Validation of a Fluid–Structure Interaction Model of a Heart Valve using the Dynamic Mesh Method in Fluent

Simulations of coupled problems such as fluid–structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

Evaluation of an aortic valve prosthesis: Fluid-structure interaction or structural simulation?

Bio-inspired polymeric heart valves (PHVs) are excellent candidates to mimic the structural and the fluid dynamic features of the native valve. PHVs can be implanted as prosthetic alternative to currently clinically used mechanical and biological valves or as potential candidate for a minimally invasive treatment, like the transcatheter aortic valve implantation. Nevertheless, PHVs are not currently used for clinical applications due to their lack of reliability. In order to investigate the main features of this new class of prostheses, pulsatile tests in an in-house pulse duplicator were carried out and reproduced in silico with both structural Finite-Element (FE) and Fluid-Structure interaction (FSI) analyses. Valve kinematics and geometric orifice area (GOA) were evaluated to compare the in vitro and the in silico tests. Numerical results showed better similarity with experiments for the FSI than for the FE simulations. The maximum difference between experimental and FSI GOA at maximum opening time was only 5%, as compared to the 46.5% between experimental and structural FE GOA. The stress distribution on the valve leaflets clearly reflected the difference in valve kinematics. Higher stress values were found in the FSI simulations with respect to those obtained in the FE simulation. This study demonstrates that FSI simulations are more appropriate than FE simulations to describe the actual behaviour of PHVs as they can replicate the valve-fluid interaction while providing realistic fluid dynamic results.     

Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in fluent

Simulations of coupled problems such as fluid-structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Fluid-structure interaction simulation of artificial textile reinforced aortic heart valve: Validation with an in-vitro test

Prosthetic heart valves deployed in the left heart (aortic and mitral) are subjected to harsh hemodynamical conditions. Most of the tissue engineered heart valves have been developed for the low pressure pulmonary position because of the difficulties in fabricating a mechanically strong valve, able to withstand the systemic circulation. This necessitates the use of reinforcing scaffolds, resulting in a tissue-engineered textile reinforced tubular aortic heart valve. Therefore, to better design these implants, material behaviour of the composite, valve kinematics and its hemodynamical response need to be evaluated. Experimental assessment can be immensely time consuming and expensive, paving way for numerical studies. In this work, the material properties obtained using the previously proposed multi-scale numerical method for textile composites was evaluated for its accuracy. An in silico immersed boundary (IB) fluid structure interaction (FSI) simulation emulating the in vitro experiment was set-up to evaluate and compare the geometric orifice area and flow rate for one beat cycle. Results from the in silico FSI simulation were found to be in good coherence with the in vitro test during the systolic phase, while mean deviation of approximately 9% was observed during the diastolic phase of a beat cycle. Merits and demerits of the in silico IB-FSI method for the presented case study has been discussed with the advantages outweighing the drawbacks, indicating the potential towards an effective use of this framework in the development and analysis of heart valves.     

Accuracy vs. computational time: translating aortic simulations to the clinic

State of the art simulations of aortic haemodynamics feature full fluid-structure interaction (FSI) and coupled 0D boundary conditions. Such analyses require not only significant computational resource but also weeks to months of run time, which compromises the effectiveness of their translation to a clinical workflow. This article employs three computational fluid methodologies, of varying levels of complexity with coupled 0D boundary conditions, to simulate the haemodynamics within a patient-specific aorta. The most comprehensive model is a full FSI simulation. The simplest is a rigid walled incompressible fluid simulation while an alternative middle-ground approach employs a compressible fluid, tuned to elicit a response analogous to the compliance of the aortic wall. The results demonstrate that, in the context of certain clinical questions, the simpler analysis methods may capture the important characteristics of the flow field.     

Systolic fluid–structure interaction model of the congenitally bicuspid aortic valve: assessment of modelling requirements

A transient fluid–structure interaction (FSI) model of a congenitally bicuspid aortic valve has been developed which allows simultaneous calculation of fluid flow and structural deformation. The valve is modelled during the systolic phase (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the bicuspid aortic valve in two dimensions. A congenital bicuspid valve is compared within the aortic root only and within the aortic arch. Symmetric and asymmetric cusps were simulated, along with differences in mechanical properties. A moving arbitrary Lagrange–Euler mesh was used to allow FSI. The FSI model requires blood flow to induce valve opening and induced strains in the region of 10%. It was determined that bicuspid aortic valve simulations required the inclusion of the ascending aorta and aortic arch. The flow patterns developed were sensitive to cusp asymmetry and differences in mechanical properties. Stiffening of the valve amplified peak velocities, and recirculation which developed in the ascending aorta. Model predictions demonstrate the need to take into account the category, including any existing cusp asymmetry, of a congenital bicuspid aortic valve when simulating its fluid flow and mechanics.     

External tissue support and fluid–structure simulation in blood flows

The objective of this work is to address the formulation of an adequate model of the external tissue environment when studying a portion of the arterial tree with fluid–structure interaction. Whereas much work has already been accomplished concerning flow and pressure boundary conditions associated with truncations in the fluid domain, very few studies take into account the tissues surrounding the region of interest to derive adequate boundary conditions for the solid domain. In this paper, we propose to model the effect of external tissues by introducing viscoelastic support conditions along the artery wall, with two—possibly distributed—parameters that can be adjusted to mimic the response of various physiological tissues. In order to illustrate the versatility and effectiveness of our approach, we apply this strategy to perform patient-specific modeling of thoracic aortae based on clinical data, in two different cases and using a distinct fluid–structure interaction methodology for each, namely an Arbitrary Lagrangian–Eulerian (ALE) approach with prescribed inlet motion in the first case and the coupled momentum method in the second case. In both cases, the resulting simulations are quantitatively assessed by detailed comparisons with dynamic image sequences, and the model results are shown to be in very good adequacy with the data.     

Does clinical data quality affect fluid-structure interaction simulations of patient-specific stenotic aortic valve models?

Numerical models are increasingly used in the cardiovascular field to reproduce, study and improve devices and clinical treatments. The recent literature involves a number of patient-specific models replicating the transcatheter aortic valve implantation procedure, a minimally invasive treatment for high-risk patients with aortic diseases. The representation of the actual patient’s condition with truthful anatomy, materials and working conditions is the first step toward the simulation of the clinical procedure.The aim of this work is to quantify how the quality of routine clinical data, from which the patient-specific models are built, affects the outputs of the numerical models representing the pathological condition of stenotic aortic valve.Seven fluid–structure interaction (FSI) simulations were performed, completed with a sensitivity analysis on patient-specific reconstructed geometries and boundary conditions. The structural parts of the models consisted of the aortic root, native tri-leaflets valve and calcifications. Ventricular and aortic pressure curves were applied to the fluid domain.The differences between clinical data and numerical results for the aortic valve area were less than 2% but reached 12% when boundary conditions and geometries were changed. The difference in the aortic stenosis jet velocity between measured and simulated values was less than 11% reaching 27% when the geometry was changed. The CT slice thickness was found to be the most sensitive parameter on the presented FSI numerical model.In conclusion, the results showed that the segmentation and reconstruction phases need to be carefully performed to obtain a truthful patient-specific domain to be used in FSI analyses.     

Non-linear rotation-free shell finite-element models for aortic heart valves

Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann–Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.     

An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.     

Effect of exercise on blood flow through the aortic valve: a combined clinical and numerical study

The aim of this study was to measure the cardiac output and stroke volume for a healthy subject by coupling an echocardiogram Doppler (echo-Doppler) method with a fluid–structure interaction (FSI) simulation at rest and during exercise. Blood flow through aortic valve was measured by Doppler flow echocardiography. Aortic valve geometry was calculated by echocardiographic imaging. An FSI simulation was performed, using an arbitrary Lagrangian–Eulerian mesh. Boundary conditions were defined by pressure loads on ventricular and aortic sides. Pressure loads applied brachial pressures with (stage 1) and without (stage 2) differences between brachial, central and left ventricular pressures. FSI results for cardiac output were 15.4% lower than Doppler results for stage 1 (r = 0.999). This difference increased to 22.3% for stage 2. FSI results for stroke volume were undervalued by 15.3% when compared to Doppler results at stage 1 and 26.2% at stage 2 (r = 0.94). The predicted mean backflow of blood was 4.6%. Our results show that numerical methods can be combined with clinical measurements to provide good estimates of patient-specific cardiac output and stroke volume at different heart rates.     

Numerical simulation of flow in mechanical heart valves: grid resolution and the assumption of flow symmetry

A numerical method is developed for simulating unsteady, 3-D, laminar flow through a bileaflet mechanical heart valve with the leaflets fixed. The method employs a dual-time-stepping artificial-compressibility approach together with overset (Chimera) grids and is second-order accurate in space and time. Calculations are carried out for the full 3-D valve geometry under steady inflow conditions on meshes with a total number of nodes ranging from 4 x 10(5) to 1.6 x 10(6). The computed results show that downstream of the leaflets the flow is dominated by two pairs of counter-rotating vortices, which originate on either side of the central orifice in the aortic sinus and rotate such that the common flow of each pair is directed away from the aortic wall. These vortices intensify with Reynolds number, and at a Reynolds number of approximately 1200 their complex interaction leads to the onset of unsteady flow and the break of symmetry with respect to both geometric planes of symmetry. Our results show the highly 3-D structure of the flow; question the validity of computationally expedient assumptions of flow symmetry; and demonstrate the need for highly resolved, fully 3-D simulations if computational fluid dynamics is to accurately predict the flow in prosthetic mechanical heart valves.     

Fluid–structure interaction simulation of the brain–skull interface for acute subdural haematoma prediction

Traumatic brain injury is a leading cause of disability and mortality. Finite element-based head models are promising tools for enhanced head injury prediction, mitigation and prevention. The reliability of such models depends heavily on adequate representation of the brain–skull interaction. Nevertheless, the brain–skull interface has been largely simplified in previous three-dimensional head models without accounting for the fluid behaviour of the cerebrospinal fluid (CSF) and its mechanical interaction with the brain and skull. In this study, the brain–skull interface in a previously developed head model is modified as a fluid–structure interaction (FSI) approach, in which the CSF is treated on a moving mesh using an arbitrary Lagrangian–Eulerian multi-material formulation and the brain on a deformable mesh using a Lagrangian formulation. The modified model is validated against brain–skull relative displacement and intracranial pressure responses and subsequently imposed to an experimentally determined loading known to cause acute subdural haematoma (ASDH). Compared to the original model, the modified model achieves an improved validation performance in terms of brain–skull relative motion and is able to predict the occurrence of ASDH more accurately, indicating the superiority of the FSI approach for brain–skull interface modelling. The introduction of the FSI approach to represent the fluid behaviour of the CSF and its interaction with the brain and skull is crucial for more accurate head injury predictions.

     

Allogenic heart valve bank in the Department of Cardiovascular Surgery and Transplantology of Jagiellonian University in Cracow – 23 years experience in the treatment of aortic valve or aortic root diseases.

Allogenic aortic valves are widely used in case of native aortic valve or root disease as well as failed prosthetic valves with great success. At the Department of Cardiovascular Surgery and Transplantology of the Jagiellonian University in Cracow, aortic valve or aortic root replacement with allogenic aortic valve has been performed for 23 years. Allogenic heart valve bank was founded in 1980. In the bank we prepare both aortic allografts for adult cardiac surgical procedures and pulmonary allografts that are mostly used for repair of congenital heart disease.Allogenic aortic valves implantation was usually considered in our clinic for older patients, patients with infective endocarditis of the native or prosthetic valve, young women in reproductive age and patients with Marfan syndrome. Allografts exhibit excellent clinical performance and acceptable durability with no early failure if properly inserted. Between 1980 and 1992, allografts were obtained only from cadavers during routine autopsies. More than 10% of prepared allografts were exported to other cardiac surgery centres in Poland and foreign countries.Aortic valve replacement using allogenic aortic valves can be performed with acceptable mortality and good long-term results. The procedure although surgically more challenging has the advantage of not requiring anticoagulation therapy, hemodynamic performance of the allogenic valve is excellent, it demonstrates freedom from thromboembolism and infective endocarditis. We would like to emphasize the importance and advantages of the fact that allogenic heart valve bank is placed in the department of cardiovascular surgery and it is able to supply the department in heart valve allografts 24 h a day.     

Investigation of left heart flow using a numerical correlation to model heart wall motion

A three-dimensional computational fluid dynamics (CFD) method has been developed to model the flow in the left heart including atrium and ventricle. Since time resolution of the medical scans does not fit the requirements of the CFD calculations, the main challenge in a numerical simulation of heart chambers is wall motion modeling. This study employs a novel three-dimensional approximation scheme to correlate the wall boundary and grid movement in systole and diastole. It uses a geometry extracted from medical images in the literature and deformed based on the reported flow rates. The opening and closing of the mitral (MV) and the aortic valve (AV) considered as simultaneous events. Unstructured tetragonal grids were used for the meshing of the domain. The calculation was performed by a Navier–Stokes solver using the arbitrary Lagrange–Euler (ALE) formulation. Results show that the proposed correlation for the wall motion could predict the main features of heart flows.     

Comparison of the hemodynamic and thrombogenic performance of two bileaflet mechanical heart valves using a CFD/FSI model

The hemodynamic and the thrombogenic performance of two commercially available bileaflet mechanical heart valves (MHVs)--the ATS Open Pivot Valve (ATS) and the St. Jude Regent Valve (SJM), was compared using a state of the art computational fluid dynamics-fluid structure interaction (CFD-FSI) methodology. A transient simulation of the ATS and SJM valves was conducted in a three-dimensional model geometry of a straight conduit with sudden expansion distal the valves, including the valve housing and detailed hinge geometry. An aortic flow waveform (60 beats/min, cardiac output 4 l/min) was applied at the inlet. The FSI formulation utilized a fully implicit coupling procedure using a separate solver for the fluid problem (FLUENT) and for the structural problem. Valve leaflet excursion and pressure differences were calculated, as well as shear stress on the leaflets and accumulated shear stress on particles released during both forward and backward flow phases through the open and closed valve, respectively. In contrast to the SJM, the ATS valve opened to less than maximal opening angle. Nevertheless, maximal and mean pressure gradients and velocity patterns through the valve orifices were comparable. Platelet stress accumulation during forward flow indicated that no platelets experienced a stress accumulation higher than 35 dyne x s/cm2, the threshold for platelet activation (Hellums criterion). However, during the regurgitation flow phase, 0.81% of the platelets in the SJM valve experienced a stress accumulation higher than 35 dyne x s/cm2, compared with 0.63% for the ATS valve. The numerical results indicate that the designs of the ATS and SJM valves, which differ mostly in their hinge mechanism, lead to different potential for platelet activation, especially during the regurgitation phase. This numerical methodology can be used to assess the effects of design parameters on the flow induced thrombogenic potential of blood recirculating devices.     

Dynamic Behavior of Reciprocating Plunger Pump Discharge Valve Based on Fluid Structure Interaction and Experimental Analysis

The influence of spring stiffness and valve quality on the motion behaviors of reciprocating plunger pump discharge valves was investigated by fluid structure interaction (FSI) simulation and experimental analysis. The mathematical model of the discharge valve motion of a 2000-fracturing pump was developed and the discrete differential equations were solved according to FSI and results obtained by ANDINA software. Results indicate that spring stiffness influences the maximum lift, the opening resistance and shut-off lag angle, as well as the fluid velocity of the clearance, the impact stress and the volume efficiency of the pump valve in relation to the valve quality. An optimal spring stiffness parameter of 14.6 N/mm was obtained, and the volumetric efficiency of the pumping valve increased by 4‰ in comparison to results obtained with the original spring stiffness of 10.09N/mm. The experimental results indicated that the mathematical model and FSI method could provide an effective approach for the subsequent improvement of valve reliability, volumetric efficiency and lifespan.     

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.     

Tomographic PIV in a model of the left ventricle: 3D flow past biological and mechanical heart valves

Left ventricular flow is intrinsically complex, three-dimensional and unsteady. Its features are susceptible to cardiovascular pathology and treatment, in particular to surgical interventions involving the valves (mitral valve replacement). To improve our understanding of intraventricular fluid mechanics and the impact of various types of prosthetic valves thereon, we have developed a custom-designed versatile left ventricular phantom with anatomically realistic moving left ventricular membrane. A biological, a tilting disc and a bileaflet valve (in two different orientations) were mounted in the mitral position and tested under the same settings. To investigate 3D flow within the phantom, a four-view tomographic particle image velocimetry setup has been implemented. The results compare side-by-side the evolution of the 3D flow topology, vortical structures and kinetic energy in the left ventricle domain during the cardiac cycle. Except for the tilting disc valve, all tested prosthetic valves induced a crossed flow path, where the outflow crosses the inflow path, passing under the mitral valve. The biological valve shows a strong jet with a peak velocity about twice as high compared to all mechanical heart valves, which makes it easier to penetrate deeply into the cavity. Accordingly, the peak kinetic energy in the left ventricle in case of the biological valve is about four times higher than the mechanical heart valves. We conclude that the tomographic particle imaging velocimetry setup provides a useful ground truth measurement of flow features and allows a comparison of the effects of different valve types on left ventricular flow patterns.