Valve Dynamics Research Articles

A simplified model for mitral valve dynamics

Located between the left atrium and the left ventricle, the mitral valve controls flow between these two cardiac chambers. Mitral valve dysfunction is a major cause of cardiac dysfunction and its dynamics are little known.A simple non-linear rotational spring model is developed and implemented to capture the dynamics of the mitral valve. A measured pressure difference curve was used as the input into the model, which represents an applied torque to the anatomical valve chords. A range of mechanical model hysteresis states were investigated to find a model that best matches reported animal data of chord movement during a heartbeat. The study is limited by the use of one dataset found in the literature due to the highly invasive nature of getting this data. However, results clearly highlight fundamental physiological issues, such as the damping and chord stiffness changing within one cardiac cycle, that would be directly represented in any mitral valve model and affect behaviour in dysfunction. Very good correlation was achieved between modeled and experimental valve angle with 1–10% absolute error in the best case, indicating good promise for future simulation of cardiac valvular dysfunction, such as mitral regurgitation or stenosis. In particular, the model provides a pathway to capturing these dysfunctions in terms of modeled stiffness or elastance that can be directly related to anatomical, structural defects and dysfunction.

Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve

We investigate the behaviour of a dynamic fluid-structure interaction model of a chorded polyurethane mitral valve prosthesis, focusing on the effects on valve dynamics of including descriptions of the bending stiffnesses of the valve leaflets and artificial chordae tendineae. Each of the chordae is attached at one end to the valve annulus and at the other to one of two chordal attachment points. These attachment points correspond to the positions where the chords of the real prosthesis would attach to the left-ventricular wall, although in the present study, these attachment points are kept fixed in space to facilitate comparison between our simulations and earlier results obtained from an experimental test rig. In our simulations, a time-dependent pressure difference derived from experimental measurements drives flow through the model valve during diastole and provides a realistic pressure load during systole. In previous modelling studies of this valve prosthesis, the valve presents an unrealistically large orifice at beginning of diastole and does not close completely at the end of diastole. We show that including a description of the chordal bending stiffness enables the model valve to close properly at the end of the diastolic phase of the cardiac cycle. Valve over-opening is eliminated only by incorporating a description of the bending stiffnesses of the valve leaflets into the model. Thus, bending stiffness plays a significant role in the dynamic behaviour of the polyurethane mitral valve prosthesis.

Mathematical modelling of a hydraulic free-piston engine considering hydraulic valve dynamics

This paper describes the design of a single piston compression ignition hydraulic free-piston engine. An engine simulation model considering hydraulic valve dynamics is built. Extensive simulated results are presented and the major features of the engine are discussed. Experimental results from a full-cycle test of a prototype are also included and analysed integrated with simulation as well. The good agreement between experiments and simulations confirms the model can predict the engine performance. The engine takes more time in the suck phase for one cycle, which is helpful in sucking the low-pressure oil into the pump chamber. The dynamics of valves on the hydraulic chambers affect the chamber pressures. The pump chamber valve response lag compared with the piston displacement affects not only the chamber volumetric efficiency but also the engine fuel economy. The unchangeable piston motion trajectory makes the engine possible to get a high volumetric efficiency with fixed check valves. The rebound changes the compression stroke length and should be considered in the engine control. Asymmetric strokes appear when the engine is running under the piston self-excited vibration frequency.

In Vitro Characterization of the Mechanisms Responsible for Functional Tricuspid Regurgitation

Functional tricuspid regurgitation (TR) is increasingly recognized as a source of morbidity. Current repair strategies focus on annular remodeling because annular dilatation is common in patients with TR. Although papillary muscle (PM) displacement is recognized in functional mitral regurgitation, its role in TR is less well characterized. The objective of this in vitro study was to further clarify the mechanisms by which TR occurs as an effect of annular dilatation and PM displacement. Porcine tricuspid valves (n=16) were studied in an in vitro right heart simulator. The valve dynamics were quantified with isolated annular dilatation starting with a normal annular size (6 cm(2)) and incrementally dilated up to 100%, isolated PM displacement, and a combination of the 2. All valves lost competence at 40% dilatation, resulting in a TR of 7.9 ± 3.4 mL (P ≤ 0.05) compared with baseline and central residual leaflet length of 0.5 ± 0.2 cm. Multidirectional displacement of the anterior and posterior/septal PMs and all PMs significantly (P ≤ 0.05) increased TR, with normal annular area. Malcoaptation was observed where the 3 leaflets joined with all significant levels of TR. The anterior leaflet had the greatest percent change in residual leaflet length, whereas PM displacement caused a reduction in residual leaflet length for the septal leaflet for all conditions. This study shows that although annular dilatation alone leads to TR, isolated PM displacement can also cause TR; annular remodeling strategies should be tailored in the setting of severe PM displacement.

Integrated Control Design of Pneumatic Servo Table Considering the Dynamics of Pipelines and Servo Valve

In this paper, integrated control design for the pneumatic servo table system considering the dynamics of pipelines and servo valve is studied. The table is mainly composed by a pneumatic actuator, a highperformance pneumatic servo valve and pipelines. The pneumatic actuator utilizes a pneumatic cylinder with air bearings. The servo valve has high dynamics up to 300 Hz and is connected to the pneumatic actuator by pipelines. The system is pneumatically driven, providing the advantages of low heat generation and non-magnetic, nature suited to precise positioning. To simulate the system, we designed a linear model considering pipelines and servo valve dynamics. Comparison results showed that with a 7thorder linear model, the discrepancy between experiment and simulation results was much smaller than when using a 3rdorder model. The model’s complexity made it necessary to reduce the model’s order. Two poles are much further from the imaginary axis compared with other five poles in the pole loci of the 7thorder model, so the model is reduced to a 5thorder. A comparison of simulation and experiment results showed that the 5thorder model matches the real system well.

FSI simulation of asymmetric mitral valve dynamics during diastolic filling

In this article, we present a fluid–structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.

Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions.

The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid–structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibility of the coupled fluid–structure system in Eulerian form. Interaction between Lagrangian and Eulerian variables is mediated by integral equations with Dirac delta function kernels. The IB method provides a unified formulation for fluid–structure interaction models involving both thin elastic boundaries and also thick viscoelastic bodies. In this work, we describe the application of an adaptive, staggered-grid version of the IB method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve. Our model describes the thin leaflets of the aortic valve as immersed elastic boundaries, and describes the wall of the aortic root as a thick, semi-rigid elastic structure. A physiological left-ventricular pressure waveform is used to drive flow through the model valve, and dynamic pressure loading conditions are provided by a reduced (zero-dimensional) circulation model that has been fit to clinical data. We use this model and method to simulate aortic valve dynamics over multiple cardiac cycles. The model is shown to approach rapidly a periodic steady state in which physiological cardiac output is obtained at physiological pressures. These realistic flow rates are not specified in the model, however. Instead, they emerge from the fluid–structure interaction simulation.

Experimental investigation of the discharge valve dynamics in a reciprocating compressor for trans-critical CO2 refrigeration cycle

The self-acting valve has a significant influence on the efficiency and reliability of the reciprocating compressor. In the trans-critical CO2 cycle, the large density and high pressure difference across the valve cause serious bending and impact stresses in the valve, offering great challenges for successful valve design. Experimental investigation of the valve dynamics is required in order to design a self-acting valve with a high efficiency and long life span for the trans-critical CO2 compressor. A semi-hermetic reciprocating compressor was developed for application in CO2 refrigeration, and a test system was incorporated into the compressor performance test rig, with a focus on investigating the dynamics of the discharge valves. With the experimental results, the movement of the valve was discussed in detail for the trans-critical CO2 compressor, allowing for the study of the thermodynamic performance of the compressor. While varying design parameters such as pressure ratio, valve lift, spring stiffness and compressor speed, the movement of the discharge valve in the reciprocating CO2 compressor was measured in order to investigate the major factors that influence the valve dynamics. The average valve speed increased from 0.71 m/s to 0.81 m/s as the discharge pressure changed from 7.8 MPa to 12 MPa. The experimental methods and results discussed in this paper could provide useful information for both valve testing and the optimization of their reliability in trans-critical CO2 compressors.

Numerical modeling of startup and shutdown transients in reciprocating compressors

Several phenomena that affect energy consumption, noise level and reliability of compressors are associated with transient effects that occur during the compressor startup and shutdown. This paper presents a simulation methodology, experimentally validated, developed to analyze the compressor in such transients. Because the time scale associated with the compressor thermal behavior is much larger than that related to the mechanical physics, a thermal equilibrium condition has been considered herein for convenience. Results for valve displacement, piston motion, pressure in the compression chamber and resistive torques are provided to illustrate the application of the methodology and to assist an understanding of the physical aspects that affect the compressor performance throughout the startup and shutdown. It is observed that the dynamics of suction and discharge valves are greatly affected. Moreover, the model is employed to estimate the minimum voltage required for the compressor startup as a function of the equalized pressure and the auxiliary coil actuation time.

Aortic Root Physiology Late After a “Perfect” Ross Operation: Magnetic Resonance Imaging Study of Three Operative Techniques

In order to define physiological properties of the autograft root, magnetic resonance imaging (MRI) findings relative to three different operative techniques were compared with those of control subjects. Twenty-three patients, 18/5 M/F, aged 32 ± 9 years, underwent MRI assessment of the aortic root. Patients with normally functioning autograft valve and at least 4 years of follow-up (average 5.6 ± 1.9, range 4-10 years) were selected for each technique: six subcoronary (Group 1), nine inclusion (Group 2), and eight freestanding root (Group 3). Results were compared among patient groups and with seven control subjects, 6/1 M/F, aged 30 ± 2 years (P = ns). Morphological and functional properties were defined using transverse and paracoronal views, during systole and diastole. Mean aortic size in each group was greater than control, except for the LV-aortic junction and the sinus of Valsalva in Group 1 (26 ± 5 vs. 23 ± 3 mm, P = 0.2 and 33 ± 6 vs. 30 ± 5 mm, P = 0.3). Aortic valve plane rotation (P = 0.02) and root dilatation (P = 0.02) were more common in Group 3. Altered valve opening dynamics and asymmetrical aortic flow profile were also more common in Group 2 (P = 0.03) and Group 3 (P = 0.04). Distensibility was significantly reduced at sinus level in Group 2 and 3 compared with control (4.1 ± 3.5% and 3.6 ± 4.4% vs. 9.0 ± 4.7%, P = 0.03). Asymmetrical aortic flow profile was more common in patients with aortic dilatation (P = 0.05) and with severely reduced (<4%) root elasticity (P = 0.06). Among the three techniques, only subcoronary grafting allows preservation of physiological autograft valve dynamics, aortic flow and distensibility, at all root levels, late after operation. These findings may have relevant implications in the selection of the ideal Ross technique.

Influence of piston on effective areas of reed-type valves of small reciprocating compressors

Most simulation models for reciprocating compressors adopt the concept of effective force and flow areas to characterize the valve dynamics and the mass flow rate through the valve. However, in the discharge process, the proximity between the piston and the cylinder head may have a significant impact on the flow field and, hence, should be taken into account in the evaluation of both effective areas. For instance, there is an additional viscous friction loss associated with the radial flow through the very narrow clearance left in the cylinder when the piston is close to the top dead center. In addition, the flow exiting the clearance may even affect the size of recirculating flow regions in the discharge port and on the valve seat. In the present study, a computational fluid dynamics model is employed to analyze the influence of the piston on the effective flow and force areas of a discharge valve of simplified geometry. Based on the results, a method is then proposed to evaluate the effective flow and force areas by considering the piston position. Results for the indicator diagram and valve dynamics obtained from the simulation of a reciprocating compressor shows the importance of the new method.

A Fully Flexible Valve Actuation System for Internal Combustion Engines

The automotive industry has been under continued pressure to improve fuel efficiency because of air pollution, global warming, and rising gasoline prices. One technology to address this need is electronic valve timing. It promises to achieve fuel savings of 10%-15% by reducing pumping losses, introducing cylinder deactivation, and enabling new combustion strategies, like homogeneous charge compression ignition. To date, valve actuators for this application primarily rely on resonant spring arrangements to achieve the necessary dynamics. This leads to a fixed amplitude of the valve trajectory and only allows for variable valve timing. In this paper, a fully flexible valve actuation system for intake valves is introduced that provides variable lift in addition to variable timing, without reducing valve dynamics or energy efficiency. Optimization procedures for the mechanical system, the servo motor selection, and the valve trajectory are presented. The combined effect of these optimizations leads to valve accelerations that are an order of magnitude higher than conventional electric servo systems. Simulations and an experimental test bed are used to validate the system performance. A comparison with other electronic valve actuation systems confirms the excellent performance of this approach.

Object-oriented simulation of reciprocating compressors: Numerical verification and experimental comparison

Numerical simulation of reciprocating compressors is important for the design, development, improvement and optimization of the elements constituting the compressor circuit. In this work, an object-oriented unstructured modular numerical simulation of reciprocating compressors is presented. Pressure correction approach is applied for the resolution of tubes, chambers and compression chambers, while valve dynamics are modelled assuming a spring-mass system having single degree of freedom. The modular approach offers advantages of handling complex circuitry (e.g. parallel paths, multiple compressor chambers, etc.), coupling different simulation models for each element and adaptability to different configurations without changing the program. The code has been verified with some basic tests for assuring asymptotic behaviour to guarantee error free code and physically realistic results. Cases with different compressor configurations and working fluids (R134a, R600a and R744) have also been worked out. Numerical results are compared with experimental data and illustrative cases of multi-stage compression are also presented.

Investigation of the dynamics of electromagnetic valves by a coupled magneto‐mechanical algorithm including contact mechanics

PurposeThe fast and flexible development of fast switching electromagnetic valves as used in modern gasoline engine demands the availability of efficient and accurate simulation tools. The purpose of this paper is to provide an enhanced computational scheme of these actuators including all relevant physical effects of magneto‐mechanical systems and including contact mechanics.Design/methodology/approachThe finite element (FE) method is applied to efficiently solve the arising coupled system of partial differential equations describing magneto‐mechanical systems. The algorithm for contact mechanics is based on the cross‐constraint method using an energy‐ and momentum‐conserving time‐discretisation scheme. Although solving separately for the electromagnetic and mechanical system, a strong coupling is ensured within each time step by an iterative process with stopping criterion.FindingsThe numerical simulations of the full switching cycle of an electromagnetic direct injection valve, including the bouncing during the closing state, are just feasible with an enhanced and robust mechanical contact algorithm. Furthermore, the solution of the nonlinear electromagnetic and mechanical equations needs a Newton scheme with a line search scheme for the relaxation of the step size.Originality/valueThe paper provides a numerical simulation scheme based on the FE method, which includes all relevant physical effects in magneto‐mechanical systems, and which is robust even for long‐term contact periods with multitude re‐opening phases.

Numerical calculation and experimental validation of safety valve flows at pressures up to 600 bar

AbstractA numerical valve model has been validated to predict the discharge capacity in accordance to the requirements of valve sizing method EN ISO 4126‐1 and the opening characteristic of high‐pressure safety valves. The valve is modeled with computational fluid dynamics software ANSYS CFX, and the model is extended with the Soave‐ Redlich–Kwong real‐gas equation of state to allow calculations at pressures up to 3600 bar. A unique test facility has been constructed to perform valve function and capacity tests at operating pressures up to 600 bar with water and nitrogen. For gas flows, the numerical results and the experimental data on mass flow rates agree within 3%, whereas deviations in flow force are 12% on average. The inclusion of fluid‐structure interaction in the numerical method improves the results for the flow force well and also gives insight into the valve dynamics of an opening safety valve. In a comparison between the experimentally and numerically determined liquid mass flow rates, a model extension accounting for cavitation reduces overpredictions by a factor of 2–20% for smaller disk lifts and decreases the deviations in flow force from 35 to 7%. At higher disk lifts, the effect of cavitation is less, and experimental and numerical mass flow rates agree within 4% and flow forces within 5%. © 2011 American Institute of Chemical Engineers AIChE J, 2011

In Vitro Fluid Dynamics of the Ahmed Glaucoma Valve Modified with Expanded Polytetrafluoroethylene

Purpose: Long-term intraocular pressure reduction by glaucoma drainage devices (GDDs) is often limited by the fibrotic capsule that forms around them. Prior work demonstrates that modifying a GDD with a porous membrane promotes a vascularized and more permeable capsule. This work examines the in vitro fluid dynamics of the Ahmed valve after enclosing the outflow tract with a porous membrane of expanded polytetrafluoroethylene (ePTFE).Materials and Methods: The control and modified Ahmed implants (termed porous retrofitted implant with modified enclosure or PRIME-Ahmed) were submerged in saline and gelatin and perfused in a system that monitored flow (Q) and pressure (P). Flow rates of 1–50 μl/min were applied and steady state pressure recorded. Resistance was calculated by dividing pressure by flow.Results: Modifying the Ahmed valve implant outflow with expanded ePTFE increased pressure and resistance. Pressure at a flow of 2 μl/min was increased in the PRIME-Ahmed (11.6 ± 1.5 mm Hg) relative to the control implant (6.5 ± 1.2 mm Hg). Resistance at a flow of 2 μl/min was increased in the PRIME-Ahmed (5.8 ± 0.8 mm Hg/μl/min) when compared to the control implant (3.2 ± 0.6 mm Hg/μl/min).Conclusions: Modifying the outflow tract of the Ahmed valve with a porous membrane adds resistance that decreases with increasing flow. The Ahmed valve implant behaves as a variable resistor. It is partially open at low pressures and provides reduced resistance at physiologic flow rates.

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

BackgroundValve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions.MethodsA cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate "open on pressure, close on flow" law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle.ResultsSimulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends.ConclusionsThe resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves.

Hemodynamic Assessment of Severe Aortic Stenosis

Direct magnetic resonance imaging (MRI) planimetry of the maximal systolic aortic valve area does not consider temporal variations of the opening area during the ejection period. We evaluated an MRI-based methodology for the assessment of valvular dynamics in patients with severe aortic stenosis by measuring the systolic variability of the valvular blood stream, that is, the "vena contracta." With institutional review board approval, we examined 22 patients (13 male, 9 female; mean age, 68 ±10 years) with severe aortic stenosis using 1.5 T MRI and a standardized scanning protocol consisting of gradient-echo phase-contrast velocity imaging and steady-state free precession-cine MRI before and after valve replacement therapy. Temporal changes of the aortic valve area, represented by systolic variations of the area of poststenotic turbulent flow at its smallest convergence, that is, the proximal vena contracta, were determined by MRI and quantified by a calculated parameter of temporal valve dynamics (T). T was defined as the period which the aortic valve spent over its maximal opening area (>85%) during systole. MRI was also used to determine left ventricular hypertrophy before (LVMI) and its regression (LVMR) after valve replacement. Findings were compared with transthoracic echocardiography and cardiac catheterization. All patients had an echocardiographic effective orifice area, EOATTE, of <1.0 cm2. The comparison of T to LVMI and LVMR revealed significant correlations (LVMI: r = -0.62; P = 0.002; LVMR: r = 0.62; P = 0.002). Further significant correlations with aortic stenosis severity were observed in the comparison with manual planimetry, invasive measurements, and echocardiographic valve areas, as well as with pressure gradients. MRI can measure systolic variations of the aortic valve area. Quantitative parameters of the hemodynamic relevance of valve dynamics obtained by this method correlate with established parameters of aortic stenosis severity and LVMR.

Experimental Characterization and Diagnosis of Different Problems in Control Valves

AbstractIn the perspective of developing an integrated system able to include loop performance assessment and early diagnosis of anomalies, an experimental characterization of more common problems encountered in industrial valves has been carried out on a pilot scale plant. The primary scope was to investigate the possibility of detecting different types of valve anomalies from the analysis of routine data, by taking into account additional variables made available by intelligent instrumentation and field bus communication systems. Experimental results show that different problems (as: stiction, change in valve dynamics, air leakage and periodic disturbances), cannot be easily detected by referring to classical loop variables. On the contrary, their presence can be promptly identified by means of Travel Deviation and Drive Signal values, made available by the valve positioner. A key role is plaid by the availability of the valve stem position.

A Novel Model for Optimized Development and Application of Switching Valves in Closed Loop Control

In this paper a novel and validated model to describe the dynamics of switching valves is presented and used to analyse the behaviour of switching valves. The paper starts with a brief discussion of the state of the art and the characteristics of switching valves, continuing with investigations of their dynamics, the development of the novel model and an analysis of the characteristics of switching valves based on the introduced model. The different operation modes which appear when fast switching control signals are applied are introduced and discussed. Additionally the application of the proposed model in closed loop simulations is pointed out and compared to state of the art models. It is demonstrated that the novel model offers a good trade-off between model accuracy and model complexity.