A three-dimensional computational analysis of fluid-structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valve's behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.     

Analysis of flow in a cone-and-plate apparatus with respect to spatial and temporal effects on endothelial cells

Endothelial cells, covering the inner surface of vessels and the heart, are permanently exposed to fluid flow, which affects the endothelial structure and the function. The response of endothelial cells to fluid shear stress is frequently investigated in cone-plate systems. For this type of device, we performed an analytical and numerical analysis of the steady, laminar, three-dimensional flow of a Newtonian fluid at low Reynolds numbers. Unsteady oscillating and pulsating flow was studied numerically by taking the geometry of a corresponding experimental setup into account. Our investigation provides detailed information with regard to shear-stress distribution at the plate as well as secondary flow. We show that: (i) there is a region on the plate where shear stress is almost constant and an analytical approach can be applied with high accuracy; (ii) detailed information about the flow in a real cone-plate device can only be obtained by numerical simulations; (iii) the pulsating flow is quasi-stationary; and (iv) there is a time lag on the order of 10(-3) s between cone rotation and shear stress generated on the plate.     

A fully coupled fluid-structure interaction model of the secondary lymphatic valve

Abstract

The secondary lymphatic valve is a bi-leaflet structure frequent throughout collecting vessels that serves to prevent retrograde flow of lymph. Despite its vital function in lymph flow and apparent importance in disease development, the lymphatic valve and its associated fluid dynamics have been largely understudied. The goal of this work was to construct a physiologically relevant computational model of an idealized rat mesenteric lymphatic valve using fully coupled fluid-structure interactions to investigate the relationship between three-dimensional flow patterns and stress/deformation within the valve leaflets. The minimum valve resistance to flow, which has been shown to be an important parameter in effective lymphatic pumping, was computed as 268?g/mm⁴?s. Hysteretic behavior of the lymphatic valve was confirmed by comparing resistance values for a given transvalvular pressure drop during opening and closing. Furthermore, eddy structures were present within the sinus adjacent to the valve leaflets in what appear to be areas of vortical flow; the eddy structures were characterized by non-zero velocity values (up to ～4?mm/s) in response to an applied unsteady transvalvular pressure. These modeling capabilities present a useful platform for investigating the complex interplay between soft tissue motion and fluid dynamics of lymphatic valves and contribute to the breadth of knowledge regarding the importance of biomechanics in lymphatic system function.     

Enhancing Cell Viability with Pulsating Flow in a Hollow Fiber Bioartificial Liver

A pulsating flow of medium was used to alleviate diffusion and transport limitations in a hollow fiber bioreactor containing a human hepatoblastoma cell line. The strategy is easy to implement but effective. The pulsating flow is introduced by a solenoid pinch valve at the outlet of the bioreactor and regulated by a timing circuit. In a permeability test, the system with pulsating flow had much less membrane fouling as compared to the control, a conventional hollow fiber unit. In hepatocyte culture test runs, the pulsating-flow bioreactor demonstrated the ability to maintain a higher cell viability. Histological sections indicated significantly smaller necrotic regions in the pulsating-flow bioreactor as compared to the conventional unit.     

A two-dimensional fluid-structure interaction model of the aortic valve [correction of value

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increases the durability of these valves by unloading the delicate parts of the leaflets, maintaining their physiological functioning. The interaction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has, so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structure interaction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domain method based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. The model has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed video recordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are well predicted for different leaflet thicknesses.     

New insights into the assessment of the prosthetic valve performance in the presence of subaortic stenosis through a fluid-structure interaction model

The aim of this study was to contribute to improving the accuracy of clinical assessments of valve performance in situations involving the concomitant presence of a prosthetic valve and subaortic stenosis (SAS). Physiological flow in a two-dimensional model for a bileaflet mechanical heart valve was investigated numerically in terms of the fluid-structure interactions. The fluid dynamics in a model with SAS of the left ventricle outflow tract were compared with those given by a healthy model. The results show that in the model with SAS, one leaflet did not close during the observed systolic phase, whereas the other one showed similar behaviour to that of the leaflet in the healthy model. In addition, the main flow did not occur along the central axis and a deviated jet was set up between leaflets, contrary to what occurred in the model without SAS. Current clinical diagnostic indices, which are mainly based on the central jet flow velocities, are therefore unsuitable for use in this pathological situation and should be used with great caution.     

Distribution of mass transfer rate and wall shear stress behind simple rectangular stenosis in pulsating flow

The distributions of mass transfer rate and wall shear stress in sinusoidal laminar pulsating flow through a two-dimensional asymmetric stenosed channel have been studied experimentally and numerically. The distributions are measured by the electrochemical method. The measurement is conducted at a Reynolds number of about 150, a Schmidt number of about 1000, a nondimensional pulsating frequency of 3.40, and a nondimensional flow amplitude of 0.3. It is suggested that the deterioration of an arterial wall distal to stenosis may be greatly enhanced by fluid dynamic effects.     

The effects of a glycerin-based blood analog on the testing of bioprosthetic heart valves

Detailed comparisons of aortic valvular flow using saline, with that using a glycerin-based blood analog in a pulse duplicator are reported. The experiments were carried out to determine whether exposure to glycerin caused stiffening of bioprosthetic valve leaflets. For two pericardial bioprostheses and for a mechanical valve we observed a fluid-dependent systolic volume flow, a fluid-dependent regurgitation volume, and fluid-dependent systolic pressure differences. Volume flow changes, both forward and reverse, are independent of valve type. The observed pressure differences, while proportional to fluid density for the mechanical valve, are fluid dependent in a more complicated way for the pericardial valves. However, no trend of changing valvular performance was observed over as much as 80 days of glycerin exposure, indicating that it is unlikely that the fluid-dependent performance was caused by glycerin absorption by the valve leaflets. We conclude that valid performance comparisons between mechanical and bioprosthetic valves may be made using a glycerin-based fluid. Furthermore, it appears that any detailed analysis of the physical mechanisms of valvular flow dissipation will require a properly matched blood analog.     

A Model for Fluid Drainage by the Lymphatic System

This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.     

Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture

This work presents a validation of a fluid-structure interaction computational model simulating the flow conditions in an in vitro mock heart chamber modeling mitral valve regurgitation during the ejection phase during which the trans-valvular pressure drop and valve displacement are not as large. The mock heart chamber was developed to study the use of 2D and 3D color Doppler techniques in imaging the clinically relevant complex intra-cardiac flow events associated with mitral regurgitation. Computational models are expected to play an important role in supporting, refining, and reinforcing the emerging 3D echocardiographic applications. We have developed a 3D computational fluid-structure interaction algorithm based on a semi-implicit, monolithic method, combined with an arbitrary Lagrangian-Eulerian approach to capture the fluid domain motion. The mock regurgitant mitral valve corresponding to an elastic plate with a geometric orifice, was modeled using 3D elasticity, while the blood flow was modeled using the 3D Navier-Stokes equations for an incompressible, viscous fluid. The two are coupled via the kinematic and dynamic conditions describing the two-way coupling. The pressure, the flow rate, and orifice plate displacement were measured and compared with numerical simulation results. In-line flow meter was used to measure the flow, pressure transducers were used to measure the pressure, and a Doppler method developed by one of the authors was used to measure the axial displacement of the orifice plate. The maximum recorded difference between experiment and numerical simulation for the flow rate was 4%, the pressure 3.6%, and for the orifice displacement 15%, showing excellent agreement between the two.     

Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.     

Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method

Current artificial heart valves either have limited lifespan or require the recipient to be on permanent anticoagulation therapy. In this paper, effort is made to assess a newly developed bileaflet valve prosthesis made of synthetic flexible leaflet materials, whose geometry and material properties are based on those of the native mitral valve, with a view to providing superior options for mitral valve replacement. Computational analysis is employed to evaluate the geometric and material design of the valve, by investigation of its mechanical behaviour and unsteady flow characteristics. The immersed boundary (IB) method is used for the dynamic modelling of the large deformation of the valve leaflets and the fluid-structure interactions. The IB simulation is first validated for the aortic prosthesis subjected to a hydrostatic loading. The predicted displacement fields by IB are compared with those obtained using ANSYS, as well as with experimental measurements. Good quantitative agreement is obtained. Moreover, known failure regions of aortic prostheses are identified. The dynamic behaviour of the valve designs is then simulated under four physiological pulsatile flows. Experimental pressure gradients for opening and closure of the valves are in good agreement with IB predictions for all flow rates for both aortic and mitral designs. Importantly, the simulations predicted improved physiological haemodynamics for the novel mitral design. Limitation of the current IB model is also discussed. We conclude that the IB model can be developed to be an extremely effective dynamic simulation tool to aid prosthesis design.     

Modeling technique of prosthetic heart valves

This paper demonstrates a modeling technique of prosthetic heart valves. In the modeling, a pumping cycle is divided into four phases, in which the state of the valve and flow is different. The pressure-flow relation across the valve is formulated separately in each phase. This technique is developed to build a mathematical model used in the real time estimation of the hemodynamic state under artificial heart pumping. The model built by this technique is simple enough for saving the computational time in the real time estimation. The model is described by the first-order ordinary differential equation with 12 parameters. These parameters can be uniquely determined beforehand from in-vitro experimental data. It is shown that the model can adapt, with sufficient accuracy, to a change in the practical pumping condition and the viscosity of the fluid in their practical range, and is also demonstrated that the estimated backflow volume by model agrees closely with the actual one.     

Anatomy of the oral valve in nymphalid butterflies and a functional model for fluid uptake in Lepidoptera

The food canal of the proboscis of Lepidoptera serves for the uptake of nutrient fluids and the discharge of saliva. A valve was discovered at the entrance to the sucking pump in the head that separates these countercurrent flows in nymphalid butterflies. Three species of Nymphalidae were examined by dissections and light microscopic serial semithin sections. The sucking pump is a unit composed of three structures: (1) the oral valve, which is a projection of the epipharynx extending into the anterior cibarial lumen, (2) the expandable lumen, and (3) the posterior sphincter valve which controls influx into the oesophagus. Based on the microanatomical results, a functional model is presented to account for the uptake and swallowing of fluids and for the control of the salivary flow into the food canal of the proboscis. Dilator muscles of the sucking pump expand the lumen by pulling on the muscular dorso-anterior side. This opens the oral valve and fluid can be drawn into the lumen from the food canal of the proboscis. Circular compressor muscles which attach to both sides of the sclerotized ventro-posterior wall of the sucking pump reduce the size of the lumen; passively they close the oral valve and press fluid through the relaxed posterior sphincter opening into the oesophagus. According to this model saliva can be discharged into the food canal during the swallowing phase. The oral valve and pumping unit are similar in all studied species despite the fact that saliva presumably plays a special role in the derived pollen-feeding behaviour of one of them, viz. Heliconius melpomene.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

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 central axis prosthetic cardiac valve: an in vitro study of pressure drop assessment under steady-state flow conditions

In this work, a new mechanical prosthetic heart valve, the central axis valve, is presented. This new prosthesis has been tested in vitro, and compared with four other common prosthetic cardiac valves (Starr-Edwards 6120, Bjork-Shiley monostrut, Medtronic-Hall, and St Jude Medical valves). All valves studied have the same orifice diameter of 22 mm. The prostheses were installed inside a transparent mitral test chamber, which enables pressure drop measurement to be made under steady-state flow conditions using a blood analogue fluid. Pressure drop loss is one important factor affecting the overall performance of a prosthetic heart valve. Steady-state flow tests are essential to predict certain flow characteristics and pressure gradient loss before more complicated, expensive, and difficult-to-interpret pulsatile flow tests are conducted. All experiments were performed in vitro and at steady volumetric flow rates of 10 to 30 l/min. The Starr-Edwards SE 6120 showed the highest values for pressure drop. The St Jude Medical valve offers the minimum resistance to flow. The central axis valve comes second to the Starr-Edwards valve for this type of measurement. The new valve is promising. A complete valve evaluation programme, covering initial conceptional design through to clinical use, is in progress. Materials for the fabrication of the new valve are also under consideration.     

Near valve flows and potential blood damage during closure of a bileaflet mechanical heart valve

Blood damage and thrombosis are major complications that are commonly seen in patients with implanted mechanical heart valves. For this in vitro study, we isolated the closing phase of a bileaflet mechanical heart valve to study near valve fluid velocities and stresses. By manipulating the valve housing, we gained optical access to a previously inaccessible region of the flow. Laser Doppler velocimetry and particle image velocimetry were used to characterize the flow regime and help to identify the key design characteristics responsible for high shear and rotational flow. Impact of the closing mechanical leaflet with its rigid housing produced the highest fluid stresses observed during the cardiac cycle. Mean velocities as high as 2.4 m/s were observed at the initial valve impact. The velocities measured at the leaflet tip resulted in sustained shear rates in the range of 1500-3500 s(-1), with peak values on the order of 11,000-23,000 s(-1). Using velocity maps, we identified regurgitation zones near the valve tip and through the central orifice of the valve. Entrained flow from the transvalvular jets and flow shed off the leaflet tip during closure combined to generate a dominant vortex posterior to both leaflets after each valve closing cycle. The strength of the peripheral vortex peaked within 2 ms of the initial impact of the leaflet with the housing and rapidly dissipated thereafter, whereas the vortex near the central orifice continued to grow during the rebound phase of the valve. Rebound of the leaflets played a secondary role in sustaining closure-induced vortices.     

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.