Jan 21, 2014

Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems

BMC Medical Informatics and Decision Making
Anton BurykinAry L Goldberger

Abstract

Physiologic signals, such as cardiac interbeat intervals, exhibit complex fluctuations. However, capturing important dynamical properties, including nonstationarities may not be feasible from conventional time series graphical representations. We introduce a simple-to-implement visualisation method, termed dynamical density delay mapping ("D3-Map" technique) that provides an animated representation of a system's dynamics. The method is based on a generalization of conventional two-dimensional (2D) Poincaré plots, which are scatter plots where each data point, x(n), in a time series is plotted against the adjacent one, x(n + 1). First, we divide the original time series, x(n) (n = 1,…, N), into a sequence of segments (windows). Next, for each segment, a three-dimensional (3D) Poincaré surface plot of x(n), x(n + 1), h[x(n),x(n + 1)] is generated, in which the third dimension, h, represents the relative frequency of occurrence of each (x(n),x(n + 1)) point. This 3D Poincaré surface is then chromatised by mapping the relative frequency h values onto a colour scheme. We also generate a colourised 2D contour plot from each time series segment using the same colourmap scheme as for the 3D Poincaré surface. Finally, the original time ...Continue Reading

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Mentioned in this Paper

Fluctuation
Atrial Fibrillation
Data Interpretation, Statistical
Chaos Theory
Pulse Rate

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