Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods.

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

3D Experimental and Computational Analysis of Eccentric Mitral Regurgitant Jets in a Mock Imaging Heart Chamber.

Mitral valve regurgitation (MR) is a disorder of the heart in which the mitral valve does not close properly. This causes an abnormal leaking of blood backwards from the left ventricle into the left atrium during the systolic contractions of the left ventricle. Noninvasive assessment of MR using echocardiography is an ongoing challenge. In particular, a major problem are eccentric or Coanda regurgitant jets which hug the walls of the left atrium and appear smaller in the color Doppler image of regurgitant flow. This manuscript presents a comprehensive investigation of Coanda regurgitant jets and the associated intracardiac flows by using a combination of experimental and computational approaches. An anatomically correct mock heart chamber connected to a pulsatile flow loop is used to generate the physiologically relevant flow conditions, and the influence of two clinically relevant parameters (orifice aspect ratio and regurgitant volume) on the onset of Coanda effect is studied. A two parameter bifurcation diagram showing transition to Coanda jets is obtained, indicating that: (1) strong wall hugging jets occur in long and narrow orifices with moderate to large regurgitant volumes, and (2) short orifices with moderate to large regurgitant volumes produce strong 3D flow features such as vortex rolls, giving rise to the velocities that are orthogonal to the 2D plane associated with the apical color Doppler views, making them "invisible" to the single plane color Doppler assessment of MR. This is the first work in which the presence of vortex rolls in the left atrium during regurgitation is reported and identified as one of the reasons for under-estimation of regurgitant volume. The results of this work can be used for better design of imaging strategies in noninvasive assessment of MR, and for better understanding of LA remodeling that may be associated with the presence of maladapted vortex dynamics. This introduces a new concept in clinical imaging, which emphasizes that the quality and not only the quantity of regurgitant flow matters in the assessment of severity of mitral valve regurgitation.

Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives.

Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.

Mathematical Model analysis of Wallstent and Aneurx: dynamic responses of bare-metal endoprosthesis compared with those of stent-graft.

We performed this study in order to analyze the mechanical properties of bare-metal Wallstent endoprostheses and of AneuRx stent-grafts and to compare their responses to hemodynamic forces. Mathematical modeling, numerical simulations, and experimental measurements were used to study the 2 structurally different types of endoprostheses. Our findings revealed that a single bare-metal Wallstent endoprosthesis is 10 times more flexible (elastic) than is the wall of the aneurysmal abdominal aorta. Graphs showing the changes in the diameter and length of the stent when exposed to a range of internal and external pressures were obtained. If the aorta is axially stiff and resists length change, a force as large as 1 kg can act in the axial direction on the aortic wall. If the stent is not firmly anchored, it will migrate. In contrast, a fabric-covered, fully supported, stent-graft such as the AneuRx is significantly less compliant than the aorta or the bare-metal stent. During each cardiac cycle, the stent frame tends to move due to its higher elasticity, while the fabric resists movement, which might break the sutures that join the fabric to the frame. Elevated local transmural pressure, detected along the prosthesis graft, can contribute to material fatigue.

Emerging trends in heart valve engineering: Part II. Novel and standard technologies for aortic valve replacement.

The engineering of technologies for heart valve replacement (i.e., heart valve engineering) is an exciting and evolving field. Since the first valve replacement, technology has progressed by leaps and bounds. Innovations emerge frequently and supply patients and physicians with new, increasingly efficacious and less invasive treatment options. As much as any other field in medicine the treatment of heart valve disease has experienced a renaissance in the last 10 years. Here we review the currently available technologies and future options in the surgical and transcatheter treatment of aortic valve disease. Different valves from major manufacturers are described in details with their applications.

Emerging trends in heart valve engineering: Part I. Solutions for future.

As the first section of a multi-part review series, this section provides an overview of the ongoing research and development aimed at fabricating novel heart valve replacements beyond what is currently available for patients. Here we discuss heart valve replacement options that involve a biological component or process for creation, either in vitro or in vivo (tissue-engineered heart valves), and heart valves that are fabricated from polymeric material that are considered permanent inert materials that may suffice for adults where growth is not required. Polymeric materials provide opportunities for cost-effective heart valves that can be more easily manufactured and can be easily integrated with artificial heart and ventricular assist device technologies. Tissue engineered heart valves show promise as a regenerative patient specific model that could be the future of all valve replacement. Because tissue-engineered heart valves depend on cells for their creation, understanding how cells sense and respond to chemical and physical stimuli in their microenvironment is critical and therefore, is also reviewed.

Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies.

In this final portion of an extensive review of heart valve engineering, we focus on the computational methods and experimental studies related to heart valves. The discussion begins with a thorough review of computational modeling and the governing equations of fluid and structural interaction. We then move onto multiscale and disease specific modeling. Finally, advanced methods related to in vitro testing of the heart valves are reviewed. This section of the review series is intended to illustrate application of computational methods and experimental studies and their interrelation for studying heart valves.

Emerging trends in heart valve engineering: Part III. Novel technologies for mitral valve repair and replacement.

In this portion of an extensive review of heart valve engineering, we focus on the current and emerging technologies and techniques to repair or replace the mitral valve. We begin with a discussion of the currently available mechanical and bioprosthetic mitral valves followed by the rationale and limitations of current surgical mitral annuloplasty methods; a discussion of the technique of neo-chordae fabrication and implantation; a review the procedures and clinical results for catheter-based mitral leaflet repair; a highlight of the motivation for and limitations of catheter-based annular reduction therapies; and introduce the early generation devices for catheter-based mitral valve replacement.

Longitudinal displacement in viscoelastic arteries: a novel fluid-structure interaction computational model, and experimental validation.

Recent in vivo studies, utilizing ultrasound contour and speckle tracking methods, have identified significant longitudinal displacements of the intima-media complex, and viscoelastic arterial wall properties over a cardiac cycle. Existing computational models that use thin structure approximations of arterial walls have so far been limited to models that capture only radial wall displacements. The purpose of this work is to present a simple fluid-struture interaction (FSI) model and a stable, partitioned numerical scheme, which capture both longitudinal and radial displacements, as well as viscoelastic arterial wall properties. To test the computational model, longitudinal displacement of the common carotid artery and of the stenosed coronary arteries were compared with experimental data found in literature, showing excellent agreement. We found that, unlike radial displacement, longitudinal displacement in stenotic lesions is highly dependent on the stenotic geometry. We also showed that longitudinal displacement in atherosclerotic arteries is smaller than in healthy arteries, which is in line with the recent in vivo measurements that associate plaque burden with reduced total longitudinal wall displacement. This work presents a first step in understanding the role of longitudinal displacement in physiology and pathophysiology of arterial wall mechanics using computer simulations.

Numerical characterization of hemodynamics conditions near aortic valve after implantation of Left Ventricular Assist Device.

Left Ventricular Assist Devices (LVADs) are implantable mechanical pumps that temporarily aid the function of the left ventricle. The use of LVADs has been associated with thrombus formation next to the aortic valve and close to the anastomosis region, especially in patients in which the native cardiac function is negligible and the aortic valve remains closed. Stagnation points and recirculation zones have been implicated as the main fluid dynamics factors contributing to thrombus formation. The purpose of the present study was to develop and use computer simulations based on a fluid-structure interaction (FSI) solver to study flow conditions corresponding to different strategies in LVAD ascending aortic anastomosis providing a scenario with the lowest likelihood of thrombus formation. A novel FSI algorithm was developed to deal with the presence of multiple structures corresponding to different elastic properties of the native aorta and of the LVAD cannula. A sensitivity analysis of different variables was performed to assess their impact of flow conditions potentially leading to thrombus formation. It was found that the location of the anastomosis closest to the aortic valve (within 4 cm away from the valve) and at the angle of 30 minimizes the likelihood of thrombus formation. Furthermore, it was shown that the rigidity of the dacron anastomosis cannula plays almost no role in generating pathological conditions downstream from the anastomosis. Additionally, the flow analysis presented in this manuscript indicates that compliance of the cardiovascular tissue acts as a natural inhibitor of pathological flow conditions conducive to thrombus formation and should not be neglected in computer simulations.

Mechanical behavior of fully expanded commercially available endovascular coronary stents.

The mechanical behavior of endovascular coronary stents influences their therapeutic efficacy. Through computational studies, researchers can analyze device performance and improve designs. We developed a 1-dimensional finite element method, net-based algorithm and used it to analyze the effects of radial loading and bending in commercially available stents. Our computational study included designs modeled on the Express, Cypher, Xience, and Palmaz stents.We found that stents that did not fully expand were less rigid than the fully expanded stents and, therefore, exhibited larger displacement. Stents with an open-cell design, such as Express-like or Xience-like stents, had a higher bending flexibility. Stents with in-phase circumferential rings, such as the Xience-like stent, had the smallest longitudinal extension when exposed to radial compression forces. Thus, the open-cell model that had in-phase circumferential rings connected by straight horizontal struts exhibited radial stiffness, bending flexibility, and the smallest change in stent length during radial forcing. The Palmaz-like stent was the most rigid of all. These findings are supported by clinical experience.Computer simulations of the mechanical properties of endovascular stents offer sophisticated insights into the mechanical behavior of different stent designs and should be used whenever possible to help physicians decide which stent is best for treating a given lesion. Our 1-dimensional finite element method model is incomparably simpler, faster, and more accurate than the classical 3-dimensional approaches. It can facilitate stent design and may aid in stent selection in the clinical setting.

A comparison between fractured Xience-like and Palmaz-like stents using a novel computational model.

We developed a novel mathematical model to study the mechanical properties of endovascular stents in their expanded state. The model is based on the one-dimensional theory of slender curved rods. Stent struts are modeled as linearly elastic curved rods that satisfy the kinematic and dynamic contact conditions at the vertices where the struts meet. A Finite Element Method for a numerical computation of its solution was developed and used to study mechanical properties of two commonly used coronary stents (Palmaz-like and Xience-like stent) in their expanded, fractured state. A simple fracture (separation), corresponding to one stent strut being disconnected from one vertex in a stent, was considered. Our results show a drastic difference in the response of the two stents to the physiologically reasonable uniform compression and bending forces. In particular, deformation of a fractured Xience-like stent (with one strut separated from one vertex) is significantly larger than that of a fractured Palmaz-like stent when exposed to uniform compression and bending. This presents conditions which may be a precursor for the clinically observed complications associated with in-stent thrombosis and in-stent restenosis of fractured coronary stents.

Use of auricular chondrocytes for lining artificial surfaces: a mathematical model.

Auricular elastic cartilage is a potential source for lining of luminal surfaces of implantable vascular devices, such as stents and left ventricular assist devices with the purpose to improve their biocompatibility. Auricular chondrocytes are easily accessible, harvested, and isolated, and they have been shown to provide a strong adherent cell lining for left ventricular assist devices. Additionally, Dr. Rosenstrauch have shown that it is possible to genetically engineer auricular chondrocytes to produce antithrombogenic factors. Thus, implantable vascular devices, such as coronary stents covered with genetically engineered auricular chondrocytes might lower restenosis rates and provide a long-lasting biocompatible prosthesis. In this paper, to optimize the process of lining of artificial surfaces with auricular cartilage, we devise a mathematical model that describes the rate of cell division and growth of extracellular matrix as a function of the initial cell count, proximity to other cells, and the type of artificial surface. Our mathematical model was experimentally tested using two different cell cultures (auricular chondrocytes and dermal fibroblasts) seeded on different artificial surfaces (tc-treated polystyrene and aluminum foil). Excellent agreement between the model and experiment was obtained. This mathematical model can be used to, for example, determine the optimum number of initially seaded cells that would provide fastest coverage of a given artificial surface.

Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics, and experimental validation.

The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier-Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, "one-and-a-half dimensional" model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow - vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.