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


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

Atrial Fibrillation
Data Interpretation, Statistical
Chaos Theory
Pulse Rate

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