L ISA D RISKELL

Graduate Student Department of Mathematics Purdue University Office: MATH 441 ldriskel@math.purdue.edu 150 N. University Street West Lafayette, IN 47907 (765) 494.5964 How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality? - Albert Einstein

C URRICULUM V ITAE CV, updated October 2009. T EACHING This year I am supported by a research grant and will not be teaching. Last Semester: Graded for MA 50400 and MA 22300. Previous Semesters (at Purdue): Taught MA 22300 (Business Calculus I), MA 22400 (Business Calculus II), and MA 15300 (College Algebra). R ESEARCH Advisor: Greg Buzzard In General: - - Applied Math - - Dynamical Systems - - Mathematical Biology - - Cardiac Electrophysiology Abstract : An arrhythmia is any disturbance from the normal periodicity of the heart beat, and alternans is one type of arrhythmia which can be a precursor to potentially fatal conditions of the heart. Dynamical systems have the ability to describe cardiac action potentials and are thus an invaluable tool in the pursuit to understand cardiac electrical activity. We deveolped a two-variable model as a modification of the popular Fitzhugh-Nagumo and Mitchell-Schaeffer models for electrical activity in excitable cells. Our model captures the major components of cardiac behavior while allowing for an explicit analysis of the propagation of electrical impulses in cardiac tissue. We examine the existence and stability of such traveling waves. Further, we use techniques of singular perturbation theory to derive and analyze an equation describing the onset and development of alternans in cardiac tissue. Files: - - Slides (motivation and background) - - Poster Advertisement - - Poster L INKS Purdue University Program in Quantitative Physiology Purdue NSF Quantitative Physiology Scholars Wiki The Virtual Heart Scholarpedia: Cardiac Arrhythmias American Mathematical Society Purdue Mathematics Deptartment Purdue University