Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure

Association of the CXCL9-CXCR3 and CXCL13-CXCR5 axes with B-cell trafficking in giant cell arteritis and polymyalgia rheumatica

OBJECTIVE: B-cells are present in the inflamed arteries of giant cell arteritis (GCA) patients and a disturbed B-cell homeostasis is reported in peripheral blood of both GCA and the overlapping disease polymyalgia rheumatica (PMR). In this study, we aimed to investigate chemokine-chemokine receptor axes governing the migration of B-cells in GCA and PMR. METHODS: We performed Luminex screening assay for serum levels of B-cell related chemokines in treatment-naïve GCA (n = 41), PMR (n = 31) and age- and sex matched healthy controls (HC, n = 34). Expression of chemokine receptors on circulating B-cell subsets were investigated by flow cytometry. Immunohistochemistry was performed on GCA temporal artery (n = 14) and aorta (n = 10) and on atherosclerosis aorta (n = 10) tissue. RESULTS: The chemokines CXCL9 and CXCL13 were significantly increased in the circulation of treatment-naïve GCA and PMR patients. CXCL13 increased even further after three months of glucocorticoid treatment. At baseline CXCL13 correlated with disease activity markers. Peripheral CXCR3+ and CXCR5+ switched memory B-cells were significantly reduced in both patient groups and correlated inversely with their complementary chemokines CXCL9 and CXCL13. At the arterial lesions in GCA, CXCR3+ and CXCR5+ B-cells were observed in areas with high CXCL9 and CXCL13 expression. CONCLUSION: Changes in systemic and local chemokine and chemokine receptor pathways related to B-cell migration were observed in GCA and PMR mainly in the CXCL9-CXCR3 and CXCL13-CXCR5 axes. These changes can contribute to homing and organization of B-cells in the vessel wall and provide further evidence for an active involvement of B-cells in GCA and PMR

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Indication of activated senescence pathways in the temporal arteries of patients with giant cell arteritis

OBJECTIVES: Giant cell arteritis (GCA) affects almost exclusively individuals above 50 years old, suggesting a role of aging-related changes such as cellular senescence in its pathobiology. p21 WAF1/CIP1 and p16/INK4A play key roles in two distinct pathways leading to senescence. The proinflammatory molecules Interleukin (IL)-6 and Granulocyte-Macrophage Colony-Stimulating Factor (GM-CSF), which are key components of the senescence-associated secretory phenotype (SASP), are effective targets of treatment in GCA. Here, we aim to investigate the presence of p21 and p16 positive cells producing these SASP cytokines in temporal artery biopsies (TABs) of patients with GCA.METHODS: Eight patients with GCA and 14 age-matched, non-GCA individuals who underwent a TAB were included. Immunohistochemical staining of p21, p16, IL-6 and GM-CSF was performed. Multiplex immunofluorescent staining was performed to investigate the colocalization of p21 and p16 with IL-6, GM-CSF, and immune cell markers (CD68, CD3, CD20).RESULTS: p16, p21, IL-6 and GM-CSF were elevated in the TABs of patients with GCA. Both p16 and p21 expressing cells were mainly found near the internal lamina elastica, especially among giant cells and macrophages, although p21 and p16 expression could be found in all three layers of the vessels. Expression of p16 and p21 was occasionally found in T cells but not B cells. p16+ and p21+ cells expressing GM-CSF/IL-6 were detected throughout the TABs.CONCLUSION: Our data suggests the presence of activated senescence pathways at the site of vascular inflammation in GCA and support further research into the role of senescence in the pathophysiology of GCA. This article is protected by copyright. All rights reserved.</p

Cytokine producing B-cells and their capability to polarize macrophages in giant cell arteritis

OBJECTIVE: The lack of disease-specific autoantibodies in giant cell arteritis (GCA) suggests an alternative role for B-cells readily detected in the inflamed arteries. Here we study the cytokine profile of tissue infiltrated and peripheral blood B-cells of patients with GCA. Moreover, we investigate the macrophage skewing capability of B-cell-derived cytokines.METHODS: The presence of various cytokines in B-cell areas in temporal artery (n = 11) and aorta (n = 10) was identified by immunohistochemistry. PBMCs of patients with GCA (n = 11) and polymyalgia rheumatica (n = 10), and 14 age- and sex-matched healthy controls (HC) were stimulated, followed by flow cytometry for cytokine expression in B-cells. The skewing potential of B-cell-derived cytokines (n = 6 for GCA and HC) on macrophages was studied in vitro.RESULTS: The presence of IL-6, GM-CSF, TNFα, IFNγ, LTβ and IL-10 was documented in B-cells and B-cell rich areas of GCA arteries. In vitro, B-cell-derived cytokines (from both GCA and HC) skewed macrophages towards a pro-inflammatory phenotype with enhanced expression of IL-6, IL-1β, TNFα, IL-23, YKL-40 and MMP-9. In vitro stimulated peripheral blood B-cells from treatment-naïve GCA patients showed an enhanced frequency of IL-6+ and TNFα+IL-6+ B-cells compared to HCs. This difference was no longer detected in treatment-induced remission. Erythrocyte sedimentation rate positively correlated with IL-6+TNFα+ B-cells.CONCLUSION: B-cells are capable of producing cytokines and steering macrophages towards a pro-inflammatory phenotype. Although the capacity of B-cells in skewing macrophages is not GCA specific, these data support a cytokine-mediated role for B-cells in GCA and provide grounds for B-cell targeted therapy in GCA.</p

Massive B-Cell Infiltration and Organization Into Artery Tertiary Lymphoid Organs in the Aorta of Large Vessel Giant Cell Arteritis

Giant cell arteritis (GCA) can be classified into Cranial(C)-GCA and Large Vessel(LV)-GCA. Based on analysis of temporal arteries, GCA is postulated to be T-cell-mediated. Recently, a disturbed B-cell homeostasis was documented in newly diagnosed GCA patients. In the current study, we assessed the presence of B-cells and their level of ectopic organization in the aorta of LV-GCA patients. Aorta tissue samples of 9 histologically-proven LV-GCA patients and 22 age-and sex-matched atherosclerosis patients who underwent aortic aneurysm surgery were studied by immunohistochemistry. Sections were stained for B-cells, T-cells, follicular dendritic cells, high endothelial venules, germinal center B-cells, proliferating B-cells, macrophages, and plasma cells. Aortas of LV-GCA patients showed massive infiltration of B-cells, which clearly outnumbered T-cells, as opposed to C-GCA patients where, as previously reported, T-cells outnumber B-cells. B-cells were mainly found in the adventitia of the vessel wall and were organized into artery tertiary lymphoid organs. These tertiary lymphoid organs had germinal centers, proliferating B-cells and plasma cell niches. In conclusion, we found massive and organized B-cell infiltrates in the aorta of LV-GCA patients, which is in line with the previously documented decrease of circulating B-cells in active GCA. Our data indicate a role for B-cells in the pathogenesis of GCA and thus evoke further investigation into the factors determining the tissue tropism and organization of B-cells in GCA

Reoperations after first lumbar disc herniation surgery; a special interest on residives during a 5-year follow-up

BACKGROUND: The overall rate of operations after recurrent lumbar disc herniation has been shown to be 3–11%. However, little is known about the rate of residives. Thus the aim of this study was to explore the cumulative rates of re-operations and especially residive disc herniations at the same side and level as the primary disc herniation after first lumbar disc herniation surgery and the factors that influence the risk of re-operations over a five year follow-up study. METHODS: 166 virgin lumbar disc herniation patients (mean age 42 years, 57% males) were studied. Data on patients' initial disc operations and type and timing of re-operations during the follow-up were collected from patient files. Back and leg pain on visual analog scale and employment status were collected by questionnaires. RESULTS: The cumulative rate of re-operations for lumbar disc herniation was 10.2% (95% Cl 6.0 to 15.1). The rate of residives at initial site was 7.4% (95% Cl 3.7 to 11.3) and rate of lumbar disc herniations at other sites was 3.1% (95% Cl 0.6 to 6.2). The occurrence of residive lumbar disc herniations was evenly distributed across the 5 years. Neither age, gender, preoperative symptoms, physical activity nor employment had effect on the probability of re-operation. CONCLUSION: Seven percent of the lumbar disc patients had a residive lumbar disc operation within five years of their first operation. No specific factors influencing the risk for re-operation were found

Effect of defects on reaction of NiO surface with Pb-contained solution

In order to understand the role of defects in chemical reactions, we used two types of samples, which are molecular beam epitaxy (MBE) grown NiO(001) film on Mg(001) substrate as the defect free NiO prototype and NiO grown on Ni(110) single crystal as the one with defects. In-situ observations for oxide-liquid interfacial structure and surface morphology were performed for both samples in water and Pb-contained solution using high-resolution X-ray reflectivity and atomic force microscopy. For the MBE grown NiO, no significant changes were detected in the high-resolution X-ray reflectivity data with monotonic increase in roughness. Meanwhile, in the case of native grown NiO on Ni(110), significant changes in both the morphology and atomistic structure at the interface were observed when immersed in water and Pb-contained solution. Our results provide simple and direct experimental evidence of the role of the defects in chemical reaction of oxide surfaces with both water and Pb-contained solution.ope