BMC Med Inform Decis Mak - Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems.


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CKGROUND: 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.METHODS: 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) Poincar? 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) Poincar? 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 Poincar? 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 Poincar? surface. Finally, the original time series graph, the colourised 3D Poincar? surface plot, and its projection as a colourised 2D contour map for each segment, are animated to create the full "D3-Map."RESULTS: We first exemplify the D3-Map method using the cardiac interbeat interval time series from a healthy subject during sleeping hours. The animations uncover complex dynamical changes, such as transitions between states, and the relative amount of time the system spends in each state. We also illustrate the utility of the method in detecting hidden temporal patterns in the heart rate dynamics of a patient with atrial fibrillation. The videos, as well as the source code, are made publicly available.CONCLUSIONS: Animations based on density delay maps provide a new way of visualising dynamical properties of complex systems not apparent in time series graphs or standard Poincar? plot representations. Trainees in a variety of fields may find the animations useful as illustrations of fundamental but challenging concepts, such as nonstationarity and multistability. For investigators, the method may facilitate data exploration.

Resumo Limpo

ckground physiolog signal cardiac interbeat interv exhibit complex fluctuat howev captur import dynam properti includ nonstationar may feasibl convent time seri graphic representationsmethod introduc simpletoimpl visualis method term dynam densiti delay map dmap techniqu provid anim represent system dynam method base general convent twodimension d poincar plot scatter plot data point xn time seri plot adjac one xn first divid origin time seri xn n n sequenc segment window next segment threedimension d poincar surfac plot xn xn hxnxn generat third dimens h repres relat frequenc occurr xnxn point d poincar surfac chromatis map relat frequenc h valu onto colour scheme also generat colouris d contour plot time seri segment use colourmap scheme d poincar surfac final origin time seri graph colouris d poincar surfac plot project colouris d contour map segment anim creat full dmapresult first exemplifi dmap method use cardiac interbeat interv time seri healthi subject sleep hour anim uncov complex dynam chang transit state relat amount time system spend state also illustr util method detect hidden tempor pattern heart rate dynam patient atrial fibril video well sourc code made public availableconclus anim base densiti delay map provid new way visualis dynam properti complex system appar time seri graph standard poincar plot represent traine varieti field may find anim use illustr fundament challeng concept nonstationar multist investig method may facilit data explor

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