Multiscale stabilization for convection-dominated diffusion in heterogeneous media

We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not be sufficient to stabilize multiscale systems. We seek a local reduced-order model for this kind of multiscale transport problems and thus, develop a systematic approach for finding reduced-order approximations of the solution. We start from a Petrov-Galerkin framework using optimal weighting functions. We introduce an auxiliary variable to a mixed formulation of the problem. The auxiliary variable stands for the optimal weighting function. The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full solution on the dimensionally reduced space that approximates the solution. To find the test space, we reformulate some recent mixed Generalized Multiscale Finite Element Methods. We introduce snapshots and local spectral problems that appropriately define local weight and trial spaces. In particular, we use energy minimizing snapshots and local spectral decompositions in the natural norm associated with the auxiliary variable. The resulting spectral decomposition adaptively identifies and builds the optimal multiscale space to stabilize the system. We discuss the stability and its relation to the approximation property of the test space. We design online basis functions, which accelerate convergence in the test space, and consequently, improve stability. We present several numerical examples and show that one needs a few test functions to achieve an error similar to the projection error in the primal variable irrespective of the Peclet number

Capacity Estimation for Vehicle-to-Grid Frequency Regulation Services with Smart Charging Mechanism

Due to various green initiatives, renewable energy will be massively incorporated into the future smart grid. However, the intermittency of the renewables may result in power imbalance, thus adversely affecting the stability of a power system. Frequency regulation may be used to maintain the power balance at all times. As electric vehicles (EVs) become popular, they may be connected to the grid to form a vehicle-to-grid (V2G) system. An aggregation of EVs can be coordinated to provide frequency regulation services. However, V2G is a dynamic system where the participating EVs come and go independently. Thus it is not easy to estimate the regulation capacities for V2G. In a preliminary study, we modeled an aggregation of EVs with a queueing network, whose structure allows us to estimate the capacities for regulation-up and regulation-down, separately. The estimated capacities from the V2G system can be used for establishing a regulation contract between an aggregator and the grid operator, and facilitating a new business model for V2G. In this paper, we extend our previous development by designing a smart charging mechanism which can adapt to given characteristics of the EVs and make the performance of the actual system follow the analytical model.Comment: 11 pages, Accepted for publication in IEEE Transactions on Smart Gri

Effect of fiber inclination on crack bridging stress in brittle fiber reinforced brittle matrix composites

behavior of brittle matrix composites is strongly affected by the bridging of cracks by fibers. In random fiber composites, fibers can lie at an angle to the crack plane. Under such conditions, the bridging stress for a certain crack opening is governed by various micromechanisms including fiber debonding, fiber bending and rupture as well as matrix spalling. While fiber debonding has been widely investigated, the coupled fiber bending/matrix spalling mechanism has received little attention. In this paper, the fiber bending/matrix spalling mechanism is analyzed by treating the fiber as a beam bent on an elastic foundation with variable stiffness and the possibility of spalling. The foundation stiffness and spalling criterion are derived from a finite element analysis. The bridging stress due to bending alone as well as the total bridging stress are then obtained for the case with brittle fibers. Through this analysis, the effect of various microstructural parameters (such as fiber and matrix moduli, matrix spalling strain and fiber/matrix interfacial friction) on the behavior of random fiber composites can be studied. Prediction of maximum bridging stress for inclined fibers based on the present model is shown to be in good agreement with experimental results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29939/1/0000296.pd

TRPV4 mediates cell damage induced by hyperphysiological compression and regulates COX2/PGE2 in intervertebral discs

Background Aberrant mechanical loading of the spine causes intervertebral disc (IVD) degeneration and low back pain. Current therapies do not target the mediators of the underlying mechanosensing and mechanotransduction pathways, as these are poorly understood. This study investigated the role of the mechanosensitive transient receptor potential vanilloid 4 (TRPV4) ion channel in dynamic compression of bovine nucleus pulposus (NP) cells in vitro and mouse IVDs in vivo. Methods Degenerative changes and the expression of the inflammatory mediator cyclooxygenase 2 (COX2) were examined histologically in the IVDs of mouse tails that were dynamically compressed at a short repetitive hyperphysiological regime (vs sham). Bovine NP cells embedded in an agarose-collagen hydrogel were dynamically compressed at a hyperphysiological regime in the presence or absence of the selective TRPV4 antagonist GSK2193874. Lactate dehydrogenase (LDH) and prostaglandin E2 (PGE2) release, as well as phosphorylation of mitogen-activated protein kinases (MAPKs), were analyzed. Degenerative changes and COX2 expression were further evaluated in the IVDs of trpv4-deficient mice (vs wild-type; WT). Results Dynamic compression caused IVD degeneration in vivo as previously shown but did not affect COX2 expression. Dynamic compression significantly augmented LDH and PGE2 releases in vitro, which were significantly reduced by TRPV4 inhibition. Moreover, TRPV4 inhibition during dynamic compression increased the activation of the extracellular signal-regulated kinases 1/2 (ERK) MAPK pathway by 3.13-fold compared to non-compressed samples. Trpv4-deficient mice displayed mild IVD degeneration and decreased COX2 expression compared to WT mice. Conclusions TRPV4 therefore regulates COX2/PGE2 and mediates cell damage induced by hyperphysiological dynamic compression, possibly via ERK. Targeted TRPV4 inhibition or knockdown might thus constitute promising therapeutic approaches to treat patients suffering from IVD pathologies caused by aberrant mechanical stress

Expression and Activity of TRPA1 and TRPV1 in the Intervertebral Disc: Association with Inflammation and Matrix Remodeling

Transient receptor potential (TRP) channels have emerged as potential sensors and transducers of inflammatory pain. The aims of this study were to investigate (1) the expression of TRP channels in intervertebral disc (IVD) cells in normal and inflammatory conditions and (2) the function of Transient receptor potential ankyrin 1 (TRPA1) and Transient receptor potential vanilloid 1 (TRPV1) in IVD inflammation and matrix homeostasis. RT-qPCR was used to analyze human fetal, healthy, and degenerated IVD tissues for the gene expression of TRPA1 and TRPV1. The primary IVD cell cultures were stimulated with either interleukin-1 beta (IL-1β) or tumor necrosis factor alpha (TNF-α) alone or in combination with TRPA1/V1 agonist allyl isothiocyanate (AITC, 3 and 10 µM), followed by analysis of calcium flux and the expression of inflammation mediators (RT-qPCR/ELISA) and matrix constituents (RT-qPCR). The matrix structure and composition in caudal motion segments from TRPA1 and TRPV1 wild-type (WT) and knock-out (KO) mice was visualized by FAST staining. Gene expression of other TRP channels (A1, C1, C3, C6, V1, V2, V4, V6, M2, M7, M8) was also tested in cytokine-treated cells. TRPA1 was expressed in fetal IVD cells, 20% of degenerated IVDs, but not in healthy mature IVDs. TRPA1 expression was not detectable in untreated cells and it increased upon cytokine treatment, while TRPV1 was expressed and concomitantly reduced. In inflamed IVD cells, 10 µM AITC activated calcium flux, induced gene expression of IL-8, and reduced disintegrin and metalloproteinase with thrombospondin motifs 5 (ADAMTS5) and collagen 1A1, possibly via upregulated TRPA1. TRPA1 KO in mice was associated with signs of degeneration in the nucleus pulposus and the vertebral growth plate, whereas TRPV1 KO did not show profound changes. Cytokine treatment also affected the gene expression of TRPV2 (increase), TRPV4 (increase), and TRPC6 (decrease). TRPA1 might be expressed in developing IVD, downregulated during its maturation, and upregulated again in degenerative disc disease, participating in matrix homeostasis. However, follow-up studies with larger sample sizes are needed to fully elucidate the role of TRPA1 and other TRP channels in degenerative disc disease

Exploiting Interference for Energy Harvesting: A Survey, Research Issues, and Challenges

Interference is one of the fundamental aspects that makes wireless communication challenging, which has attracted great research attention for decades. To solve this interference problem, many interference management (IM) techniques h

Development of a standardized histopathology scoring system using machine learning algorithms for intervertebral disc degeneration in the mouse model—An ORS spine section initiative

Mice have been increasingly used as preclinical model to elucidate mechanisms and test therapeutics for treating intervertebral disc degeneration (IDD). Several intervertebral disc (IVD) histological scoring systems have been proposed, but none exists that reliably quantitate mouse disc pathologies. Here, we report a new robust quantitative mouse IVD histopathological scoring system developed by building consensus from the spine community analyses of previous scoring systems and features noted on different mouse models of IDD. The new scoring system analyzes 14 key histopathological features from nucleus pulposus (NP), annulus fibrosus (AF), endplate (EP), and AF/NP/EP interface regions. Each feature is categorized and scored; hence, the weight for quantifying the disc histopathology is equally distributed and not driven by only a few features. We tested the new histopathological scoring criteria using images of lumbar and coccygeal discs from different IDD models of both sexes, including genetic, needle-punctured, static compressive models, and natural aging mice spanning neonatal to old age stages. Moreover, disc sections from common histological preparation techniques and stains including H&E, SafraninO/Fast green, and FAST were analyzed to enable better cross-study comparisons. Fleiss\u27s multi-rater agreement test shows significant agreement by both experienced and novice multiple raters for all 14 features on several mouse models and sections prepared using various histological techniques. The sensitivity and specificity of the new scoring system was validated using artificial intelligence and supervised and unsupervised machine learning algorithms, including artificial neural networks, k-means clustering, and principal component analysis. Finally, we applied the new scoring system on established disc degeneration models and demonstrated high sensitivity and specificity of histopathological scoring changes. Overall, the new histopathological scoring system offers the ability to quantify histological changes in mouse models of disc degeneration and regeneration with high sensitivity and specificity

N-cadherin is key to expression of the nucleus pulposus cell phenotype under selective substrate culture conditions

published_or_final_versio

SOX9 Governs Differentiation Stage-Specific Gene Expression in Growth Plate Chondrocytes via Direct Concomitant Transactivation and Repression

Cartilage and endochondral bone development require SOX9 activity to regulate chondrogenesis, chondrocyte proliferation, and transition to a non-mitotic hypertrophic state. The restricted and reciprocal expression of the collagen X gene, Col10a1, in hypertrophic chondrocytes and Sox9 in immature chondrocytes epitomise the precise spatiotemporal control of gene expression as chondrocytes progress through phases of differentiation, but how this is achieved is not clear. Here, we have identified a regulatory element upstream of Col10a1 that enhances its expression in hypertrophic chondrocytes in vivo. In immature chondrocytes, where Col10a1 is not expressed, SOX9 interacts with a conserved sequence within this element that is analogous to that within the intronic enhancer of the collagen II gene Col2a1, the known transactivation target of SOX9. By analysing a series of Col10a1 reporter genes in transgenic mice, we show that the SOX9 binding consensus in this element is required to repress expression of the transgene in non-hypertrophic chondrocytes. Forced ectopic Sox9 expression in hypertrophic chondrocytes in vitro and in mice resulted in down-regulation of Col10a1. Mutation of a binding consensus motif for GLI transcription factors, which are the effectors of Indian hedgehog signaling, close to the SOX9 site in the Col10a1 regulatory element, also derepressed transgene expression in non-hypertrophic chondrocytes. GLI2 and GLI3 bound to the Col10a1 regulatory element but not to the enhancer of Col2a1. In addition to Col10a1, paired SOX9–GLI binding motifs are present in the conserved non-coding regions of several genes that are preferentially expressed in hypertrophic chondrocytes and the occurrence of pairing is unlikely to be by chance. We propose a regulatory paradigm whereby direct concomitant positive and negative transcriptional control by SOX9 ensures differentiation phase-specific gene expression in chondrocytes. Discrimination between these opposing modes of transcriptional control by SOX9 may be mediated by cooperation with different partners such as GLI factors