Transient localized wave patterns and their application to migraine

Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by a ghost near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and therefore occur not only in migraine with aura (MA) but also in migraine without aura (MO), i.e., in the two major migraine subforms. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves' forms, according to which (i) activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area anti-correlated to both SD duration and total affected cortical area such that headache would be less severe in MA than in MO (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation, and (iii) the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation.Comment: 14 pages, 11 figure

Time-delayed feedback in neurosystems

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure

The quest for hot gas in the halo of NGC 1511

XMM-Newton observations of the starburst galaxy NGC 1511 reveal the presence of a previously unknown extended hot gaseous phase of its ISM, which partly extends out of the disk plane. The emission distribution is asymmetric, being brightest in the eastern half of the galaxy, where also radio continuum observations suggest the highest level of star formation. Spectral analysis of the integral 0.2-12 keV X-ray emission from NGC 1511 indicates a complex emission composition. A model comprising a power law plus thermal plasma component, both absorbed by foreground gas, cannot explain all details of the observed spectrum, requiring a third spectral component to be added. This component can be a second thermal plasma, but other spectral models can be fitted as well. Its X-ray properties characterize NGC 1511 as a starburst galaxy. The X-ray-to-infrared luminosity ratio is consistent with this result. Together with the X-ray data, XMM-Newton obtained UV images of NGC 1511, tracing massive stars heating the ambient gas, which is then seen in H\alpha emission. UV, H\alpha and near-infrared imagery suggest that NGC 1511 is disturbed, most likely by its two small companions, NGC 1511a and NGC 1511b.Comment: 7 pages, 7 figures, accepted for publication in A&

ECoG-based short-range recurrent stimulation techniques to stabilize tissue at risk of progressive damage: Theory based on clinical observations

We introduce theoretical concepts based on chaos control to stabilize in acute stroke the tissue at risk of progressive damage by preventing adverse effects of waves of mass neuronal depolarization. Moreover, we present clinical electrocorticography (ECoG) recordings of relevant signals suggested for the feedback control. The recordings are performed in combination with novel subdural opto-electrode technology for simultaneous laser-Doppler flowmetry in patients with aneurysmal subarachnoid haemorrhage (aSAH). In aSAH patients waves of spreading depolarization (SD) have a high incidence and cause hypoxia in tissue at risk, and, importantly, the haemodynamic response is the inverse of that seen in healthy tissue. In previous clinical studies, clusters of prolonged SDs have been measured in aSAH patients in close proximity to structural brain damage as assessed by neuroimaging, and, in theoretical studies, a mechanism was presented, suggesting how a failure of internal feedback could be a putative mechanism of such SD cluster patterns in acute stroke. 

This failing internal feedback control is now suggested to be replaced by ECoG-based short-range recurrent functional stimulation that initiates the normal hyperperfusion haemodynamic response in a demand-controlled way and stabilizes the tissue at risk during the critical phase of SD passage. The suggested method has three key features: (i) it is short-range, i.e., in the order of the distance of the ECoG electrode strip, (ii) it is demand-controlled, and (iii) it uses no prior knowledge of the target state, in particular, it adapts to conditions in the healthy physiological range. On-demand type stimulation provides minimal invasive feedback as the control force is off when the target state is reached, i.e., the tissue at risk is without SD or it is back to the physiological range (out of risk). These last two features (ii-iii) are shared with classical methods of chaos control, where major progress was made in the last years with respect to extensions for spatio-temporal wave patterns. A detailed bifurcation analysis of the nonlinear model is presented, in particular, the SD cluster forming cortical state is suggested to be caused by a delay-induced saddle-node bifurcation.
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Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback

The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change of RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example step-wise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain

Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

X-ray Emission from NGC 1808: More than a Complex Starburst

Earlier observations of NGC 1808 in various wavebands (X-ray, optical, near-infrared, radio) provided evidence for the existence of either a starburst or a Seyfert 2 nucleus. We here present the results of multiwavelength XMM-Newton and Chandra observations, which directly prove the co-existence of thermal diffuse plasma and non-nuclear unresolved point-like sources associated with the starburst activity, along with a Low Luminosity Active Galactic Nucleus (LLAGN) or an Ultra Luminous X-ray source (ULX). The broad bandwidth of XMM-Newton allows us to show that the unresolved nuclear source in NGC 1808 dominates the hard X-ray spectrum, while the emission in the soft regime, below 1 keV, is dominated by a thermal component associated to an extended starburst. Both EPIC and RGS data provide reliable detections of a number of emission lines from heavy elements, with abundances ranging from roughly 0.7 to 2.2 Z_sol for different elements. However, no 6.4 keV Fe K-alpha fluorescence line emission was detected. The analysis of the nuclear region of NGC 1808 allows us to detect and disentangle the contribution of an unresolved nuclear X-ray source and the starburst region, but the exact nature of the nucleus remains unknown. The observed luminosity of NGC 1808 is L(2-10 keV)=(1.61+/-0.06)E+40 erg/s. A comparison of our OM 212 nm image with a CTIO 4-m telescope H-alpha frame shows a good general correspondence between the emission from massive stars and warm ionized gas, with minor deviations near the ends of the bar in NGC 1808. An aditional, very soft thermal spectral component with kT~0.1 keV has been discovered in the XMM-Newton spectral analysis, which most likely originates from the halo of NGC 1808.Comment: 18 pages, 14 figures. Accepted for publication in Astronomy & Astrophysics (Figures 1, 3, 4, 12, 13 & 14 at lower resolution than accepted version

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]>>1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale