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

Background. 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), hx(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\'e 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\'e surface. Finally, the original time series graph, the colourised 3D Poincar\'e 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\'e 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

Generating Signals with Multiscale Time Irreversibility: The Asymmetric Weierstrass Function

Time irreversibility (asymmetry with respect to time reversal) is an important property of many time series derived from processes in nature. Some time series (e.g., healthy heart rate dynamics) demonstrate even more complex, multiscale irreversibility, such that not only the original but also coarse-grained time series are asymmetric over a wide range of scales. Several indices to quantify multiscale asymmetry have been introduced. However, there has been no simple generator of model time series with ' 'tunable' ' multiscale asymmetry to test such indices. We introduce an asymmetric Weierstrass function W A (constructed from asymmetric sawtooth functions instead of cosine waves) that can be used to construct time series with any given value of the multiscale asymmetry. We show that multiscale asymmetry appears to be independent of other multiscale complexity indices, such as fractal dimension and multiscale entropy. We further generalize the concept of multiscale asymmetry by introducing time-dependent (local) multiscale asymmetry and provide examples of such time series. The W A function combines two essential features of complex fluctuations, namely fractality (self-similarity) and irreversibility (multiscale time asymmetry); moreover, each of these features can be tuned independently. The proposed family of functions can be used to compare and refine multiscale measures of time series asymmetry

Multiscale Poincaré plots for visualizing the structure of heartbeat time series

Background: Poincaré delay maps are widely used in the analysis of cardiac interbeat interval (RR) dynamics. To facilitate visualization of the structure of these time series, we introduce multiscale Poincaré (MSP) plots. Methods: Starting with the original RR time series, the method employs a coarse-graining procedure to create a family of time series, each of which represents the system’s dynamics in a different time scale. Next, the Poincaré plots are constructed for the original and the coarse-grained time series. Finally, as an optional adjunct, color can be added to each point to represent its normalized frequency. Results: We illustrate the MSP method on simulated Gaussian white and 1/f noise time series. The MSP plots of 1/f noise time series reveal relative conservation of the phase space area over multiple time scales, while those of white noise show a marked reduction in area. We also show how MSP plots can be used to illustrate the loss of complexity when heartbeat time series from healthy subjects are compared with those from patients with chronic (congestive) heart failure syndrome or with atrial fibrillation. Conclusions: This generalized multiscale approach to Poincaré plots may be useful in visualizing other types of time series

What Really Prevents Proton Transport through Aquaporin? Charge Self-Energy versus Proton Wire Proposals

The nature of the control of water/proton selectivity in biological channels is a problem of a fundamental importance. Most studies of this issue have proposed that an interference with the orientational requirements of the so-called proton wire is the source of selectivity. The elucidation of the structures of aquaporins, which have evolved to prevent proton transfer (PT), provided a clear benchmark for exploring the selectivity problem. Previous simulations of this system have not examined, however, the actual issue of PT, but only considered the much simpler task of the transfer of water molecules. Here we take aquaporin as a benchmark and quantify the origin of the water/proton selectivity in this and related systems. This is done by evaluating in a consistent way the free energy profile for transferring a proton along the channel and relating this profile to the relevant PT rate constants. It is found that the water/proton selectivity is controlled by the change in solvation free energy upon moving the charged proton from water to the channel. The reason for the focus on the elegant concept of the proton wire and the related Grotthuss-type mechanism is also considered. It is concluded that these mechanisms are clearly important in cases with flat free energy surfaces (e.g., in bulk water, in gas phase water chains, and in infinitely long channels). However, in cases of biological channels, the actual PT mechanism is much less important than the energetics of transferring the proton charge from water to different regions in the channels

On the origin of the electrostatic barrier for proton transport in aquaporin

AbstractThe nature of the electrostatic barrier for proton transport in aquaporins is analyzed by semimacroscopic and microscopic models. It is found that the barrier is associated with the loss of the generalized solvation energy upon moving from the bulk solvent to the center of the channel. It is clarified that our solvation concept includes the effect of the protein polar groups and ionized residues. The nature of the contributions to the solvation barrier is examined by using the linear response approximation. It is found that the residues in the NPA region contribute much less than what would be deduced from calculations that do not consider the protein reorganization. It is clarified that the contributions of different structural or electrostatic elements to the solvation barrier can be established by removing these elements and examining the corresponding effect on the barrier height. Using this definition and “mutating” the NPA residues to their non-polar analogues establishes that these residues do not provide the major contribution to the solvation barrier

Toward optimal display of physiologic status in critical care: I. Recreating bedside displays from archived physiologic data

BACKGROUND: Physiologic data display is essential to decision making in critical care. Current displays echo first-generation hemodynamic monitors dating to the 1970s and have not kept pace with new insights into physiology or the needs of clinicians who must make progressively more complex decisions about their patients. The effectiveness of any redesign must be tested before deployment. Tools that compare current displays with novel presentations of processed physiologic data are required. Regenerating conventional physiologic displays from archived physiologic data is an essential first step. OBJECTIVES: The purposes of the study were to (1) describe the SSSI (single sensor single indicator) paradigm that is currently used for physiologic signal displays, (2) identify and discuss possible extensions and enhancements of the SSSI paradigm, and (3) develop a general approach and a software prototype to construct such "extended SSSI displays" from raw data. RESULTS: We present Multi Wave Animator (MWA) framework-a set of open source MATLAB (MathWorks, Inc., Natick, MA, USA) scripts aimed to create dynamic visualizations (eg, video files in AVI format) of patient vital signs recorded from bedside (intensive care unit or operating room) monitors. Multi Wave Animator creates animations in which vital signs are displayed to mimic their appearance on current bedside monitors. The source code of MWA is freely available online together with a detailed tutorial and sample data sets

Postreperfusion cardiac arrest and resuscitation during orthotopic liver transplantation: dynamic visualization and analysis of physiologic recordings

We recently reported on the Multi Wave Animator (MWA), a novel open-source tool with capability of recreating continuous physiologic signals from archived numerical data and presenting them as they appeared on the patient monitor. In this report, we demonstrate for the first time the power of this technology in a real clinical case, an intraoperative cardiopulmonary arrest following reperfusion of a liver transplant graft. Using the MWA, we animated hemodynamic and ventilator data acquired before, during, and after cardiac arrest and resuscitation. This report is accompanied by an online video that shows the most critical phases of the cardiac arrest and resuscitation and provides a basis for analysis and discussion. This video is extracted from a 33-min, uninterrupted video of cardiac arrest and resuscitation, which is available online. The unique strength of MWA, its capability to accurately present discrete and continuous data in a format familiar to clinicians, allowed us this rare glimpse into events leading to an intraoperative cardiac arrest. Because of the ability to recreate and replay clinical events, this tool should be of great interest to medical educators, researchers, and clinicians involved in quality assurance and patient safety

Plasticity of the systemic inflammatory response to acute infection during critical illness: development of the riboleukogram.

Diagnosis of acute infection in the critically ill remains a challenge. We hypothesized that circulating leukocyte transcriptional profiles can be used to monitor the host response to and recovery from infection complicating critical illness.A translational research approach was employed. Fifteen mice underwent intratracheal injections of live P. aeruginosa, P. aeruginosa endotoxin, live S. pneumoniae, or normal saline. At 24 hours after injury, GeneChip microarray analysis of circulating buffy coat RNA identified 219 genes that distinguished between the pulmonary insults and differences in 7-day mortality. Similarly, buffy coat microarray expression profiles were generated from 27 mechanically ventilated patients every two days for up to three weeks. Significant heterogeneity of VAP microarray profiles was observed secondary to patient ethnicity, age, and gender, yet 85 genes were identified with consistent changes in abundance during the seven days bracketing the diagnosis of VAP. Principal components analysis of these 85 genes appeared to differentiate between the responses of subjects who did versus those who did not develop VAP, as defined by a general trajectory (riboleukogram) for the onset and resolution of VAP. As patients recovered from critical illness complicated by acute infection, the riboleukograms converged, consistent with an immune attractor.Here we present the culmination of a mouse pneumonia study, demonstrating for the first time that disease trajectories derived from microarray expression profiles can be used to quantitatively track the clinical course of acute disease and identify a state of immune recovery. These data suggest that the onset of an infection-specific transcriptional program may precede the clinical diagnosis of pneumonia in patients. Moreover, riboleukograms may help explain variance in the host response due to differences in ethnic background, gender, and pathogen. Prospective clinical trials are indicated to validate our results and test the clinical utility of riboleukograms