2015英特爾ISEF獲獎作品摘要 數學 Intel Finalist Abstract Mathematics

獲獎作品基本信息

年份	2015
學科	數學 Mathematics
國家/州	United States of America

獲獎作品名稱

Mathematical Modeling and Simulation of Cardiac Tissue Electrophysiology: Effect of Cardiac Deformation on Action Potential Duration

獲獎作品摘要

The purpose of this project was to determine the effect of heart tissue deformation on cardiac action potential duration (APD).? The hypothesis was that deformation of the heart tissue would cause the APD to increase. The levels of the independent variable were no deformation (control), and 1 to 5% stretch and APD was the dependent variable.

A mathematical model calculating the variation of transmembrane potential during the heartbeat cycle was developed by solving the system of cardiac reaction-diffusion partial differential equations. A computer program in the C language solving the system of partial differential equations, using the forward Euler for time discretization, and center-difference methods for spatial discretization was created. The program calculated ion currents, stretch currents, and diffusion components for each node at every integration time step.

The 1.05 deformation yielded the shortest APD while no deformation yielded the longest. The regression r-values were high for all deformation levels. Regression t-tests indicated that the difference in data between deformations and control was significant.

The model was extended to study the effects of periodic deformation on spiral wave dynamics and APD using the S1-S2 stimulation protocol. A tip-tracking algorithm to locate points of phase singularities was developed to analyze periodic deformation amplitude and frequency parameters. An increase in amplitude and frequency of the deformation increased the chaos of the spiral waves and the abnormality of the heartbeat.

The data collected does not support the hypothesis. This analysis could be extended to study the breaking and meandering of spiral waves.

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高中生科研學術活動 英特爾 Intel ISEF 簡介

英特爾國際科學與工程大獎賽，簡稱 "ISEF"，由美國 Society for Science and the Public（科學和公共服務協會）主辦，英特爾公司冠名贊助，是全球規模最大、等級最高的中學生的科研科創賽事。ISEF 的學術活動學科包括了所有數學、自然科學、工程的全部領域和部分社會科學。ISEF 素有全球青少年科學學術活動的“世界杯”之美譽，旨在鼓勵學生團隊協作，開拓創新，長期專一深入地研究自己感興趣的課題。

學科簡介：數學 Mathematics

The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. The deductive study of numbers, geometry, and various abstract constructs, or structures.

Subcategories:

Algebra (ALB): The study of algebraic operations and/or relations and the structures which arise from them. An example is given by (systems of) equations which involve polynomial functions of one or more variables. Analysis (ANL): The study of infinitesimal processes in mathematics, typically involving the concept of a limit. This begins with differential and integral calculus, for functions of one or several variables, and includes differential equations.

Combinatorics, Graph Theory, and Game Theory (CGG): The study of combinatorial structures in mathematics, such as finite sets, graphs, and games, often with a view toward classification and/or enumeration. Geometry and Topology (GEO): The study of the shape, size, and other properties of figures and spaces. Includes such subjects as Euclidean geometry, non-Euclidean geometries (spherical, hyperbolic, Riemannian, Lorentzian), and knot theory (classification of knots in 3-space). Number

Theory (NUM): The study of the arithmetic properties of integers and related topics such as cryptography. Probability and Statistics (PRO): Mathematical study of random phenomena and the study of statistical tools used to analyze and interpret data. Other (OTH): Studies that cannot be assigned to one of the above subcategories. If the project involves multiple subcategories, the principal subcategory should be chosen instead of Other.