Topological and Geometric Investigations of Electrocardiogram

Abstract

Electrocardiogram abbreviated as ecg is a test that measures the electrical activity of the heartbeat[5]. It is crucial to diagnose Arrhythmia. Theres an huge advantage no pain or risk associated with having an ecg. But, there is an certain ambiguity of diagnosis with looking at ecg. In order to establish quantitative diagnostic criteria, We approach to it using topological and geometric ways. Given that ECG is periodic, we embed ECG into three dimensional space taking some procedure. Then, we define topological and geometric invariant of ECG, namely curvature and linking number. Previous researches in topological data analysis mainly focused on computing homology groups. As far as I know, It is the first trial to use linking numbers to analyze data. Curvatures are computed by definitions. Linking numbers are computed by stable formula. Three diseases and normal case are considered, Atrial fibrillation(AFIB),Premature atrial contractions(PAC), Sinus arrhythmia(SA) and Normal sinus rhythm(S1). We observe how these invariant classify heart diseases.

이 논문에서는 심장병 진단에 수치적 기준을 제시하기 위해 수학적인 방법을사용한다. 위상수학적 개념인 연환수와 기하학적 개념인 곡률을 심전도의 불변량으로 정의한다. 주기적인 형태를 보이는 심전도의 특성을 고려하여 삼차원에 임베딩한다. 임베딩된 심전도는 그 특성 때문에 고리 모양을 보인다. 이 고리들의 연환수와 곡률을 계산하여 각 질병이 어떤 특성을 갖는지 분류한다.