Mathematical Modeling of Heart Electrical Instabilities by Using Topology, Convex Analysis, Conceptual Spaces, Graph Theory

The graph theory, topology, convex analysis have been studied and applied to medicine, cardiology. Heart electrical instability has various causes. The di?erential diagnosis of it is based on qualitative and quantitative electrocardiogram (ECG) assessment. The purpose of this study was to formulate model, an algorithm for making diagnosis of heart electrical instability as oxymoron, fractal and anti-fractal, Moebius strip like processes by using discrete mathematics, graph theory, topology, convex analysis, multiple testing. We used algorithm for diagnosing heart electrical instability, which reduces to qualitative and quantitative analysis of ECG in standard, inverted, 3D (as rotation bodies of ECG's elements) forms; constructing graphs, including "Gift wrapping" algorithm; calculation distances between points, angles between graphs, and others; comparison of qualitative and quantitative characteristics of these graphs by selective multiple testing; formulation of the diagnostic conclusion. Characteristics of ECG by distance between points, perimeters, and angles of polygons of complexes allowed to determine peculiarities of electromagnetic picture, triggers and resonators of heart electrical instabilities. Thus, complex using of discrete mathematics, graph theory, topology, convex analysis, multiple testing allowed us to formulate an algorithm for making diagnosis of heart electrical instability as oxymoron, fractal and anti-fractal, Moebius strip like processes. Analysis of graphs as networks of node-waves with their ribs can be the basis for improving the quality of diagnosis and treatment the patients with heart rhythm and conduction disorders.