Quicklists
public 01:34:50

Suncica Canic : Mathematical modeling for cardiovascular stenting

  -   Applied Math and Analysis ( 193 Views )

The speaker will talk about several projects that are taking place in an interdisciplinary endeavor between the researchers in the Mathematics Department at the University of Houston, the Texas Heart Institute, Baylor College of Medicine, the Mathematics Department at the University of Zagreb, and the Mathematics Department of the University of Lyon 1. The projects are related to non-surgical treatment of aortic abdominal aneurysm and coronary artery disease using endovascular prostheses called stents and stent-grafts. Through a collaboration between mathematicians, cardiovascular specialists and engineers we have developed a novel mathematical model to study blood flow in compliant (viscoelastic) arteries treated with stents and stent-grafts. The mathematical tools used in the derivation of the effective, reduced equations utilize asymptotic analysis and homogenization methods for porous media flows. The existence of a unique solution to the resulting fluid-structure interaction model is obtained by using novel techniques to study systems of mixed, hyperbolic-parabolic type. A numerical method, based on the finite element approach, was developed, and numerical solutions were compared with the experimental measurements. Experimental measurements based on ultrasound and Doppler methods were performed at the Cardiovascular Research Laboratory located at the Texas Heart Institute. Excellent agreement between the experiment and the numerical solution was obtained. This year marks a giant step forward in the development of medical devices and in the development of the partnership between mathematics and medicine: the FDA (the United States Food and Drug Administration) is getting ready to, for the first time, require mathematical modeling and numerical simulations to be used in the development of peripheral vascular devices. The speaker acknowledges research support from the NSF, NIH, and Texas Higher Education Board, and donations from Medtronic Inc. and Kent Elastomer Inc.

public 01:14:39

Lucy Zhang : Modeling and Simulations of Fluid and Deformable-Structure Interactions in Bio-Mechanical Systems

  -   Applied Math and Analysis ( 164 Views )

Fluid-structure interactions exist in many aspects of our daily lives. Some biomedical engineering examples are blood flowing through a blood vessel and blood pumping in the heart. Fluid interacting with moving or deformable structures poses more numerical challenges for its complexity in dealing with transient and simultaneous interactions between the fluid and solid domains. To obtain stable, effective, and accurate solutions is not trivial. Traditional methods that are available in commercial software often generate numerical instabilities.

In this talk, a novel numerical solution technique, Immersed Finite Element Method (IFEM), is introduced for solving complex fluid-structure interaction problems in various engineering fields. The fluid and solid domains are fully coupled, thus yield accurate and stable solutions. The variables in the two domains are interpolated via a delta function that enables the use of non-uniform grids in the fluid domain, which allows the use of arbitrary geometry shapes and boundary conditions. This method extends the capabilities and flexibilities in solving various biomedical, traditional mechanical, and aerospace engineering problems with detailed and realistic mechanics analysis. Verification problems will be shown to validate the accuracy and effectiveness of this numerical approach. Several biomechanical problems will be presented: 1) blood flow in the left atrium and left atrial appendage which is the main source of blood in patients with atrial fibrillation. The function of the appendage is determined through fluid-structure interaction analysis, 2) examine blood cell and cell interactions under different flow shear rates. The formation of the cell aggregates can be predicted when given a physiologic shear rate.

public 01:14:36

Andrew J. Bernoff : Domain Relaxation in Langmuir Films

  -   Applied Math and Analysis ( 143 Views )

We report on an experimental and theoretical study of a molecularly thin polymer Langmuir layers on the surface of a Stokesian subfluid. Langmuir layers can have multiple phases (fluid, gas, liquid crystal, isotropic or anisotropic solid); at phase boundaries a line tension force is observed. By comparing theory and experiment we can estimate this line tension. We first consider two co-existing fluid phases; specifically a localized phase embedded in an infinite secondary phase. When the localized phase is stretched (by a transient stagnation flow), it takes the form of a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape relaxes to the minimum energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is thin. We model these experiments by taking previous descriptions of the full hydrodynamics (primarily those of Stone & McConnell and Lubensky & Goldstein), identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem where motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. The problem has a boundary integral formulation which allows us to numerically simulate the tether relaxation; comparison with the experiments allows us to estimate the line tension in the system. We also report on incorporating dipolar repulsion into the force balance and simulating the formation of "labyrinth" patterns.

public 01:29:47

Elisabetta Matsumoto : Biomimetic 4D Printing

  -   Applied Math and Analysis ( 134 Views )

The nascent technique of 4D printing has the potential to revolutionize manufacturing in fields ranging from organs-on-a-chip to architecture to soft robotics. By expanding the pallet of 3D printable materials to include the use stimuli responsive inks, 4D printing promises precise control over patterned shape transformations. With the goal of creating a new manufacturing technique, we have recently introduced a biomimetic printing platform that enables the direct control of local anisotropy into both the elastic moduli and the swelling response of the ink.

We have drawn inspiration from nastic plant movements to design a phytomimetic ink and printing process that enables patterned dynamic shape change upon exposure to water, and possibly other external stimuli. Our novel fiber-reinforced hydrogel ink enables local control over anisotropies not only in the elastic moduli, but more importantly in the swelling. Upon hydration, the hydrogel changes shape accord- ing the arbitrarily complex microstructure imparted during the printing process.

To use this process as a design tool, we must solve the inverse problem of prescribing the pattern of anisotropies required to generate a given curved target structure. We show how to do this by constructing a theory of anisotropic plates and shells that can respond to local metric changes induced by anisotropic swelling. A series of experiments corroborate our model by producing a range of target shapes inspired by the morphological diversity of flower petals.