Bioprosthetic aortic valve diameter and thickness are directly related to leaflet fluttering: Results from a combined experimental and computational modeling study

Analysis of Fluid-Structure Interaction Mechanisms for a Native Aortic Valve, Patient-Specific Ozaki Procedure, and a Bioprosthetic Valve

The Ozaki procedure is a surgical technique which avoids to implant foreign aortic valve prostheses in human heart, using the patient's own pericardium. Although this approach has well-identified benefits, it is still a topic of debate in the cardiac surgical community, which prevents its larger use to treat valve pathologies. This is linked to the actual lack of knowledge regarding the dynamics of tissue deformations and surrounding blood flow for this autograft pericardial valve. So far, there is no numerical study examining the coupling between the blood flow characteristics and the Ozaki leaflets dynamics. To fill this gap, we propose here a comprehensive comparison of various performance criteria between a healthy native valve, its pericardium-based counterpart, and a bioprosthetic solution, this is done using a three-dimensional fluid-structure interaction solver. Our findings reveal similar physiological dynamics between the valves but with the emergence of fluttering for the Ozaki leaflets and higher velocity and wall shear stress for the bioprosthetic heart valve.

Can mechanical heart valves perform similarly to tissue valves? An in vitro study

Current surgical aortic valve (AV) replacement options include bioprosthetic and mechanical heart valves (MHVs), each with inherent limitations. Bioprosthetic valves offer superior hemodynamics but suffer from durability issues, typically initiating deterioration within 7-8 years. MHVs, while durable, necessitate lifelong anticoagulation therapy, presenting risks such as severe bleeding and thromboembolic events. The need for anticoagulants is caused by non-physiological flow through the hinge area during the closed phase and large spikes of regional backflow velocity (RBV) during the closing phase that produces high shear events. This study introduces the iValve, a novel MHV designed to combine the hemodynamic benefits of bioprosthetic valves with the durability of MHVs without requiring anticoagulation. The iValve features eye-like leaflets, a saddle-shaped housing, and an optimized hinge design to enhance blood flow and minimize thrombotic risk. Fabricated using 6061-T6 aluminum and polyether ether ketone (PEEK), twelve iValve iterations were evaluated for their opening and closing dynamics. The reported top-performing prototypes demonstrated competitive performance against industry standards. The proposed iValve prototype exhibited a mean RBV of -4.34 m/s with no spikes in RBV, performing similarly to bioprosthetic valves and significantly outperforming existing MHVs. The iValve's optimized design showed a 7-10% reduction in closing time and a substantial decrease in RBV spikes, potentially reducing the need for anticoagulation therapy. This study highlights the iValve's potential to revolutionize prosthetic heart valve technology by offering a durable, hemodynamically superior solution that mitigates the drawbacks of current MHVs.

Comparison of Immersed Boundary Simulations of Heart Valve Hemodynamics Against In Vitro 4D Flow MRI Data

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator.

In Vitro Proof of Concept of a First-Generation Growth-Accommodating Heart Valved Conduit for Pediatric Use

Currently available heart valve prostheses have no growth potential, requiring children with heart valve diseases to endure multiple valve replacement surgeries with compounding risks. This study demonstrates the in vitro proof of concept of a biostable polymeric trileaflet valved conduit designed for surgical implantation and subsequent expansion via transcatheter balloon dilation to accommodate the growth of pediatric patients and delay or avoid repeated open-heart surgeries. The valved conduit is formed via dip molding using a polydimethylsiloxane-based polyurethane, a biocompatible material shown here to be capable of permanent stretching under mechanical loading. The valve leaflets are designed with an increased coaptation area to preserve valve competence at expanded diameters. Four 22 mm diameter valved conduits are tested in vitro for hydrodynamics, balloon dilated to new permanent diameters of 23.26 ± 0.38 mm, and then tested again. Upon further dilation, two valved conduits sustain leaflet tears, while the two surviving devices reach final diameters of 24.38 ± 0.19 mm. After each successful dilation, the valved conduits show increased effective orifice areas and decreased transvalvular pressure differentials while maintaining low regurgitation. These results demonstrate concept feasibility and motivate further development of a polymeric balloon-expandable device to replace valves in children and avoid reoperations.

A Doppler-exclusive non-invasive computational diagnostic framework for personalized transcatheter aortic valve replacement

Given the associated risks with transcatheter aortic valve replacement (TAVR), it is crucial to determine how the implant will affect the valve dynamics and cardiac function, and if TAVR will improve or worsen the outcome of the patient. Effective treatment strategies, indeed, rely heavily on the complete understanding of the valve dynamics. We developed an innovative Doppler-exclusive non-invasive computational framework that can function as a diagnostic tool to assess valve dynamics in patients with aortic stenosis in both pre- and post-TAVR status. Clinical Doppler pressure was reduced by TAVR (52.2 ± 20.4 vs. 17.3 ± 13.8 [mmHg], p < 0.001), but it was not always accompanied by improvements in valve dynamics and left ventricle (LV) hemodynamics metrics. TAVR had no effect on LV workload in 4 patients, and LV workload post-TAVR significantly rose in 4 other patients. Despite the group level improvements in maximum LV pressure (166.4 ± 32.2 vs 131.4 ± 16.9 [mmHg], p < 0.05), only 5 of the 12 patients (41%) had a decrease in LV pressure. Moreover, TAVR did not always improve valve dynamics. TAVR did not necessarily result in a decrease (in 9 out of 12 patients investigated in this study) in major principal stress on the aortic valve leaflets which is one of the main contributors in valve degeneration and, consequently, failure of heart valves. Diastolic stresses increased significantly post-TAVR (34%, 109% and 81%, p < 0.001) for each left, right and non-coronary leaflets respectively. Moreover, we quantified the stiffness and material properties of aortic valve leaflets which correspond with the reduced calcified region average stiffness among leaflets (66%, 74% and 62%; p < 0.001; N = 12). Valve dynamics post-intervention should be quantified and monitored to ensure the improvement of patient conditions and prevent any further complications. Improper evaluation of biomechanical valve features pre-intervention as well as post-intervention may result in harmful effects post-TAVR in patients including paravalvular leaks, valve degeneration, failure of TAVR and heart failure.

A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis because they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

A Nodal Immersed Finite Element-Finite Difference Method

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve.

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid-structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

Biomechanical Engineering Analysis of Pulmonary Valve Leaflet Hemodynamics and Kinematics in the Ross Procedure

The Ross procedure using the inclusion technique with anticommissural plication (ACP) is associated with excellent valve hemodynamics and favorable leaflet kinematics. The objective was to evaluate individual pulmonary cusp's biomechanics and fluttering by including coronary flow in the Ross procedure using an ex vivo three-dimensional-printed heart simulator. Ten porcine and five human pulmonary autografts were harvested from a meat abattoir and heart transplant patients. Five porcine autografts without reinforcement served as controls. The other autografts were prepared using the inclusion technique with and without ACP (ACP and NACP). Hemodynamic and high-speed videography data were measured using the ex vivo heart simulator. Although porcine autografts showed similar leaflet rapid opening and closing mean velocities, human ACP compared to NACP autografts demonstrated lower leaflet rapid opening mean velocity in the right (p = 0.02) and left coronary cusps (p = 0.003). The porcine and human autograft leaflet rapid opening and closing mean velocities were similar in all three cusps. Porcine autografts showed similar leaflet flutter frequencies in the left (p = 0.3) and noncoronary cusps (p = 0.4), but porcine NACP autografts versus controls demonstrated higher leaflet flutter frequency in the right coronary cusp (p = 0.05). The human NACP versus ACP autografts showed higher flutter frequency in the noncoronary cusp (p = 0.02). The leaflet flutter amplitudes were similar in all three cusps in both porcine and human autografts. The ACP compared to NACP autografts in the Ross procedure was associated with more favorable leaflet kinematics. These results may translate to the improved long-term durability of the pulmonary autografts.

Patient-Specific Immersed Finite Element-Difference Model of Transcatheter Aortic Valve Replacement

Transcatheter aortic valve replacement (TAVR) first received FDA approval for high-risk surgical patients in 2011 and has been approved for low-risk surgical patients since 2019. It is now the most common type of aortic valve replacement, and its use continues to accelerate. Computer modeling and simulation (CM&S) is a tool to aid in TAVR device design, regulatory approval, and indication in patient-specific care. This study introduces a computational fluid-structure interaction (FSI) model of TAVR with Medtronic's CoreValve Evolut R device using the immersed finite element-difference (IFED) method. We perform dynamic simulations of crimping and deployment of the Evolut R, as well as device behavior across the cardiac cycle in a patient-specific aortic root anatomy reconstructed from computed tomography (CT) image data. These IFED simulations, which incorporate biomechanics models fit to experimental tensile test data, automatically capture the contact within the device and between the self-expanding stent and native anatomy. Further, we apply realistic driving and loading conditions based on clinical measurements of human ventricular and aortic pressures and flow rates to demonstrate that our Evolut R model supports a physiological diastolic pressure load and provides informative clinical performance predictions.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

Computational Fluid Dynamics (CFD) is used to assist in designing artificial valves and planning procedures, focusing on local flow features. However, assessing the impact on overall cardiovascular function or predicting longer-term outcomes may requires more comprehensive whole heart CFD models. Fitting such models to patient data requires numerous computationally expensive simulations, and depends on specific clinical measurements to constrain model parameters, hampering clinical adoption. Surrogate models can help to accelerate the fitting process while accounting for the added uncertainty. We create a validated patient-specific four-chamber heart CFD model based on the Navier-Stokes-Brinkman (NSB) equations and test Gaussian Process Emulators (GPEs) as a surrogate model for performing a variance-based global sensitivity analysis (GSA). GSA identified preload as the dominant driver of flow in both the right and left side of the heart, respectively. Left-right differences were seen in terms of vascular outflow resistances, with pulmonary artery resistance having a much larger impact on flow than aortic resistance. Our results suggest that GPEs can be used to identify parameters in personalized whole heart CFD models, and highlight the importance of accurate preload measurements.

Fluid-structure interaction simulation of calcified aortic valve stenosis

Calcified aortic valve stenosis (CAVS) is caused by calcium buildup and tissue thickening that impede the blood flow from left ventricle (LV) to aorta. In recent years, CAVS has become one of the most common cardiovascular diseases. Therefore, it is necessary to study the mechanics of aortic valve (AV) caused by calcification. In this paper, based on a previous idealized AV model, the hybrid immersed boundary/finite element method (IB/FE) is used to study AV dynamics and hemodynamic performance under normal and calcified conditions. The computational CAVS model is realized by dividing the AV leaflets into a calcified region and a healthy region, and each is described by a specific constitutive equation. Our results show that calcification can significantly affect AV dynamics. For example, the elasticity and mobility of the leaflets decrease due to calcification, leading to a smaller opening area with a high forward jet flow across the valve. The calcified valve also experiences an increase in local stress and strain. The increased loading due to AV stenosis further leads to a significant increase in left ventricular energy loss and transvalvular pressure gradients. The model predicted hemodynamic parameters are in general consistent with the risk classification of AV stenosis in the clinic. Therefore, mathematical models of AV with calcification have the potential to deepen our understanding of AV stenosis-induced ventricular dysfunction and facilitate the development of computational engineering-assisted medical diagnosis in AV related diseases.

Computational modeling of drug dissolution in the human stomach: Effects of posture and gastroparesis on drug bioavailability

The oral route is the most common choice for drug administration because of several advantages, such as convenience, low cost, and high patient compliance, and the demand and investment in research and development for oral drugs continue to grow. The rate of dissolution and gastric emptying of the dissolved active pharmaceutical ingredient (API) into the duodenum is modulated by gastric motility, physical properties of the pill, and the contents of the stomach, but current in vitro procedures for assessing dissolution of oral drugs are limited in their ability to recapitulate this process. This is particularly relevant for disease conditions, such as gastroparesis, that alter the anatomy and/or physiology of the stomach. In silico models of gastric biomechanics offer the potential for overcoming these limitations of existing methods. In the current study, we employ a biomimetic in silico simulator based on the realistic anatomy and morphology of the stomach (referred to as "StomachSim") to investigate and quantify the effect of body posture and stomach motility on drug bioavailability. The simulations show that changes in posture can potentially have a significant (up to 83%) effect on the emptying rate of the API into the duodenum. Similarly, a reduction in antral contractility associated with gastroparesis can also be found to significantly reduce the dissolution of the pill as well as emptying of the API into the duodenum. The simulations show that for an equivalent motility index, the reduction in gastric emptying due to neuropathic gastroparesis is larger by a factor of about five compared to myopathic gastroparesis.

On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method's performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretization combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta functions). Earlier work with this methodology suggested that such coarse structural meshes can yield improved accuracy for shear-dominated cases and, further, found that accuracy improves when the structural mesh spacing is increased. However, these results were limited to simple test cases that did not include substantial pressure loading on the structure. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations in a broader range of tests. Our results indicate that kernels satisfying a commonly imposed even-odd condition require higher resolution to achieve similar accuracy as kernels that do not satisfy this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, and that structural meshes that are substantially coarser than the Cartesian grid can yield high accuracy for shear-dominated cases but not for cases with large normal forces. We verify our results in a large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a pulse duplicator.

Effects of membrane and flexural stiffnesses on aortic valve dynamics: identifying the mechanics of leaflet flutter in thinner biological tissues

Valvular pathologies that induce deterioration in the aortic valve are a common cause of heart disease among aging populations. Although there are numerous available technologies to treat valvular conditions and replicate normal aortic function by replacing the diseased valve with a bioprosthetic implant, many of these devices face challenges in terms of long-term durability. One such phenomenon that may exacerbate valve deterioration and induce undesirable hemodynamic effects in the aorta is leaflet flutter, which is characterized by oscillatory motion in the biological tissues. While this behavior has been observed for thinner bioprosthetic valves, the specific underlying mechanics that lead to leaflet flutter have not previously been identified. This work proposes a computational approach to isolate the fundamental mechanics that induce leaflet flutter in thinner biological tissues during the cardiac cycle. The simulations in this work identify reduced flexural stiffness as the primary factor that contributes to increased leaflet flutter in thinner biological tissues, while decreased membrane stiffness and mass of the thinner tissues do not directly induce flutter in these valves. The results of this study provide an improved understanding of the mechanical tissue properties that contribute to flutter and offer significant insights into possible developments in the design of bioprosthetic tissues to account for and reduce the incidence of flutter.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid-Structure Interaction Simulation

Built on the hybrid immersed boundary/finite element (IB/FE) method, fluid-structure interaction (FSI) simulations of aortic valve (AV) dynamics are performed with three different constitutive laws and two different fiber architectures for the AV leaflets. An idealized AV model is used and mounted in a straight tube, and a three-element Windkessel model is further attached to the aorta. After obtaining ex vivo biaxial tensile testing of porcine AV leaflets, we first determine the constitutive parameters of the selected three constitutive laws by matching the analytical stretch-stress relations derived from constitutive laws to the experimentally measured data. Both the average error and relevant R-squared value reveal that the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions could be more suitable for characterizing the mechanical behaviors of the AV leaflets. We then thoroughly compare the simulation results from both structural mechanics and hemodynamics. Compared to the other two constitutive laws, the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions shows the larger leaflet displacements at the opened state, the largest forward jet flow, the smaller regurgitant flow. We further analyze hemodynamic parameters of the six different cases, including the regurgitant fraction, the mean transvalvular pressure gradient, the effective orifice area, and the energy loss of the left ventricle. We find that the fiber architecture with body-fitted orientation shows better dynamic behaviors in the leaflets, especially with the constitutive law using exponential terms for both the fiber and cross-fiber directions. In conclusion, both constitutive laws and fiber architectures can affect AV dynamics. Our results further suggest that the strain energy function with exponential terms for both the fiber and cross-fiber directions could be more suitable for describing the AV leaflet mechanical behaviors. Future experimental studies are needed to identify competent constitutive laws for the AV leaflets and their associated fiber orientations with controlled experiments. Although limitations exist in the present AV model, our results provide important information for selecting appropriate constitutive laws and fiber architectures when modeling AV dynamics.