Signatures of Subacute Potentially Catastrophic Illness in the ICU: Model Development and Validation.

OBJECTIVES: Patients in ICUs are susceptible to subacute potentially catastrophic illnesses such as respiratory failure, sepsis, and hemorrhage that present as severe derangements of vital signs. More subtle physiologic signatures may be present before clinical deterioration, when treatment might be more effective. We performed multivariate statistical analyses of bedside physiologic monitoring data to identify such early subclinical signatures of incipient life-threatening illness. DESIGN: We report a study of model development and validation of a retrospective observational cohort using resampling (Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis type 1b internal validation) and a study of model validation using separate data (type 2b internal/external validation). SETTING: University of Virginia Health System (Charlottesville), a tertiary-care, academic medical center. PATIENTS: Critically ill patients consecutively admitted between January 2009 and June 2015 to either the neonatal, surgical/trauma/burn, or medical ICUs with available physiologic monitoring data. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We analyzed 146 patient-years of vital sign and electrocardiography waveform time series from the bedside monitors of 9,232 ICU admissions. Calculations from 30-minute windows of the physiologic monitoring data were made every 15 minutes. Clinicians identified 1,206 episodes of respiratory failure leading to urgent unplanned intubation, sepsis, or hemorrhage leading to multi-unit transfusions from systematic individual chart reviews. Multivariate models to predict events up to 24 hours prior had internally validated C-statistics of 0.61-0.88. In adults, physiologic signatures of respiratory failure and hemorrhage were distinct from each other but externally consistent across ICUs. Sepsis, on the other hand, demonstrated less distinct and inconsistent signatures. Physiologic signatures of all neonatal illnesses were similar. CONCLUSIONS: Subacute potentially catastrophic illnesses in three diverse ICU populations have physiologic signatures that are detectable in the hours preceding clinical detection and intervention. Detection of such signatures can draw attention to patients at highest risk, potentially enabling earlier intervention and better outcomes.

Accurate automated apnea analysis in preterm infants.

OBJECTIVE: In 2006 the apnea of prematurity (AOP) consensus group identified inaccurate counting of apnea episodes as a major barrier to progress in AOP research. We compare nursing records of AOP to events detected by a clinically validated computer algorithm that detects apnea from standard bedside monitors. STUDY DESIGN: Waveform, vital sign, and alarm data were collected continuously from all very low-birth-weight infants admitted over a 25-month period, analyzed for central apnea, bradycardia, and desaturation (ABD) events, and compared with nursing documentation collected from charts. Our algorithm defined apnea as > 10 seconds if accompanied by bradycardia and desaturation. RESULTS: Of the 3,019 nurse-recorded events, only 68% had any algorithm-detected ABD event. Of the 5,275 algorithm-detected prolonged apnea events > 30 seconds, only 26% had nurse-recorded documentation within 1 hour. Monitor alarms sounded in only 74% of events of algorithm-detected prolonged apnea events > 10 seconds. There were 8,190,418 monitor alarms of any description throughout the neonatal intensive care unit during the 747 days analyzed, or one alarm every 2 to 3 minutes per nurse. CONCLUSION: An automated computer algorithm for continuous ABD quantitation is a far more reliable tool than the medical record to address the important research questions identified by the 2006 AOP consensus group.

A mathematical model of Cheyne-Stokes or periodic breathing.

Cheyne-Stokes Breathing is a periodic cycle of apnea followed by hyperventilation. A theory of this phenomenon is developed based on a minimal set of physiological assumptions. The rate of loss of CO2 from venous blood is proportional to the CO2 concentration in the lungs times the respiration rate; the respiration rate is a linear function of arterial CO2 concentration above a threshold, and zero below that threshold. A time delay between blood in lungs and respiratory response allows the system to go into oscillation. These assumptions lead to a single nonanalytic delay-differential equation containing only three parameters, which we call respiratory recovery coefficients, (α,ß,γ). A detailed study of the solutions to this equation is presented here. For ß below a first threshold, breathing becomes steady, and any disturbance recovers exponentially to the steady state (∼overdamped oscillator). Above the first threshold, breathing recovers to the steady state by decaying oscillations (∼underdamped oscillator). Above a second threshold, oscillations grow to reach a limit cycle, and when that cycle is sufficiently large, it represents the Cheyne-Stokes cycle of hyperventilation and apnea. Fourier analysis shows that the transition to growing oscillations is a forward or soft Hopf bifurcation. In the Cheyne-Stokes region (sufficiently large ß), the equation predicts the shapes of the curves representing the time-dependence of arterial CO2 and the respiration rate. From these shapes, we infer the values of the respiratory recovery coefficients for several groups of patients. With additional approximations, we infer the values of other physiological parameters, including cardiac output, CO2 chemosensitivity, and volume of blood between lungs and detectors.

Predictive monitoring for respiratory decompensation leading to urgent unplanned intubation in the neonatal intensive care unit.

BACKGROUND: Infants admitted to the neonatal intensive care unit (NICU), and especially those born with very low birth weight (VLBW; <1,500 g), are at risk for respiratory decompensation requiring endotracheal intubation and mechanical ventilation. Intubation and mechanical ventilation are associated with increased morbidity, particularly in urgent unplanned cases. METHODS: We tested the hypothesis that the systemic response associated with respiratory decompensation can be detected from physiological monitoring and that statistical models of bedside monitoring data can identify infants at increased risk of urgent unplanned intubation. We studied 287 VLBW infants consecutively admitted to our NICU and found 96 events in 51 patients, excluding intubations occurring within 12 h of a previous extubation. RESULTS: In order of importance in a multivariable statistical model, we found that the characteristics of reduced O(2) saturation, especially as heart rate was falling; increased heart rate correlation with respiratory rate; and the amount of apnea were all significant independent predictors. The predictive model, validated internally by bootstrap, had a receiver-operating characteristic area of 0.84 ± 0.04. CONCLUSION: We propose that predictive monitoring in the NICU for urgent unplanned intubation may improve outcomes by allowing clinicians to intervene noninvasively before intubation is required.

Anemia, apnea of prematurity, and blood transfusions.

OBJECTIVE: To compare the frequency and severity of apneic events in very low birth weight (VLBW) infants before and after blood transfusions using continuous electronic waveform analysis. STUDY DESIGN: We continuously collected waveform, heart rate, and oxygen saturation data from patients in all 45 neonatal intensive care unit beds at the University of Virginia for 120 weeks. Central apneas were detected using continuous computer processing of chest impedance, electrocardiographic, and oximetry signals. Apnea was defined as respiratory pauses of >10, >20, and >30 seconds when accompanied by bradycardia (<100 beats per minute) and hypoxemia (<80% oxyhemoglobin saturation as detected by pulse oximetry). Times of packed red blood cell transfusions were determined from bedside charts. Two cohorts were analyzed. In the transfusion cohort, waveforms were analyzed for 3 days before and after the transfusion for all VLBW infants who received a blood transfusion while also breathing spontaneously. Mean apnea rates for the previous 12 hours were quantified and differences for 12 hours before and after transfusion were compared. In the hematocrit cohort, 1453 hematocrit values from all VLBW infants admitted and breathing spontaneously during the time period were retrieved, and the association of hematocrit and apnea in the next 12 hours was tested using logistic regression. RESULTS: Sixty-seven infants had 110 blood transfusions during times when complete monitoring data were available. Transfusion was associated with fewer computer-detected apneic events (P < .01). Probability of future apnea occurring within 12 hours increased with decreasing hematocrit values (P < .001). CONCLUSIONS: Blood transfusions are associated with decreased apnea in VLBW infants, and apneas are less frequent at higher hematocrits.

Escape of trajectories from a vase-shaped cavity.

We consider the escape of ballistic trajectories from an open, vase-shaped cavity. Such a system serves as a model for microwaves escaping from a cavity or electrons escaping from a microjunction. Fixing the initial position of a particle and recording its escape time as a function of the initial launch direction, the resulting escape-time plot shows "epistrophic fractal" structure--repeated structure within structure at all levels of resolution with new features appearing in the fractal at longer time scales. By launching trajectories simultaneously in all directions (modeling an outgoing wave), a detector placed outside the cavity would measure a train of escaping pulses. We connect the structure of this chaotic pulse train with the fractal structure of the escape-time plot.

Stochastic modeling of central apnea events in preterm infants.

A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm-stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events-may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge.

Quantification of periodic breathing in premature infants.

Periodic breathing (PB), regular cycles of short apneic pauses and breaths, is common in newborn infants. To characterize normal and potentially pathologic PB, we used our automated apnea detection system and developed a novel method for quantifying PB. We identified a preterm infant who died of sudden infant death syndrome (SIDS) and who, on review of her breathing pattern while in the neonatal intensive care unit (NICU), had exaggerated PB.We analyzed the chest impedance signal for short apneic pauses and developed a wavelet transform method to identify repetitive 10-40 second cycles of apnea/breathing. Clinical validation was performed to distinguish PB from apnea clusters and determine the wavelet coefficient cutoff having optimum diagnostic utility. We applied this method to analyze the chest impedance signals throughout the entire NICU stays of all 70 infants born at 32 weeks' gestation admitted over a two-and-a-half year period. This group includes an infant who died of SIDS and her twin.For infants of 32 weeks' gestation, the fraction of time spent in PB peaks 7-14 d after birth at 6.5%. During that time the infant that died of SIDS spent 40% of each day in PB and her twin spent 15% of each day in PB.This wavelet transform method allows quantification of normal and potentially pathologic PB in NICU patients.

Very long apnea events in preterm infants.

Apnea is nearly universal among very low birth weight (VLBW) infants, and the associated bradycardia and desaturation may have detrimental consequences. We describe here very long (>60 s) central apnea events (VLAs) with bradycardia and desaturation, discovered using a computerized detection system applied to our database of over 100 infant years of electronic signals. Eighty-six VLAs occurred in 29 out of 335 VLBW infants. Eighteen of the 29 infants had a clinical event or condition possibly related to the VLA. Most VLAs occurred while infants were on nasal continuous positive airway pressure, supplemental oxygen, and caffeine. Apnea alarms on the bedside monitor activated in 66% of events, on average 28 s after cessation of breathing. Bradycardia alarms activated late, on average 64 s after cessation of breathing. Before VLAs oxygen saturation was unusually high, and during VLAs oxygen saturation and heart rate fell unusually slowly. We give measures of the relative severity of VLAs and theoretical calculations that describe the rate of decrease of oxygen saturation. A clinical conclusion is that very long apnea (VLA) events with bradycardia and desaturation are not rare. Apnea alarms failed to activate for about one-third of VLAs. It appears that neonatal intensive care unit (NICU) personnel respond quickly to bradycardia alarms but not consistently to apnea alarms. We speculate that more reliable apnea detection systems would improve patient safety in the NICU. A physiological conclusion is that the slow decrease of oxygen saturation is consistent with a physiological model based on assumed high values of initial oxygen saturation.

Topological analysis of chaotic transport through a ballistic atom pump.

We examine a system consisting of two reservoirs of particles connected by a channel. In the channel are two oscillating repulsive potential-energy barriers. It is known that such a system can transport particles from one reservoir to the other, even when the chemical potentials in the reservoirs are equal. We use computations and the theory of chaotic transport to study this system. Chaotic transport is described by passage around or through a heteroclinic tangle. Topological properties of the tangle are described using a generalization of homotopic lobe dynamics, which is a theory that gives some properties of intermediate-time behavior from properties of short-time behavior. We compare these predicted properties with direct computation of trajectories.

Matter, energy, and heat transfer in a classical ballistic atom pump.

A ballistic atom pump is a system containing two reservoirs of neutral atoms or molecules and a junction connecting them containing a localized time-varying potential. Atoms move through the pump as independent particles. Under certain conditions, these pumps can create net transport of atoms from one reservoir to the other. While such systems are sometimes called "quantum pumps," they are also models of classical chaotic transport, and their quantum behavior cannot be understood without study of the corresponding classical behavior. Here we examine classically such a pump's effect on energy and temperature in the reservoirs, in addition to net particle transport. We show that the changes in particle number, of energy in each reservoir, and of temperature in each reservoir vary in unexpected ways as the incident particle energy is varied.

Chaotic escape from an open vase-shaped cavity. II. Topological theory.

We present part II of a study of chaotic escape from an open two-dimensional vase-shaped cavity. A surface of section reveals that the chaotic dynamics is controlled by a homoclinic tangle, the union of stable and unstable manifolds attached to a hyperbolic fixed point. Furthermore, the surface of section rectifies escape-time graphs into sequences of escape segments; each sequence is called an epistrophe. Some of the escape segments (and therefore some of the epistrophes) are forced by the topology of the dynamics of the homoclinic tangle. These topologically forced structures can be predicted using the method called homotopic lobe dynamics (HLD). HLD takes a finite length of the unstable manifold and a judiciously altered topology and returns a set of symbolic dynamical equations that encode the folding and stretching of the unstable manifold. We present three applications of this method to three different lengths of the unstable manifold. Using each set of dynamical equations, we compute minimal sets of escape segments associated with the unstable manifold, and minimal sets associated with a burst of trajectories emanating from a point on the vase's boundary. The topological theory predicts most of the early escape segments that are found in numerical computations.

Chaotic escape from an open vase-shaped cavity. I. Numerical and experimental results.

We present part I in a two-part study of an open chaotic cavity shaped as a vase. The vase possesses an unstable periodic orbit in its neck. Trajectories passing through this orbit escape without return. For our analysis, we consider a family of trajectories launched from a point on the vase boundary. We imagine a vertical array of detectors past the unstable periodic orbit and, for each escaping trajectory, record the propagation time and the vertical detector position. We find that the escape time exhibits a complicated recursive structure. This recursive structure is explored in part I of our study. We present an approximation to the Helmholtz equation for waves escaping the vase. By choosing a set of detector points, we interpolate trajectories connecting the source to the different detector points. We use these interpolated classical trajectories to construct the solution to the wave equation at a detector point. Finally, we construct a plot of the detector position versus the escape time and compare this graph to the results of an experiment using classical ultrasound waves. We find that generally the classical trajectories organize the escaping ultrasound waves.

Breath-by-breath analysis of cardiorespiratory interaction for quantifying developmental maturity in premature infants.

In healthy neonates, connections between the heart and lungs through brain stem chemosensory pathways and the autonomic nervous system result in cardiorespiratory synchronization. This interdependence between cardiac and respiratory dynamics can be difficult to measure because of intermittent signal quality in intensive care settings and variability of heart and breathing rates. We employed a phase-based measure suggested by Schäfer and coworkers (Schäfer C, Rosenblum MG, Kurths J, Abel HH. Nature 392: 239-240, 1998) to obtain a breath-by-breath analysis of cardiorespiratory interaction. This measure of cardiorespiratory interaction does not distinguish between cardiac control of respiration associated with cardioventilatory coupling and respiratory influences on the heart rate associated with respiratory sinus arrhythmia. We calculated, in sliding 4-min windows, the probability density of heartbeats as a function of the concurrent phase of the respiratory cycle. Probability density functions whose Shannon entropy had a <0.1% chance of occurring from random numbers were classified as exhibiting interaction. In this way, we analyzed 18 infant-years of data from 1,202 patients in the Neonatal Intensive Care Unit at University of Virginia. We found evidence of interaction in 3.3 patient-years of data (18%). Cardiorespiratory interaction increased several-fold with postnatal development, but, surprisingly, the rate of increase was not affected by gestational age at birth. We find evidence for moderate correspondence between this measure of cardiorespiratory interaction and cardioventilatory coupling and no evidence for respiratory sinus arrhythmia, leading to the need for further investigation of the underlying mechanism. Such continuous measures of physiological interaction may serve to gauge developmental maturity in neonatal intensive care patients and prove useful in decisions about incipient illness and about hospital discharge.

A new algorithm for detecting central apnea in neonates.

Apnea of prematurity is an important and common clinical problem, and is often the rate-limiting process in NICU discharge. Accurate detection of episodes of clinically important neonatal apnea using existing chest impedance (CI) monitoring is a clinical imperative. The technique relies on changes in impedance as the lungs fill with air, a high impedance substance. A potential confounder, however, is blood coursing through the heart. Thus, the cardiac signal during apnea might be mistaken for breathing. We report here a new filter to remove the cardiac signal from the CI that employs a novel resampling technique optimally suited to remove the heart rate signal, allowing improved apnea detection. We also develop an apnea detection method that employs the CI after cardiac filtering. The method has been applied to a large database of physiological signals, and we prove that, compared to the presently used monitors, the new method gives substantial improvement in apnea detection.

Cardiovascular oscillations at the bedside: early diagnosis of neonatal sepsis using heart rate characteristics monitoring.

We have applied principles of statistical signal processing and nonlinear dynamics to analyze heart rate time series from premature newborn infants in order to assist in the early diagnosis of sepsis, a common and potentially deadly bacterial infection of the bloodstream. We began with the observation of reduced variability and transient decelerations in heart rate interval time series for hours up to days prior to clinical signs of illness. We find that measurements of standard deviation, sample asymmetry and sample entropy are highly related to imminent clinical illness. We developed multivariable statistical predictive models, and an interface to display the real-time results to clinicians. Using this approach, we have observed numerous cases in which incipient neonatal sepsis was diagnosed and treated without any clinical illness at all. This review focuses on the mathematical and statistical time series approaches used to detect these abnormal heart rate characteristics and present predictive monitoring information to the clinician.

Predictive monitoring for early detection of subacute potentially catastrophic illnesses in critical care.

We wish to save lives of patients admitted to ICUs. Their mortality is high enough based simply on the severity of the original injury or illness, but is further raised by events during their stay. We target those events that are subacute but potentially catastrophic, such as infection. Sepsis, for example, is a bacterial infection of the bloodstream, that is common in ICU patients and has a >25% risk of death. Logically, early detection and treatment with antibiotics should improve outcomes. Our fundamental precepts are (1) some potentially catastrophic medical and surgical illnesses have subclinical phases during which early diagnosis and treatment might have life-saving effects, (2) these phases are characterized by changes in the normal highly complex but highly adaptive regulation and interaction of the nervous system and other organs such as the heart and lungs, (3) teams of clinicians and quantitative scientists can work together to identify clinically important abnormalities of monitoring data, to develop algorithms that match the clinicians' eye in detecting abnormalities, and to undertake the clinical trials to test their impact on outcomes.

Periodic heart rate decelerations in premature infants.

The pacemaking system of the heart is complex; a healthy heart constantly integrates and responds to extracardiac signals, resulting in highly complex heart rate patterns with a great deal of variability. In the laboratory and in some pathological or age-related states, however, dynamics can show reduced complexity that is more readily described and modeled. Reduced heart rate complexity has both clinical and dynamical significance - it may provide warning of impending illness or clues about the dynamics of the heart's pacemaking system. In this paper, we describe simple and interesting heart rate dynamics that we have observed in premature human infants - reversible transitions to large-amplitude periodic oscillations - and we show that the appearance and disappearance of these periodic oscillations can be described by a simple mathematical model, a Hopf bifurcation.

Motion of an electron from a point source in parallel electric and magnetic fields.

Negative ions undergoing near-threshold photodetachment in a weak laser field provide an almost pointlike, isotropic source of low-energy electrons. External fields exert forces on the emitted coherent electron wave and direct its motion. Here, we examine the spatial distribution of photodetached electrons in uniform, parallel electric and magnetic fields. The interplay of the electric and magnetic forces leads to a surprising intricate shape of the refracted electron wave, and multiple interfering trajectories generate complex fringe patterns in the matter wave. The exact quantum solution is best understood in terms of the classical electron motion.