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.

Remembrance of time series past: simple chromatic method for visualizing trends in biomedical signals.

Analysis of biomedical time series plays an essential role in clinical management and basic investigation. However, conventional monitors streaming data in real-time show only the most recent values, not referenced to past dynamics. We describe a chromatic approach to bring the 'memory' of the physiologic system's past behavior into the current display window.The method employs the estimated probability density function of a time series segment to colorize subsequent data points.For illustrative purposes, we selected open-access recordings of continuous: (1) fetal heart rate during the pre-partum period, and (2) heart rate and systemic blood pressure from a critical care patient during a spontaneous breathing trial. The colorized outputs highlight changes from the 'baseline' reference state, the latter defined as the mode value assumed by the signal, i.e. the maximum of its probability density function.A colorization method may facilitate the recognition of relevant features of time series, especially shifts in baseline dynamics and other trends (including transient and longer-term deviation from baseline values) which may not be as readily noticed using traditional displays. This method may be applicable in clinical monitoring (real-time or off-line) and in research settings. Prospective studies are needed to assess the utility of this approach.

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) 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 series graph, the colourised 3D Poincaré 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 Poincaré 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.

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.

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.

Using "off-the-shelf" tools for terabyte-scale waveform recording in intensive care: computer system design, database description and lessons learned.

Until now, the creation of massive (long-term and multichannel) waveform databases in intensive care required an interdisciplinary team of clinicians, engineers and informaticians and, in most cases, also design-specific software and hardware development. Recently, several commercial software tools for waveform acquisition became available. Although commercial products and even turnkey systems are now being marketed as simple and effective, the performance of those solutions is not known. The additional expense upfront may be worthwhile if commercial software can eliminate the need for custom software and hardware systems and the associated investment in teams and development. We report the development of a computer system for long-term large-scale recording and storage of multichannel physiologic signals that was built using commercial solutions (software and hardware) and existing hospital IT infrastructure. Both numeric (1 Hz) and waveform (62.5-500 Hz) data were captured from 24 SICU bedside monitors simultaneously and stored in a file-based vital sign data bank (VSDB) during one-year period (total DB size is 4.21TB). In total, vital signs were recorded from 1,175 critically ill patients. Up to six ECG leads, all other monitored waveforms, and all monitored numeric data were recorded in most of the cases. We describe the details of building blocks of our system, provide description of three datasets exported from our VSDB and compare the contents of our VSDB with other available waveform databases. Finally, we summarize lessons learned during recording, storage, and pre-processing of physiologic signals.

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.

Predicting clinical physiology: a Markov chain model of heart rate recovery after spontaneous breathing trials in mechanically ventilated patients.

Analysis of heart rate (HR) dynamics before, during, and after a physiologic stress has clinical importance. For example, the celerity of heart rate recovery (HRR) after a cardiac stress test (eg, treadmill exercise test) has been shown to be an independent predictor of all-cause mortality. Heart rate dynamics are modulated, in part, by the autonomic nervous system. These dynamics are commonly abstracted using metrics of heart rate variability (HRV), which are known to be sensitive to the influence of the autonomic nervous system on HR. The patient-specific modulators of HR should be reflected both in the response to stress as well as in the recovery from stress. We therefore hypothesized that the patient-specific HR response to stress could be used to predict the HRR after the stress. We devised a Markov chain model to predict the poststress HRR dynamics using the parameters (transition matrix) calculated from HR data during the stress. The model correctly predicts the exponential shape of poststress HRR. This model features a simple analytical relationship linking poststress HRR time constant (T(off)) with a standard measure of HRV, namely the correlation coefficient of the Poincaré plot (first return map) of the HR recorded during the stress. A corresponding relationship exists between the time constant (T(on)) of R-R interval decrease at the onset of stress and the correlation coefficient of the Poincaré plot of prestress R-R intervals. Consequently, the model can be used for the prediction of poststress HRR using the HRV measured during the stress. This direct relationship between the event-to-event microscopic fluctuations (HRV) during the stress and the macroscopic response (HRR) after the stress terminates can be interpreted as an instance of a fluctuation-dissipation relationship. We have thus applied the fluctuation-dissipation theorem to the analysis of heart rate dynamics. The approach is specific neither to cardiac physiology nor to transitions between mechanical and free ventilation as a specific stress. It may therefore have wider applicability to physiologic systems subject to modest stresses.

Using systems biology to simplify complex disease: immune cartography.

What if there was a rapid, inexpensive, and accurate blood diagnostic that could determine which patients were infected, identify the organism(s) responsible, and identify patients who were not responding to therapy? We hypothesized that systems analysis of the transcriptional activity of circulating immune effector cells could be used to identify conserved elements in the host response to systemic inflammation, and furthermore, to discriminate between sterile and infectious etiologies. We review herein a validated, systems biology approach demonstrating that 1) abdominal and pulmonary sepsis diagnoses can be made in mouse models using microarray (RNA) data from circulating blood, 2) blood microarray data can be used to differentiate between the host response to Gram-negative and Gram-positive pneumonia, 3) the endotoxin response of normal human volunteers can be mapped at the level of gene expression, and 4) a similar strategy can be used in the critically ill to follow septic patients and quantitatively determine immune recovery. These findings provide the foundation of immune cartography and demonstrate the potential of this approach for rapidly diagnosing sepsis and identifying pathogens. Further, our data suggest a new approach to determine how specific pathogens perturb the physiology of circulating leukocytes in a cell-specific manner. Large, prospective clinical trails are needed to validate the clinical utility of leukocyte RNA diagnostics (e.g., the riboleukogram).

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

BACKGROUND: 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. METHODOLOGY/PRINCIPAL FINDINGS: 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. CONCLUSIONS/SIGNIFICANCE: 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.

Realistic simulations of proton transport along the gramicidin channel: demonstrating the importance of solvation effects.

The nature of proton transduction (PTR) through a file of water molecules, along the gramicidin A (gA) channel, has long been considered as being highly relevant to PTR in biological systems. Previous attempts to model this process implied that the so-called Grotthuss mechanism and the corresponding orientation of the water file plays a major role. The present work reexamines the PTR in gA by combining a fully microscopic empirical valence bond (EVB) model and a recently developed simplified EVB-based model with Langevin dynamics (LD) simulations. The full model is used first to evaluate the free energy profile for a stepwise PTR process. The corresponding results are then used to construct the effective potential of the simplified EVB. This later model is then used in Langevin dynamics simulations, taking into account the correct physics of possible concerted motions and the effect of the solvent reorganization. The simulations reproduce the observed experimental trend and lead to a picture that is quite different from that assumed previously. It is found that the PTR in gA is controlled by the change in solvation energy of the transferred proton along the channel axis. Although the time dependent electrostatic fluctuations of the channel and water dipoles play their usual role in modulating the proton-transfer process (Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 444), the PTR rate is mainly determined by the free energy profile. Furthermore, the energetics of the reorientation of the unprotonated water file do not appear to provide a consistent way of assessing the activation barrier for the PTR process. It seems to us that in the case of gA, and probably other systems with significant electrostatic barriers for the transfer of the proton charge, the PTR rate is controlled by the electrostatic barrier. This finding has clear consequences with regards to PTR processes in biological systems.

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

The 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.

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.

Exploring the origin of the ion selectivity of the KcsA potassium channel.

The availability of structural information about biological ion channels provides an opportunity to gain a detailed understanding of the control of ion selectivity by biological systems. However, accomplishing this task by computer simulation approaches is very challenging. First, although the activation barriers for ion transport can be evaluated by microscopic simulations, it is hard to obtain accurate results by such approaches. Second, the selectivity is related to the actual ion current and not directly to the individual activation barriers. Thus, it is essential to simulate the ion currents and this cannot be accomplished at present by microscopic MD approaches. In order to address this challenge, we developed and refined an approach capable of evaluating ion current while still reflecting the realistic features of the given channel. Our method involves generation of semimacroscopic free energy surfaces for the channel/ions system and Brownian dynamics (BD) simulations of the corresponding ion current. In contrast to most alternative macroscopic models, our approach is able to reproduce the difference between the free energy surfaces of different ions and thus to address the selectivity problem. Our method is used in a study of the selectivity of the KcsA channel toward the K+ and Na+ ions. The BD simulations with the calculated free energy profiles produce an appreciable selectivity. To the best of our knowledge, this is the first time that the trend in the selectivity in the ion current is produced by a computer simulation approach. Nevertheless, the calculated selectivity is still smaller than its experimental estimate. Recognizing that the calculated profiles are not perfect, we examine how changes in these profiles can account for the observed selectivity. It is found that the origin of the selectivity is more complex than generally assumed. The observed selectivity can be reproduced by increasing the barrier at the exit and the entrance of the selectivity filter, but the necessary changes in the barrier approach the limit of the error in the PDLD/S-LRA calculations. Other options that can increase the selectivity are also considered, including the difference between the Na+...Na+ and K+...K+ interaction. However, this interesting effect does not appear to lead to a major difference in selectivity since the Na+ ions at the limit of strong interaction tend to move in a less concerted way than the K+ ions. Changes in the relative binding energies at the different binding sites are also not so effective in changing the selectivity. Finally, it is pointed out that using the calculated profiles as a starting point and forcing the model to satisfy different experimentally based constraints, should eventually provide more detailed understanding of the different complex factors involved in ion selectivity of biological channels.