On occurrence of spectral edges for periodic operators inside the Brillouin zone

The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the (reduced) Brillouin zone only, rather than the whole zone? Or, do the edges of the spectrum occur necessarily at the set of ``corner'' high symmetry points? This is known to be true in 1D, while no apparent reasons exist for this to be happening in higher dimensions. In many practical cases, though, this appears to be correct, which sometimes leads to the claims that this is always true. There seems to be no definite answer in the literature, and one encounters different opinions about this problem in the community. In this paper, starting with simple discrete graph operators, we construct a variety of convincing multiply-periodic examples showing that the spectral edges might occur deeply inside the Brillouin zone. On the other hand, it is also shown that in a ``generic'' case, the situation of spectral edges appearing at high symmetry points is stable under small perturbations. This explains to some degree why in many (maybe even most) practical cases the statement still holds.Comment: 25 pages, 10 EPS figures. Typos corrected and a reference added in the new versio

Implantation of Mouse Embryonic Stem Cell-Derived Cardiac Progenitor Cells Preserves Function of Infarcted Murine Hearts

Stem cell transplantation holds great promise for the treatment of myocardial infarction injury. We recently described the embryonic stem cell-derived cardiac progenitor cells (CPCs) capable of differentiating into cardiomyocytes, vascular endothelium, and smooth muscle. In this study, we hypothesized that transplanted CPCs will preserve function of the infarcted heart by participating in both muscle replacement and neovascularization. Differentiated CPCs formed functional electromechanical junctions with cardiomyocytes in vitro and conducted action potentials over cm-scale distances. When transplanted into infarcted mouse hearts, CPCs engrafted long-term in the infarct zone and surrounding myocardium without causing teratomas or arrhythmias. The grafted cells differentiated into cross-striated cardiomyocytes forming gap junctions with the host cells, while also contributing to neovascularization. Serial echocardiography and pressure-volume catheterization demonstrated attenuated ventricular dilatation and preserved left ventricular fractional shortening, systolic and diastolic function. Our results demonstrate that CPCs can engraft, differentiate, and preserve the functional output of the infarcted heart

Decomposition cross-correlation for analysis of collagen matrix deformation by single smooth muscle cells

Microvascular remodeling is known to depend on cellular interactions with matrix tissue. However, it is difficult to study the role of specific cells or matrix elements in an in vivo setting. The aim of this study is to develop an automated technique that can be employed to obtain and analyze local collagen matrix remodeling by single smooth muscle cells. We combined a motorized microscopic setup and time-lapse video microscopy with a new cross-correlation based image analysis algorithm to enable automated recording of cell-induced matrix reorganization. This method rendered 60–90 single cell studies per experiment, for which collagen deformation over time could be automatically derived. Thus, the current setup offers a tool to systematically study different components active in matrix remodeling

Computational methodology to determine fluid related parameters on non regular three-dimensional scaffolds

The application of three-dimensional (3D) biomaterials to facilitate the adhesion, proliferation, and differentiation of cells has been widely studied for tissue engineering purposes. The fabrication methods used to improve the mechanical response of the scaffold produce complex and non regular structures. Apart from the mechanical aspect, the fluid behavior in the inner part of the scaffold should also be considered. Parameters such as permeability (k) or wall shear stress (WSS) are important aspects in the provision of nutrients, the removal of metabolic waste products or the mechanically-induced differentiation of cells attached in the trabecular network of the scaffolds. Experimental measurements of these parameters are not available in all labs. However, fluid parameters should be known prior to other types of experiments. The present work compares an experimental study with a computational fluid dynamics (CFD) methodology to determine the related fluid parameters (k and WSS) of complex non regular poly(L-lactic acid) scaffolds based only on the treatment of microphotographic images obtained with a microCT (lCT). The CFD analysis shows similar tendencies and results with low relative difference compared to those of the experimental study, for high flow rates. For low flow rates the accuracy of this prediction reduces. The correlation between the computational and experimental results validates the robustness of the proposed methodology.The authors gratefully acknowledge research support from the Spanish Ministry of Science and Innovation through research project DPI2010-20399-C04-01. The Instituto de Salud Carlos III (ISCIII) through the CIBER initiative and the Platform for Biological Tissue Characterization of the Centro de Investigacion Biomedica en Red en Bioingenieria, Biomateriales y Nanomedicina (CIBER-BBN) are also gratefully acknowledged.Acosta Santamaría, VA.; Malvé, M.; Duizabo, A.; Mena Tobar, A.; Gallego Ferrer, G.; García Aznar, J.; Doblare Castellano, M.... (2013). Computational methodology to determine fluid related parameters on non regular three-dimensional scaffolds. Annals of Biomedical Engineering. 41(11):2367-2380. https://doi.org/10.1007/s10439-013-0849-8S236723804111Acosta Santamaría, V., H. Deplaine, D. Mariggió, A. R. Villanueva-Molines, J. M. García-Aznar, J. L. Gómez Ribelles, M. Doblaré, G. Gallego Ferrer, and I. Ochoa. Influence of the macro and micro-porous structure on the mechanical behavior of poly(l-lactic acid) scaffolds. J. Non-Cryst. Solids 358(23):3141–3149, 2012.Adachi, T., Y. Osako, M. Tanaka, M. Hojo, and S. J. Hollister. 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MR fluoroscopy in vascular and cardiac interventions (review)

Vascular and cardiac disease remains a leading cause of morbidity and mortality in developed and emerging countries. Vascular and cardiac interventions require extensive fluoroscopic guidance to navigate endovascular catheters. X-ray fluoroscopy is considered the current modality for real time imaging. It provides excellent spatial and temporal resolution, but is limited by exposure of patients and staff to ionizing radiation, poor soft tissue characterization and lack of quantitative physiologic information. MR fluoroscopy has been introduced with substantial progress during the last decade. Clinical and experimental studies performed under MR fluoroscopy have indicated the suitability of this modality for: delivery of ASD closure, aortic valves, and endovascular stents (aortic, carotid, iliac, renal arteries, inferior vena cava). It aids in performing ablation, creation of hepatic shunts and local delivery of therapies. Development of more MR compatible equipment and devices will widen the applications of MR-guided procedures. At post-intervention, MR imaging aids in assessing the efficacy of therapies, success of interventions. It also provides information on vascular flow and cardiac morphology, function, perfusion and viability. MR fluoroscopy has the potential to form the basis for minimally invasive image–guided surgeries that offer improved patient management and cost effectiveness

Imaging Long-Term Fate of Intramyocardially Implanted Mesenchymal Stem Cells in a Porcine Myocardial Infarction Model

The long-term fate of stem cells after intramyocardial delivery is unknown. We used noninvasive, repetitive PET/CT imaging with [18F]FEAU to monitor the long-term (up to 5 months) spatial-temporal dynamics of MSCs retrovirally transduced with the sr39HSV1-tk gene (sr39HSV1-tk-MSC) and implanted intramyocardially in pigs with induced acute myocardial infarction. Repetitive [18F]FEAU PET/CT revealed a biphasic pattern of sr39HSV1-tk-MSC dynamics; cell proliferation peaked at 33–35 days after injection, in periinfarct regions and the major cardiac lymphatic vessels and lymph nodes. The sr39HSV1-tk-MSC–associated [18F]FEAU signals gradually decreased thereafter. Cardiac lymphography studies using PG-Gd-NIRF813 contrast for MRI and near-infrared fluorescence imaging showed rapid clearance of the contrast from the site of intramyocardial injection through the subepicardial lymphatic network into the lymphatic vessels and periaortic lymph nodes. Immunohistochemical analysis of cardiac tissue obtained at 35 and 150 days demonstrated several types of sr39HSV1-tk expressing cells, including fibro-myoblasts, lymphovascular cells, and microvascular and arterial endothelium. In summary, this study demonstrated the feasibility and sensitivity of [18F]FEAU PET/CT imaging for long-term, in-vivo monitoring (up to 5 months) of the fate of intramyocardially injected sr39HSV1-tk-MSC cells. Intramyocardially transplanted MSCs appear to integrate into the lymphatic endothelium and may help improve myocardial lymphatic system function after MI

Genome-wide association study of REM sleep behavior disorder identifies polygenic risk and brain expression effects

Rapid-eye movement (REM) sleep behavior disorder (RBD), enactment of dreams during REM sleep, is an early clinical symptom of alpha-synucleinopathies and defines a more severe subtype. The genetic background of RBD and its underlying mechanisms are not well understood. Here, we perform a genome-wide association study of RBD, identifying five RBD risk loci near SNCA, GBA, TMEM175, INPP5F, and SCARB2. Expression analyses highlight SNCA-AS1 and potentially SCARB2 differential expression in different brain regions in RBD, with SNCA-AS1 further supported by colocalization analyses. Polygenic risk score, pathway analysis, and genetic correlations provide further insights into RBD genetics, highlighting RBD as a unique alpha-synucleinopathy subpopulation that will allow future early intervention