JBiomech.com
Papillary muscle and annulus size effect on anterior and posterior annulus tension of the mitral valve: An insight into annulus dilatation Zhaoming He, Shamik Bhattacharya Department of Mechanical Engineering, Texas Tech University, 7th and Boston, PO Box 41021, Lubbock, TX 79409-1021, USA Accepted 6 May 2008
Abstract Mitral valve (MV) annulus mechanics and its effect on annulus dilatation are not well understood. The objective of the current study was to understand annulus tension (AT) during valve closure. A porcine MV rested on top of annulus rings with papillary muscles (PMs) held at slack, normal and taut conditions. The annulus was held by strings in the periphery during valve closure under static trans-mitral pressures. String tensions were measured and further used to calculate the anterior and posterior ATs. Three rings of different sizes were used to simulate normal and dilatated annuli. Fourteen MVs were tested. The anterior ATs were 37.21711.03, 53.86714.98 and 58.87715.72 N/m, respectively, at the slack, normal and taut PM positions in the normal annulus at the trans-mitral pressure of 16.3 kPa (122 mmHg). The posterior ATs were 24.5275.68, 36.2978.89 and 42.32711.82 N/m, respectively, at the slack, normal and taut PM positions in the normal annulus at the trans-mitral pressure of 16.3 kPa (122 mmHg). AT increased as the PM changed from slack to normal, then to taut PM positions. The AT increases with the increase of annulus area and linearly with the increase of trans-mitral pressure. The AT increases with the increases of apical PM displacement and dilatated annulus area, and reduces the potential of annulus dilatation. Low trans-mitral pressure due to existent mitral regurgitation, and MV prolapse increase the potential of annulus dilatation. Published by Elsevier Ltd. Keywords: Annulus tension; Annulus dilatation; Tissue mechanics; Left ventricle
1. Introduction The mitral valve (MV) annulus is an anatomical structure joining the leaflets and left ventricle wall. The MV annulus is a dynamic structure that varies in size and shape during a cardiac cycle. It has a ‘‘sphincteric’’ function when the MV closes, thus helping leaflet coaptation by reducing the annulus orifice area (Ormiston et al., 1981). It also changes saddle height due to contraction or relaxation of the left ventricle (Levine et al., 1989; Gorman et al., 1996; Flachskampf et al., 2000; Timek et al., 2005). The MV leaflets are supported by the annulus and chordae at MV closure. The annulus pulls the MV leaflets and prevents them from shrinking towards center of the MV orifice during systole. Trans-mitral pressure acts on the leaflets and induces leaflet tension, which is transferred to the annulus and chordae (Arts et al., 1983). The leaflet Corresponding author. Tel.: +806 742 3563x225; fax: +806 742 3540.
E-mail address: [email protected] (Z. He). 0021-9290/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jbiomech.2008.05.006
tension at the annulus per unit length is defined as annulus tension (AT). Chordae pull MV leaflets apically and prevent them from prolapsing, and further transfer chordal tensions to papillary muscles (PMs) (He et al., 2000). Even when the MV is fully open during diastole, inflow drag force and chordae tension on the leaflets pulls the leaflets and hence the annulus (Kheradvar and Gharib, 2007). The AT is an interaction force in the equilibrium state between the leaflets and the myocardium. Alteration in either one due to pathologies will break the equilibrium and change the AT, which ultimately results in annulus geometry change such as annulus dilatation. Ischemic heart disease is a disease in which the coronary arteries are blocked partially or completely. This disease leads to left ventricular dilation, which tethers PMs away from the MV annulus. This PM tethering alters MV mechanics and sometimes causes a tented MV, in which MV leaflets look like a tent during closure and do not coaptate, and causes ischemic mitral regurgitation. The peak stresses in the anterior leaflet increase with PM
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displacement (Kunzelman et al., 1998; He et al., 2005). On the other hand, a minimum annulo-papillary length is also required to allow proper MV closure (Espino et al., 2007). PM position influences MV function in a complicated way. Annulus dilatation is a consequence caused by left ventricle remodeling and worsens the MV function. Annulus dilatation occurs primarily in the myocardium annulus and secondarily in the fibrous annulus (Tibayan et al., 2003). This asymmetrical dilatation in the annulus increases specifically septal–lateral annulus diameter, which may be a plausible reason for functional mitral regurgitation (Qin et al., 2002). Annulus dilatation is related to AT and its interaction with the myocardium. AT is on the annulus plane and restricts MV annulus size, while out-ofplane AT components determine MV annulus shape (Jimenez et al., 2003). Annulus dilatation increases leaflet stresses and thus AT (Kunzelman et al., 1993; Quick et al., 1997). The effect of PM displacement and/or annulus dilatation on MV mechanics and function is not well understood. We aim to understand PM position effect on annulus dilatation from the viewpoint of mechanics. It is hypothesized that the AT is one of the important
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mechanisms that control annulus size under different PM positions. This hypothesis can be tested by AT analysis in the PM displacement and annulus dilatation conditions. The objective of the present study was to quantify the MV AT in the annulus dilatation and PM displacement conditions and to understand how the AT interacts with MV annulus dilatation and PM positions in MV coaptation. 2. Methods 2.1. Left heart simulator A left heart simulator, as shown in Fig. 1, was designed to simulate the coaptating MV in systole at a static trans-mitral pressure. It was made up of a annulus-mounting plate, two PM holders and a vacuum pump. The annulus-mounting plate was made of plexiglas and had a plastic ring glued on it. The ring was made to be the same size as the annulus of selected MVs. A porcine MV annulus was placed on the plastic ring. The atrium chamber below the MV was connected to the vacuum pump. The MV and chordae were open to the air. A humidifier was used to spray cold wet air on the MV continuously during the experiment to prevent the MVs from drying. The PMs were sutured to two PM holders. The vacuum pump created a trans-mitral pressure that forced the valve to close. Atrial
Annulus tissue suture
Anterior leaflet ө
ө
Posterior leaflet
ө * * * * ө
ө
* : post with force transducer
* * * ө
θ : post without force transducer
Porcine annulus resting on a ring ө
ө
Cylinder support for force transducers
Papillary muscle holder
Papillary muscle
Annulus-mounting plate
Chordae Leaflet Suture at the annulus edge
Suture at the transducer
Annulus ring
Force transducer
To the valve Pressure transducer Air is drawn from vacuum pump
Tuning valve
Fig. 1. (a) Front (top) and lateral (bottom) pictures of the MV with strings in the annulus; (b) schematic of the left heart simulator and AT measurement system. The left heart simulator consisted of an annulus-mounting plate, two PM holders and a vacuum pump. The annulus-mounting plate had a ring to support the MV annulus, which was also held by multiple strings in the periphery. Two PM holders secured PMs in the slack, normal and taut positions. String tensions were measured and used to calculate the ATs.
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pressure was monitored by a pressure transducer (25KPGAV, Fujikura Amrican Inc. Houston, TX).
2.2. AT measurement A porcine MV was mounted on the left heart simulator. The MV annulus perimeter was connected through thin strings to posts installed at the periphery of the MV in a circular way. The strings were approximately perpendicular to the ring perimeter. The plane formed by all the strings was approximately parallel to the MV annulus plane. The MV annulus tissue could slide freely on the plastic ring. When the MV closed under trans-mitral pressure, all the strings in the MV annulus were in tension, preventing the MV annulus from shrinking towards the MV orifice center. The strings that connected the anterior and posterior annulus were attached to force transducers (Load Cell Central, Monroeton, PA) that were used to measure string tensions. The capacity of the load cell was 5.89 N (600 g). Combined error was 0.02%. A data acquisition (DAQ) board & Labview 8.0 software (National Instruments Corporation, Austin, TX) was used to record the tensions. Force transducers were placed inline with the strings attached to the annulus. Four transducers were placed at the anterior, while three were placed at the posterior. Spacing between strings was approximately 5 mm. The string tensions were divided by the distance between stitches in the annulus to obtain the AT. The friction between the MV annulus and the ring was eliminated by averaging string tensions during the loading and unloading processes. Average tension per unit length of the annulus was calculated and averaged along the anterior and posterior annulus sections in the unit of N/m, referred to as the AT (He and Bhattacharya, 2008). The ATs are presented as mean7standard deviation.
2.3. Experiment preparation and data analysis Fresh porcine hearts were obtained from local slaughterhouses and were stored in a freezer for less than a week before the MVs were harvested. The MVs of annulus size M36 measured by a ring sizer (Edwards Lifescience, Irvine, CA) were selected. Only the MV with a normal geometry of chord and leaflet structure was used in the
Normal annulus size
1.25 times dilatation
1.5 times dilatation
Fig. 2. A picture of the three rings used to support the MV annulus: one normal and two dilatated sizes. The ring was identical to the MV annulus. A normal ring was made according to M36 in an Edwards ring sizer with 7.63 cm2 in area. Two dilatated rings were 1.25 and 1.5 times the normal annulus area. The dilatated rings were similar to pathologies with enlarged septal–lateral diameters and the same commissure-to-commissure diameter.
experiment. PMs were set up in the normal state controlled by PM holders which could be adjusted three-dimensionally. Normal PM position was achieved when the chordae were approximately perpendicular to the annulus plane with neither tension nor slackness in the chordae (He et al., 2003). Slack and taut PM positions were set up with 5 mm displacement to and from the annulus, respectively. Trans-mitral pressures of 11.1, 13.6, 16.3 and 19.6 kPa (83, 102, 122 and 147 mmHg, respectively) were used in the experiment. Three rings were used in the experiment as shown in Fig. 2: one normal and two dilatated sizes. A ring of normal size was made according to M36 on the Edwards ring sizer. The normal annulus area was 7.63 cm2. Two dilatated ring sizes were 1.25 and 1.5 times the normal annulus area. The dilatated rings were similar to pathologies with enlarged septal–lateral diameters and the same commissure-to-commissure diameter. The MV annuli themselves were enlarged to match the enlarged rings during the experiment. A total of 14 MVs were tested. Statistical analysis assumed the observations of the ATs followed a normal distribution. For the comparison of anterior and posterior ATs in the different PM positions, a paired two-sample t-test for means was used. The p-value is based on two-tail distribution, with po0.05 used as the accepted value for significance.
3. Results Most of MVs coaptated normally and built up transmitral pressure in the experiment. One of the 14 MVs did not coaptate normally in the 1.25 times dilatated annulus. Four of 14 MVs did not coaptate normally in the 1.5 times dilatated annulus. The data from these regurgitant MVs were excluded because of low trans-mitral pressures. Fig. 3 is the averaged anterior and posterior ATs under a series of trans-mitral pressures in the 3 PM positions and normal annulus. The error bars are in the format of 71/2 standard deviation centered on the averaged values. It can be seen that the anterior and posterior ATs increased approximately linearly with the increase of trans-mitral pressures for all 3 PM positions in the normal annulus. Linear regression of the anterior and posterior ATs vs. trans-mitral pressure data in the normal annulus all demonstrated R240.98 for the slack, normal and taut PM positions. Both the anterior and posterior ATs increased with apical PM displacement, i.e., from slack to normal to taut PM positions. The taut and slack PM positions demonstrated the highest and lowest anterior ATs in any annulus size. The differences in the anterior and posterior ATs between the slack and normal, and normal and taut PM positions were significant, and all p-values were less than 0.0003. The difference in the anterior and posterior ATs between the normal and taut PM positions was less than that between the normal and slack PM positions in 3 annuli. Fig. 4(a) is the anterior ATs in 3 PM positions and 3 annuli at the trans-mitral pressure of 16.3 kPa (122 mmHg). The anterior ATs were 37.21711.03, 53.86714.98 and 58.87715.72 N/m in the slack, normal and taut PM positions, respectively, in the normal annulus. The slack and taut PM positions demonstrated a 30.9% decrease and a 9.3% increase, respectively, in anterior ATs if compared with the anterior AT in the normal PM position for the normal annulus. The anterior ATs also increased with the increase of annulus area in all the 3 PM positions.
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ATs in 3 PM positions in the normal annulus Anterior AT in the normal PM position Anterior AT in the slack PM position Posterior AT in the taut PM position
Anterior AT in the taut PM position Posterior AT in the normal PM position Posterior AT in the slack PM position
Annulus tension (N/m)
70
50
30
10
90
80
100 110 120 130 Trans-mitral pressure (mmHg or 0.133 kPa)
140
150
Fig. 3. Averaged anterior and posterior ATs in three PM positions under a series of trans-mitral pressures and the normal annulus. The error bars are in the format of 71/2 standard deviation centered on the averaged values. The anterior and posterior ATs increased linearly with the increase of trans-mitral pressures in three PM positions. The anterior and posterior ATs also increased when PM positions changed from the slack to normal, then to taut positions.
Anterior ATs in 3 PM positiions at the trans-mitral pressure of 16.3 kPa (122 mmHg) Slack P<0.00001
Annulus tension (N/m)
80.00 70.00
P<0.00001 53.86
60.00 50.00 40.00
Normal
P<0.00001
Taut
P=0.0065
P=0.0016
63.67
61.52
58.87
67.28
58.15 41.84
40.27
37.2
P<0.00001
30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 16.3 kPa (122 mmHg) Slack
Normal
Taut
80.00 P<0.00001 P<0.00001
Annulus tension (N/m)
70.00 60.00
P<0.00001
P<0.00001
P<0.00001
50.00
42.32
39.66
36.29
40.00 30.00
P<0.00001
24.52
51.47 46.48
45.69
28.18
31.15
20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 4. The anterior and posterior ATs in the three PM positions at the trans-mitral pressure of 16.3 kPa (122 mmHg) in the normal annulus. In all three PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
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Anterior ATs in 3 PM positiions at the trans-mitral pressure of 19.6 kPa (147 mmHg) Slack
Annulus tension (N/m)
80.00
P<0.00001
70.00
60.06
60.00 50.00
P<0.00001
Taut
P<0.00001 P<0.00001
65.51
42.11
Normal
63.93
P<0.00001
P=0.01463
69.83
67.79
73.09
45.90
44.27
40.00 30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 19.6 kPa (147 mmHg) Slack 80.00 Annulus tension (N/m)
70.00
P<0.00049
P=0.00002
P<0.00001
P=0.02791
46.80
43.23 29.23
56.62 53.23
52.09
48.54
50.00
Taut
P<0.00001
P<0.00001
60.00
40.00
Normal
35.30
32.09
30.00 20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 5. The anterior and posterior ATs in the 3 PM positions and the normal annulus at the trans-mitral pressure of 19.6 kPa (147 mmHg). In all 3 PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
Regarding the anterior AT change with PM position and annulus size, the anterior AT in the 1.5 times dilatated annulus was 63.67712.04 N/m in the normal PM position and greater than the anterior AT of 58.87715.72 N/m in the normal annulus in the taut PM position. Fig. 4(b) shows the posterior ATs in 3 PM positions and 3 annuli at the trans-mitral pressure of 16.3 kPa (122 mmHg). The posterior ATs were similar to the anterior ATs. The posterior ATs were 24.5275.68, 36.2978.89 and 42.32711.82 N/m in the slack, normal and taut PM positions, respectively, in the normal annulus. The slack and taut PM positions demonstrated a 32.4% decrease and a 16.6% increase, respectively, in the posterior ATs if compared with the posterior AT in the normal PM position for the normal annulus. The posterior AT also increased with the increase of annulus area in all 3 PM positions. Regarding the posterior AT change with PM position and annulus size, the posterior ATs in the 1.5 times dilatated annulus was 46.48710.73 N/m in the normal annulus and the normal PM position and greater than the posterior AT of 42.32711.82 N/m in the normal annulus in the taut PM position.
Figs. 5 and 6 show the anterior and posterior ATs for all 3 PM positions and all 3 annuli at the trans-mitral pressures 13.6 and 19.6 kPa (102 and 147 mmHg). The results were similar to those at the trans-mitral pressure of 16.3 kPa (122 mmHg). The anterior and posterior ATs at the trans-mitral pressure of 19.6 kPa (147 mmHg) were 60.06716.26 and 43.23711.09 N/m, respectively, in the normal annulus and normal PM position. Generally, both anterior and posterior AT increased with the PM change from the slack to normal, and then to taut position, and increased with the increase of the annulus area. Effects of annulus size, trans-mitral pressure and PM position on the anterior and posterior ATs followed the pattern in the ATs: 1.5 times dilatated annulus4trans-mitral pressure of 19.6 kPa (147 mmHg)4taut PM position (5 mm away from the normal PM position).
4. Discussion In the current study, we presented the detailed study of the MV ATs in the anterior and posterior annulus sections
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Anterior ATs in 3 PM positiions at the trans-mitral pressure of 13.6 kPa (102 mmHg) Slack
Normal
Taut
Annulus tension (N/m)
80.00 70.00
P<0.00001 P<0.00001
60.00 46.22
50.00 40.00
P=0.00003
P<0.00001
P=0.02081
50.59
32.14
P=0.00003
49.93
55.56
52.38
60.15
33.89
30.00
21.49
20.00 10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Posterior ATs in 3 PM positions at the trans-mitral pressure of 13.6 kPa (102 mmHg) Slack
Normal
Taut
80.00 Annulus tension (N/m)
70.00 60.00 50.00
P<0.00001
P=0.00004
40.00
P=0.00016
P=0.00001 44.31
40.15 34.04
32.16
29.00
30.00 20.00
P=0.00267
P=0.00002
19.65
35.32 24.11
21.41
10.00 0.00 Normal annulus
1.25 times dilatation Annulus size
1.5 times dilatation
Fig. 6. The anterior and posterior ATs in the 3 PM positions and the normal annulus at the trans-mitral pressure of 13.6 kPa (102 mmHg). In all 3 PM positions, the anterior and posterior ATs increased when the PM changed from the slack to normal, then to taut positions.
in the 3 PM positions. We summarize our key findings as follows: 1. The AT increases with the increase of annulus area and linearly with increase of trans-mitral pressure in the 3 PM positions. 2. The AT increases with apical PM displacement, i.e., from slack to normal to taut PM positions. 3. The AT increases with change from a normal state (normal annulus, normal PM position, normal transmitral pressure 122 mmHg) to any one of three extreme conditions alone (1.5 times dilatated annulus, taut PM position or 147 mmHg trans-mitral pressure). So far as any one of the three extreme conditions is concerned with other two conditions in the normal state, the AT is greatest in the 1.5 times dilatated annulus while the AT is lowest in the taut PM position. AT can be understood by MV spatial configuration, pressure on the MV and chordal tension in the coaptation. The AT addressed in the current paper is leaflet tension at the anterior and posterior annulus sections. In order to
obtain a clear concept of MV mechanics, we analyze a control volume of the MV, the region outlined by dashed lines in Fig. 7. The ATs, chordal tensions and air pressures are on the control surfaces. The AT has two components: one in the annulus plane and the other normal to the annulus plane. The AT angle is leaflet angle with respect to the annulus plane. The AT components in annulus and in out-of-annulus planes can be calculated with the AT angle. The AT angle changes with PM positions. Leaflet positions in the slack and taut PM positions are shown in the figure by the dotted lines. The AT angle is negative, approximately zero and positive in the slack, normal and taut PM positions, respectively. The AT component in the annulus plane is balanced by chordal tension component and transmitral pressure force on the leaflet in the annulus plane. The leaflet coaptation force is defined as a force in the lateral direction to push the leaflets close together. It is balanced primarily by the AT component in the annulus plane as well as secondarily by chordal tension components in the annulus plane because the chordae are approximately perpendicular to the annulus plane. The leaflet coaptation force is determined primarily by the product of
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Papillary muscle Chordae
Control volume Anterior leaflet in the taut, normal and slack PM positions
Posterior leaflet in the taut, normal and slack PM positions String
String tension String tension AT angle
Annulus-mounting plate
Annulus ring Fig. 7. MV control volume. The ATs, chordal tensions and air pressures act on the control surfaces. The ATs are primarily within the annulus plane in the normal valve configuration. The chordae and their tensions are approximately perpendicular to the annulus plane. Apical force components on the MV are generated by trans-mitral pressure and are balanced primarily by chordal tensions. The leaflet coaptation force, which pushes the leaflets close together in the lateral direction is balanced primarily by the ATs as well as secondarily by chordal tension components in the annulus plane.
the MV leaflet profile area and trans-mitral pressure. The MV leaflet profile area is defined as a projection of the leaflet surface area on a cylinder surface in annulus diameter. The leaflet height and thus MV leaflet profile area is greatest and smallest in the taut and slack PM positions, respectively. Therefore, the AT component in the annulus plane is greatest and smallest in the taut and slack PM positions, respectively. Our results demonstrated agreement with the mechanics analysis based on the control volume. But the AT change did not change linearly with PM position. This fact might be due to differences in chordal structure, AT angle or leaflet coaptation depth in 3 PM positions. The results demonstrated that the anterior AT was consistently higher than the posterior AT in the 3 PM positions and 3 annuli. The difference between the anterior and posterior ATs was caused by the difference in area between (the larger) anterior and (the smaller) posterior leaflets covering the annulus orifice, as well as by the chord structure. For the same reason, the AT increased with the increase of the annulus area, which is supported by the numerical study that the leaflet stresses increased with the annular dilatation for both the anterior and posterior leaflets (Quick et al., 1997). Annulus configuration is determined by two mechanical contributions: leaflet restriction and myocardium force in the annulus. The myocardium force is a force on MV annulus by the left ventricle tissue around annulus, and forms a balance with the AT in the annulus. Our results showed the extent to which the MV leaflets restrict the annulus although the myocardium contribution is unknown. The AT is a force pulling the anterior and posterior annulus sections to each other and balanced by the myocardium in the septal–lateral direction. The force helps prevent the annulus from expanding in the septal–lateral
direction. It is proposed that annulus dilatation is a consequence of imbalance between the AT and myocardium force. This force increases as the left ventricle pressure increases. The low trans-mitral pressure reduces the leaflet restriction force. Less restriction on the annulus from the MV leaflets will possibly cause greater potential for annulus dilatation. This mechanism is supported by the animal experiment in which lower trans-mitral pressure from mitral regurgitation caused mitral annulus area increase (Messas et al., 2001, 2003). This process is described as a cycle: annulus dilatation–regurgitation–low trans-mitral pressure–less restriction force on the annulus–further annulus dilatation. Therefore, the annulus dilatation process is a vicious cycle, which, once it has started, accelerates in the point of view of annulus mechanics. Clinically, the slack PM position was to simulate a prolapsed MV, while the taut PM position was to simulate a dilated left ventricle disease such as ischemic MV disease. AT decreased in the slack PM position, which means less restriction on the annulus. If the AT component in the annulus plane was considered, this restriction force was even smaller. Hence, the prolapsed MV had more potential of annulus dilatation than the normal MV. On the other hand, the AT increased in the taut PM position, and the AT component in the annulus plane probably increased when the AT angle was considered. The taut PM position had a stronger septal–lateral restriction force than the normal PM position. Therefore, taut PM position reduced the potential of annulus dilatation due to the greater AT restricting the annulus expansion. As far as PM displacement, annulus dilatation and transmitral pressure are concerned, their effects on AT are different. The annulus dilatation reduced the leaflet
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coaptation depth and inclined the chordae relative to the annulus plane, and therefore increased coaptation force in the lateral direction and the chordal tension component in the annulus plane, and thus the AT. The leaflet coaptation in annulus dilatation is helped by leaflet redundancy to some extent (He et al., 1999). The taut PM position also reduced leaflet coaptation depth and increased MV lateral profile area, thus coaptation force. However, large apical PM displacement caused by ischemic heart disease can lead to a tented MV and ischemic mitral regurgitation (Messas et al., 2001; Miller, 2001). The taut PM position might not change the chord angle relative to the annulus plane, but changed leaflet profile and thus AT angle. The AT increased with apical PM displacement due to higher leaflet profile; the AT increased with the increase of annulus area (due to increase of chordae tension component in annulus plane), and of the large lateral leaflet profile area (due to the increase of annulus diameter and reduction of leaflet coaptation depth). Trans-mitral pressure increases global forces on the MV and therefore the AT increases linearly with trans-mitral pressure. 5. Limitations The differences in the left ventricle and MV geometry between a porcine heart and a human heart may cause discrepancy in the results. The ATs were measured only in the anterior and posterior annulus regions and do not describe the annulus force conditions in the other region. The chordal tensions may affect the ATs by variations in their structural configuration. Static experiment only provided peak AT without duration in a whole cardiac cycle. This setting limited the explanation of AT in a whole cardiac cycle. The AT angle relative to the annulus plane was not quantified. The lack of angle could cause error in the AT component in the annulus plane. The leakage through the gap between the annulus and the supporting ring might exist. This leaking flow shear stress might cause error in AT measurement. However, the MV tissue is compliant and easily pushed to contact the ring well when the vacuum pump started and trans-mitral pressure was built up. Leakage between the MV and the ring should be very limited. The effect of leaking on the AT would be minor for small air density. The MV geometry and mechanical properties might change due to dehydration even if a humidifier was used to spray wet air to the MV. The change might cause error in the AT measurement. 6. Summary The current study reveals the ATs in the 3 PM positions and their interaction with annulus dilatation and transmitral pressures and provides insight into annulus dilatation. The AT increases with the increase of annulus area and linearly with the increase of trans-mitral pressure in the 3 PM positions. The AT increases from the slack to normal, then to taut PM positions. The AT is greater in the
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taut PM position than that in the normal and slack PM positions. The greatest AT is in a condition of taut PM in the 1.5 times dilatated annulus at the high trans-mitral pressure. The AT increases with change from a normal state (normal annulus, normal PM position, normal transmitral pressure 122 mmHg) to any one of three extreme conditions alone (1.5 times dilatated annulus, taut PM position or 147 mmHg trans-mitral pressure). So far as any one of the three extreme conditions is concerned with other two conditions in the normal state, the AT is greatest in the 1.5 times dilatated annulus while the AT is lowest in the taut PM position. Therefore, annulus configuration is a comprehensive outcome from the trans-mitral pressure, annulus size, PM position and the left ventricular myocardium configuration. The AT increases in apical PM displacement and dilatated annuli, reducing annulus dilatation potential under normal trans-mitral pressure. Low trans-mitral pressure due to existent mitral regurgitation will increase annulus dilatation potential. Mitral regurgitation due to MV prolapse will have a great potential of annulus dilatation. Conflict of interest Dr. Zhaoming He and Shamik Bhattacharya have no potential conflict of interest. Acknowledgments The study was supported by the American Heart Association, Southcentral Affiliate (Beginning-Grant-InAid #0665055Y). The pig hearts were donated to the lab by the Department of Animal & Food Science at Texas Tech University, and Klemke Sausage Haus in Slaton, Texas. References Arts, T., Meerbaum, S., et al., 1983. Stresses in the closed mitral valve: a model study. Journal of Biomechanics 16, 539–547. Espino, D.M., Shepherd, D.E., et al., 2007. Effect of mitral valve geometry on valve competence. Heart Vessels 22, 109–115. Flachskampf, F.A., Chandra, S., et al., 2000. Analysis of shape and motion of the mitral annulus in subjects with and without cardiomyopathy by echocardiographic 3-dimensional reconstruction. Journal of the American Society of Echocardiography 13, 277–287. Gorman III, J.H., Gupta, K.B., et al., 1996. Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization. Journal of Thoracic and Cardiovascular Surgery 112, 712–726. He, Z., Bhattacharya, S., 2008. Mitral valve annulus tension in the anterior and posterior annulus: an in-vitro study. Annals of Biomedical Engineering, submitted for publication. He, S., Lemmon Jr., J.D., et al., 1999. Mitral valve compensation for annular dilatation: in vitro study into the mechanisms of functional mitral regurgitation with an adjustable annulus model. Journal of Heart Valve Disease 8, 294–302. He, S., Weston, M.W., et al., 2000. Geometric distribution of chordae tendineae: an important anatomic feature in mitral valve function. Journal of Heart Valve Disease 9, 495–501 (discussion 502–503).
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He, Z., Sacks, M.S., et al., 2003. Effects of papillary muscle position on invitro dynamic strain on the porcine mitral valve. Journal of Heart Valve Disease 12, 488–494. He, Z., Ritchie, J., et al., 2005. In vitro dynamic strain behavior of the mitral valve posterior leaflet. Journal of Biomechanical Engineering 127, 504–511. Jimenez, J.H., Soerensen, D.D., et al., 2003. Effects of a saddle shaped annulus on mitral valve function and chordal force distribution: an in vitro study. Annals of Biomedical Engineering 31, 1171–1181. Kheradvar, A., Gharib, M., 2007. Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Annals of Biomedical Engineering 35, 2050–2064. Kunzelman, K.S., Cochran, R.P., et al., 1993. Finite element analysis of the mitral valve. Journal of Heart Valve Disease 2, 326–340. Kunzelman, K.S., Quick, D.W., et al., 1998. Altered collagen concentration in mitral valve leaflets: biochemical and finite element analysis. Annals of Thoracic Surgery 66, S198–S205. Levine, R.A., Handschumacher, M.D., et al., 1989. Three-dimensional echocardiographic reconstruction of the mitral valve, with implications for the diagnosis of mitral valve prolapse. Circulation 80, 589–598. Messas, E., Guerrero, J.L., et al., 2001. Chordal cutting: a new therapeutic approach for ischemic mitral regurgitation. Circulation 104, 1958–1963.
Messas, E., Pouzet, B., et al., 2003. Efficacy of chordal cutting to relieve chronic persistent ischemic mitral regurgitation. Circulation 108 (Suppl. 1), II111–II115. Miller, D.C., 2001. Ischemic mitral regurgitation redux-to repair or to replace? Journal of Thoracic and Cardiovascular Surgery 122, 1059–1062. Ormiston, J.A., Shah, P.M., et al., 1981. Size and motion of the mitral valve annulus in man. I. A two-dimensional echocardiographic method and findings in normal subjects. Circulation 64, 113–120. Qin, J.X., Shiota, T., et al., 2002. Impact of left ventricular outflow tract area on systolic outflow velocity in hypertrophic cardiomyopathy: a real-time three-dimensional echocardiographic study. Journal of the American College of Cardiology 39, 308–314. Quick, D.W., Kunzelman, K.S., et al., 1997. Collagen synthesis is upregulated in mitral valves subjected to altered stress. American Society for Artificial Internal Organs Journal 43, 181–186. Tibayan, F.A., Rodriguez, F., et al., 2003. Annular remodeling in chronic ischemic mitral regurgitation: ring selection implications. Annals of Thoracic Surgery 76, 1549–1554 (discussion 1554–1555). Timek, T.A., Glasson, J.R., et al., 2005. Annular height-to-commissural width ratio of annulolasty rings in vivo. Circulation 112, I423–I428.