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.     

The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions

Although variability in connective tissue parameters is widely reported and recognized, systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking. As such, a sensitivity analysis was performed to consider the behavior of a three-dimensional, non-linear, finite element knee model with connective tissue material parameters that varied within a given interval. The model included the coupled mechanics of the tibio-femoral and patello-femoral degrees of freedom. Seven primary connective tissues modeled as non-linear continua, articular cartilages described by a linear elastic model, and menisci modeled as transverse isotropic elastic materials were included. In this study, a multi-factorial global sensitivity analysis is proposed, which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions. To illustrate the effect of material uncertainties on model predictions, exemplar loading conditions reported in a number of isolated experimental paradigms were used. Our findings illustrated that the inclusion of material uncertainties in a coupled tibio-femoral and patello-femoral model reveals biomechanical interactions that otherwise would remain unknown. For example, our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello-femoral kinematic and kinetic response sensitivities was significantly larger, over a range of flexion angles, when compared to variations associated with material parameters of tissues intrinsic to the patello-femoral joint. We argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response.     

Functional analysis of bioprosthetic heart valves

Glutaraldehyde-treated bovine pericardium is used successfully as bioprosthetic material in the manufacturing of heart valves leaflets. The mechanical properties of bovine pericardial aortic valve leaflets seem to influence its mechanical behaviour and the failure mechanisms. In this study the effect of orthotropy on tricuspid bioprosthetic aortic valve was analysed, using a three-dimensional finite element model, during the entire cardiac cycle. Multiaxial tensile tests were also performed to determine the anisotropy of pericardium. Seven different models of the same valve were analysed using different values of mechanical characteristics from one leaflet to another, considering pericardium as an orthotropic material. The results showed that even a small difference between values along the two axes of orthotropy can negatively influence leaflets performance as regard both displacement and stress distribution. Leaflets of bovine pericardium bioprostheses could be manufactured to be similar to natural human heart valves reproducing their well-known anisotropy. In this way it could be possible to improve the manufacturing process, durability and function of pericardial bioprosthetic valves.     

A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve

The importance of the aortic root compliance in the aortic valve performance has most frequently been ignored in computational valve modeling, although it has a significant contribution to the functionality of the valve. Aortic root aneurysm or (calcific) stiffening severely affects the aortic valve behavior and, consequently, the cardiovascular regulation. The compromised mechanical and hemodynamical performance of the valve are difficult to study both 'in vivo' and 'in vitro'. Computational analysis of the valve enables a study on system responses that are difficult to obtain otherwise. In this paper a numerical model of a fiber-reinforced stentless aortic valve is presented. In the computational evaluation of its clinical functioning the interaction of the valve with the blood is essential. Hence, the blood-tissue interaction is incorporated in the model using a combined fictitious domain/arbitrary Lagrange-Euler formulation, which is integrated within the Galerkin finite element method. The model can serve as a diagnostic tool for clinical purposes and as a design tool for improving existing valve prostheses or developing new concepts. Structural mechanical and fluid dynamical aspects are analyzed during the systolic course of the cardiac cycle. Results show that aortic root compliance largely influences the valve opening and closing configurations. Stresses in the delicate parts of the leaflets are substantially reduced if fiber-reinforcement is applied and the aortic root is able to expand.     

An approach to the simulation of fluid-structure interaction in the aortic valve

A pair of finite element models has been employed to study the interaction of blood flow with the operation of the aortic valve. A three-dimensional model of the left ventricle with applied wall displacements has been used to generate data for the spatially and time-varying blood velocity profile across the aortic aperture. These data have been used as the inlet loading conditions in a three-dimensional model of the aortic valve and its surrounding structures. Both models involve fluid-structure interaction and simulate the cardiac cycle as a dynamic event. Confidence in the models was obtained by comparison with data obtained in a pulse duplicator. The results show a circulatory flow being generated in the ventricle which produces a substantially axial flow through the aortic aperture. The aortic valve behaves in an essentially symmetric way under the action of this flow, so that the pressure difference across the leaflets is approximately uniform. This work supports the use of spatially uniform but temporally variable pressure distributions across the leaflets in dry or structural models of aortic valves. The study is a major advance through its use of truly three-dimensional geometry, spatially non-uniform loading conditions for the valve leaflets and the successful modelling of progressive contact of the leaflets in a fluid environment.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

A nonlinear anisotropic model for porcine aortic heart valves

The anisotropic property of porcine aortic valve leaflet has potentially significant effects on its mechanical behaviour and the failure mechanisms. However, due to its complex nature, testing and modelling the anisotropic porcine aortic valves remains a continuing challenge to date. This study has developed a nonlinear anisotropic finite element model for porcine heart valves. The model is based on the uniaxial experimental data of porcine aortic heart valve leaflet and the properties of nonlinear composite material. A finite element code is developed to solve this problem using the 8-node super-parameter nonlinear shells and the update Lagrangian method. The stress distribution and deformation of the porcine aortic valves with either uniform and non-uniform thicknesses in closed phase and loaded condition are calculated. The results showed significant changes in the stress distributions due to the anisotropic property of the leaflets. Compared with the isotropic valve at the same loading condition, it is found that the site of the peak stress of the anisotropic leaflet is different; the maximum longitudinal normal stress is increased, but the maximum transversal normal stress and in-plane shear stress are reduced. We conclude that it is very important to consider the anisotropic property of the porcine heart valves in order to understand the failure mechanism of such valves in vivo.     

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.     

A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations

Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input parameters. In this work, we develop a general set of tools to evaluate the sensitivity of output parameters to input uncertainties in cardiovascular simulations. Uncertainties can arise from boundary conditions, geometrical parameters, or clinical data. These uncertainties result in a range of possible outputs which are quantified using probability density functions (PDFs). The objective is to systemically model the input uncertainties and quantify the confidence in the output of hemodynamic simulations. Input uncertainties are quantified and mapped to the stochastic space using the stochastic collocation technique. We develop an adaptive collocation algorithm for Gauss-Lobatto-Chebyshev grid points that significantly reduces computational cost. This analysis is performed on two idealized problems--an abdominal aortic aneurysm and a carotid artery bifurcation, and one patient specific problem--a Fontan procedure for congenital heart defects. In each case, relevant hemodynamic features are extracted and their uncertainty is quantified. Uncertainty quantification of the hemodynamic simulations is done using (a) stochastic space representations, (b) PDFs, and (c) the confidence intervals for a specified level of confidence in each problem.     

Patient-specific simulation of a stentless aortic valve implant: the impact of fibres on leaflet performance

In some cases of aortic valve leaflet disease, the implant of a stentless biological prosthesis represents an excellent option for aortic valve replacement (AVR). In particular, if compared with the implant of mechanical valves, it provides a more physiological haemodynamic performance and a reduced thrombogeneticity, avoiding the use of anticoagulants. The clinical outcomes of AVR are strongly dependent on an appropriate choice of both prosthesis size and replacement technique, which is, at present, strictly related to surgeon's experience and skill. This represents the motivation for patient-specific finite element analysis able to virtually reproduce stentless valve implantation. With the aim of performing reliable patient-specific simulations, we remark that, on the one hand, it is not well established in the literature whether bioprosthetic leaflet tissue is isotropic or anisotropic; on the other hand, it is of fundamental importance to incorporate an accurate material model to realistically predict post-operative performance. Within this framework, using a novel computational methodology to simulate stentless valve implantation, we test the impact of using different material models on both the stress pattern and post-operative coaptation parameters (i.e. coaptation area, length and height). As expected, the simulation results suggest that the material properties of the valve leaflets affect significantly the post-operative prosthesis performance.     

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.     

A simple method to estimate the exponential material parameters of heart valve tissue based on analogy between uniaxial tension and micropipette aspiration

Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials. To estimate material parameters from MA experimental data, analytical half-space models and inverse finite element (FE) analyses are typically used. The half-space model is easy to implement but cannot account for nonlinear material properties and complex geometrical boundary conditions that are inherent to MA. Inverse FE approaches can account for geometrical and material nonlinearities, but their implementation is resource-intensive and not widely available. Here, by making analogy between an analytical uniaxial tension model and a FE model of MA, we proposed an easily implementable and accurate method to estimate the material parameters of tissues tested by MA. We first adopted a strain invariant-based isotropic exponential constitutive model and implemented it in both the analytical uniaxial tension model and the FE model. The two models were fit to experimental data generated by MA of porcine aortic valve tissue (45 spots on four leaflets) to estimate material parameters. We found no significant differences between the effective moduli estimated by the two models ( $p > 0.39$ ), with the effective moduli estimated by the uniaxial tension model correlating significantly with those estimated by the FE model ( $p < 0.001; R^{2}= 0.96$ ) with a linear regression slope that was not different than unity ( $p = 0.38$ ). Thus, the analytical uniaxial tension model, which avoids solving resource-intensive numerical problems, is as accurate as the FE model in estimating the effective modulus of valve tissue tested by MA.     

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.     

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.     

Population-specific material properties of the implantation site for transcatheter aortic valve replacement finite element simulations

Patient-specific computational models are an established tool to support device development and test under clinically relevant boundary conditions. Potentially, such models could be used to aid the clinical decision-making process for percutaneous valve selection; however, their adoption in clinical practice is still limited to individual cases. To be fully informative, they should include patient-specific data on both anatomy and mechanics of the implantation site. In this work, fourteen patient-specific computational models for transcatheter aortic valve replacement (TAVR) with balloon-expandable Sapien XT devices were retrospectively developed to tune the material parameters of the implantation site mechanical model for the average TAVR population.Pre-procedural computed tomography (CT) images were post-processed to create the 3D patient-specific anatomy of the implantation site. Balloon valvuloplasty and device deployment were simulated with finite element (FE) analysis. Valve leaflets and aortic root were modelled as linear elastic materials, while calcification as elastoplastic. Material properties were initially selected from literature; then, a statistical analysis was designed to investigate the effect of each implantation site material parameter on the implanted stent diameter and thus identify the combination of material parameters for TAVR patients.These numerical models were validated against clinical data. The comparison between stent diameters measured from post-procedural fluoroscopy images and final computational results showed a mean difference of 2.5 ± 3.9%. Moreover, the numerical model detected the presence of paravalvular leakage (PVL) in 79% of cases, as assessed by post-TAVR echocardiographic examination.The final aim was to increase accuracy and reliability of such computational tools for prospective clinical applications.     

Structural analysis of the natural aortic valve in dynamics: From unpressurized to physiologically loaded

A novel finite element model of the natural aortic valve was developed implementing anisotropic hyperelastic material properties for the leaflets and aortic tissues, and starting from the unpressurized geometry. Static pressurization of the aortic root, silicone rubber moulds and published data helped to establish the model parameters, while high-speed video recording of the leaflet motion in a left-heart simulator allowed for comparisons with simulations. The model was discretized with brick elements and loaded with time-varying pressure using an explicit commercial solver. The aortic valve model produced a competent valve whose dynamic behavior (geometric orifice area vs. time) closely matched that observed in the experiment. In both cases, the aortic valve took approximately 30 ms to open to an 800 mm² orifice and remained completely or more than half open for almost 200 ms, after which it closed within 30–50 ms. The highest values of stress were along the leaflet attachment line and near the commissure during diastole. Von Mises stress in the leaflet belly reached 600–750 kPa from early to mid-diastole. While the model using the unpressurized geometry as initial configuration was specially designed to satisfy the requirements of continuum mechanics for large deformations of hyperelastic materials, it also clearly demonstrated that dry models can be adequate to analyze valve dynamics. Although improvements are still needed, the advanced modeling and validation techniques used herein contribute toward improved and quantified accuracy over earlier simplified models.     

Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study

A simple finite element model of the L₅-S₁ intervertebral disc body has been constructed; it is circular and symmetrical about the sagittal plane. The annulus fibrosus of the model was idealized as an inhomogeneous composite of an isotropic ground substance, reinforced by helically oriented collagen fibres so that the model has six different structural components namely: cortical bone, cancellous bone, cartilaginous endplates, nucleus pulposus, ground substance and collagen fibres. A sensitivity analysis of the material properties of each structural component was carried out by varying those properties for one structural component at a time and evaluating the changes in the biomechanical response to compressive displacements. Experimentally available relations between the applied compressive force and the vertical displacements, the nucleus pulposus pressure increase and the disc lateral bulge were used to evaluate the biomechanical responses for each set of material properties. Results showed that both the Poisson's ratio and the Young's modulus of the ground substance play an important role in the prediction of the biomechanical response.     

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.     

Evaluating the Use of Global Sensitivity Analysis in Dynamic MFA

Dynamic material flow analysis (MFA) provides information about material usage over time and consequent changes in material stocks and flows. In order to understand the effect of limited data quality and model assumptions on MFA results, the use of sensitivity analysis methods in dynamic MFA studies has been on the increase. So far, sensitivity analysis in dynamic MFA has been conducted by means of a one‐at‐a‐time method, which tests parameter perturbations individually and observes the outcomes on output. In contrast to that, variance‐based global sensitivity analysis decomposes the variance of the model output into fractions caused by the uncertainty or variability of input parameters. The present study investigates interaction and time‐delay effects of uncertain parameters on the output of an archetypal input‐driven dynamic material flow model using variance‐based global sensitivity analysis. The results show that determining the main (first‐order) effects of parameter variations is often sufficient in dynamic MFA because substantial effects attributed to the simultaneous variation of several parameters (higher‐order effects) do not appear for classical setups of dynamic material flow models. For models with time‐varying parameters, time‐delay effects of parameter variation on model outputs need to be considered, potentially boosting the computational cost of global sensitivity analysis. Finally, the implications of exploring the sensitivities of model outputs with respect to parameter variations in the archetypical model are used to derive model‐ and goal‐specific recommendations on choosing appropriate sensitivity analysis methods in dynamic MFA.     

Bioprosthetic heart valve leaflet motion monitored by dual camera stereo photogrammetry

Dual camera stereo photogrammetry (DCSP) was applied to investigate the leaflet motion of bioprosthetic heart valves (BHVs) in a physiologic pulse flow loop (PFL). A 25-mm bovine pericardial valve was installed in the aortic valve position of the PFL, which was operated at a pulse rate of 70 beats/min and a cardiac output of 5 l/min. The systolic/diastolic aortic pressure was maintained at 120/80 mmHg to mimic the physiologic load experienced by the aortic valve. The leaflet of the test valve was marked with 80 India ink dots to form a fan-shaped matrix. From the acquired image sequences, 3-D coordinates of the marker matrix were derived and hence the surface contour, local mean and Gaussian curvatures at each opening and closing phase during one cardiac cycle were reconstructed. It is generally believed that the long-term failure rate of BHV is related to the uneven distribution of mechanical stresses occurring in the leaflet material during opening and closing. Unfortunately, a quantitative analysis of the leaflet motion under physiological conditions has not been reported. The newly developed technique permits frame-by-frame mapping of the leaflet surface, which is essential for dynamic analysis of stress-strain behavior in BHV.