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PATTERNS OF SYSTOLIC STRESS DISTRIBUTION ON MITRAL VALVE ANTERIOR LEAFLET CHORDAL APPARATUS.
A Structural Mechanical Theoretical Analysis
Stefano NAZARI, Fabio CARLI, Susanna SALVI, Carlo BANFI, Alessandro ALUFFI, Ziad MOURAD, Paolo BUNIVA, Giuseppe RESCIGNO.
1 - Dept of Surgery, IRCCS San Matteo, University of Pavia, 27100 Pavia, Italy
2 - Foundation Alexis Carrel, 27100 Pavia, Italy
3 - Dept of Structural Mechanics, University of Pavia, 27100 Pavia, Italy
4 - H. Européen de Paris "La Roserai", Aubervilliers, Paris
JOURNAL OF CARDIOVASCULAR SURGERY
Increasing diffusion and complexity of mitral valve repair procedures may prompt an interest in the evaluation of the patterns of stress distribution on the chords, which are, under the structural mechanical point of view, the weakest element of valve apparatus. This theoretical analysis concentrates in particular on the mitral valve anterior leaflet.
As known, the vast majority of the chordae are attached to the anterior leaflet within the coaptation area; during systole they are then necessarily parallel, aligned along the same plane as that of the leaflets' coaptation surface, to which they are attached; moreover the thickness of the chordae increases significantly from the marginal chordae to the more central ones.
In normal conditions during systole the progressively wider coaptation surface causes the increasing stress to be supported by an increasing number of progressively thicker chords which are substantially parallel and aligned on the coaptation surface plane in such a way that they can share the stress between them, according to their thickness; in other words chords form a multifilament functional unit which enrols elements of increasing thickness in response to the mounting stress.
The geometrical modifications of the valve apparatus architecture (annulus dilatation, leaflet retraction, chordal elongation or retraction) often associated with valve insufficiency due to chordal rupture, have the common result of causing, during systole, a radial disarrangement of the direction of most of the secondary chordae which are no longer parallel, aligned on the coaptation surface plane. Due to the negligible elastic module of the valve leaflet, in this new arrangement the various chordae cannot share the stress between themselves as they do in a normal physiological situation; on the contrary the thinner chordae nearer to the free margin are also loaded with the peak systolic stress, thus generating conditions favoring their rupture.
It can, therefore, be hypothesized that the anatomopathological picture of valve insufficiency due to chordal rupture may be the final event of a series of geometrical modifications of valve apparatus architecture, the common consequence of which is to load thinner marginal chords with peak systolic stress from which they are normally spared, thus favoring their rupture.
Key words: mitral valve, stress, chordae, anterior leaflet
Mitral valvuloplasty, conceived and spread into clinical practice by Carpentier (1), gives better long term results than either mechanical or biological valve replacements, without the complications associated with these procedures (thromboemboli, infections, suture dehiscence, haemolysis, functional deterioration) or the need for anticoagulative treatment (1,2). If the valve cusps are still pliable, the valve can generally be repaired, even though this may require a complex procedure.
From the structural mechanical point of view, chordae seem to be the weakest point of the mitral valve apparatus; it may then be useful to analyse, in detail, stress distribution in the chordal apparatus of a normal valve and try to anticipate its modifications in valve disease.
Many literature reports deal with stress on the chordal system (3-9), with complex mathematical methods (5,8) and accurate direct stress measurements on mitral chords (3,4,9). This study, however, focuses on a purely theoretical analysis, under the structural mechanic point of view, of the peculiar parallel arrangement which occurs physiologically between marginal and secondary chords during systole and of the functional consequences of the alterations of this parallelism induced by modifications of the valve architecture in pathological conditions.
Chords systolic stress in normal conditions
The main physiological action of the chords is to keep the free margins of the valve leaflets below the plane of the mitral annulus during systole, triggering the mechanism of coaptation; the rising systolic pressure then causes coaptation of an increasingly wide portion of the valve leaflets. At the peak of systolic pressure the coaptation surface is 1/4 to 1/3 of the height of the anterior leaflet and includes nearly all the insertions of the chordae tendineae (Fig. 1, middle and bottom).
Fig. 1.In isolated contracted pig heart a black dye stained the atrial surface of a closed mitral valve (150 mm Hg ventricular pressure), thus outlining only those parts of the leaflets which did not participate in the coaptation (Top).
The effective coaptation surface, not stained by the black dye, is thus clearly identified (Bottom).
Examining the anterior leaflet ventricular surface it can be appreciated that most of the chordae are inserted within the coaptation area; thus, during systole, these chordae are necessarily parallel, aligned on the same plane (the coaptation surface plane). It is also clear that the thicker (see tab I), stronger chordae are those closer to the atrial margin of the coaptation surface, where the stress is theoretically maximal.
During systole therefore, nearly all the secondary and marginal chordae tendineae are necessarily parallel, aligned along the same plane as that of the leaflets' coaptation surface to which they are attached (Fig. 2). In experimental conditions on animals (Fig 1, 150mmHg ventricular pressure) the most internal secondary chords, which are significantly thicker (strut chordae) (10,11), are only slightly away from the coaptation surface.
From a theoretical mechanical point of view the systolic stress is concentrated on that part of the leaflet where the chordae are inserted (rough zone). According to their different thicknesses and arrangements on the leaflet, marginal and secondary chords share the systolic stress in a particular way (Fig 2). At the beginning of systole, in fact, the still light stress is loaded on the thinner, more marginal chords which trigger the coaptation mechanism by keeping the valve leaflets below the annular plane. As the ventricular pressure rises, it causes coaptation of a wider leaflet surface, causing the alignment on the coaptation plane of thicker, more secondary chords, which can then share the increasing stress with the marginal ones, parallel to them and aligned on the same plane. At the peak of systolic pressure most of the stress is loaded on those very thick 'strut' secondary chords inserted at the atrial limit of the coaptation surface.
Fig. 2. During the peak of systolic pressure most of the chordae are aligned on the same plane, which is that of the coaptation surface, roughly parallel to the atrioventricular axis. Accordingly during systole the increasing stress is progressively supported by a growing number of increasingly thick chords which are substantially parallel and aligned on the coaptation surface plane in such a way that they can share the stress between them according to their thickness.
In summary, we may conclude that during systole the increasing stress is supported by an increasing number of progressively thicker chords which are substantially parallel and aligned on the coaptation surface plane in such a way that they can share the stress between them, according to their thickness (Fig. 3, A); in other words chords form a multifilament functional unit which enrols elements of increasing thickness in response to the mounting stress.
Fig. 3.A. The rough zone of the leaflet acts as a functional expansion of the chordae, supporting and distributing the stress between them, in such a way that the thinner marginal chords cannot elongate up to the breaking point without the stress being transferred onto the thicker ones.
B. When the rough zone is not parallel to the chordae however, this stress redistribution is no longer possible, due to the negligible elastic module of the leaflet, and the same amount of stress is loaded on all the chords. If we consider the great difference in thickness and thus resistance to stress of the marginal chords compared to the strut chords, on which the systolic stress is physiologically loaded, marginal chord rupture with abrupt valve insufficiency is not surprising.
Maximal Anterior chordae thickness
Specimen Leaflet A-P height 1st ord. 2nd ord. marginals
N cm mm mm mm
1 3.3 Post-med. Pap. m. 1.40 0.67 0.36
Ant-lat. Pap. m. 1.17 0.85-0.47 0.22
2 3.2 Post-med. Pap. m. 1.30 0.69 0.29
Ant-lat. Pap. m. 0.86 0.55 0.43
3 4.1 Post-med. Pap. m. 1.6 0.54 0.37
Ant-lat. Pap. m. 1.40 0.67 0.23
4 3.4 Post-med. Pap. m. 0.86 0.59 0.37
Ant-lat. Pap. m. 0.99 0.46 0.34
*data from 4 adult pigs.
Chords systolic stress in pathologic conditions
In spite of different underlying etiologies (1,2,12), the anatomopathological picture of valve insufficiency due to chordal rupture very frequently includes more or less marked modifications in the architecture of some or all of the components of the mitral valve apparatus. Quite frequently there is enlargement of the annulus associated with a variable degree of chordal elongation (12), but all kinds of modifications can be observed alone or in combination. It may then be interesting to attempt to predict the effects of each of the possible geometrical modifications of the valve apparatus architecture on the coaptation mechanism and on the pattern of stress distribution on the chordal system.
The essential acquired geometrical modifications of the valve apparatus which can be theoretically hypothesized may involve a) the annulus (dilatation or stenosis), b) the leaflets (retraction or augmentation) and c) the chordae tendineae (elongation or retraction). Papillary muscle modifications should theoretically also be considered; however the functional effects of their hypothesizable acquired geometrical modifications (elongation and retraction) are identical, in this regard, to the corresponding changes in the chords, and thus may be considered together.
It is interesting to note that most of these geometrical modifications of the valve apparatus have significant direct consequences on the wideness of the coaptation surface, which is reduced to variable extent; decrease of the coaptation surface necessarily involves a modification of the normal orientation of the major axis of part of the secondary chordae, which cannot be kept parallel to the marginal ones during systole, thus modifying the pattern of stress distribution. Fig. 4 illustrates these patterns assuming that each of the above geometrical modifications is present alone in an otherwise normal valve.
Fig. 4. All the hypothesized geometrical modifications of the valve apparatus components, with the exception of pure annulus stenosis and leaflet augmentation, have the common consequence of reducing the coaptation surface to some extent, thus necessarily causing a radial disarrangement of the chordae inserted on that portion of the leaflet no longer participating in the coaptation. This causes the peak systolic stress to be loaded also on the thinner less resistant marginal chords, normally spared this stress, generating conditions predisposing to their rupture. In fact, due to the leaflets' negligible elastic module, the stress can be distributed between the various chords only if they are parallel and aligned on the same plane (the coaptation plane) (see also Fig.3).
Annulus dilatation (Fig. 4, 1) which is very frequently associated with valve prolapse (5), increases the valvular orifice surface, thus necessarily causing a proportional decrease of the coaptation surface. This causes some of the secondary chordae to follow the leaflet towards the annulus and thus some of them are no longer arranged, during systole, on the same plane (the coaptation surface plane); in other words annular dilatation causes a radial disarrangement of the direction of most of the secondary chordae in such a way that the chordae nearer to the free margin, which are thinner and normally spared, are also loaded with the peak systolic stress. In fact, since the valve leaflets have negligible elastic module (13) (i.e. they are very pliable), the various chordae cannot share the stress between them as they do in a physiological situation when they are parallel and aligned on the same plane (the coaptation surface plane); on the contrary the same amount of stress is loaded on marginal chordae and all those chordae which are away from the coaptation plane (Fig. 3, B).
The opposite geometrical modification, i.e. pure annular stenosis (Fig. 4, 1"), has the effect of mildly increasing the coaptation surface, favoring the approach of most secondary chords to the coaptation plane. This presumably has no significant impact on the pattern of stress distribution which still predominantly loads all chords aligned on the same plane, in proportion to their thickness.
In the case of leaflet retraction (Fig. 4, 2), due for example to inflammatory and fibrotic leaflet reactions, the same mechanism as that observed in annular dilatation is responsible for the same consequences on chordal stress distribution .
Pure leaflet augmentation (Fig. 4, 2") does not itself involve significant reduction of the coaptation surface. On the other hand when artificially induced leaflet augmentation (i.e. by patch insertion) is carried out in a retracted leaflet, obviously it can restore a physiologically wide coaptation surface, re-establishing a normal pattern of stress distribution.
Chordal elongation (Fig. 4, 3) moves the coaptation surface upwards (towards the atrium). Minor elongation might not modify the width of the coaptation surface; however, with more significant elongation, i.e. when the leaflet insertion of the more secondary chords surpasses the level of the annulus, these chords can no longer be kept aligned with the coaptation surface; i.e. an analogous radial disarrangement of the most secondary chordae takes place, again unphysiologically exposing chords more proximal to the leaflet margin to the peak systolic stress .
Pure chordal retraction (Fig. 4, 3") moves the coaptation surface downwards (towards the ventricle), correspondingly increasing the distance between the annulus and the coaptation surface ventricular limit. The coaptation surface width is then reduced to some extent; accordingly the more secondary chords might not be kept aligned on the coaptation surface with the above mentioned consequences on chordal stress distribution.
In summary, with the exception of pure annular stenosis and leaflet augmentation, all the hypothesized modifications of the geometrical features of the valve apparatus components result in a more or less marked (Fig. 5) reduction of coaptation surface and, consequently, in radial disarrangement of the direction of the secondary chordae away from the physiological plane, which is substantially that of the coaptation surface. The invariable functional consequence of this is to expose the chordae nearer to the free margin to the peak systolic stress (Fig. 3, B) while, in a physiological situation, they would be spared from this load. The great difference in thickness ( 3 to 6 times, table I) and thus strength between strut and marginal chords makes it easy to predict that the latter will rupture when loaded with the entire systolic stress.
Fig. 5. In an attempt to predict the entity of coaptation surface reduction of geometrical modifications of various valve components, the sketches compare modifications resulting from a 1/4th reduction of leaflet and chordae and a 1/4th increase in the annulus diameter. A 1/4th reduction of the leaflet AP height makes it impossible for the leaflet to reach the coaptation plane; when there is a 1/4th increase in annular diameter, the leaflet barely reaches the coaptation plane, along a necessarily near linear path. The same proportional amount of chordal retraction affects coaptation surface width less markedly; moreover since the coaptation surface lower margin is moved downwards, the angle between the surface plane and z1 line decreases thus enhancing the preservation of coaptation surface to some extent.
Sketches are in scale, taking as reference the normal values (13). Leaflet AP height as well as all relevant lines measures shown in the figure were calculated by design software
Of course this theoretical, qualitative analysis implies many approximations.
First of all, in order to simplify the analysis, the modifications were hypothesized each as occurring alone in an otherwise normal valve, which seldom happens in a clinical setting. When geometrical modifications of other valve components are added, the radial disarrangement of secondary chords may be worsened or improved in ways that may be complex to predict. In the pure interest of speculation, Fig. 6 reports the predictable effects on secondary chords radial disarrangement of a second factor, added to each of those hypothesized above, causing decrease of coaptation surface.
In addition, quite frequently geometrical modifications involve only a part of the single valvular apparatus component; for example annular dilatation often involves predominantly the posterior part of the annulus (12), chordal elongation may involve only part of the chordae, etc. Moreover, other alterations such as increasing thickness, calcification and fusion of the mitral valve apparatus components, in particular of chordae, as well as changes in the mechanical properties of valve tissue due to pathologic processes, may also quite frequently occur and generate peculiar functional consequences on the pattern of stress distribution. These valve architecture alterations are difficult to analyze under a general point of view and were therefore intentionally excluded from this theoretical analysis.
Fig. 6.Shematic representation of the predictable effects on chords radial disarrangement of a second factor, added to each of those hypothesized above, causing decrease of coaptation surface. As can be seen the radial disarrangement may be improved or worsened by the second factor. The significance of the improvement or worsening is proportional to the predicted coaptation surface width modification (red bar).
In spite of the many and relevant approximations, these patterns of stress distribution allow us to hypothesize that the anatomopathological picture of valve insufficiency due to chordal rupture may be the final event of a series of geometrical modifications of valve apparatus architecture, the common consequence of which is to load thinner marginal chords with peak systolic stress from which they are normally spared, thus favoring their rupture. The great difference in thickness between strut and marginal chords (3 to 6 times, table I) indicates how significant the overload on the thin marginal chords can be when they are not aligned with the secondary ones at the peak of the systole; accordingly sooner or later rupture with abrupt onset of valve incompetence is not surprising.
This hypothesis may have practical implications in plastic surgery procedures. On a theoretical basis in fact, it could be important that surgery re-establishes a physiologically wide coaptation surface, not simply in order to enhance valve competence, but to ensure that systolic stress is physiologically shared by all the chords according to their thickness. This is only possible if the chordae are parallely aligned on the same plane (the coaptation plane). In fact, when this condition is not achieved, the resulting unphysiological stress load on thinner marginal chords would act as an important risk factor, predictably of the same nature as that which brought the patient to the surgeon, predisposing to late chordal rupture and recurrence of the valve insufficiency.
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