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.     

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.     

Comparative in vitro study of bileaflet and tilting disk valve behavior in the pulmonary position

A study of mechanical heart valve behavior in the pulmonary position as a function of pulmonary vascular resistance is reported for the St. Jude Medical bileaflet (SJMB) valve and the MedicalCV Omnicarbon (OTD) tilting disk valve. Tests were conducted in a pulmonic mock circulatory system and impedance was varied in terms of system pulmonary vascular resistance (PVR). An impedance spectrum was found using instantaneous pulmonary artery pressure and flow rate curves. Both valves fully opened and closed at and above a nominal PVR of 3.0 mmHg/L/min. The SJMB valve was prone to leaflet bounce at closure, but otherwise completely closed, at settings above and below this nominal setting. At PVR values at and below 2.0 mmHg/L/min, the SJMB valve exhibited two types of leaflet aberrant behavior: single leaflet only closure while the other leaflet fluttered, and incomplete closure where both leaflets flutter but neither remain fully closed. The OTD valve fully opened and closed to a PVR value of 1.6 mmHg/L/min. At lower values, the valve did not close. Valves designed for the left heart can show aberrant behavior under normal conditions as pulmonary valves.     

A mathematical model of aortic valve vibration

It has been shown experimentally that the second heart sound is produced by diastolic vibrations of the closed aortic valve. In the present paper a mathematical model of this vibration is developed from first principles. The model assumes a one dimensional but non-linear fluid behavior. The problem is coupled through a non-linear, planar valve. A solution is obtained using the method of characteristics developed in finite difference form. The resulting valve frequency and amplitude are in good agreement with patient data. The model predicts a strong dependency of response on the valve forcing function and valve stiffness; and a weaker dependency of response on valve mass.     

A respiratory valve for rapid switching between two gas mixtures.

We have devised a respiratory valve that facilitates rapid and silent breath-to-breath switching between two gas mixtures, under remote control. It utilizes two inspiratory Loven-type valve elements, one for each gas mixture, either of which can be held closed with an electromagnet. Any type of valve element can serve as the expiratory valve. We have used a small respiratory valve with goats and a larger model for both goat and human use.     

High-speed imaging of developing heart valves reveals interplay of morphogenesis and function

Knowing how mutations disrupt the interplay between atrioventricular valve (AVV) morphogenesis and function is crucial for understanding how congenital valve defects arise. Here, we use high-speed fluorescence microscopy to investigate AVV morphogenesis in zebrafish at cellular resolution. We find that valve leaflets form directly through a process of invagination, rather than first forming endocardial cushions. There are three phases of valve function in embryonic development. First, the atrioventricular canal (AVC) is closed by the mechanical action of the myocardium, rolls together and then relaxes. The growing valve leaflets serve to block the canal during the roll and, depending on the developmental stage, either expand or hang down as a leaflet to block the canal. These steps are disrupted by the subtle morphological changes that result from inhibiting ErbB-, TGFbeta-or Cox2 (Ptgs2)-dependent signaling. Cox2 inhibition affects valve development due to its effect on myocardial cell size and shape, which changes the morphology of the ventricle and alters valve geometry. Thus, different signaling pathways regulate distinct aspects of the behavior of individual cells during valve morphogenesis, thereby influencing specific facets of valve function.     

Life-saving PTMC for critical calcific mitral stenosis in cardiogenic shock with balloon impasse

A 32-year-old male patient, a case of critical calcific mitral stenosis (following closed mitral valvotomy in 1989) was admitted for mitral valve replacement in September 2001. In hospital, he developed cardiogenic shock, pulmonary oedema and oliguria precluding surgery. An emergency percutaneous transatrial balloon mitral commissurotomy as a life-saving procedure in a valve with unfavourable morphology and 'balloon impasse' is discussed.     

Preserved ligament in the Jurassic bivalve Lithiotis: adaptive and evolutionary significance

An exceptionally well-preserved specimen of Lithiotis problematica from the Lower Jurassic of NE Italy possesses multiple resilia, composed of thin fibres and joining both valves, housed in ligamental grooves. The resilia were modified to allow small changes in the reciprocal distance of the valves. This increased the area in which the extremely thin free valve flexed to allow shell closure, and reduced the risk of breakage by fatigue of the valve and/or ligament. The fact that the valves remained connected by ligament for an extended height of the ligamental area implies that (1) the free valve closed by flexing, not by articulating, (2) it did not migrate in the ventral direction as often observed in cemented bivalves, and (3) it was approximately as long as the attached one.     

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D–0D fluid–structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier–Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier–Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.     

Geometric modeling of functional trileaflet aortic valves: development and clinical applications

The dimensions of the aortic valve components condition its ability to prevent blood from flowing back into the heart. While the theoretical parameters for best trileaflet valve performance have already been established, an effective approach to describe other less optimal, but functional models has been lacking. Our goal was to establish a method to determine by how much the dimensions of the aortic valve components can vary while still maintaining proper function. Measurements were made on silicone rubber casts of human aortic valves to document the range of dimensional variability encountered in normal adult valves. Analytical equations were written to describe a fully three-dimensional geometric model of a trileaflet valve in both the open and closed positions. A complete set of analytical, numerical and graphical tools was developed to explore a range of component dimensions within functional aortic valves. A list of geometric guidelines was established to ensure safe operation of the valve during the cardiac cycle, with practical safety margins. The geometry-based model presented here allows determining quickly if a certain set of valve component dimensions results in a functional valve. This is of great interest to designers of new prosthetic heart valve models, as well as to surgeons involved in valve-sparing surgery.     

Dynamics of flow in a mechanical heart valve: the role of leaflet inertia and leaflet compliance

In this work, we examine the dynamics of fluid flow in a mechanical heart valve when the solid inertia and leaflet compliance are important. The fluid is incompressible and Newtonian, and the leaflet is an incompressible neo-Hookean material. In the case of an inertialess leaflet, we find that the maximum valve opening angle and the time that the valve remains closed increase as the shear modulus of the leaflet decreases. More importantly, the regurgitant volume decreases with decreasing shear modulus. When we examined the forces exerted on the leaflet, we found that the downward motion of the leaflet is initiated by a vertical force exerted on its right side and, later on, by a vertical force exerted on the top side of the leaflet. In the case of solid inertia, we find that the maximum valve opening angle and the regurgitant volume are larger than in the case of an inertialess leaflet. These results highlight the importance of solid compliance in the dynamics of blood flow in a mechanical heart valve. More importantly, they indicate that mechanical heart valves with compliant leaflets may have smaller regurgitant volumes and smaller shear stresses than the ones with rigid leaflets.     

The relationship of normal and abnormal microstructural proliferation to the mitral valve closure sound

BACKGROUND: Many diseases that affect the mitral valve are accompanied by the proliferation or degradation of tissue microstructure. The early acoustic detection of these changes may lead to the better management of mitral valve disease. In this study, we examine the nonstationary acoustic effects of perturbing material parameters that characterize mitral valve tissue in terms of its microstructural components. Specifically, we examine the influence of the volume fraction, stiffness and splay of collagen fibers as well as the stiffness of the nonlinear matrix in which they are embedded. METHODS AND RESULTS: To model the transient vibrations of the mitral valve apparatus bathed in a blood medium, we have constructed a dynamic nonlinear fluid-coupled finite element model of the valve leaflets and chordae tendinae. The material behavior for the leaflets is based on an experimentally derived structural constitutive equation. The gross movement and small-scale acoustic vibrations of the valvular structures result from the application of physiologic pressure loads. Material changes that preserved the anisotropy of the valve leaflets were found to preserve valvular function. By contrast, material changes that altered the anisotropy of the valve were found to profoundly alter valvular function. These changes were manifest in the acoustic signatures of the valve closure sounds. Abnormally, stiffened valves closed more slowly and were accompanied by lower peak frequencies. CONCLUSION: The relationship between stiffness and frequency, though never documented in a native mitral valve, has been an axiom of heart sounds research. We find that the relationship is more subtle and that increases in stiffness may lead to either increases or decreases in peak frequency depending on their relationship to valvular function.     

Left ventricular endocardial longitudinal and transverse changes during isovolumic contraction and relaxation: a challenge

Left ventricular (LV) longitudinal and transverse geometric changes during isovolumic contraction and relaxation are still controversial. This confusion is compounded by traditional definitions of these phases of the cardiac cycle. High-resolution sonomicrometry studies might clarify these issues. Crystals were implanted in six sheep at the LV apex, fibrous trigones, lateral and posterior mitral annulus, base of the aortic right coronary sinus, anterior and septal endocardial wall, papillary muscle tips, and edge of the anterior and posterior mitral leaflets. Changes in distances were time related to LV and aortic pressures and to mitral valve opening. At the beginning of isovolumic contraction, while the mitral valve was still open, the LV endocardial transverse diameter started to shorten while the endocardial longitudinal diameter increased. During isovolumic relaxation, while the mitral valve was closed, LV transverse diameter started to increase while the longitudinal diameter continued to decrease. These findings are inconsistent with the classic definitions of the phases of the cardiac cycle.     

A detailed fluid mechanics study of tilting disk mechanical heart valve closure and the implications to blood damage

Hemolysis and thrombosis are among the most detrimental effects associated with mechanical heart valves. The strength and structure of the flows generated by the closure of mechanical heart valves can be correlated with the extent of blood damage. In this in vitro study, a tilting disk mechanical heart valve has been modified to measure the flow created within the valve housing during the closing phase. This is the first study to focus on the region just upstream of the mitral valve occluder during this part of the cardiac cycle, where cavitation is known to occur and blood damage is most severe. Closure of the tilting disk valve was studied in a "single shot" chamber driven by a pneumatic pump. Laser Doppler velocimetry was used to measure all three velocity components over a 30 ms period encompassing the initial valve impact and rebound. An acrylic window placed in the housing enabled us to make flow measurements as close as 200 microm away from the closed occluder. Velocity profiles reveal the development of an atrial vortex on the major orifice side of the valve shed off the tip of the leaflet. The vortex strength makes this region susceptible to cavitation. Mean and maximum axial velocities as high as 7 ms and 20 ms were recorded, respectively. At closure, peak wall shear rates of 80,000 s(-1) were calculated close to the valve tip. The region of the flow examined here has been identified as a likely location of hemolysis and thrombosis in tilting disk valves. The results of this first comprehensive study measuring the flow within the housing of a tilting disk valve may be helpful in minimizing the extent of blood damage through the combined efforts of experimental and computational fluid dynamics to improve mechanical heart valve designs.     

The circadian rhythms of valve movements in the mussel <Emphasis Type="Italic">Mytilus galloprovincialis</Emphasis>

The long-term (10–30 day) continuous recording of valve movements in the mussel Mytilus galloprovincialis was carried out in the laboratory under nearly natural conditions. Fourier analysis revealed the circadian (close to the diurnal) rhythm of the valve activity, the phase of which is readily shifted by a shift in the beginning of the daytime, since the light regime is one of the main factors determining the circadian rhythm. The circadian rhythm was manifested in the daily dynamics of mussel valve activity: in the daytime, mussels hold their valves closed more often than at night. This behavior may be a protective response, namely the “shadow reflex”: mussels close their valves upon a sudden decrease in illumination, thus protecting themselves from possible predators. Circadian activity can mask a mussel’s response to environmental pollution; therefore, regular valve closure should be taken into account in early warning systems such as “MusselMonitor®” with a correction for the season of the year, time of day, and other factors.     

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)     

Computational model of aortic valve surgical repair using grafted pericardium

Aortic valve reconstruction using leaflet grafts made from autologous pericardium is an effective surgical treatment for some forms of aortic regurgitation. Despite favorable outcomes in the hands of skilled surgeons, the procedure is underutilized because of the difficulty of sizing grafts to effectively seal with the native leaflets. Difficulty is largely due to the complex geometry and function of the valve and the lower distensibility of the graft material relative to native leaflet tissue. We used a structural finite element model to explore how a pericardial leaflet graft of various sizes interacts with two native leaflets when the valve is closed and loaded. Native leaflets and pericardium are described by anisotropic, hyperelastic constitutive laws, and we model all three leaflets explicitly and resolve leaflet contact in order to simulate repair strategies that are asymmetrical with respect to valve geometry and leaflet properties. We ran simulations with pericardial leaflet grafts of various widths (increase of 0%, 7%, 14%, 21% and 27%) and heights (increase of 0%, 13%, 27% and 40%) relative to the native leaflets. Effectiveness of valve closure was quantified based on the overlap between coapting leaflets. Results showed that graft width and height must both be increased to achieve proper valve closure, and that a graft 21% wider and 27% higher than the native leaflet creates a seal similar to a valve with three normal leaflets. Experimental validation in excised porcine aortas (n=9) corroborates the results of simulations.     

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.     

Modeling active muscle contraction in mitral valve leaflets during systole: a first approach

The present study addresses the effect of muscle activation contributions to mitral valve leaflet response during systole. State-of-art passive hyperelastic material modeling is employed in combination with a simple active stress part. Fiber families are assumed in the leaflets: one defined by the collagen and one defined by muscle activation. The active part is either assumed to be orthogonal to the collagen fibers or both orthogonal to and parallel with the collagen fibers (i.e. an orthotropic muscle fiber model). Based on data published in the literature and information herein on morphology, the size of the leaflet parts that contain muscle fibers is estimated. These parts have both active and passive materials, the remaining parts consist of passive material only. Several solid finite element analyses with different maximum activation levels are run. The simulation results are compared to corresponding echocardiography at peak systole for a porcine model. The physiologically correct flat shape of the closed valve is approached as the activation levels increase. The non-physiological bulging of the leaflet into the left atrium when using passive material models is reduced significantly. These results contribute to improved understanding of the physiology of the native mitral valve, and add evidence to the hypothesis that the mitral valve leaflets not are just passive elements moving as a result of hemodynamic pressure gradients in the left part of the heart.     

Functional anatomy of the valves in the ambulacral system of sea urchins (Echinodermata,Echinoida)

Summary The water vascular system of sea urchins is examined with special reference to the valves positioned between the radial vessel and the ampullae of the tube feet. The lips of the valve protrude into the ampulla. Thus the valve functions mainly like a check valve that allows the unidirectional flow of fluid towards the ampulla. Each ampulla-tube foot compartment acts as a semi-autonomous hydraulic system. The lumina of the ampulla and the tube foot are lined with myoepithelia except for the interconnecting channels that pierce the ambulacral plate. The contraction of the ampulla results in an increasing hydraulic pressure that protrudes the tube foot, provided that the valve is closed. The retraction of the tube foot results in a backflow of fluid independent of the condition of the valve. The lips of the valve are folds of the hydrocoel epithelium. The pore slit lies in the midline. The perradial faces of the lips are covered with the squamous epithelium of the lateral water vessel. The ampullar faces are specialized parts of the ampulla myoepithelium. Turgescent cells which form incompressible cushions take the place of the support cells. The valve myocytes run parallel to the pore slit and form processes that run along the base of the ampulla and the perradial channel up to the podial retractor muscle. The findings lead to the hypothesis of multiple control of the ampulla-tube foot system: (1) The mutual activity of the ampulla and the tube foot is indirectly controlled by the lateral and podial nerves which release transmitter substances that diffuse through the connective tissue up to the muscle layers. (2) A muscle-to-muscle conduction causes the simultaneous contraction of the ampulla or the podial retractor muscles. (3) The valve muscles are directly controlled by the processes of the valve myocytes which make contact with the podial retractor. In extreme conditions a backflow of hydrocoel fluid towards the radial water vessel occurs.