Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: In this talk I will discuss the problem of elastic growth in biological material and use the growth of filamentous microorganisms as a case study. Most filamentous microorganisms belong to two groups, the eukaryotic filamentous fungi, and the prokaryotic filamentous actinomycetes. The cellular structures observed in these two groups are fundamentally different. However, they exhibit similar morphologies, growth patterns, and mycelial and aerial growth forms. Despite some earlier geometric models there is no biomechanical understanding of filamentous growth. In this talk, I will present recent experimental results and new models for the vegetative growth of filamentous bacteria. In particular, I will develop a general theory of growing elastic biomembranes to model tip growth.
Scientific Computing Seminar
University of Houston | |
Before and After Endovascular Repair: Modeling, Analysis and Numerical Simulation | |
Abstract: The complexity of the cardiovascular system features a tremendous variety of districts like large arteries, vessels of medium caliber as well as capillaries. Except for the tiny capillaries, the blood flow can be assumed to behave like a continuum, as well as incompressible, except for some severe pathological situations. The incompressible Navier-Stokes equations can be used to model the flow in large, or incompressible Stokes equations in small arteries. To analyze some relevant properties of blood flow in specific arterial districts for specific medical problems, two important effects often need to be taken into account: the pulsatile nature of the flow and the compliant nature of the vessel walls. Despite the incredible power of supercomputing now-a-days, it is still impossible to take all these effects into account in order to simulate large sections of the human cardiovascular system in a realistic time frame. This is why simplified models describing fluid-structure interaction between the pulsatile blood flow and the compliant vessel wall are crucial in fast, real-time calculations, often needed by medical specialists.
This talk will address a rigorous mathematical approach in the derivation of the simplified equations using the axi-symmetric nature of compliant arterial sections (either treated with axy-symmetric nature prostheses or not). The compliant arterial sections are modeled using the Navier equations for the linearly elastic membrane. Depending on the size of the vessel, the resulting simplified equations are either hyperbolic (derived from the coupling between the Navier-Stokes equations for the flow and the Navier equations for the vessel wall), or parabolic (derived from the coupling between the Stokes equations for the flow and the Navier equations for the vessel wall). Convergence results and error estimates will be given. They show how the solution of the reduced, simplified equation, converges to the solution of the original, 3-dimensional problem, in long and narrow axi-symmetric vessels.
In the presence of a flexible vascular prosthesis (stent) inserted into an artery, the model equations featuring discontinuous coefficients due to the jump in the elasticity properties of the compliant walls at the anchoring sites of the prostheses. New theory and numerical methods are needed to study solutions of the reduced, hyperbolic PDEs with such discontinuous coefficients. An insight into the related problems and preliminary answers will be presented.
Movies Showing numerical simulations related to the patients suffering from aortic abdominal aneurysm, treated at the Texas Heart Institute in Houston, will be shown.
Collaborators:
1. Prof. Andro Mikelic, Universite Claude Bernard Lyon 1, France,
2. Medical Doctors: Z. Krajcer, Texas Heart Institute, (St. Lukes's
Hospital)
G. Dorros, Arizona Heart Institute
3. Prof. Ravi-Chandar, Aerospace Engineering, University of Texas
in Austin
Brown University Graduate School
Dissertation Defense Information
Division of Applied Mathematics
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