Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc

ArticleThe intervertebral disc is a multicomposite structure, with an outer fibrous ring, the annulus fibrosus, retaining a gel-like core, the nucleus pulposus. The disc presents complex mechanical behaviour, and it is of high importance for spine biomechanics. Advances in multiscale modelling and disc repair raised a need for new quantitative data on the finest details of annulus fibrosus mechanics. In this work we explored inter-lamella and inter-bundle behaviour of the outer annulus using micromechanical testing and second harmonic generation microscopy. Twenty-one intervertebral discs were dissected from cow tails; the nucleus and inner annulus were excised to leave a ring of outer annulus, which was tested in circumferential loading while imaging the tissue’s collagen fibres network with sub-micron resolution. Custom software was developed to determine local tissue strains through image analysis. Inter-bundle linear and shear strains were 5.5 and 2.8 times higher than intra-bundle strains. Bundles tended to remain parallel while rotating under loading, with large slipping between them. Inter-lamella linear strain was almost 3 times the intra-lamella one, but no slipping was observed at the junction between lamellae. This study confirms that outer annulus straining is mainly due to bundles slipping and rotating. Further development of disc multiscale modelling and repair techniques should take into account this modular behaviour of the lamella, rather than considering it as a homogeneous fibre-reinforced matrix.Henry Smith Charit

Measuring visual cortical oxygenation in diabetes using functional near-infrared spectroscopy

Aims: Diabetes mellitus affects about 6% of the world’s population, and the chronic complications of the disease may result in macro- and micro-vascular changes. The purpose of the current study was to shed light on visual cortical oxygenation in diabetic individuals. We then aimed to compare the haemodynamic response (HDR) to visual stimulation with glycaemic control, given the likelihood of diabetic individuals suffering from such macro- and micro-vascular insult. Methodology: Thirty participants took part in this explorative study, fifteen of whom had diabetes and fifteen of whom were non-diabetic controls. The HDR, measured as concentrations of oxyhaemoglobin [HbO] and deoxyhaemoglobin [HbR], to visual stimulation was recorded over the primary visual cortex (V1) using a dual-channel oximeter. The stimulus comprised a pattern-reversal checkerboard presented in a block design. Participants’ mean glycated haemoglobin (HbA1c) level (±SD) was 7.2±0.6% in the diabetic group and 5.5±0.4% in the non-diabetic group. Raw haemodynamic data were normalised to baseline, and the last 15 s of data from each ‘stimulus on’ and ‘stimulus off’ condition were averaged over seven duty cycles for each participant. Results: There were statistically significant differences in ∆[HbO] and ∆[HbR] to visual stimulation between diabetic and non-diabetic groups (p<0.05). In the diabetic group, individuals with type 1 diabetes displayed an increased [HbO] (p<0.01) and decreased [HbR] (p<0.05) compared to their type 2 counterparts. There was also a linear relationship between both ∆[HbO] and ∆[HbR] as a function of HbA1c level (p<0.0005). Conclusions: Our findings suggest that fNIRS can be used as a quantitative measure of cortical oxygenation in diabetes. Diabetic individuals have a larger HDR to visual stimulation compared to non-diabetic individuals. This increase in ∆[HbO] and decrease in ∆[HbR] appears to be correlated with HbA1c level

Spontaneous curvature cancellation in forced thin sheets

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.Comment: 13 pages, 12 figures, revtex

Neutron, electron and X-ray scattering investigation of Cr1-xVx near Quantum Criticality

The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr$_{1-x}$V$_{x}$ is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr$_{1-x}$V$_{x}$ in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at x$_{c}$=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.Comment: 6 pages, 6 figures. Accepted to Physical Review

Trying to understand confinement in the Schroedinger picture

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.Comment: 21 pages, 1 figure. Lecture given at the 4th St.Petersburg Winter School in Theoretical Physics, Feb. 22-28, 199

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

The Casimir force on a surface with shallow nanoscale corrugations: Geometry and finite conductivity effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 15%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Absolute photoionization cross section measurements of the Kr I-isoelectronic sequence

Photoionization spectra have been recorded in the 4s, 4p and 3d resonance regions for the Kr Iisoelectronic sequence using both the dual laser produced plasma technique (at DCU) to produce photoabsorption spectra, and the merged ion beam and synchrotron radiation technique (at ASTRID) to measure absolute photoionization cross sections. Profile parameters are compared for the 4s − np resonances of Rb+ and Sr2+. Many new 4p " ns, md transitions are identified with the aid of Hartree-Fock calculations, and consistent quantum defects are observed for the various ns and md Rydberg series. Absolute single and double photoionization cross sections recorded in the 3d region for Rb+ and Sr2+ ions show preferential decay via double photoionization. This is only the second report where both the DLP technique and the merged beam technique have been used simultaneously to record photoionization spectra, and the advantages of both techniques (i.e. better resolution in the case of DLP and values for absolute photoionization cross sections in the case of the merged beam technique) are highlighted