2015英特尔ISEF获奖作品摘要 数学 Intel Finalist Abstract Mathematics

获奖作品基本信息

年份	2015
学科	数学 Mathematics
国家/州	United States of America

获奖作品名称

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

获奖作品摘要

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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高中生科研学术活动 英特尔 Intel ISEF 简介

英特尔国际科学与工程大奖赛，简称 "ISEF"，由美国 Society for Science and the Public（科学和公共服务协会）主办，英特尔公司冠名赞助，是全球规模最大、等级最高的中学生的科研科创赛事。ISEF 的学术活动学科包括了所有数学、自然科学、工程的全部领域和部分社会科学。ISEF 素有全球青少年科学学术活动的“世界杯”之美誉，旨在鼓励学生团队协作，开拓创新，长期专一深入地研究自己感兴趣的课题。

学科简介：数学 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.