CAREER: Dynamic Spatial Patterns: Quantitative Comparison of Equations and Experiments

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

9984370 Gray The overall goal of this career plan is to educate individuals about the wide variety of dynamic spatial patterns that occur in chemical, physical, biological and physiological systems and the common mathematical equations that govern them. Similar patterns, such as rotating spiral waves, occur in many of these systems. "Universal" mathematical equations in the form of partial differential equations (PDEs) reproduce these dynamic spatial patterns. These PDEs represent generic reaction-diffusion systems and can be studied analytically. The objectives of the plan outlined in this proposal include developing a graduate-level course that incorporates interactive learning through hands-on laboratories and immediate student feedback during homework assignments via computer software. Another objective of this proposal is to create an educational outreach program to expose elementary and high school students to the exciting aspects of research such as the thrill of discovery and the importance of research in the design of new technologies and saving lives. This will be accomplished through presentations and demonstrations and will take place within the Birmingham area public schools and local science museum to reach underprivileged populations. The research in this project incorporates high-speed video imaging technology to record the dynamic spatial patterns in a wide variety of chemical, physical, biological and physiological systems. These patterns will be analyzed with novel methods that allow a direct quantitative comparison of the experiments and the equations thought to govern their behavior. The research and education portions of the project are tightly integrated. The research will identify certain systems that are ideally suited for demonstrations and the laboratory that accompanies the graduate level course. In addition, homework assignment will be designed based on real examples identified in the research efforts. The significance of this plan is three-fold. First, college students and graduates are not familiar with nonlinear phenomenon and the mathematical representation of the dynamics of spatial patterns. The ability to use nonlinear analysis and understand the basic equations that govern spatially extended systems through interactive learning provide students with tools to quantitatively address complex spatial behavior. The ability to analyze dynamic spatial patterns is becoming increasingly important as rapid advances in optics and electronics, including lasers, charge-coupled device (CCD) detectors, fluorescence dyes, and computerized control and image-processing systems are occurring. Furthermore, secondary students are not well-trained in science and mathematics. This lack of knowledge is due, in part, to an inadequate exposure to the exciting aspects of research and its importance. Presentations involving hands-on demonstrations act to stimulate interest in science, mathematics and engineering through. Third, the study of biological phenomenon such as cardiac arrhythmias has traditionally been empirical, with investigators interpreting experimental results in terms of the physiology and the anatomy. The research proposed in this application investigates quantitative comparisons between experimental results and the mathematical equations thought to represent them. A particular emphasis is placed on cardiac arrhythmias and defibrillation due to the PIs research interests and environment. An improved understanding of the mathematical models that represent wave propagation in the heart may lead to advances in clinical therapy.