Scaling law for the transient behavior of type-II neuron models

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $\tau$ near but below the repetitive firing critical current, $\tau \simeq C (I_c-I)^{-\Delta}$. For both the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent is independent of the numerical integration time step and that both systems belong to the same universality class, with $\Delta = 1/2$. For appropriately chosen parameters, the FitzHugh-Nagumo model presents the same generic transient behavior, but the critical region is significantly smaller. We propose an experiment that may reveal nontrivial critical exponents in the squid axon.Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev.

Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators

We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system of differential equations. This avoids uncertainty about the impact of artificial boundary conditions and discretization in time. Stability results also follow from the integral version. Stable kinks have a monotone leading edge and move with a velocity larger than a critical value which depends on the damping strength.Comment: 11 figure

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally

Heat and moisture exchangers (HMEs) and heated humidifiers (HHs) in adult critically ill patients: a systematic review, meta-analysis and meta-regression of randomized controlled trials

The aims of this systematic review and meta-analysis of randomized controlled trials are to evaluate the effects of active heated humidifiers (HHs) and moisture exchangers (HMEs) in preventing artificial airway occlusion and pneumonia, and on mortality in adult critically ill patients. In addition, we planned to perform a meta-regression analysis to evaluate the relationship between the incidence of artificial airway occlusion, pneumonia and mortality and clinical features of adult critically ill patients

Factors influencing physical functional status in intensive care unit survivors two years after discharge

BACKGROUND: Studies suggest that in patients admitted to intensive care units (ICU), physical functional status (PFS) improves over time, but does not return to the same level as before ICU admission. The goal of this study was to assess physical functional status two years after discharge from an ICU and to determine factors influencing physical status in this population. METHODS: The study reviewed all patients admitted to two non-trauma ICUs during a one-year period and included patients with age ≥ 18 yrs, ICU stay ≥ 24 h, and who were alive 24 months after ICU discharge. To assess PFS, Karnofsky Performance Status Scale scores and Lawton-Instrumental Activities of Daily Living (IADL) scores at ICU admission (K-ICU and L-ICU) were compared to the scores at the end of 24 months (K-24mo and L-24mo). Data at 24 months were obtained through telephone interviews. RESULTS: A total of 1,216 patients were eligible for the study. Twenty-four months after ICU discharge, 499 (41.6%) were alive, agreed to answer the interview, and had all hospital data available. PFS (K-ICU: 86.6 ± 13.8 vs. K-24mo: 77.1 ± 19.6, p < 0.001) and IADL (L-ICU: 27.0 ± 11.7 vs. L-24mo: 22.5 ± 11.5, p < 0.001) declined in patients with medical and unplanned surgical admissions. Most strikingly, the level of dependency increased in neurological patients (K-ICU: 86 ± 12 vs. K-24mo: 64 ± 21, relative risk [RR] 2.6, 95% CI, 1.8–3.6, p < 0.001) and trauma patients (K-ICU: 99 ± 2 vs. K-24mo: 83 ± 21, RR 2.7, 95% CI, 1.6–4.6, p < 0.001). The largest reduction in the ability to perform ADL occurred in neurological patients (L-ICU: 27 ± 7 vs. L-24mo: 15 ± 12, RR 3.3, 95% CI, 2.3–4.6 p < 0.001), trauma patients (L-ICU: 32 ± 0 vs. L-24mo: 25 ± 11, RR 2.8, 95% CI, 1.5–5.1, p < 0.001), patients aged ≥ 65 years (RR 1.4, 95% CI, 1.07–1.86, p = 0.01) and those who received mechanical ventilation for ≥ 8 days (RR 1.48, 95% CI, 1.02–2.15, p = 0.03). CONCLUSIONS: Twenty-four months after ICU discharge, PFS was significantly poorer in patients with neurological injury, trauma, age ≥ 65 tears, and mechanical ventilation ≥ 8 days. Future studies should focus on the relationship between PFS and health-related quality of life in this population

Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations (survey)

Analysis and Stochastic