Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution

This study presents a three-dimensional finite element model of the mitral apparatus using a hyperelastic transversely isotropic material model for the leaflets. The objectives of this study are to illustrate the effects of the annulus shape on the chordal force distribution and on the mitral valve response during systole, to investigate the role of the anterior secondary (strut) chordae and to study the influence of thickness of the leaflets on the leaflets stresses. Hence, analyses are conducted with a moving and fixed saddle shaped annulus and with and without anterior secondary chordae. We found that the tension in the secondary chordae represents 31% of the load carried by the papillary muscles. When removing the anterior secondary chordae, the tension in the primary anterior chordae is almost doubled, the displacement of the anterior leaflet toward the left atrium is also increased. The moving annulus configuration with an increasing annulus saddle height does not give significant changes in the chordal force distribution and in the leaflet stress compared to the fixed annulus. The results also show that the maximum principle stresses in the anterior leaflet are carried by the collagen fibers. The stresses calculated in the leaflets are very sensitive to the thickness employed.     

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.     

Distribution of NADPH-diaphorase and AChE activity in the anterior leaflet of rat mitral valve

The mitral valve, as an active flap, forms the major part of the left ventricular inflow tract and therefore plays an important function in many aspects of left ventricular performance. The anterior leaflet of this valve is the largest and most ventrally placed of two leaflets that come together during ventricular systole to close the left atrioventricular orifice. Various neurotransmitters are responsible for different functions including controlling valve movement, inhibiting or causing the failure of impulse conduction in the valve and the sensation of pain. Nitric oxide acts as a gaseous free radical neurotransmitter, neuromediator and effective cardiovascular modulator. Acetyl-choline is known to function as a typical neurotransmitter. Histochemical methods for detection of nicotinamide adenine dinucleotide phosphate diaphorase (NADPH-d), as an indirect nitric oxide-synthase marker, and method for detection of acetylcholinesterase (AChE) were used. Both methods were performed on the same valve sample. A widespread distribution of nerve fibres was observed in the anterior leaflet of the mitral valve. The fine NADPH-d positive (nitrergic) nerve fibres were identified in all zones of valve leaflet. AChE positive (cholinergic) nerve fibres were identified forming dense network and fibres organized in stripes. Endocardial cells and vessels manifested heavy NADPH-d activity. Our observations suggest a different arrangement of nitrergic and cholinergic nerve fibres in the anterior leaflet of the mitral valve. The presence of nitrergic and cholinergic activity confirms the involvement of both neurotransmitters in nerve plexuses and other structures of mitral valve.Key words: NADPH-diaphorase, acetylcholinesterase, heart, mitral valve, nerve fibres, vessels, rat.     

In vitro assessment of a combined radiofrequency ablation and cryo-anchoring catheter for treatment of mitral valve prolapse

Percutaneous approaches to mitral valve repair are an attractive alternative to surgical repair or replacement. Radiofrequency ablation has the potential to approximate surgical leaflet resection by using resistive heating to reduce leaflet size, and cryogenic temperatures on a percutaneous catheter can potentially be used to reversibly adhere to moving mitral valve leaflets for reliable application of radiofrequency energy. We tested a combined cryo-anchoring and radiofrequency ablation catheter using excised porcine mitral valves placed in a left heart flow loop capable of reproducing physiologic pressure and flow waveforms. Transmitral flow and pressure were monitored during the cryo-anchoring procedure and compared to baseline flow conditions, and the extent of radiofrequency energy delivery to the mitral valve was assessed post-treatment. Long term durability of radiofrequency ablation treatment was assessed using statically treated leaflets placed in a stretch bioreactor for four weeks. Transmitral flow and pressure waveforms were largely unaltered during cryo-anchoring. Parameter fitting to mechanical data from leaflets treated with radiofrequency ablation and cryo-anchoring revealed significant mechanical differences from untreated leaflets, demonstrating successful ablation of mitral valves in a hemodynamic environment. Picrosirius red staining showed clear differences in morphology and collagen birefringence between treated and untreated leaflets. The durability study indicated that statically treated leaflets did not significantly change size or mechanics over four weeks. A cryo-anchoring and radiofrequency ablation catheter can adhere to and ablate mitral valve leaflets in a physiologic hemodynamic environment, providing a possible percutaneous alternative to surgical leaflet resection of mitral valve tissue.     

Stresses in the closed mitral valve: a model study

In the present model study on the closed mitral valve, tensile force in the chordae tendineae is related to transvalvular pressure using a mathematical model of mechanics of the closed mitral valve. Circumferential stress as well as bending stress in the valve leaflets were neglected. Without precisely knowing the mechanical properties of the leaflet material, geometry of the leaflets was estimated by applying Laplace's law, which relates leaflet stress to leaflet curvature. Independent of shape of the mitral valve orifice, under all circumstances tensile force in the chordae tendineae was calculated to be equal or greater than half the force exerted on the mitral valve orifice by the transvalvular pressure.     

Ablation of mitral annular and leaflet muscle: effects on annular and leaflet dynamics

Mitral annular (MA) and leaflet three-dimensional (3-D) dynamics were examined after circumferential phenol ablation of the MA and anterior mitral leaflet (AML) muscle. Radiopaque markers were sutured to the left ventricle, MA, and both mitral leaflets in 18 sheep. In 10 sheep, phenol was applied circumferentially to the atrial surface of the mitral annulus and the hinge region of the AML, whereas 8 sheep served as controls. Animals were studied with biplane video fluoroscopy for computation of 3-D mitral annular area (MAA) and leaflet shape. MAA contraction (MAACont) was determined from maximum to minimum value. Presystolic MAA (PS-MAACont) reduction was calculated as the percentage of total reduction occurring before end diastole. Phenol ablation decreased PS-MAACont (72 +/- 6 vs. 47 +/- 31%, P = 0.04) and delayed valve closure (31 +/- 11 vs. 57 +/- 25 ms, P = 0.017). In control, the AML had a compound sigmoid shape; after phenol, this shape was entirely concave to the atrium during valve closure. These data indicate that myocardial fibers on the atrial side of the valve influence the 3-D dynamic geometry and shape of the MA and AML.     

Straightening of curved pattern of collagen fibers under load controls aortic valve shape

The network of collagen fibers in the aortic valve leaflet is believed to play an important role in the strength and durability of the valve. However, in addition to its stress-bearing role, such a fiber network has the potential to produce functionally important shape changes in the closed valve under pressure load. We measured the average pattern of the collagen network in porcine aortic valve leaflets after staining for collagen. We then used finite element simulation to explore how this collagen pattern influences the shape of the closed valve. We observed a curved or bent pattern, with collagen fibers angled downward from the commissures toward the center of the leaflet to form a pattern that is concave toward the leaflet free edge. Simulations showed that these curved fiber trajectories straighten under pressure load, leading to functionally important changes in closed valve shape. Relative to a pattern of straight collagen fibers running parallel to the leaflet free edge, the concave pattern of curved fibers produces a closed valve with a 40% increase in central leaflet coaptation height and with decreased leaflet billow, resulting in a more physiological closed valve shape. Furthermore, simulations show that these changes in loaded leaflet shape reflect changes in leaflet curvature due to modulation of in-plane membrane stress resulting from straightening of the curved fibers. This effect appears to play an important role in normal valve function and may have important implications for the design of prosthetic and tissue engineered replacement valves.     

Mapping the spatial variation of mitral valve elastic properties using air-pulse optical coherence elastography

The mitral valve is a highly heterogeneous tissue composed of two leaflets, anterior and posterior, whose unique composition and regional differences in material properties are essential to overall valve function. While mitral valve mechanics have been studied for many decades, traditional testing methods limit the spatial resolution of measurements and can be destructive. Optical coherence elastography (OCE) is an emerging method for measuring viscoelastic properties of tissues in a noninvasive, nondestructive manner. In this study, we employed air-pulse OCE to measure the spatial variation in mitral valve elastic properties with micro-scale resolution at 1 mm increments along the radial length of the leaflets. We analyzed differences between the leaflets, as well as between regions of the valve. We found that the anterior leaflet has a higher elastic wave velocity, which is reported as a surrogate for stiffness, than the posterior leaflet, most notably at the annular edge of the sample. In addition, we found a spatial elastic gradient in the anterior leaflet, where the annular edge was found to have a greater elastic wave velocity than the free edge. This gradient was less pronounced in the posterior leaflet. These patterns were confirmed using established uniaxial tensile testing methods. Overall, the anterior leaflet was stiffer and had greater heterogeneity in its mechanical properties than the posterior leaflet. This study measures differences between the two mitral leaflets with greater resolution than previously feasible and demonstrates a method that may be suitable for assessing valve mechanics following repair or during the engineering of synthetic valve replacements.     

Aortic valve leaflet mechanical properties facilitate diastolic valve function

This work was concerned with the numerical simulation of the behaviour of aortic valves whose material can be modelled as non-linear elastic anisotropic. Linear elastic models for the valve leaflets with parameters used in previous studies were compared with hyperelastic models, incorporating leaflet anisotropy with pronounced stiffness in the circumferential direction through a transverse isotropic model. The parameters for the hyperelastic models were obtained from fits to results of orthogonal uniaxial tensile tests on porcine aortic valve leaflets. The computational results indicated the significant impact of transverse isotropy and hyperelastic effects on leaflet mechanics; in particular, increased coaptation with peak values of stress and strain in the elastic limit. The alignment of maximum principal stresses in all models follows approximately the coarse collagen fibre distribution found in aortic valve leaflets. The non-linear elastic leaflets also demonstrated more evenly distributed stress and strain which appears relevant to long-term scaffold stability and mechanotransduction.     

Dynamics of left ventricular wall and mitral valve mechanics--a model study

The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.     

In vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.     

Insights from in-vitro flow visualization into the mechanism of systolic anterior motion of the mitral valve in hypertrophic cardiomyopathy under steady flow conditions.

Hypertrophic obstructive cardiomyopathy is a heart disease characterized by a thickened interventricular septum which narrows the left ventricular outflow tract, and by systolic anterior motion (SAM) of the mitral valve which can contact the septum and create dynamic subaortic obstruction. The most common explanation for SAM has been the Venturi mechanism which postulates that septal hypertrophy, by narrowing the outflow tract, produces high velocities and thus low pressure between the mitral valve and the septum, causing the valve leaflets to move anteriorly. This hypothesis, however, fails to explain why SAM often begins early in systole, when outflow tract velocities are low or negligible or why it may occur in the absence of septal hypertrophy. The goal of this study was therefore to investigate an alternative hypothesis in which structural abnormalities of the papillary muscles act as a primary cause of SAM by altering valve restraint and thereby changing the geometry of the closed mitral apparatus and its relationship to the surrounding flow field. In order to test this hypothesis, an in vitro model of the left ventricle which included an explanted human mitral valve with intact chords and papillary muscle apparatus was constructed. Flow visualization was used to observe the ventricular flow field and the mitral valve geometry. Displacing the papillary muscles anteriorly and closer to each other, as observed clinically in patients with cardiomyopathy and obstruction produced SAM in the absence of septal hypertrophy. Flow could be seen impacting on the upstream (posterior) surface of the leaflets; such flow is capable of producing form drag forces which can initiate and maintain SAM.(ABSTRACT TRUNCATED AT 250 WORDS)     

Motion of both mitral valve leaflets: a cineroentgenographic study in intact dogs.

Motion and position of both mitral leaflets were studied in five normal dogs 1-11 wk after radiopaque markers were sutured on the valve cusps and on the mitral annulus. Cinefluorograms and cineangiograms (100-120 frames/s) of left atrium and left ventricle were used to study cusp motion and intraventricular flow patterns, and to detect mitral regurgitation during sinus rhythm (42-184 beats/min) and during isolated atrial or ventricular contractions. Time-motion of both leaflets was similar throughout diastole with the exception of delayed posterior cusp opening. Peak opening and closing speeds, opening and closing times, and time of complete closure, measured from the Q wave of the ECG, were not significantly affected by the variations in heart rate. Diastolic leaflet closure began immediately after opening, while the ventricular cavity was small, and was caused by flow eddies behind the cusps. Isolated ventricular contractions closed the valve leaflets completely and symmetric valve closure was ensured by the different rates of leaflet edge approximation. In contrast, atrial closure was slow, partial, and of very short duration.     

Probe for production and measurement of acute mitral regurgitant flow in dog.

A probe for production and measurement of acute mitral regurgitation in dogs is described. It consists of a tube that is introduced into the mitral valve through the left atrial appendage. Regurgitant flow through the tube is measured by an electromagnetic device. Variation of flow and zero flow are achieved by narrowing or occluding the tube with a rubber cuff. In animals weighing 30-50 kg, the probe does not produce significant mitral stenosis and the mitral leaflets fit closely around the probe during ventricular systole. The instantaneous relationship between mitral regurgitant flow (MRF) and the gradient between left ventricular and left atrial pressure shows a marked delay of MRF at the beginning and end of regurgitation. This delay can be attributed to some extent to electrical phase lag and to the small movement of the probe relative to the mitral valve during the cardiac cycle. Measurement of regurgitant stroke volume is affected by this movement only to a small extent.     

Cell-mediated retraction versus hemodynamic loading – A delicate balance in tissue-engineered heart valves

Preclinical studies of tissue-engineered heart valves (TEHVs) showed retraction of the heart valve leaflets as major failure of function mechanism. This retraction is caused by both passive and active cell stress and passive matrix stress. Cell-mediated retraction induces leaflet shortening that may be counteracted by the hemodynamic loading of the leaflets during diastole. To get insight into this stress balance, the amount and duration of stress generation in engineered heart valve tissue and the stress imposed by physiological hemodynamic loading are quantified via an experimental and a computational approach, respectively.     

Interlayer micromechanics of the aortic heart valve leaflet

While the mechanical behaviors of the fibrosa and ventricularis layers of the aortic valve (AV) leaflet are understood, little information exists on their mechanical interactions mediated by the GAG-rich central spongiosa layer. Parametric simulations of the interlayer interactions of the AV leaflets in flexure utilized a tri-layered finite element (FE) model of circumferentially oriented tissue sections to investigate inter-layer sliding hypothesized to occur. Simulation results indicated that the leaflet tissue functions as a tightly bonded structure when the spongiosa effective modulus was at least 25 % that of the fibrosa and ventricularis layers. Novel studies that directly measured transmural strain in flexure of AV leaflet tissue specimens validated these findings. Interestingly, a smooth transmural strain distribution indicated that the layers of the leaflet indeed act as a bonded unit, consistent with our previous observations (Stella and Sacks in J Biomech Eng 129:757–766, 2007) of a large number of transverse collagen fibers interconnecting the fibrosa and ventricularis layers. Additionally, when the tri-layered FE model was refined to match the transmural deformations, a layer-specific bimodular material model (resulting in four total moduli) accurately matched the transmural strain and moment-curvature relations simultaneously. Collectively, these results provide evidence, contrary to previous assumptions, that the valve layers function as a bonded structure in the low-strain flexure deformation mode. Most likely, this results directly from the transverse collagen fibers that bind the layers together to disable physical sliding and maintain layer residual stresses. Further, the spongiosa may function as a general dampening layer while the AV leaflets deforms as a homogenous structure despite its heterogeneous architecture.     

Biaxial mechanical properties of bovine jugular venous valve leaflet tissues

Venous valve incompetence has been implicated in diseases ranging from chronic venous insufficiency (CVI) to intracranial venous hypertension. However, while the mechanical properties of venous valve leaflet tissues are central to CVI biomechanics and mechanobiology, neither stress–strain curves nor tangent moduli have been reported. Here, equibiaxial tensile mechanical tests were conducted to assess the tangent modulus, strength and anisotropy of venous valve leaflet tissues from bovine jugular veins. Valvular tissues were stretched to 60% strain in both the circumferential and radial directions, and leaflet tissue stress–strain curves were generated for proximal and distal valves (i.e., valves closest and furthest from the right heart, respectively). Toward linking mechanical properties to leaflet microstructure and composition, Masson’s trichrome and Verhoeff–Van Gieson staining and collagen assays were conducted. Results showed: (1) Proximal bovine jugular vein venous valves tended to be bicuspid (i.e., have two leaflets), while distal valves tended to be tricuspid; (2) leaflet tissues from proximal valves exhibited approximately threefold higher peak tangent moduli in the circumferential direction than in the orthogonal radial direction (i.e., proximal valve leaflet tissues were anisotropic; \(p<0.01\)); (3) individual leaflets excised from the same valve apparatus appeared to exhibit different mechanical properties (i.e., intra-valve variability); and (4) leaflets from distal valves exhibited a trend of higher soluble collagen concentrations than proximal ones (i.e., inter-valve variability). To the best of the authors’ knowledge, this is the first study reporting biaxial mechanical properties of venous valve leaflet tissues. These results provide a baseline for studying venous valve incompetence at the tissue level and a quantitative basis for prosthetic venous valve design.     

Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.