Dynamical instability determines the effect of ongoing noise on neural firing.
ABSTRACT: At low stimulation rates, electrically stimulated auditory nerve fibers typically fire regularly, in lock-step to the applied stimulus. At high stimulation rates, however, these same fibers fire irregularly. Firing irregularity has been attributed to the random opening and closing of voltage-gated sodium channels at the spike generation site. We demonstrate, however, that the nonlinear dynamics of neural excitation and refractoriness embodied in the FitzHugh-Nagumo (FN) model produce realistic firing irregularity at high stimulus rates, even in the complete absence of ongoing physiological noise. Indeed, we show that ongoing noise can actually regularize the response at low discharge rates. The degree of stimulus-dependent irregularity is determined not so much by the level of ongoing physiological noise as by the dynamical instability. Our work suggests that the dynamical instability, quantified by the Lyapunov exponent, controls neural sensitivity to input signals and to physiological noise, as well the amount of mutual desynchronization between similarly stimulated fibers. This instability, quantified by the value of the Lyapunov exponent, may play a critical role in determining modulation sensitivity and dynamic range in cochlear implants.
Project description:The response of the auditory nerve to electrical stimulation is highly sensitive to small modulations (<0.5%). This report demonstrates that dynamical instability (i.e., a positive Lyapunov exponent) can account for this sensitivity in a modified FitzHugh-Nagumo model of spike generation, so long as the input noise is not too large. This finding suggests both that spike generator instability is necessary to account for auditory nerve sensitivity and that the amplitude of physiological noise, such as that produced by the random behavior of voltage-gated sodium channels, is small. Based on these results with direct electrical stimulation, it is hypothesized that spike generator instability may be the mechanism that reconciles high sensitivity with the cross-fiber independence observed under acoustic stimulation.
Project description:Most cortical neurons fire regularly when excited by a constant stimulus. In contrast, irregular-spiking (IS) interneurons are remarkable for the intrinsic variability of their spike timing, which can synchronize amongst IS cells via specific gap junctions. Here, we have studied the biophysical mechanisms of this irregular spiking in mice, and how IS cells fire in the context of synchronous network oscillations. Using patch-clamp recordings, artificial dynamic conductance injection, pharmacological analysis and computational modeling, we show that spike time irregularity is generated by a nonlinear dynamical interaction of voltage-dependent sodium and fast-inactivating potassium channels just below spike threshold, amplifying channel noise. This active irregularity may help IS cells synchronize with each other at gamma range frequencies, while resisting synchronization to lower input frequencies.
Project description:BACKGROUND:The role of ischemia reperfusion contributing to functional impairment in lower extremity peripheral arterial disease (PAD) patients has not previously been elucidated. The evaluation of gait variability patterns has proven useful in many pathologic populations. Therefore, the purpose of this study is to isolate and determine the specific effect of the acute reperfusion phase of ischemia-reperfusion on gait variability in young individuals with no vascular disease. MATERIALS AND METHODS:Thirty healthy young individuals walked on a treadmill during baseline and the acute reperfusion phase of ischemia-reperfusion conditions while lower extremity joint kinematics were captured. Stride to stride variability was assessed using the largest Lyapunov exponent, approximate entropy, standard deviation, and coefficient of variation. Differences in gait variability between conditions were assessed using dependent t-tests. RESULTS:The largest Lyapunov exponent values and approximate entropy values were significantly higher in the acute reperfusion phase of ischemia-reperfusion condition for the ankle, knee, and the hip. Coefficient of variation was significantly higher at the hip and standard deviation was higher at the knee and the hip during the acute reperfusion phase of ischemia-reperfusion condition. CONCLUSIONS:The acute reperfusion phase of the ischemia-reperfusion cycle alters gait variability patterns at the ankle, knee, and the hip in healthy young individuals. Our findings indicate increased noise and irregularity of gait variability patterns post-ischemia. In young healthy individuals who do not have neuromuscular impairments, significant gait alterations are present during walking after a period of interruption of blood flow.
Project description:Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%), 23 with moderate stenosis (<70%), and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R(2): 0.35) and largest Lyapunov exponent (p<0.001, adjusted R(2): 0.6). Baroreflex sensitivity also predicted the correlation dimension values (p?=?0.05), and the LLE (p?=?0.08). Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.
Project description:Cortical spike trains are highly irregular both during ongoing, spontaneous activity and when driven at high firing rates. There is uncertainty about the source of this irregularity, ranging from intrinsic noise sources in neurons to collective effects in large-scale cortical networks. Cortical interneurons display highly irregular spike times (coefficient of variation of the interspike intervals >1) in response to dc-current injection in vitro. This is in marked contrast to cortical pyramidal cells, which spike highly irregularly in vivo, but regularly in vitro. We show with in vitro recordings and computational models that this is due to the fast activation kinetics of interneuronal K(+) currents. This explanation holds over a wide parameter range and with Gaussian white, power-law, and Ornstein-Uhlenbeck noise. The intrinsically irregular spiking of interneurons could contribute to the irregularity of the cortical network.
Project description:The influence of attention on the dynamical structure of postural sway was examined in 30 healthy young adults by manipulating the focus of attention. In line with the proposed direct relation between the amount of attention invested in postural control and regularity of center-of-pressure (COP) time series, we hypothesized that: (1) increasing cognitive involvement in postural control (i.e., creating an internal focus by increasing task difficulty through visual deprivation) increases COP regularity, and (2) withdrawing attention from postural control (i.e., creating an external focus by performing a cognitive dual task) decreases COP regularity. We quantified COP dynamics in terms of sample entropy (regularity), standard deviation (variability), sway-path length of the normalized posturogram (curviness), largest Lyapunov exponent (local stability), correlation dimension (dimensionality) and scaling exponent (scaling behavior). Consistent with hypothesis 1, standing with eyes closed significantly increased COP regularity. Furthermore, variability increased and local stability decreased, implying ineffective postural control. Conversely, and in line with hypothesis 2, performing a cognitive dual task while standing with eyes closed led to greater irregularity and smaller variability, suggesting an increase in the "efficiency, or "automaticity" of postural control". In conclusion, these findings not only indicate that regularity of COP trajectories is positively related to the amount of attention invested in postural control, but also substantiate that in certain situations an increased internal focus may in fact be detrimental to postural control.
Project description:Low-intensity pulsed ultrasound stimulation (LIPUS) can inhibit seizures associated with temporal lobe epilepsy (TLE), which is the most common epileptic syndrome in adults and accounts for more than half of the cases of intractable epilepsy. Electroencephalography (EEG) signal analysis is an important method for studying epilepsy. The nonlinear dynamics of epileptic EEG signals can be used as biomarkers for the prediction and diagnosis of epilepsy. However, how ultrasound modulates the nonlinear dynamic characteristics of EEG signals in TLE is still unclear. Here, we used low-intensity pulsed ultrasound to stimulate the CA3 region of kainite (KA)-induced TLE mice, simultaneously recorded local field potentials (LFP) in the stimulation regions before, during, and after LIPUS. The nonlinear characteristics, including complexity, approximate entropy of different frequency bands, and Lyapunov exponent of the LFP, were calculated. Compared with the control group, the experimental group showed that LIPUS inhibited TLE seizure and the complexity, approximate entropy of the delta (0.5-4 Hz) and theta (4-8 Hz) frequency bands, and Lyapunov exponent of the LFP significantly increased in response to ultrasound stimulation. The values before ultrasound stimulation were higher ?1.87 (complexity), ?1.39 (approximate entropy of delta frequency bands), ?1.13 (approximate entropy of theta frequency bands) and ?1.46 times (Lyapunov exponent) than that after ultrasound stimulation (p < 0.05). The above results demonstrated that LIPUS can alter nonlinear dynamic characteristics and provide a basis for the application of ultrasound stimulation in the treatment of epilepsy.
Project description:Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.
Project description:The persistence of a spatially structured population is determined by the rate of dispersal among habitat patches. If the local dynamic at the subpopulation level is extinction-prone, the system viability is maximal at intermediate connectivity where recolonization is allowed, but full synchronization that enables correlated extinction is forbidden. Here we developed and used an algorithm for agent-based simulations in order to study the persistence of a stochastic metapopulation. The effect of noise is shown to be dramatic, and the dynamics of the spatial population differs substantially from the predictions of deterministic models. This has been validated for the stochastic versions of the logistic map, the Ricker map and the Nicholson-Bailey host-parasitoid system. To analyze the possibility of extinction, previous studies were focused on the attractiveness (Lyapunov exponent) of stable solutions and the structure of their basin of attraction (dependence on initial population size). Our results suggest that these features are of secondary importance in the presence of stochasticity. Instead, optimal sustainability is achieved when decoherence is maximal. Individual-based simulations of metapopulations of different sizes, dimensions and noise types, show that the system's lifetime peaks when it displays checkerboard spatial patterns. This conclusion is supported by the results of a recently published Drosophila experiment. The checkerboard strategy provides a technique for the manipulation of migration rates (e.g., by constructing corridors) in order to affect the persistence of a metapopulation. It may be used in order to minimize the risk of extinction of an endangered species, or to maximize the efficiency of an eradication campaign.
Project description:Deep brain stimulation (DBS) provides dramatic tremor relief when delivered at high-stimulation frequencies (more than ?100 Hz), but its mechanisms of action are not well-understood. Previous studies indicate that high-frequency stimulation is less effective when the stimulation train is temporally irregular. The purpose of this study was to determine the specific characteristics of temporally irregular stimulus trains that reduce their effectiveness: long pauses, bursts, or irregularity per se. We isolated these characteristics in stimulus trains and conducted intraoperative measurements of postural tremor in eight volunteers. Tremor varied significantly across stimulus conditions (P < 0.015), and stimulus trains with pauses were significantly less effective than stimulus trains without (P < 0.002). There were no significant differences in tremor between trains with or without bursts or between trains that were irregular or periodic. Thus the decreased effectiveness of temporally irregular DBS trains is due to long pauses in the stimulus trains, not the degree of temporal irregularity alone. We also conducted computer simulations of neuronal responses to the experimental stimulus trains using a biophysical model of the thalamic network. Trains that suppressed tremor in volunteers also suppressed fluctuations in thalamic transmembrane potential at the frequency associated with cerebellar burst-driver inputs. Clinical and computational findings indicate that DBS suppresses tremor by masking burst-driver inputs to the thalamus and that pauses in stimulation prevent such masking. Although stimulation of other anatomic targets may provide tremor suppression, we propose that the most relevant neuronal targets for effective tremor suppression are the afferent cerebellar fibers that terminate in the thalamus.