The 7th Annual UNCG Regional Mathematics and Statistics Conference
Saturday, November 5, 2011

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Morning Plenary Lecture

Excitable tissues in fluids

presented by

Laura Miller

Assistant Professor
University of North Carolina Chapel Hill

Abstract: A wide range of numerical, analytical, and experimental work in recent years has focused on understanding the interaction between fluids and elastic structures in the context of cardiovascular flows, animal swimming and flying, cellular flows, and other biological problems. While great progress has been made in understanding such systems, less is known about how these excitable tissues modulate their mechanical properties in response to fluid forces and other environmental cues. The broad goal of this work is to develop a framework to integrate the conduction of action potentials with the contraction of muscles, to the movement of organs and organisms, to the motion of the fluid, and back to the nervous system through environmental cues. Such coupled models can then be used to understand how small changes in tissue physics can result in large changes in performance at the organ and organism level. Two examples will be discussed in this presentation. The first example considers how active contractions generated by the cardiac conduction system can enhance flows in tubular hearts, particularly at low Reynolds numbers. The second example considers how the interactions between pacemakers in the upside down jellyfish can alter feeding currents generated by the bell pulsations. In both cases, the ultimate goal is to simulate the electropotentials in the nervous system that trigger mechanical changes in 1D fibers representing the muscular bands. The muscular contractions then apply forces to the boundaries that interacts with the fluid modeled by the Navier-Stokes equations. The computational framework used to solve these problems is the immersed boundary method originally developed by Charles Peskin.

Biosketch: Dr. Laura Miller received her Ph.D. from the Courant Institute of Mathematics at New York University in 2004. She was advised by Charles Peskin and her dissertation topic was "The aerodynamics of tiny insect flight." Dr. Miller then continued her work in mathematical biomechanics and physiology at the University of Utah from 2004-2006. In 2006, Miller received a Burroughs Wellcome Fund Career Award at the Scientific Interface to pursue problems related to the mathematical modeling of insect flight and the fluid dynamics of the developing embryonic heart. She then joined the faculty in the Department of Mathematics at the University of North Carolina at Chapel Hill in January of 2007. Using her training in both mathematics and biology, she continues to apply mathematical modeling and computational fluid dynamics to better understand how organisms interact with their environments. Her current research interests include the feeding mechanics of jellyfish, the coupled electromechanical problem of tubular heart pumping, and the mechanical properties of trees that allows them to withstand hurricane force winds and avalanches. She teaches classes that integrate mathematics, mechanical engineering, and biology.

 

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