Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.
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Fluid‐structure interaction simulations of venous valves: A monolithic ALE method for large structural displacements
Venous valves are bicuspidal valves that ensure that blood in veins only flows back to the heart. To prevent retrograde blood flow, the two intraluminal leaflets meet in the center of the vein and occlude the vessel. In fluid‐structure interaction (FSI) simulations of venous valves, the large structural displacements may lead to mesh deteriorations and entanglements, causing instabilities of the solver and, consequently, the numerical solution to diverge. In this paper, we propose an arbitrary Lagrangian‐Eulerian (ALE) scheme for FSI simulations designed to solve these instabilities. A monolithic formulation for the FSI problem is considered, and due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation. The method relies on the introduction of a staggered in time velocity to improve stability, and on fictitious springs to model the contact force of the valve leaflets. Because the large structural displacements may compromise the quality of the fluid mesh as well, a smoother fluid displacement, obtained with the introduction of a scaling factor that measures the distance of a fluid element from the valve leaflet tip, guarantees that there are no mesh entanglements in the fluid domain. To further improve stability, a streamline upwind Petrov‐Galerkin (SUPG) method is employed. The proposed ALE scheme is applied to a two‐dimensional (2D) model of a venous valve. The presented simulations show that the proposed method deals well with the large structural displacements of the problem, allowing a reconstruction of the valve behavior in both the opening and closing phase.
more » « less- NSF-PAR ID:
- 10077373
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Biomedical Engineering
- Volume:
- 35
- Issue:
- 2
- ISSN:
- 2040-7939
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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BACKGROUND: Almost 95% of the venous valves are micron scale found in veins smaller than 300μm diameter. The fluid dynamics of blood flow and transport through these micro venous valves and their contribution to thrombosis is not yet well understood or characterized due to difficulty in making direct measurements in murine models. OBJECTIVE: The unique flow patterns that may arise in physiological and pathological non-actuating micro venous valves are predicted. METHODS: Computational fluid and transport simulations are used to model blood flow and oxygen gradients in a microfluidic vein. RESULTS: The model successfully recreates the typical non-Newtonian vortical flow within the valve cusps seen in preclinical experimental models and in clinic. The analysis further reveals variation in the vortex strengths due to temporal changes in blood flow. The cusp oxygen is typically low from the main lumen, and it is regulated by systemic venous flow. CONCLUSIONS: The analysis leads to a clinically-relevant hypothesis that micro venous valves may not create a hypoxic environment needed for endothelial inflammation, which is one of the main causes of thrombosis. However, incompetent micro venous valves are still locations for complex fluid dynamics of blood leading to low shear regions that may contribute to thrombosis through other pathways.more » « less
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The motion of cells orthogonal to the direction of main flow is of importance in natural and engineered systems. The lateral movement of red blood cells (RBCs) distal to sudden expansion is considered to influence the formation and progression of thrombosis in venous valves, aortic aneurysms, and blood-circulating devices and is also a determining parameter for cell separation applications in flow-focusing microfluidic devices. Although it is known that the unique geometry of venous valves alters the blood flow patterns and cell distribution in venous valve sinuses, the interactions between fluid flow and RBCs have not been elucidated. Here, using a dilute cell suspension in an in vitro microfluidic model of a venous valve, we quantified the spatial distribution of RBCs by microscopy and image analysis, and using micro-particle image velocimetry and 3D computational fluid dynamics simulations, we analyzed the complex flow patterns. The results show that the local hematocrit in the valve pockets is spatially heterogeneous and is significantly different from the feed hematocrit. Above a threshold shear rate, the inertial separation of streamlines and lift forces contribute to an uneven distribution of RBCs in the vortices, the entrapment of RBCs in the vortices, and non-monotonic wall shear stresses in the valve pockets. Our experimental and computational characterization provides insights into the complex interactions between fluid flow, RBC distribution, and wall shear rates in venous valve mimics, which is of relevance to understanding the pathophysiology of thrombosis and improving cell separation efficiency.
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Computational cardiovascular flow analysis can provide valuable information to medical doctors in a wide range of patientspecific cases, including cerebral aneurysms, aortas and heart valves. The computational challenges faced in this class of flow analyses also have a wide range. They include unsteady flows, complex cardiovascular geometries, moving boundaries and interfaces, such as the motion of the heart valve leaflets, contact between moving solid surfaces, such as the contact between the leaflets, and the fluid–structure interaction between the blood and the cardiovascular structure. Many of these challenges have been or are being addressed by the Space–Time Variational Multiscale (ST-VMS) method, Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) method, and the VMS-based Immersogeometric Analysis (IMGA-VMS), which serve as the core computational methods, and the special methods used in combination with them. We provide an overview of the core and special methods and present examples of challenging computations carried out with these methods, including aorta and heart valve flow analyses. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.more » « less
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Abstract Deep vein thrombosis (DVT) and its consequences are lethal, but current models cannot completely dissect its determinants—endothelium, flow, and blood constituents—together called Virchow's triad. Most models for studying DVT forego assessment of venous valves that serve as the primary sites of DVT formation. Therefore, the knowledge of DVT formed at the venous cusps has remained obscure due to lack of experimental models. Here, organ‐on‐chip methodology is leveraged to create a Vein‐Chip platform integrating fully vascularized venous valves and its hemodynamic, as seen in vivo. These Vein‐Chips reveal that vascular endothelium of valve cusps adapts to the locally disturbed microenvironment by expressing a different phenotype from the regions of uniform flow. This spatial adaptation of endothelial function recreated on the in vitro Vein‐Chip platform is shown to protect the vein from thrombosis from disturbed flow in valves, but interestingly, cytokine stimulation reverses the effect and switches the valve endothelium to becoming prothrombotic. The platform eventually modulates the three factors of Virchow's triad and provides a systematic approach to investigate the determinants of fibrin and platelet dynamics of DVT. Therefore, this Vein‐Chip offers a new preclinical approach to study venous pathophysiology and show effects of antithrombotic drug treatment.
