Rana Zakerzadeh

A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis

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.

Computational methods for the aortic heart valve and its replacements

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. While the most popular replacement heart valve continues to be the bioprosthetic heart valve (BHV), its durability remains limited. There is thus a continued need to develop a general understanding of the underlying mechanisms limiting BHV durability to facilitate development of a more durable prosthesis. In this regard, computational models can play a pivotal role as they can evaluate our understanding of the underlying mechanisms and be used to optimize designs that may not always be intuitive. Areas covered: This review covers recent progress in computational models for the simulation of BHV, with a focus on aortic valve (AV) replacement. Recent contributions in valve geometry, leaflet material models, novel methods for numerical simulation, and applications to BHV optimization are discussed. This information should serve not only to infer reliable and dependable BHV function, but also to establish guidelines and insight for the design of future prosthetic valves by analyzing the influence of design, hemodynamics and tissue mechanics. Expert commentary: The paradigm of predictive modeling of heart valve prosthesis are becoming a reality which can simultaneously improve clinical outcomes and reduce costs. It can also lead to patient-specific valve design.

Fluid-structure interaction in arteries with a poroelastic wall model

The objective of this work is modeling the interaction between pulsatile blood flow and arterial walls. We model blood flow in arteries as an incompressible viscous fluid with Newtonian rheology, confined by a poroelastic arterial wall modeled with the Biot equations. We propose loosely coupled solution strategy of the fluid-structure interaction problem, which allows solving the Navier-Stokes and Biot equations separately. In this way, we uncouple the original problem into two parts defined on separate subregions. At the end, the partitioned scheme is exploited as a preconditioner for the monolithic method, leading to a more accurate calculation of the numerical solution. The theoretical results are complemented by numerical simulations.

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.

Effects of Poroelasticity on Fluid-Structure Interaction in Arteries: a Computational Sensitivity Study

We model blood flow in arteries as an incompressible Newtonian fluid confined by a poroelastic wall. The blood and the artery are coupled at multiple levels. Fluid forces affect the deformation of the artery. In turn, the mechanical deformation of the wall influences both blood flow and transmural plasma filtration. We analyze these phenomena using a two layer model for the artery, where the inner layers (the endothelium and the intima) behave as a thin membrane modeled as a linearly elastic Koiter shell, while the outer part of the artery (accounting for the media and the adventitia) is described by the Biot model. We assume that the membrane can transduce displacements and stresses to the artery and it is permeable to flow.

A material modeling approach for the effective response of planar soft tissues for efficient computational simulations

One of the most crucial aspects of biomechanical simulations of physiological systems that seek to predict the outcomes of disease, injury, and surgical interventions is the underlying soft tissue constitutive model. Soft tissue constitutive modeling approaches have become increasingly complex, often utilizing meso- and multi-scale methods for greater predictive capability and linking to the underlying biological mechanisms. However, such modeling approaches are associated with substantial computational costs. One solution is to use effective constitutive models in place of meso- and multi-scale models in numerical simulations but derive their responses by homogenizing the responses of the underlying meso- or multi-scale models. A robust effective constitutive model can thus drastically increase the speed of simulations for a wide range of meso- and multi-scale models. However, there is no consensus on how to develop a single effective constitutive model and optimal methods for parameter estimation for a wide range of soft tissue responses. In the present study, we developed an effective constitutive model which can fully reproduce the response of a wide range of planar soft tissues, along with a method for robust and fast-convergent parameter estimation. We then evaluated our approach and demonstrated its ability to handle materials of widely varying degrees of stiffness and anisotropy. Furthermore, we demonstrated the robutst performance of the meso-structural to effective constitutive model framework in finite element simulations of tri-leaflet heart valves. We conclude that the effective constitutive modeling approach has significant potential for improving the computational efficiency and numerical robustness of multi-scale and meso-scale models, facilitating efficient soft tissue simulations in such demanding applications as inverse modeling and growth.

Hyperbolic–Parabolic Coupling and the Occurrence of Resonance in Partially Dissipative Systems

It is well known that elastic solids, when subjected to a time-periodic load of frequency ω, may respond with a drastic increase of the magnitude of basic kinematic and dynamic quantities, such as displacement, velocity and energy, whenever ω is near to one of the “proper frequencies” of the solid. This phenomenon is briefly described as resonance. Objective of our analysis is to investigate whether the interaction of an elastic solid with a dissipative agent can affect and possibly prevent the occurrence of resonance. We shall study this problem in a broad class of dynamical systems that we call partially dissipative, and whose dynamics is governed by strongly continuous semigroups of contractions. For such systems we will provide sharp necessary and sufficient conditions for the occurrence of resonance. Afterward, we shall furnish a number of applications to physically relevant problems including thermo- and magneto-elasticity, as well as several liquid–structure interaction models.