A cohesive interface approach to model the inter-lamellar behaviour of the intervertebral disc annulus fibrosus

INTRODUCTION - The method of representing the inter-lamellar behaviour in Finite Element (FE) models of the disc has been shown to affect the gross disc mechanics [1]. This study aim was to develop an approach to produce inter-lamellar models of the Annulus Fibrosus, i.e. constitutive models of interaction between lamellae. METHODS (Figure 1) - Mature ovine intervertebral discs were used in the present study as a model for the discs of the human lumbar spine. The annulus fibrosus was dissected and radial slices were subjected to mechanical tests. Images were taken under conventional and differential interference contrast (DIC) microscopy. The images before and during loading were used to produce 2D computational models of the annulus structural behaviour. The DIC images were analysed (ImageJ, U.S. N.I.H., USA) to extract the edges between lamellae and converted into quadrilateral FE meshes (ScanIP 5.1, Simpleware Ltd, UK, and Abaqus 6.12, Dassault Systèmes). Each lamella was modelled with Holzapfel’s anisotropic hyperelastic constitutive behaviour, with one fibre orientation per lamella. For this, model parameters were identified to fit to experimental data on the behaviour of tissue components (the proteoglycan matrix and the collagen fibres) [1]. Several modelling hypotheses were tested for the inter-lamellar behaviour: fully bonded conditions, simple frictionless behaviour, friction behaviour with a Coulomb contact, and delamination behaviour, with or without friction, through the use of a cohesive interface model. Displacement boundary conditions were applied reproducing the measured external displacement on the conventional microscopy images. Adequacy of the inter-lamellar behaviour model was assessed by comparing computational and experimental deformed geometries, specifically the change in lamellar interfaces

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure

The origin and composition of carbonatite-derived carbonate-bearing fluorapatite deposits

Carbonate-bearing fluorapatite rocks occur at over 30 globally distributed carbonatite complexes and represent a substantial potential supply of phosphorus for the fertiliser industry. However, the process(es) involved in forming carbonate-bearing fluorapatite at some carbonatites remain equivocal, with both hydrothermal and weathering mechanisms inferred. In this contribution, we compare the paragenesis and trace element contents of carbonate-bearing fluorapatite rocks from the Kovdor, Sokli, Bukusu, Catalão I and Glenover carbonatites in order to further understand their origin, as well as to comment upon the concentration of elements that may be deleterious to fertiliser production. The paragenesis of apatite from each deposit is broadly equivalent, comprising residual magmatic grains overgrown by several different stages of carbonate-bearing fluorapatite. The first forms epitactic overgrowths on residual magmatic grains, followed by the formation of massive apatite which, in turn, is cross-cut by late euhedral and colloform apatite generations. Compositionally, the paragenetic sequence corresponds to a substantial decrease in the concentration of rare earth elements (REE), Sr, Na and Th, with an increase in U and Cd. The carbonate-bearing fluorapatite exhibits a negative Ce anomaly, attributed to oxic conditions in a surficial environment and, in combination with the textural and compositional commonality, supports a weathering origin for these rocks. Carbonate-bearing fluorapatite has Th contents which are several orders of magnitude lower than magmatic apatite grains, potentially making such apatite a more environmentally attractive feedstock for the fertiliser industry. Uranium and cadmium contents are higher in carbonate-bearing fluorapatite than magmatic carbonatite apatite, but are much lower than most marine phosphorites

Comprehensive molecular characterization of the hippo signaling pathway in cancer

Hippo signaling has been recognized as a key tumor suppressor pathway. Here, we perform a comprehensive molecular characterization of 19 Hippo core genes in 9,125 tumor samples across 33 cancer types using multidimensional “omic” data from The Cancer Genome Atlas. We identify somatic drivers among Hippo genes and the related microRNA (miRNA) regulators, and using functional genomic approaches, we experimentally characterize YAP and TAZ mutation effects and miR-590 and miR-200a regulation for TAZ. Hippo pathway activity is best characterized by a YAP/TAZ transcriptional target signature of 22 genes, which shows robust prognostic power across cancer types. Our elastic-net integrated modeling further reveals cancer-type-specific pathway regulators and associated cancer drivers. Our results highlight the importance of Hippo signaling in squamous cell cancers, characterized by frequent amplification of YAP/TAZ, high expression heterogeneity, and significant prognostic patterns. This study represents a systems-biology approach to characterizing key cancer signaling pathways in the post-genomic era

Traversing the intact/fibrillated joint surface: a biomechanical interpretation

Cartilage taken from the osteoarthritic bovine patellae was used to investigate the progression of change in the collagenous architecture associated with the development of fibrillated lesions. Differential interference contrast optical microscopy using fully hydrated radial sections revealed a continuity in the alteration of the fibrillar architecture in the general matrix consistent with the progressive destructuring of a native radial arrangement of fibrils repeatedly interconnected in the transverse direction via a non-entwinement-based linking mechanism. This destructuring is shown to occur in the still intact regions adjacent to the disrupted lesion thus rendering them more vulnerable to radial rupture. Two contrasting modes of surface rupture were observed and these are explained in terms of the absence or presence of a skewed structural weakening of the intermediate zone. A mechanism of surface rupture initiation based on simple bi-layer theory is proposed to account for the intensification of surface ruptures observed in the intact regions on advancing towards the fibrillation front. Focusing specifically on the primary collagen architecture in the cartilage matrix, this study proposes a pathway of change from intact to overt disruption within a unified structural framework

Derivation of inter-lamellar behaviour of the intervertebral disc annulus

The inter-lamellar connectivity of the annulus fibrosus in the intervertebral disc has been shown to affect the prediction of the overall disc behaviour in computational models. Using a combined experimental and computational approach, the inter-lamellar mechanical behaviour of the disc annulus was investigated under conditions of radial loading. Twenty-seven specimens of anterior annulus fibrosus were dissected from twelve discs taken from four frozen ovine thoracolumbar spines. Specimens were grouped depending on their radial provenance within the annulus fibrosus. Standard tensile tests were performed. In addition, micro-tensile tests under microscopy were used to observe the displacement of the lamellae and inter-lamellar connections. Finite elements models matching the experimental protocols were developed with specimen-specific geometries and boundary conditions assuming a known lamellar behaviour. An optimisation process was used to derive the interface stiffness values for each group. The assumption of a linear cohesive interface was used to model the behaviour of the inter-lamellar connectivity. The interface stiffness values derived from the optimisation process were consistently higher than the corresponding lamellar values. The interface stiffness values of the outer annulus were 43% to 75% higher than those of the inner annulus. Tangential stiffness values for the interface were 6% to 39% higher than normal stiffness values within each group and similar to values reported by other investigators. These results reflect the intricate fibrous nature of the inter-lamellar connectivity and provide values for the representation of the inter-lamellar behaviour at a continuum level