Standing and travelling waves in a spherical brain model: The Nunez model revisited

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, center manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.The authors would like to thank Stephan van Gils for his valuable input on the manuscript, and Paul Nunez for discussions about experimental and clinical issues. We are also grateful to the anonymous referees for their constructive comments. SV and SC were supported by the European Commission through the FP7 Marie Curie Initial Training Network 289146, NETT: Neural Engineering Transformative Technologies. Moreover, SV was generously supported by the Wellcome Trust Institutional Strategic Support Award (WT105618MA)

Geometrical structure of two-dimensional crystals with non-constant dislocation density

We outline mathematical methods which seem to be necessary in order to discuss crystal structures with non-constant dislocation density tensor(ddt) in some generality. It is known that, if the ddt is constant (in space), then material points can be identified with elements of a certain Lie group, with group operation determined in terms of the ddt - the dimension of the Lie group equals that of the ambient space in which the body resides, in that case. When the ddt is non-constant, there is also a relevant Lie group (given technical assumptions), but the dimension of the group is strictly greater than that of the ambient space. The group acts on the set of material points, and there is a non-trivial isotropy group associated with the group action. We introduce and discuss the requisite mathematical apparatus in the context of Davini's model of defective crystals, and focus on a particular case where the ddt is such that a three dimensional Lie group acts on a two dimensional crystal state - this allows us to construct corresponding discrete structures too

Group elastic symmetries common to continuum and discrete defective crystals

The Lie group structure of crystals which have uniform continuous distributions of dislocations allows one to construct associated discrete structures—these are discrete subgroups of the corresponding Lie group, just as the perfect lattices of crystallography are discrete subgroups of R 3 , with addition as group operation. We consider whether or not the symmetries of these discrete subgroups extend to symmetries of (particular) ambient Lie groups. It turns out that those symmetries which correspond to automorphisms of the discrete structures do extend to (continuous) symmetries of the ambient Lie group (just as the symmetries of a perfect lattice may be embedded in ‘homogeneous elastic’ deformations). Other types of symmetry must be regarded as ‘inelastic’. We show, following Kamber and Tondeur, that the corresponding continuous automorphisms preserve the Cartan torsion, and we characterize the discrete automorphisms by a commutativity condition, (6.14), that relates (via the matrix exponential) to the dislocation density tensor. This shows that periodicity properties of corresponding energy densities are determined by the dislocation density

Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f)

Insights into oscillator network dynamics using a phase-isostable framework

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolution of its phase and slowest decaying isostable coordinate have previously been shown to capture bifurcations and dynamics of the network, which cannot be explained through standard phase reduction. An alternative framework using isostable coordinates to obtain higher-order phase reductions has also demonstrated a similar descriptive ability for two oscillators. In this work, we consider the phase-isostable network equations for an arbitrary but finite number of identical coupled oscillators, obtaining conditions required for the stability of phase-locked states including synchrony. For the mean-field complex Ginzburg–Landau equation where the solutions of the full system are known, we compare the accuracy of the phase-isostable network equations and higher-order phase reductions in capturing bifurcations of phase-locked states. We find the former to be the more accurate and, therefore, employ this to investigate the dynamics of globally linearly coupled networks of Morris–Lecar neuron models (both two and many nodes). We observe qualitative correspondence between results from numerical simulations of the full system and the phase-isostable description demonstrating that in both small and large networks, the phase-isostable framework is able to capture dynamics that the first-order phase description cannot

Cancer Treatment and Bone Health

Considerable advances in oncology over recent decades have led to improved survival, while raising concerns about long-term consequences of anticancer treatments. In patients with breast or prostate malignancies, bone health is a major issue due to the high risk of bone metastases and the frequent prolonged use of hormone therapies that alter physiological bone turnover, leading to increased fracture risk. Thus, the onset of cancer treatment-induced bone loss (CTIBL) should be considered by clinicians and recent guidelines should be routinely applied to these patients. In particular, baseline and periodic follow-up evaluations of bone health parameters enable the identification of patients at high risk of osteoporosis and fractures, which can be prevented by the use of bone-targeting agents (BTAs), calcium and vitamin D supplementation and modifications of lifestyle. This review will focus upon the pathophysiology of breast and prostate cancer treatment-induced bone loss and the most recent evidence about effective preventive and therapeutic strategies

A comparison of proximal and distal high-frequency jet ventilation in an experimental animal model

High-frequency jet ventilation using either a proximal or a distal endotracheal injection site through a triple-lumen endotracheal tube was studied in 10 adult cats. The comparative effects on pulmonary gas exchange, tracheal pressure, heart rate, and blood pressure were examined for each injection site at both high (8–12 pounds per square inch [PSI] and low (5–8 PSI) jet-driving pressures in normal and lung-injured cats. Lung injury was created by modification of a surfactant washout technique previously demonstrated in rabbits. Alveolar ventilation (Paco 2 ) was found to be significantly better with distal than with proximal jet injection under all experimental conditions. At high jet-driving pressures, peak inspiratory pressure was higher in both normal (p = 0.03) and lung-injured cats (p = 0.002) with distal high-frequency jet ventilation. In addition, lung-injured animals were observed to have higher distal mean airway pressures at high jet-driving pressures (p < 0.01). No differences in oxygenation were found in any circumstances. The results of this animal study suggest that distal high-frequency jet ventilation may be more effective in those situations in which improvement in alveolar ventilation is the major goal and that during proximal high-frequency jet ventilation airway pressures should be monitored as far distally as possible.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38592/1/1950020410_ftp.pd