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Author

Rana Zakerzadeh

Bio: Rana Zakerzadeh is an academic researcher from RMIT University. The author has contributed to research in topics: Poromechanics & Fluid–structure interaction. The author has an hindex of 8, co-authored 20 publications receiving 311 citations. Previous affiliations of Rana Zakerzadeh include University of Pittsburgh & University of Texas at Austin.

Papers
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Journal ArticleDOI
TL;DR: This work presents a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid–structure interaction (FSI) analysis and parameterizes the leaflet geometry using several key design parameters.
Abstract: Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid-structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian-Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient-specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.

94 citations

Journal ArticleDOI
TL;DR: In this work, a loosely coupled scheme for Stokes–Biot equations is developed and thoroughly analyzed, based on Nitsche’s method for enforcing interface conditions, and the application of the loosely coupling scheme as a preconditioner for the monolithic approach is considered.

82 citations

Journal ArticleDOI
TL;DR: The relative simplicity of the Lee-Sacks model is attractive for computationally-demanding applications such as FSI analysis and it is used to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.

60 citations

Posted Content
TL;DR: In this paper, a loosely coupled time advancing scheme for Stokes-Darcy coupled systems is proposed, which is based on Nitsche's method for enforcing interface conditions, and the stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem.
Abstract: We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it shares common traits with fluid-structure interaction. On the other hand it resembles the Stokes-Darcy coupling. For these reasons, the numerical simulation of the Stokes-Biot coupled system is a challenging task. The need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners are typical shortcomings of classical discretization methods applied to this problem. The application of loosely coupled time advancing schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others. In this work we develop and thoroughly analyze a loosely coupled scheme for Stokes-Biot equations. The scheme is based on Nitsche's method for enforcing interface conditions. Once the interface operators corresponding to the interface conditions have been defined, time lagging allows us to build up a loosely coupled scheme with good stability properties. The stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem. The error of the resulting method is also analyzed, showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes. In order to restore good approximation properties, while maintaining the computational efficiency of the loosely coupled approach, we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach. Both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand.

49 citations

Journal ArticleDOI
TL;DR: This review covers recent progress in computational models for the simulation of BHV, with a focus on aortic valve (AV) replacement, and recommends guidelines and insight for the design of future prosthetic valves by analyzing the influence of design, hemodynamics and tissue mechanics.
Abstract: Introduction: Replacement with a prosthetic device remains a major treatment option for the patients suffering from heart valve disease, with prevalence growing resulting from an ageing population....

48 citations


Cited by
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01 Jan 2016
TL;DR: In this article, a numerical approximation of partial differential equations was used to detect harmful downloads of books on the Internet, where people have search hundreds of times for their chosen novels like this numerical approximation, but end up in harmful downloads.
Abstract: Thank you very much for reading numerical approximation of partial differential equations. Maybe you have knowledge that, people have search hundreds times for their chosen novels like this numerical approximation of partial differential equations, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some harmful virus inside their laptop.

246 citations

Journal ArticleDOI
TL;DR: This article reviews immersed methods for both elastic structures and structures with prescribed kinematics using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces.
Abstract: Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

149 citations

Journal ArticleDOI
TL;DR: An unmet clinical need remains for valve replacements with regenerative, remodelling and growth potential, and next-generation tissue-engineered heart valves (TEHVs) are a promising therapeutic option for patients with valvular heart disease.
Abstract: Valvular heart disease is a major cause of morbidity and mortality worldwide. Surgical valve repair or replacement has been the standard of care for patients with valvular heart disease for many decades, but transcatheter heart valve therapy has revolutionized the field in the past 15 years. However, despite the tremendous technical evolution of transcatheter heart valves, to date, the clinically available heart valve prostheses for surgical and transcatheter replacement have considerable limitations. The design of next-generation tissue-engineered heart valves (TEHVs) with repair, remodelling and regenerative capacity can address these limitations, and TEHVs could become a promising therapeutic alternative for patients with valvular disease. In this Review, we present a comprehensive overview of current clinically adopted heart valve replacement options, with a focus on transcatheter prostheses. We discuss the various concepts of heart valve tissue engineering underlying the design of next-generation TEHVs, focusing on off-the-shelf technologies. We also summarize the latest preclinical and clinical evidence for the use of these TEHVs and describe the current scientific, regulatory and clinical challenges associated with the safe and broad clinical translation of this technology.

104 citations

Journal ArticleDOI
TL;DR: In this work, a loosely coupled scheme for Stokes–Biot equations is developed and thoroughly analyzed, based on Nitsche’s method for enforcing interface conditions, and the application of the loosely coupling scheme as a preconditioner for the monolithic approach is considered.

82 citations

Journal ArticleDOI
TL;DR: In this article, an iterative scheme for solving a coupled geomechanics and flow problem in a fractured poroelastic medium is proposed, where fractures are treated as possibly non-planar interfaces.
Abstract: We consider an iterative scheme for solving a coupled geomechanics and flow problem in a fractured poroelastic medium. The fractures are treated as possibly non-planar interfaces. Our iterative scheme is an adaptation due to the presence of fractures of a classical fixed stress-splitting scheme. We prove that the iterative scheme is a contraction in an appropriate norm. Moreover, the solution converges to the unique weak solution of the coupled problem.

82 citations