Lévy walks in random scattering and growth of waves

Random spatial wave scattering and stochastic wave growth are studied where one or both of the random processes can be described by a Lévy walk. This analysis extends previous work on randomly growing and scattering waves where both the random processes are modeled by Gaussian diffusive statistics. Both random spatial scattering and stochastic wave growth modeled by Lévy walks are studied separately, together, and in combination with Gaussian processes. Transmission coefficients, lasing thresholds, and energy densities in the medium are obtained for the different permutations.

Estimation of multiscale neurophysiologic parameters by electroencephalographic means

It is shown that new model-based electroencephalographic (EEG) methods can quantify neurophysiologic parameters that underlie EEG generation in ways that are complementary to and consistent with standard physiologic techniques. This is done by isolating parameter ranges that give good matches between model predictions and a variety of experimental EEG-related phenomena simultaneously. Resulting constraints range from the submicrometer synaptic level to length scales of tens of centimeters, and from timescales of around 1 ms to 1 s or more, and are found to be consistent with independent physiologic and anatomic measures. In the process, a new method of obtaining model parameters from the data is developed, including a Monte Carlo implementation for use when not all input data are available. Overall, the approaches used are complementary to other methods, constraining allowable parameter ranges in different ways and leading to much tighter constraints overall. EEG methods often provide the most restrictive individual constraints. This approach opens a new, noninvasive window on quantitative brain analysis, with the ability to monitor temporal changes, and the potential to map spatial variations. Unlike traditional phenomenologic quantitative EEG measures, the methods proposed here are based explicitly on physiology and anatomy.

Statistics of polarization and Stokes parameters of stochastic waves

Several theories now exist to describe the probability distribution functions (PDFs) for the electric field strength, intensity, and power of signals. In this work, a model is developed for the PDFs of the polarization properties of the superposition of multiple transverse wave populations. The polarization of each transverse wave population is described by a polarization ellipse with fixed axial ratio and polarization angle, and PDFs for the field strength and phase. Wave populations are vectorially added, and expressions found for the Stokes parameters I , U , Q , and V , as well as the degrees of linear and circular polarization, and integral expressions for their statistics. In this work, lognormal distributions are chosen for the electric field, corresponding to stochastic growth, and polarization PDFs are numerically calculated for the superposition of orthonormal mode populations, which might represent the natural modes emitted by a source. Examples are provided of the superposition of linear, circular, and elliptically polarized wave populations in cases where the component field strength PDFs are the same, and where one field strength PDF is dominant.

Spatially uniform and nonuniform analyses of electroencephalographic dynamics,with application to the topography of the alpha rhythm

Corticothalamic dynamics are investigated using a model in which spatial nonuniformities are incorporated via the coupling of spatial eigenmodes. Comparison of spectra generated using the nonuniform analysis with those generated using a uniform one demonstrates that, for most frequencies, local activity is only weakly dependent on activity elsewhere in the cortex; however, dispersion of low-wave-number activity ensures that distant dynamics influence local dynamics at low frequencies (below approximately 2 Hz ), and at the alpha frequency (approximately 10 Hz ), where propagating signals are inherently weakly damped, and wavelengths are large. When certain model parameters have similar spatial profiles, as is expected from physiology, the low-frequency discrepancies tend to cancel, and the uniform analysis with local parameter values is an adequate approximation to the full nonuniform one across the whole spectrum, at least for large-scale nonuniformities. After comparing the uniform and nonuniform analyses, we consider one possible application of the nonuniform analysis: studying the phenomenon of occipital alpha dominance, whereby the alpha frequency and power are greater at the back of the head (occipitally) than at the front. In order to infer realistic nonuniformities in the model parameters, the uniform version of the model is first fitted to data recorded from 98 normal subjects in a waking, eyes-closed state. This yields a set of parameters at each of five electrode sites along the midline. The inferred parameter nonuniformities are consistent with anatomical and physiological constraints. Introducing these spatial profiles into the full nonuniform model then quantitatively reproduces observed site-dependent variations in the alpha power and frequency. The results confirm that the frequency shift is mainly due to a decrease in the corticothalamic propagation delay, but indicate that the delay nonuniformity cannot account for the observed occipital increase in alpha power; the occipital alpha dominance is due to decreased cortical gains and increased thalamic gains in occipital regions compared to frontal ones.

The effect of gender on Helicobacter felis-mediated gastritis, epithelial cell proliferation, and apoptosis in the mouse model

The murine Helicobacter felis model has been extensively used to investigate the importance of host factors in the development of chronic gastritis. The effect of gender in this murine model is unknown. Male and female C57BL/6J mice were infected with H felis for up to 1 year. At 4, 8, 19, 36, and 52 weeks post-infection, gastric histopathology, epithelial cell proliferation, and apoptosis were examined and compared with age- and gender-matched controls. In female mice, infection with H felis resulted in an earlier onset of chronic gastric inflammation, epithelial hyperplasia, and oxyntic cell loss than males. In females, there was a trend towards increased gastric pathology compared with males, with long-term-infected female mice having significantly greater (p < 0.05) chronic inflammation than male mice. The histopathological differences in male and female mice did not relate to the density of H felis infection. Female mice infected with H felis had significantly increased gastric epithelial cell proliferation in the cardia and corpus at both 8 and 52 weeks post-infection (p < 0.05). Epithelial cell apoptosis in the glandular mucosa of the corpus at 36 and 52 weeks post-infection was significantly increased (p < 0.05) in female mice compared with uninfected gender controls. In contrast, there was no significant increase in epithelial cell proliferation or apoptosis in any area of the stomach at any time point after H felis infection in male mice. These results demonstrate that there are gender differences in the gastric inflammatory and epithelial response to H felis in the murine model. The functional importance of gender should be considered in future murine studies on H felis- and H pylori-induced chronic gastritis.

Nonuniform corticothalamic continuum model of electroencephalographic spectra with application to split-alpha peaks

Recent theoretical work has successfully predicted electroencephalographic spectra from physiology using a model corticothalamic system with spatially uniform parameters. The present work incorporates parameter nonuniformities into this model via the coupling they induce between spatial eigenmodes. Splitting of the spectral alpha peak, an effect seen in a small percentage of the normal population, is investigated as an illustrative special case. It is confirmed that weak splitting can arise from mode structure if the peak is sufficiently sharp, even for uniform parameters. However, it is further demonstrated that greater splitting can result from nonuniformities, and it is argued that this mechanism for split alpha is better able to account quantitatively for this effect than previously suggested alternatives of pacemakers or purely cortical resonances. On introducing nonuniformities in corticothalamic loop time delays, we find that the alpha frequency also varies as one moves from the front to the back of the head, in accord with observations, and that analogous (but less distinct) variations are seen in the beta peak. Analysis shows realistic variations of around +/-10 ms relative to the mean loop delay of approximately 80 ms can account for observed splittings of about 1 Hz. It is also suggested that subjects who display clear alpha splitting form the tail of a distribution of magnitude of cortical inhomogeneity, rather than a separate population.

Effects of disorder in two-dimensional photonic crystal waveguides

The effects of randomness on the guiding properties of waveguides embedded in disordered two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index, and position are considered for both straight and 90 degrees bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties. A smaller range of position disorder is also considered. For strong disorder in radius and refractive index, the guide effectively closes. These results were obtained by a Monte Carlo simulation method, and the performance of this method is analyzed. The method requires at least ten realizations in some cases for convergence to commence; substantially more realizations are required for moderate and strong disorder to achieve accurate results.

Neurophysical modeling of brain dynamics

A recent neurophysical model of brain electrical activity is outlined and applied to EEG phenomena. It incorporates single-neuron physiology and the large-scale anatomy of corticocortical and corticothalamic pathways, including synaptic strengths, dendritic propagation, nonlinear firing responses, and axonal conduction. Small perturbations from steady states account for observed EEGs as functions of arousal. Evoked response potentials (ERPs), correlation, and coherence functions are also reproduced. Feedback via thalamic nuclei is critical in determining the forms of these quantities, the transition between sleep and waking, and stability against seizures. Many disorders correspond to significant changes in EEGs, which can potentially be quantified in terms of the underlying physiology using this theory. In the nonlinear regime, limit cycles are often seen, including a regime in which they have the characteristic petit mal 3 Hz spike-and-wave form.

Simulated electrocortical activity at microscopic, mesoscopic, and global scales

Simulation of electrocortical activity requires (a) determination of the most crucial features to be modelled, (b) specification of state equations with parameters that can be determined against independent measurements, and (c) explanation of electrical events in the brain at several scales. We report our attempts to address these problems, and show that mutually consistent explanations, and simulation of experimental data can be achieved for cortical gamma activity, synchronous oscillation, and the main features of the EEG power spectrum including the cerebral rhythms and evoked potentials. These simulations include consideration of dendritic and synaptic dynamics, AMPA, NMDA, and GABA receptors, and intracortical and cortical/subcortical interactions. We speculate on the way in which Hebbian learning and intrinsic reinforcement processes might complement the brain dynamics thus explained, to produce elementary cognitive operations.

Increased zinc finger protein zFOC1 transcripts in gastric cancer compared with normal gastric tissue

BACKGROUND

Screening of cDNA arrays of the IMAGE library identified human zFOC1 as a differentially expressed cDNA that was upregulated in KATO III gastric cancer cells following stimulation with the gastric pathogen Helicobacter pylori.

AIMS

To determine the expression of zFOC1 in gastric mucosa with and without H pylori infection and in patients with gastric cancer.

RESULTS

zFOC1 is localised on chromosome 12q24.3 and encodes a zinc finger protein. Expression studies in human H pylori infected and uninfected gastric biopsies, gastric tumours, and gastric cancer cell lines revealed that zFOCI gene transcripts are significantly higher in gastric cancer than in non-cancerous gastric tissues.

CONCLUSIONS

The zFOC1 gene appears to be a tumour marker associated with gastric cancer.

Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals

Correlation and coherence functions of electroencephalographic signals are calculated using a recent continuum theory that has previously yielded excellent agreement with observations of electroencephalographic spectra. The predicted properties of these functions are found to be in semiquantitative agreement with observations for parameters consistent with those used in previous studies of spectra. The corresponding results for electrocorticographic signals point to an additional contribution at characteristic scales of around 6mm, as has been previously inferred, and are consistent with a crossover to the long-range behavior seen in scalp data. Analysis within the framework of the model enables constraints on the relative strengths of the two contributions to be inferred, and makes it plausible that the short-range component reflects the point-spread function of external stimuli and corticothalamic feedback reaching the cortex.

Wave-number spectrum of electrocorticographic signals

A physiologically based continuum model of corticothalamic electrodynamics is generalized and used to derive the theoretical form of the electrocorticographic (ECoG) wave-number spectrum. A one-dimensional projection of the spectrum is derived, as is the azimuthally averaged two-dimensional spectrum for isotropic and anisotropic cortices. The predicted spectra are found to consist of a low-k plateau followed by three regions of power-law decrease, which result from filtering of the electrical activity through physical structures at different scales in the cortex. The magnitude of the maximum theoretical power-law exponent is larger for the two-dimensional (2D) spectrum than for its 1D counterpart. The predicted spectra agree well with experimental data obtained from 1D and 2D recording arrays on the cortical surface, enabling the structures in the brain that are important in determining spatial cortical dynamics to be identified. The cortical dispersion relation predicted by our model is also investigated, providing insight into the relationships between temporal and spatial brain dynamics.

Self-organized criticality in ant brood tending

A new stochastic lattice gas model of ant brood tending is formulated to examine the role played by repulsive ant-ant interactions in the even distribution of care among brood members. The deterministic limit of the model is known to be self-organized critical. Numerical simulations of the model show that the ant-ant repulsion facilitates an even distribution of brood care in the middle of the brood. This provides a possible explanation for the fact that ants sort their brood so that the youngest brood (which are most in need of care) are placed in the middle. Simulations show that the uniformity of brood care distribution is optimal when ants operate in a regime intermediate between completely random and completely deterministic. A certain degree of randomness helps ants to avoid becoming trapped in suboptimal configurations but does not destroy the long-range correlations that are inherent to self-organized critical systems.

Self-organized criticality and emergent oscillations in models of termite architecture with crowding

The termite architecture model of O'Toole et'al. (1999) is extended to incorporate arbitrary halting time-scales. It is shown that this also means that the assumption of synchronous building must be relaxed. Numerical simulations show that ordered nest architecture emerges under a wide range of time-scales but also that there is an optimal region of halting times. This optimal region is explained by the emergence of synchronized periods of termite activity. The correlation length of the building distribution is shown to diverge providing strong evidence that the model is self-organized critical.

Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology

Detrended fluctuation analysis has recently demonstrated the existence of two approximate temporal scaling regimes in locally detrended human electroencephalographic (EEG) fluctuations, and has suggested a connection between the location of the breakpoint between regimes and the alpha resonance near 10 Hz. It is shown here that these scalings can be explained in terms of the filtering of the underlying power spectrum implied by the detrending process. Using a recent physiologically based model of EEG generation, the main features of the scalings, and deviations from them, are related to the underlying physiology of dendritic propagation and muscle electrical activity, and it is concluded that the effects of such physiological features are usually clearer in spectra.

Diffusion and anomalous diffusion of light in two-dimensional photonic crystals

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified. It is shown that the transport velocity upsilon(E) can be as much as 10(8) times less than its free space value, while just outside the cluster upsilon(E) can be 0.3c. The effects of weak and strong disorders on the transport velocity are investigated. Different regimes of the wave transport-ordered propagation, diffusion, and anomalous diffusion-are demonstrated, and it is inferred that Anderson localization is incipient in the latter regime. Exact numerical calculations from the Helmholtz equation are shown to be in good agreement with the diffusion approximation.

Field statistics of two vectorially superposed wave populations

Field statistics of observed waves and radiation constrain the physics of the emission process and source region. However, data often contain two or more superposed signals or a signal superposed on a noise background, creating difficulties for interpretation. Here, the combined probability distribution of the field formed by vector superposition of two signals, each with specified statistics, is written as a double integral with integrable singularities. The analytic result and its numerical solutions for combinations of Gaussian and lognormally distributed signals show that these predictions differ from those for field or intensity convolution and from the individual wave distributions. At high fields, the combined distribution takes the qualitative form of the dominant individual distribution (which is localized or otherwise extends to larger fields) but develops a significant tail at low fields due to vector superposition of almost antiparallel fields with similar magnitudes. It is shown that very nearly power-law distributions can develop in significant field domains, despite neither component distribution being power law. This is relevant to alternative interpretations in terms of self-organized criticality and certain modulational wave instabilities. The formalism is then applied to observations of the Vela pulsar, resulting in greatly improved fits to data and different interpretations. Specifically, the results are strong evidence that stochastic growth theory (SGT) is relevant and that the approximate power-law statistics found at some phases are not intrinsic but rather due to vector convolution of a Gaussian background with a lognormal; the latter is interpretable in terms of SGT. The field statistics are consistent with the emission mechanism being a direct linear instability or indirect generation via linear mode conversion of nonescaping waves driven by a linear instability. They are inconsistent with nonlinear self-focusing instabilities generating the observed pulsar radiation. This formalism and its results should also be widely applicable to other types of wave growth in inhomogeneous media.

Wave-number spectrum of electroencephalographic signals

A recently developed, physiologically based continuum model of corticothalamic electrodynamics is used to derive the theoretical form of the electroencephalographic wave-number spectrum and its projection onto a one-dimensional recording array. The projected spectrum is found to consist of a plateau followed by regions of power-law decrease with various exponents, which are dependent on both model parameters and temporal frequency. The theoretical spectrum is compared with experimental results obtained in other studies, showing good agreement. The model provides a framework for understanding the nature of the spatial power spectrum by linking the underlying physiology with the large-scale dynamics of the brain.

Helicobacter pylori-stimulated EGF receptor transactivation requires metalloprotease cleavage of HB-EGF

Helicobacter pylori has a major aetiological role in human gastric carcinogenesis but the cellular and molecular pathways by which infection promotes transformation remain to be resolved. This study demonstrates that H. pylori exposure to MKN-1, ST42, and MKN-28 gastric epithelial tumour cells results in the activation of HB-EGF gene expression and EGFR tyrosine phosphorylation. These cell responses are induced by both cagPAI positive and cagPAI negative H. pylori strains and are dependent on cell surface expression of the HB-EGF precursor. The induction of HB-EGF gene transcription by H. pylori requires metalloprotease-, EGFR-, and Mek1-activities, indicating the involvement of the "triple membrane passing signal" (TMPS) for EGFR transactivation. Moreover, the release of the inflammatory cytokine IL-8 by cells exposed to H. pylori is significantly impaired by inhibitors of TMPS pathway elements. Our findings support a model in which H. pylori triggers constitutive EGFR signal activation, which enhances IL-8 production, and initiates neoplastic transformation of gastric epithelial cells.

Unified neurophysical model of EEG spectra and evoked potentials

Evoked potentials -- the brain's transient electrical responses to discrete stimuli -- are modeled as impulse responses using a continuum model of brain electrical activity. Previous models of ongoing brain activity are refined by adding an improved model of thalamic connectivity and modulation, and by allowing for two populations of excitatory cortical neurons distinguished by their axonal ranges. Evoked potentials are shown to be modelable as an impulse response that is a sum of component responses. The component occurring about 100 ms poststimulus is attributed to sensory activation, and this, together with positive and negative feedback pathways between the cortex and thalamus, results in subsequent peaks and troughs that semiquantitatively reproduce those of observed evoked potentials. Modulation of the strengths of positive and negative feedback, in ways consistent with psychological theories of attentional focus, results in distinct responses resembling those seen in experiments involving attentional changes. The modeled impulse responses reproduce key features of typical experimental evoked response potentials: timing, relative amplitude, and number of peaks. The same model, with further modulation of feedback, also reproduces experimental spectra. Together, these results mean that a broad range of ongoing and transient electrocortical activity can be understood within a common framework, which is parameterized by values that are directly related to physiological and anatomical quantities.

Dynamics of large-scale brain activity in normal arousal states and epileptic seizures

Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms-mainly slow wave, delta, theta, alpha, and sleep spindle-with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

Unexpected benefit of sorbitol placebo in Mg intervention study of premenstrual symptoms: implications for choice of placebo in RCTs

We carried out a randomized, double-blind, crossover study of 85 women, designed to investigate the dose-response of daily Mg supplementation on premenstrual symptoms. Each woman took one of four treatments: Mg (200, 350 or 500 mg/day) or sorbitol (placebo) for 2 months. This was followed by a washout of 1 month, and then each woman received one of the three remaining treatments for a further 2 months. Unexpectedly, sorbitol (1305 mg) reduced anxiety-related and total premenstrual symptoms after 2 months compared with Mg treatments (P<0.001 and P<0.001, respectively). We conclude that low-dose sorbitol reduces premenstrual symptoms beyond that expected of a placebo. After 2 months of treatment, sorbitol also reduced urinary Mg excretion compared to baseline (no intervention) and Mg treatments (P=0.005). A follow-up study on 17 healthy volunteers confirmed lack of effect on urinary Mg output of a similar sorbitol intervention regime compared with either baseline or cellulose placebo. It appears that sorbitol may influence Mg homeostasis in women suffering premenstrual symptoms, but not in healthy individuals. Implications for placebo choice in RCTs are discussed.

Redo carotid endarterectomy versus primary carotid endarterectomy

BACKGROUND AND PURPOSE

Several authorities have recently advocated carotid stenting for recurrent carotid stenosis because of the perception that redo surgery has a higher complication rate than primary carotid endarterectomy (CEA). This study compares the early and late results of reoperations versus primary CEA.

METHODS

All reoperations for recurrent carotid stenosis performed during a recent 7-year period by a single vascular surgeon were compared with primary CEA. Because all redo CEAs were done with polytetrafluoroethylene (PTFE) or vein patch closure, we only analyzed those primary CEAs that used the same patch closures. A Kaplan-Meier life-table analysis was used to estimate stroke-free survival rates and freedom from >/=50% recurrent stenosis.

RESULTS

Of 547 primary CEAs, 265 had PTFE or saphenous vein patch closure, and 124 reoperations had PTFE or vein patch closure during the same period. Both groups had similar demographic characteristics. The indications for reoperation and primary CEA were symptomatic stenosis in 78% and 58% of cases and asymptomatic >/=80% stenosis in 22% and 42% of cases, respectively (P<0.001). The 30-day perioperative stroke and transient ischemic attack rates for reoperation and primary CEA were 4.8% versus 0.8% (P=0.015) and 4% versus 1.1%, respectively, with no perioperative deaths in either group. Cranial nerve injury was noted in 17% of reoperation patients versus 5.3% of primary CEA patients; however, most of these injuries were transient (P<0.001). Mean hospital stay was 1.8 days for reoperation versus 1.6 days for primary CEA. Cumulative rates of stroke-free survival and freedom from >/=50% recurrent stenosis for reoperation and primary CEA at 1, 3, and 5 years were 96%, 91%, and 82% and 98%, 96%, and 95% versus 94%, 92%, and 91% and 98%, 96%, and 96%, respectively (no significant differences).

CONCLUSIONS

Reoperation carries higher perioperative stroke and cranial nerve injury rates than primary CEA. However, reoperations are durable and have stroke-free survival rates that are similar to primary CEA. These considerations should be kept in mind when carotid stenting is recommended instead of reoperation.