Dynamic Markers for Chaotic Motion in C. elegans.

We describe the locomotion of Caenorhabditis elegans (C. elegans) using nonlinear dynamics. C. elegans is a commonly studied model organism based on ease of maintenance and simple neurological structure. In contrast to traditional microscopic techniques, which require constraining motion to a 2D microscope slide, dynamic diffraction allows the observation of locomotion in 3D as a time series of the intensity at a single point in the diffraction pattern. The electric field at any point in the far-field diffraction pattern is the result of a superposition of the electric fields bending around the worm. As a result, key features of the motion can be recovered by analyzing the intensity time series. One can now apply modern nonlinear techniques; embedding and recurrence plots, providing valuable insight for visualizing and comparing data sets. We found significant markers of low-dimensional chaos. Next, we implemented a minimal biomimetic simulation of the central pattern generator of C. elegans with FitzHugh-Nagumo neurons, which exhibits undulatory oscillations similar to those of the real C. elegans. Finally, we briefly describe the construction of a biomimetic version of the Izquierdo and Beer robotic worm using Keener's implementation of the Nagumo et al. circuit.

Pacemaker-Based Cardiac Neuromodulation Therapy in Patients With Hypertension: A Pilot Study.

Background In prior unblinded studies, cardiac neuromodulation therapy (CNT) employing a sequence of variably timed short and longer atrioventricular intervals yielded sustained reductions of systolic blood pressure (SBP) in patients with hypertension. The effects of CNT on SBP were investigated in this double-blind randomized pilot study. Methods and Results Eligible patients had daytime ambulatory SBP (aSBP) ≥130 mm Hg and office SBP ≥140 mm Hg despite taking ≥1 antihypertensive medication, and an indication for a dual-chamber pacemaker. Patients underwent Moderato device implantation, which was programmed as a standard pacemaker during a 1-month run-in phase. Patients whose daytime aSBP was ≥125 mm Hg at the end of this period were randomized (1:1, double blind) to treatment (CNT) or control (CNT inactive). The primary efficacy end point was the between-group difference of the change in 24-hour aSBP at 6 months. Of 68 patients initially enrolled and who underwent implantation with the Moderato system, 47 met criteria for study continuation and were randomized (26 treatment, 21 control). The mean age was 74.0±8.7 years, 64% were men, left ventricular ejection fraction was 59.2%±5.7%, and aSBP averaged 141.0±10.8 mm Hg despite the use of 3.3±1.5 antihypertensive medications; 81% had isolated systolic hypertension. Six months after randomization, aSBP was 11.1±10.5 mm Hg (95% CI, -15.2 to -8.1 mm Hg) lower than prerandomization in the treatment group compared with 3.1±9.5 mm Hg (-7.4 to 1.2 mm Hg) lower in controls, yielding a net treatment effect of 8.1±10.1 mm Hg (-14.2 to -1.9 mm Hg) (P=0.012). There were no Moderato device- or CNT-related adverse events. Conclusions CNT significantly reduced 24-hour aSBP in patients with hypertension with a clinical indication for a pacemaker. The majority of patients had isolated systolic hypertension, a particularly difficult group of patients to treat. Registration URL: https://www.clinicaltrials.gov; Unique identifier: NCT02837445.

Chaotic markers in dynamic diffraction.

In a dynamic far-field diffraction experiment, we calculate the largest Lyapunov exponent of a time series obtained from the optical fluctuations in a dynamic diffraction pattern. The time series is used to characterize the locomotory predictability of an oversampled microscopic species. We use a live nematode, Caenorhabditis elegans, as a model organism to demonstrate our method. The time series is derived from the intensity at one point in the diffraction pattern. This single time series displays chaotic markers in the locomotion of the Caenorhabditis elegans by reconstructing the multidimensional phase space. The average largest Lyapunov exponent (base e) associated with the dynamic diffraction of 10 adult wildtype (N2) Caenorhabditis elegans is 1.27±0.03s-1.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

Fishing Quotas, Induced Allee Effect, and Fluctuation-Driven Extinction.

We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level). In the presence of environmental noise, fish population dynamics is similar to a random walk with (non-linear) drift. The expected survival time (first passage time to collapse) is shown to depend sensitively upon the amount of environmental noise and size of the 'safe zone' between the deterministic steady state population and the critical population level at which the system collapses; more precisely it is exponential in the cube of the size of the safe zone divided by the variance of the noise process. Similar scaling can be expected for more survival in more general systems with multiple steady states. Our calculations imply an amplification effect under which small increases in harvest yield large decreases in expected survival time, and one should be cautious in changes in harvesting, especially in fisheries with poor or limited data and fisheries affected by climate change.

Oregonator Scaling Motivated by the Showalter-Noyes Limit.

The Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. We investigate here a new scaling of the Oregonator model of BZ chemical kinetics and use this scaling to elucidate fundamental properties of BZ dynamics. In particular, the Showalter-Noyes criterion for oscillation, that the product [BrO3-][H+] exceeds a critical value, arises naturally as a subcritical Hopf bifurcation in this setting, as does the reduction to a two-variable model. We thus provide chemical explanations of the role of time scales in the BZ reaction.

Weaning of extracorporeal membrane oxygenation using continuous hemodynamic transesophageal echocardiography.

BACKGROUND: Venoarterial extracorporeal membrane oxygenation (VA ECMO) has been used for profound cardiogenic shock to bridge to decision, ventricular assist device(s) (VADs), or transplant. To assess ventricular function and volume status along with hemodynamics during ECMO weaning, we developed a standardized weaning protocol, guided by a miniaturized transesophageal echocardiography probe designed for continuous hemodynamic monitoring (hemodynamic transesophageal echocardiography [hTEE]). We reviewed our experience with this weaning protocol with hTEE guidance to assess if we could predict patient outcomes. METHODS: During the academic year of 2011, hTEE-guided ECMO weaning was performed in 21 patients on VA ECMO. Left and right ventricular function and volume status were assessed by continuous hTEE, while attempting to wean ECMO after a standardized protocol. The clinical outcomes, management, and positive predictive value of the device were investigated and analyzed for this cohort of patients. RESULTS: Of the 21 patients, 6 (29%) had left and right ventricular recovery and underwent optimal medical therapy or revascularization for underlying coronary artery disease; 7 (33%) had nonrecoverable left and right ventricular function; and 8 (38%) had right ventricular recovery without improvement of the left ventricular function. These 8 patients underwent left VAD placement; none subsequently developed profound right ventricular failure. The positive predictive value for ventricular recovery by hTEE was 100% using our standardized ECMO weaning protocol (95% confidence interval, 73%-100%). CONCLUSIONS: The hTEE-guided ECMO weaning protocol accurately predicted the ability to wean ECMO to decision. This protocol can be applied by cardiac intensivists as a part of standard bedside intensive care unit assessment.

Dynamics of human atrial cell models: restitution, memory, and intracellular calcium dynamics in single cells.

Mathematical models of cardiac cells have become important tools for investigating the electrophysiological properties and behavior of the heart. As the number of published models increases, it becomes more difficult to choose a model appropriate for the conditions to be studied, especially when multiple models describing the species and region of the heart of interest are available. In this paper, we will review and compare two detailed ionic models of human atrial myocytes, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models include the same transmembrane currents and are largely based on the same experimental data from human atrial cells, the two models exhibit vastly different properties, especially in their dynamical behavior, including restitution and memory effects. The CM produces pronounced rate adaptation of action potential duration (APD) with limited memory effects, while the NM exhibits strong rate dependence of resting membrane potential (RMP), limited APD restitution, and stronger memory, as well as delayed afterdepolarizations and auto-oscillatory behavior upon cessation of rapid pacing. Channel conductance modifications based on experimentally measured changes during atrial fibrillation modify rate adaptation and memory in both models, but do not change the primary rate-dependent properties of APD and RMP for the CM and NM, respectively. Two sets of proposed changes to the NM that yield a spike-and-dome action potential morphology qualitatively similar to the CM at slow pacing rates similarly do not change the underlying dynamics of the model. Moreover, interchanging the formulations of all transmembrane currents between the two models while leaving calcium handling and ionic concentrations intact indicates that the currents strongly influence memory and the rate adaptation of RMP, while intracellular calcium dynamics primarily determine APD rate adaptation. Our results suggest that differences in intracellular calcium handling between the two human atrial myocyte models are responsible for marked dynamical differences and may prevent reconciliation between the models by straightforward channel conductance modifications.

Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction.

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.

Controlled excitations of the Belousov-Zhabotinsky reaction: Experimental procedures.

The purpose of this research was to explore the unstirred, ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction as an experimental model for the response of excitable media to small perturbations (slightly larger than the threshold for excitations). Following Showalter et al. (Showalter, K.; Noyes, R. M.; Turner, H. J.Am. Chem. Soc. 1979, 101, 7463-69), we used a positively biased silver electrode to release silver ions into a BZ reaction mixture, removing bromide ions and causing an excitation if sufficient bromide was removed. We found (1) a scaling region in which the delay before activation increased linearly as the size of the perturbation decreased, qualitatively consistent with but not fully explained by the Oregonator of Field et al. (Field, R. J.; Körõs, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649-64); (2) evidence for a 10 s oligomerization time scale; and (3) that activations were always delayed until after the end of a pulse of current, with the delay essentially constant for sufficiently long pulses, an effect not seen in simple ODE models but consistent with the anomalously large current apparently required for activation (Showalter, K.; Noyes, R. M. J. Am. Chem. Soc. 1976, 98, 3730-31) and explainable by bromide transport. Overall, the BZ system appeared to be well-suited as an experimental prototype, despite its complexity.

Oxidation state of BZ reaction mixtures.

The unstirred, ferroin (Fe(phen)(3)2+)-catalyzed Belousov-Zhabotinsky (BZ) reaction1-4 is the prototype oscillatory chemical system. After an induction period of several minutes, one sees "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and a red, reduced state (low [Fe(phen)(3)3+]). The reaction medium appears red (reduced) during the induction phase, and the pacemaker sites generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Korös, and Noyes (FKN), a robust, reduced model which captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here, we show that including reaction R8 of the FKN mechanism, not incorporated in the original Oregonator, accounts for bromide release during the induction phase, thus producing the observed red oxidation state.

The relationship of fall school opening and emergency department asthma visits in a large metropolitan area.

BACKGROUND: Asthma morbidity is seasonal, with the fewest exacerbations occurring in summer and the most exacerbations in early fall. OBJECTIVE: To determine if the fall increase in pediatric asthma emergency department (ED) visits is related to the school year start. DESIGN: Time-series study of daily asthma ED visits taken from an administrative claims database for the years 1991 to 2002. SETTING: Eleven municipal hospitals in New York City, NY. Patients Emergency department visits with asthma as the primary diagnosis among children aged 2 to 4, 5 to 11, and 12 to 17 years and adults with asthma aged 22 to 45 years as comparative group. Main Outcome Measure Rate of asthma ED visits after the September school opening compared with before the opening, during a 60-day window of each year. The delayed effect of school opening was examined by the lagged school-opening indicator for lag 0 through 9 days. The model adjusted for factors that may influence morbidity. There were 86 731 ED visits within the study period. RESULTS: Asthma ED visits for children aged 5 to 11 years were significantly associated with school opening day, with the highest lagged rate ratio being 1.46 (95% confidence interval [CI], 1.29-1.65). For children aged 2 to 4 years, the highest rate ratio was 1.19 (95% CI, 1.06-1.35), and for children aged 12 to 17 years, the highest lagged rate ratio was 1.13 (95% CI, 0.98-1.31). The rise in adult ED visits following school opening was less substantial, with the highest lagged rate ratio being 1.07 (95% CI, 1.00-1.14). CONCLUSION: The start of the September school year was associated with increases in pediatric asthma ED visits, particularly among grade school children.

Spatiotemporal clustering and temporal order in the excitable BZ reaction.

The prototype experimental example of "spontaneous" pattern formation in an unstirred chemical medium is the oscillatory Belousov-Zhabotinsky (BZ) reaction: target patterns of outward-moving concentric rings are readily observed when the reaction is run in a thin layer in a Petri dish. In many experimental runs, new target centers appeared to form closer to pre-existing target centers than expected in a randomized model. Here we describe a simple direct test for the presence of temporal order in the spatiotemporal dynamics of target nucleation, and apply this test to detect significant temporal order in target formation in the ferroin-catalyzed BZ reaction. We also describe how mixing heterogeneity can generate temporal order, even in the absence of heterogeneous physical nucleating centers.

Age-related seasonal patterns of emergency department visits for acute asthma in an urban environment.

STUDY OBJECTIVE: Asthma morbidity is greater in younger patients. The reasons are not fully understood, although identifying demographic patterns of seasonality may help determine causes and potential prevention. The objective of this study is to determine the relationship between age and seasonal asthma periodicity in patients presenting to the emergency department (ED). METHODS: We conducted a retrospective study of ED visits from 1991 to 2000 in 11 municipal hospitals in New York City, with 911 receiving facilities. There were 673,141 patients who presented to the ED during the study period and had a primary diagnosis of acute asthma. RESULTS: Distinct seasonal patterns were observed, with the highest number of visits occurring in the fall and the fewest in the summer. Seasonal fluctuations of ED visits were highest in children aged 13 years or younger (coefficient of variation [CV] 37.8%; 95% confidence interval [CI] 37.5% to 38.1%), with a peak in CV occurring at approximately age 7 years (CV 43.3%; 95% CI 43.0% to 43.6%). Less variability was noted with increasing age, and the population aged 30 years and older appeared to be the least susceptible to seasonal influences (CV 11.7%; 95% CI 11.3% to 12.1%). Although the total number of asthma visits decreased by more than 30% from 1991 to 2000, the CVs for each year remained within a relatively narrow range of 24.2% to 30.5%. CONCLUSION: In an urban population, seasonal variability of asthma episodes requiring ED visits are closely linked to age, which may be important in understanding the causes of asthma and developing disease-management strategies for the prevention of asthma episodes.

Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs.

We describe a useful setting for interactive, real-time study of mathematical models of cardiac electrical activity, using implicit and explicit integration schemes implemented in JAVA. These programs are intended as a teaching aid for the study and understanding of general excitable media. Particularly for cardiac cell models and the ionic currents underlying their basic electrical dynamics. Within the programs, excitable media properties such as thresholds and refractoriness and their dependence on parameter values can be analyzed. In addition, the cardiac model applets allow the study of reentrant tachyarrhythmias using premature stimuli and conduction blocks to induce or to terminate reentrant waves of electrical activation in one and two dimensions. The role of some physiological parameters in the transition from tachycardia to fibrillation also can be analyzed by varying the maximum conductances of ion channels associated with a given model in real time during the simulations. These applets are available for download at http://arrhythmia.hofstra.edu or its mirror site http://stardec.ascc.neu.edu/~fenton.

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity.

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.