",isbn:"978-1-80356-678-8",printIsbn:"978-1-80356-677-1",pdfIsbn:"978-1-80356-679-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,isSalesforceBook:!1,isNomenclature:!1,hash:"6dcb071a2e978694b6b1cb9c20afc1a3",bookSignature:"Prof. Hai-Zhi Song",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/11494.jpg",keywords:"Electric Field Effect, Nano-Materials, Electric Field Design, Antenna, Microelectronics, Optoelectronics, Electric Field Stimulation, Brain and Nerve, Electric Field Imaging, Atomic Electric Field, Space Science, Climate",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"March 22nd 2022",dateEndSecondStepPublish:"May 26th 2022",dateEndThirdStepPublish:"July 25th 2022",dateEndFourthStepPublish:"October 13th 2022",dateEndFifthStepPublish:"December 12th 2022",dateConfirmationOfParticipation:null,remainingDaysToSecondStep:"a day",secondStepPassed:!0,areRegistrationsClosed:!1,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"A pioneering researcher in the fields of new materials, optoelectronic devices, and quantum information processing, appointed vice director of the Science and Technology Committee of SWITP, author/co-author of more than 170 research papers, and holder of 40 patents.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"196114",title:"Prof.",name:"Hai-Zhi",middleName:null,surname:"Song",slug:"hai-zhi-song",fullName:"Hai-Zhi Song",profilePictureURL:"https://mts.intechopen.com/storage/users/196114/images/system/196114.jpg",biography:"Curriculum Vitae\n\nName: Hai-Zhi Song \nGender: male\nDate of Birth: Oct. 20, 1968\nPlace of Birth: Shanxi, China\nAffiliation and Address: \nSouthwest Institute of Technical Physics\nNo.7, Section 4, Renminnan Road, Chengdu 610041, China\nAnd\nInstitute of Fundamental and Frontier Sciences,\nUniversity of Electronic Science and Technology of China,\nNo. 4, Section 2, Jianshebei Road, Chengdu 610054, China\n\nWork Phone: +86-28-68180751, +86-28-83208728\nMobile Phone: +86-158-28239155\nFax: +86-28-83201896\nE-mail: hzsong1296@163.com, hzsong@uestc.edu.cn\n \nEducation \nSept, 1990 – July, 1995:Peking University, PhD, Thesis “Visible luminescence of porous silicon and its mechanism”, Researches on hydrogen-influenced Schottky diodes and silicon-based light-emitting materials. \nSept, 1986 – July, 1990:Nanjing University, Bachelor of Science, Thesis “Study of refractory metal silicides”, Research on Ohmic contact of semiconductors.\n\nWork Experience \nJuly, 1995 – Sept. 1997: Nanjing University, Nanjing, China, Postdoctoral Researcher, Research on silicon-based light-emitting materials. \nOct, 1997 – Sept. 1998: Catholic University Leuven, Leuven, Belgium, Visiting free Researcher, Research on amorphous semiconductors. \nOct, 1998 – Sept. 2001: Tsukuba University, Tsukuba, Japan, Assistant Professor, Research on semiconductor quantum dots. \nOct, 2001 – March 2012: Fujitsu Lab. Ltd., Atsugi, Japan, Researcher/Senior Researcher, Researches on Semiconductor Quantum Dots for Quantum Information, Semiconductor Optoelectronic Materials and Devices. \nApril, 2012 – March 2014: University of Tokyo, Tokyo, Japan, Senior Researcher, Researches on Quantum Information Processing Devices. \nApril, 2014 – now: Southwest Institute of Technical Physics, Chengdu, China, Professor, Researches on Semiconductor Optoelectronic Materials and Devices. \nJune, 2015 – now: University of Electronic Science and Technology, Chengdu, China, Professor, Researches on Nanoscaled Semiconductors and Quantum Information Processing Devices.\n \nAchievements\nSystematically studied the property of porous silicon materials and verified their mechanism; found green and ultraviolet luminescence, and clarified the multiple luminescence mechanisms of nanocrystalline-silicon embedded in SiO2, which is valuable to silicon-based optoelectronic integration; realized enhanced hole mobility in amorphous silicon, verified the existence of deep trap states in amorphous selenium, providing ways to improve amorphous optoelectronic materials. \nDiscovered lateral coupling between self-assembled quantum dots (QDs) and their tuning effect to 2D electron gas; illustrated and deeply explained the metal-insulator transition in 2D ordered QD arrays, all of which are worth in optoelectronic application of semiconductor QDs. \nDeveloped Sb-free technique to double the InAs/GaAs QD density and suppress the atomic interdiffusion, helped producing 1.3 um QD lasers, which won Japanese national prizes and had been merchandized; developed 1.06 um quantum-well lasers, which have been used to produce pure-green lasers robust against high temperature. \nFound a way to access buried QDs by scanning tunneling microscope; achieved a way to prepare diluted QDs by post-annealing and clarified its mechanisms; invented a technique to control the size and site of QDs by atomic-force microscopy lithography, and an apparatus to detect single electron spin states by optically-detected magnetic resonance; designed a few types of micropillar cavities applicable to realize 1.55 um highly-efficient, even coherent (strongly coupled) InAs/InP QD single photon sources; produced fiber-integrated photon-entangled sources, all of which are very useful to the applications of QDs in quantum information processing. \nDeveloped focal-plane single-photon avalanche detectors, providing central devices for 3D laser detecting and ranging system; explored antimonide middle- and long-wavelength infrared detectors and the surface plasmon enhancement effect in such detectors; advanced the acetone-sensing function of Eu-doped SnO2 nano-belt; found Nickle Phosphide serving as a good catalyst in hydrogen-producing. Realized a series of optoelectronic quantum devices for quantum information processing, such as fiber-integrated photon-pair-entangler, chiplet heralded single photon emitter, fiber quantum memories, quantum number generator, etc.\n\nHonor and Group Memberships \nSelected Scholar of the Recruitment Program of Global Experts, China\nEditorial member of “Laser Technology”\nEditorial member of “Journal of Electronic Science and Technology”\nEditorial member of “Internal J. Mat. Sci. Appl”\nMember of APS (American Physics Society)\nMember of OSA (Optical Society of America)\nPermanent Member of China Physical Science and Technology\nPermanent Member of the Chinese Optical Society\nTechnical committee member of PIERS, organizing a series of “quantum information processing and devices” sessions\nTechnical committee member of ICICM",institutionString:"Southwest University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Southwest University",institutionURL:null,country:{name:"China"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"20",title:"Physics",slug:"physics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"453623",firstName:"Silvia",lastName:"Sabo",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/453623/images/20396_n.jpg",email:"silvia@intechopen.com",biography:null}},relatedBooks:[{type:"book",id:"8356",title:"Metastable, Spintronics Materials and Mechanics of Deformable Bodies",subtitle:"Recent Progress",isOpenForSubmission:!1,hash:"1550f1986ce9bcc0db87d407a8b47078",slug:"solid-state-physics-metastable-spintronics-materials-and-mechanics-of-deformable-bodies-recent-progress",bookSignature:"Subbarayan Sivasankaran, Pramoda Kumar Nayak and Ezgi Günay",coverURL:"https://cdn.intechopen.com/books/images_new/8356.jpg",editedByType:"Edited by",editors:[{id:"190989",title:"Dr.",name:"Subbarayan",surname:"Sivasankaran",slug:"subbarayan-sivasankaran",fullName:"Subbarayan Sivasankaran"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophile",surname:"Theophanides",slug:"theophile-theophanides",fullName:"Theophile Theophanides"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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1. Introduction
Spinal Cord Injury (SCI) is a devastating trauma and according to the National Spinal Cord Injury Statistical Center (NSCISC) there are approximately 294,000 people living with SCI in the United States [1]. After spinal SCI there is immediate cell death caused directly from the insult followed by a cascade of inflammation that leads to additional cell death and a much larger scar formation that impedes axonal regeneration [2, 3]. Although there are several positive effects of inflammation after SCI, the extensive infiltration of immune cells is a principal contributor to neural degeneration [4, 5]. These immune cells are guided to the lesion site from the periphery via many signaling cues including several interleukins (ILs) released by microglia, astrocytes, and peripheral macrophages within the lesion [5, 6].
Throughout the first hours after injury, polymorphonuclear leukocytes are the predominant infiltrating cells and over-activation of these cells causes tissue destruction through the release of significant amounts of neurotoxins including reactive oxygen species (ROS), reactive nitrogen species (RNS), chemokines, and enzymes [5, 7, 8]. Microglia, the resident macrophages, are also activated and migrate to the site of injury, proliferate, and transform from the ramified phenotype to amoeboid phagocytic cells [9]. These activated microglia and peripheral macrophages make up the majority of inflammatory cells present at the site of the lesion. Although in normal wound healing macrophages sequentially change and reduce inflammation, after SCI macrophages persist in an inflammatory state for prolonged periods resulting in progressive tissue degeneration [10, 11]. However these microglia/macrophages can be activated toward an anti-inflammatory phenotype and ILs are important signaling cues in the extracellular environment that help dictate this contrasting phenotype. The goal of this chapter is to examine the role ILs have on the dynamic inflammatory process that occurs after SCI.
2. Interleukins involved in inflammation after SCI
There are numerous known ILs and several of these ILs are shown to be involved in inflammation after SCI. Throughout this chapter we will discuss the ILs that have been investigated after SCI and whether their role is predominately inflammatory or anti-inflammatory. It is important to note, the role an IL plays after injury is not as simple as just inflammatory or anti-inflammatory. For many of the ILs there are multiple factors that determine whether they will have a beneficial role or a detrimental role, including the extent of initial injury, concentration of IL, other associated molecules in the injury, and the response of immune cells and glial cells [12, 13].
Although there is a broad spectrum of signaling molecules including cytokines, chemokines, and other reactive species after SCI, this chapter will just focus on ILs and only the ILs that are known to play a role in inflammation after SCI [14]. These ILs will be discussed in terms of the cell types that produce them, receptors they bind, cell types they target, timeline of upregulation, and ultimately their effect on inflammation after SCI.
2.1 Interleukin-1 family cytokines
IL-1α, IL-1β, and IL-33 are members of the IL-1 family that have been studied after SCI and all are predominantly inflammatory [15]. IL-1 is released via activated macrophages and microglia largely in response to disease, infection, or inflammatory events. IL-1 has two structurally and biologically similar isoforms, IL-1α and IL-1β [13]. These two isoforms share roughly 30% amino acid sequence homology and although they perform similar biological functions, IL-1β plays a more substantial role post-SCI [16, 17]. IL-1β has been shown to contribute to the exaggerated neuroinflammation following SCI that leads to secondary neural degeneration and cell death [16]. IL-1 signaling following SCI is diverse and complex, resulting in a recruitment of neurotoxins or immune system molecules that contribute to the inflammatory response [13].
The primary receptor for signaling of both IL-1 isoforms is the type-I interleukin-1 receptor (IL-1RI). IL-1 signaling is further regulated by a decoy receptor (IL-1RII) and a receptor antagonist (IL-1ra) [13]. The expression of these receptors mediates the inflammatory response to SCI and their mechanisms have been widely studied following SCI. After SCI in rats, IL-1R1 expression is elevated as early as 4 hours, peaks at 8 hours to 1-day and remains elevated for 7 days post-injury [13]. Another study tested the role of IL-1ra as a regulatory molecule following SCI and observed that increased expression of IL-1ra suppressed IL-1β levels and increased locomotor function following SCI, suggesting that IL-1β and IL-1RI play critical roles in secondary tissue damage and impaired functional recovery post-SCI [16]. Likewise, administration of IL-1β suppressed the expression of IL-1ra following SCI indicating the regulatory nature of IL-1β interactions with its receptor antagonist [16]. Similarly, a study using IL-1 knockout mice observed a significantly smaller lesion area and improved locomotor function after SCI in comparison to wild-type mice [18].
The signaling cascade of the IL-1β/IL-1RI pathway is complex and yet to be completely understood, however it is widely understood that it stimulates the production of toxic intermediates that cause neural degeneration and cell death [13]. These toxic inflammatory mediators include prostaglandins, cyclooxygenase 2, and phospholipase A2 [13]. However, there are studies showing benefits of IL-1, where IL-1β null mice failed to remyelinate as rapidly as wild-type mice [19]. These different roles IL-1 plays are likely due to several factors including extent of injury as well as IL-1 concentration and timing of upregulation, but at present are not well understood.
Another member of the IL-1 family, IL-33, predominantly induces type-2 immune responses against allergens and infectious diseases [20]. IL-33 is upregulated in response to SCI and tends to localize in spinal cord astrocytes to reduce T cell infiltration and overexaggerated inflammation that leads to neuronal cell death [21]. IL-33 is classified as an alarm signal (alarmin) and is released by epithelial cells upon signals of cell or tissue death, but the exact in vivo mechanism of release is not fully understood [22]. After its release, IL-33 binds to ST2 receptors (IL-1RL1) that are present on multiple immune cells as an alert signal for immunologic and neurologic damage or inflammation [22].
One study that treated SCI injury in mice with administration of recombinant IL-33 indicated an attenuation of spinal cord encephalomyelitis progression and a significant decrease in neural tissue death, decrease in demyelination, and an overexaggerated astrocyte infiltration at the lesion site of the contused spinal cord [21]. These results yielded a significant increase in functional recovery and a dramatic decrease of the expression of TNF-α in the spinal cord for as long as 42 days post-SCI. In addition to suppression of pro-inflammatory cytokine release, IL-33 administration promoted the activation of anti-inflammatory M2 macrophage/microglia [21].
2.2 Interleukin-2 family cytokines
Cytokines from the IL-2 family, IL-2, IL-4, IL-7, IL-15, and IL-21, all share a common receptor subunit (gammac), which plays a major role in promoting and maintaining T lymphocyte populations [23]. IL-2 is a pro-inflammatory cytokine made up of four α helixes and is produced mainly by CD4+ cells when activated. At an mRNA level, signals from T-cell receptor (TCR) and CD28 closely regulate the production of IL-2 [24]. After synthesis, IL-2 binds to a receptor complex, which consists of three subunits, IL-2Rα, IL-2Rβ, and the common γ-chain [24]. All three subunits are needed to achieve high affinity binding. These receptors are located on regulatory T cells and antigen-activated T lymphocytes [25]. To produce an IL-2-dependent response, IL-2 must be produced and IL-2R must be expressed within the same microenvironments [25].
IL-2 and its receptor, IL-2R, are crucial to maintaining the balance of the timing and adequacy of an immune response [26]. The primary role of IL-2 is to perpetuate the proper response of memory T-cells to invading pathogens [27]. In addition, IL-2 is vital to the survival, as well as death, of lymphocytes, which has an effect on the development of the immune system. By properly maintaining the life of regulatory T cells (T reg) and activation-induced cell death, IL-2 is able to eliminate self-reactive T cells as a preventative measure against autoimmune diseases [27]. After SCI in a rat, IL-2 levels were significantly lower than intact controls from 3 days to 2 weeks post-SCI [14]. In addition, the interaction of IL-2 with its receptor after SCI contributes to the proliferation of T-helpers, which also have an effect on the proliferation of cytotoxic T cells, natural killer cells, lymphokine-activated killers, B cells, and macrophages [14].
IL-4 and IL-13 are related anti-inflammatory cytokines that regulate many aspects of inflammation and have also been shown to induce alternative macrophage activation (Figure 1) [28]. IL-4 is a cytokine that is involved in regulating immunity, and is secreted by Th2 cells, eosinophils, basophils, and mast cells [29]. IL-4 is also involved in allergic inflammation by utilizing Th2 lymphocytes, differentiated from Th cells, which can then be used in the production of effector cytokines [30]. IL-4 binds to its receptor IL-4Rα, and will dimerize with either γc (the common cytokine-receptor γ-chain) and produce the type-1 signaling complex, or with IL-13Rα1 and produce the type-2 signaling complex (Figure 1) [29, 31]. Although IL-4 has a major impact on immunity, it also affects cognition based on T-cells mediated by IL-4. When administered within a short period post injury, IL-4 exhibits anti-inflammatory effects; however, it can exert a pro-inflammatory response when macrophages possessing IL-4 are undergoing pro-inflammatory stimulation [29].
Figure 1.
IL-4, IL-13, and IL-10 pathways and effects.
Lima et al. (2017) performed a study to understand the effect of the acute and sub-acute treatment using IL-4 on various populations of neural cells and on functional recovery in vivo. In the injured spinal cord, treatment using a systemic delivery of IL-4 (0.35 μg/kg) for 7 days, led to an upregulation of the anti-inflammatory IL-10 and a reduction in area of macrophage/microglia expressing inflammation markers CD11b and inducible nitric oxide synthase (iNOS) [32]. After systemic IL-4 treatment, they also observed an increase in the number of O4-positive cells (a marker for both type I and type II oligodendrocytes) and neuronal markers βIII-tubulin and NeuN, suggesting that IL-4 has a role in neuroprotection. This overall reduction in inflammation resulted in improved hind limb function in rats after SCI. Although they observed several positive effects, systemic IL-4 did not have an effect on the number of astrocytes or lesion size [32]. In another study a delayed intraspinal injection of IL-4 (100 ng of recombinant IL-4, 48 hours after injury) was given after a spinal cord contusion in mice [33]. The intraspinal injection of IL-4 resulted in an increase in microglia/macrophages expressing antigens characteristic of an anti-inflammatory M2 phenotype, reduced tissue damage, and improved hind limb function in mice after SCI [33]. These studies suggest that therapies using IL-4 could be a valuable treatment for improving function after SCI.
IL-13 is produced by different T cell subsets, dendritic cells, and activated Th2 cells [34]. Although the IL-13α2 receptor was originally thought to be a “decoy” receptor that serves as a neutralizer (Figure 1) [35], Fichtner-Feigl et al. showed a role for IL-13Rα2-mediated signaling that required the cytoplasmic tail of IL-13Rα2 in the production of transforming growth factor beta (TGF-β), an anti-inflammatory shown to down-regulate inflammatory cytokines, providing evidence for IL -13Ra2-mediated signaling (Figure 1) [31, 36]. Furthermore, after SCI it was shown that transplanted mesenchymal stem cells continuously expressing IL-13 improved functional recovery and decreased lesion size. In addition, IL-13 increased the amount of ARG-1-expressing macrophages [37].
IL-7 is a homeostatic cytokine that plays a key role in the survival of multiple immune cells and acts on lymphocytes [38]. The IL-7 receptor complex is composed of two chains, IL-7Rα and γc (the common cytokine-receptor γ-chain), which signal downstream to the JAK/STAT5 pathway, and assists in regulating the survival and development of immune cells [38]. IL-7 is produced by stromal cells in lymphoid organs and is necessary for T-cell development and their survival in the periphery [39].
After SCI in mice, IL-7 is promptly upregulated and displays as a strong chemotactic property for macrophages [40]. An intraspinal injection of IL-7 after SCI in mice, resulted in an increase in pro-inflammatory cytokines IL-1β, IL-6, and TNF-α, and a decrease in the anti-inflammatory cytokine IL-10 [38]. The increase in IL-7 also led to an increase in apoptosis, macrophage infiltration, and a decrease in hind limb function in mice after SCI [38]. Moreover, blocking the IL-7 receptor after SCI in mice, resulted in suppression of pro-inflammatory cytokines IFN-γ and TNF-α, an increase in IL-4 and IL-13, more macrophages expressing antigens characteristic of an anti-inflammatory M2 phenotype, an increase in spared white matter, and an improvement in hind limb function [40]. During SCI, the JAK/STAT5 pathway is activated, and IL-7 post-SCI also contributes to the activation of the JAK/STAT5 pathway, which upholds a crucial role in the inflammatory response and secondary damage [38]. When the JAK/STAT5 pathway was inhibited by pimozide, the effects of IL-7 discontinued, which emphasizes the relationship between the JAK/STAT5 pathway and IL-7 function [38]. Therefore, Yuan et al. (2019) concluded that the IL-7/JAK/STAT5 axis targeted by antagonists may represent a potential therapeutic treatment for SCI [38].
Similar to IL-2, IL-15 is a pro-inflammatory cytokine that is also part of the four α helix cytokine family. The main function of IL-15 is to provide a long-term immune response to invading pathogens by contributing to the homeostasis of natural killer cells and CD8+ memory T cells that express IL-2/IL-15Rβ and γc [27]. IL-15 has three receptors, IL-15Rα, IL-2Rβ, and γc, and shares two of the receptors with IL-2 (IL-2Rβ and γc) [41]. Although IL-15 has not been well studied after SCI, it has been shown to be involved in the development of neuropathic pain from nerve injury [42]. After sciatic nerve injury, IL-15 expression was observed in the spinal cord in astrocytes and microglia, and it is also present in neurons located in the dorsal and ventral horn [42].
IL-21 is a pleiotropic cytokine expressed by many immune cells including natural killer T cells and activated CD4+ T cells [43]. Similar to other inflammatory mediators, IL-21 is upregulated after SCI [44, 45]. Fu et al. (2017) studied peripheral blood-derived mesenchymal stem cells (PBMSCs) as a therapy for SCI and their role in the lesion microenvironment by analyzing the neuroprotection, differentiation, and immunoregulation of PBMSCs that were engrafted. When IL-21 was inhibited, a decrease in the secretion of IL-23a and IL-22 occurred [44]. When investigating the potential Th17/Treg-relative mechanism of PBMSCs therapy after SCI, Fu et al. (2017) discovered that the M1 macrophage migrated to lesion site and resulted in the pro-inflammatory secretion of IL-6 and IL-21, which led to CD4 + T cells differentiating into CD4 + IL17 + Th17 cells [44]. Furthermore it has been shown that IL-17 production is stimulated by the combination of IL-21 and TGF-β [45].
2.3 β common chain cytokines IL-3, and IL-5
The β common cytokine family, including IL-3 and IL-5, is defined by a shared receptor structure, comprising of a specific α chain and a common β chain that is essential for cytokine-specific receptor signaling [46]. IL-3 is a cytokine that is produced by activated T cell lymphocytes, which then induces the production of various hematopoietic cell types that are crucial to the immune response [47]. IL-5 is cytokine that is produced by hematopoietic and non-hematopoietic cells, including granulocytes, T cells, and natural helper cells [48]. IL-5 is also a mediator for eosinophilic inflammation by providing stimulation, differentiation, recruitment and activity of eosinophils. Due to their roles with eosinophils, IL-3 and IL-5 have been primarily studied in asthma, and their roles after SCI are not clear. However, both of them co-express in TH2 cells, which is a subset of CD4+ cells. These TH2 cells are characterized by the production of IL-4, IL-5, IL-10 and IL-13 and thus, may be beneficial in exerting anti-inflammatory effects after SCI [49, 50].
2.4 IL-6 and IL-11
IL-6 and IL-11 are grouped into one cytokine family because the receptor complex of each cytokine contains two of the signaling receptor subunit gp130 (Figure 2) [51]. For both IL-6 and IL-11 there are membrane bound receptors as well as soluble receptors and after ligand binding to either the membrane bound receptor or the soluble receptor, they form a complex with two gp130 receptors leading to Jak/STAT pathway signaling (Figure 2) [52, 53].
Figure 2.
Classic and trans-signaling. Cells that express the IL-6R or IL-11R will undergo classic signaling when IL-6 or IL-11 bind to the corresponding receptor, inducing gp130 dimerization and initiating intracellular signal transduction. Trans-signaling occurs when the ligand and soluble receptor complex (IL-6/sIL-6R or IL-11/sIL-11R) associate with gp130 inducing gp130 dimerization and initiating intracellular signal transduction.
IL-6 is predominantly an inflammatory cytokine. After SCI in a mouse model, Pineau et al. observed IL-6 mRNA expression in astrocytes, microglia/ macrophages, and neurons, starting at 3 hours post-injury, peaking at 12 hours and continuing for 4 days post-injury [54]. Similarly after SCI in humans IL-6 is strongly upregulated. IL-6 levels in cerebrospinal fluid of SCI patients changed from undetectable (<4 pg./ml) in non-injured controls to an average of almost 30,000 pg./mL in the subset of patients with complete SCI [55]. Furthermore, the cerebrospinal levels of IL-6 correlated with the extent of spinal cord damage in humans, which demonstrates the importance of IL-6 after SCI.
IL-6 leads to recruitment of immune cells. Delivery of IL-6/sIL-6 receptor fusion protein to injury sites induced a sixfold increase in neutrophils and a twofold increase of macrophages/microglial [56]. Mice treated with an antibody against IL-6 receptor showed a reduction in neutrophil and monocyte/macrophage invasion [57, 58]. It was also shown that blocking IL-6 signaling after SCI reduces the damaging inflammatory activity by promoting the formation of alternatively activated M2 macrophages [59]. Taken together these data suggest IL-6 signaling is an activator of inflammation and a strong recruiter of immune cells after SCI.
After SCI astrocytes proliferate and migrate to the injury leading to a dense astroglial scar surrounding the lesion. It has been shown in vitro that IL-6 signaling acts on neural stem cells to induce their differentiation into astrocytes [60]. This was supported by several in vivo studies including, IL-6 knockout mice that showed suppression of astrogliosis following SCI [61], mice with an excessive expression of IL-6 and IL-6R showed abundant astrogliosis suggesting that astrocytes were selectively affected in these mice [62], and the development of astrogliosis was inhibited in mice given an IL-6 receptor blocker after SCI [58].
Several studies have shown that blocking IL-6 signaling improves functional recovery after SCI [57, 58, 59]. It has also been shown that delivery of IL-6/IL-6 receptor resulted in a four fold decrease in axon growth [56]. However there are studies showing that IL-6 is neuroprotective and aids in axonal regeneration [63, 64]. The differences in IL-6 effect may depend on the level of expression and timeline of IL-6 upregulation. The studies using an IL-6 blocker were performed in the sub-acute timeframe after SCI. In the sub-acute SCI, any neurotrophic effects of IL-6 appear to be overwhelmed by its proinflammatory features. Taken together, the aforementioned data demonstrates the importance of IL-6 after SCI. IL-6 upregulates inflammatory cytokines, recruits immune cells, effects macrophage phenotype, effects astrocyte activation, effects axonal regeneration, and effects functional recovery.
IL-11 has been shown to be primarily anti-inflammatory. Recombinant IL-11 administered to activated macrophages inhibited the production of pro-inflammatory cytokines TNF-α, IL-1β, IL-12, and nitric oxide production [65, 66, 67]. Furthermore, IL-11 has been shown to play an anti-inflammatory role in the airways for asthma [68], play a role in decreasing mucosal damage in inflammatory bowel disease [69], and importantly IL-11 has a neuroprotective role in multiple sclerosis [70]. Due to these anti-inflammatory roles, Cho et al. analyzed the role of IL-11 after SCI using IL-11Rα knockout mice [71]. In wild type mice, they observed a significant upregulation in IL-11 with a peak gene expression 24 hours after injury and a significant upregulation of IL-11Rα at 3 and 7 days after SCI. Somewhat surprisingly, they did not observe significant differences in functional recovery or histopathology in IL-11Rα knockout mice as compared to wild type mice after SCI. The authors speculate that since “the peak in IL-11Rα expression is on the order of days after SCI, suggests that IL-11 signaling may not play as significant a role in the acute inflammatory response after injury, but more in the long-term sequelae such as oligodendrocyte survival”. Maheshwari et al. used a cuprizone induced mouse model of demyelination in the central nervous system to analyze the effects of overexpression of IL-11 on demyelination/remyelination [72]. Overexpression of IL-11 was able to limit cuprizone-induced demyelination by reducing oligodendrocyte cell death, decrease microglial activation, and enhance spontaneous remyelination. Maheshwari’s results further suggest that IL-11 likely plays a role in the long-term remyelination efforts after SCI and is not as involved in the sub-acute stage [72].
2.5 Interleukin-8 and interleukin-16
IL-8, also known as neutrophil chemotactic factor or CXCL8, primarily induces chemotaxis in neutrophils and granulocytes. IL-8 is a member of the chemokine family that acts on CXCR1 and CXCR2 receptors (il8ra and il8rb, respectively), which have been primarily studied on polymorphonuclear leukocytes. However many other cell types express these receptors including neurons [73]. Several studies have shown that IL-8 can be released by a wide variety of cells including monocytes endothelial cells, T lymphocytes, and macrophages [73]. After SCI in rat, GRO, the rat analogue of human IL-8, is strongly upregulated for at least 14 days and the upregulation of GRO strongly correlates with the extent of injury [14, 74, 75]. Furthermore IL-8 is upregulated in the cerebrospinal fluid of dogs and humans after SCI, and for humans the IL-8 levels are also shown to correlate with the extent of damage [55, 76, 77]. Although IL-8 clearly plays a role in neutrophil infiltration and overall inflammation after SCI, as shown by its significant upregulation, it has not been extensively studied after SCI.
IL-16 is a proinflammatory cytokine that is produced by mast and leukemic cells, fibroblasts, endothelial cells, granulocytes, dendritic cells, CD4+ and CD8+ T lymphocytes, monocytes, and microglial cells. IL-16 plays a role in the release of other proinflammatory cytokines (IL-1β, IL-6, IL-15, and TNFα), the increase of intracellular Ca++ or inositol-(1,4,5)-triphosphatase, and the translocation of protein kinase C [78]. These processes occur after IL-16 binds to the signal-transducing CD4 receptor molecule [79]. Moreover, IL-16 promotes lymphocyte migration and modulates apoptosis [80].
Following spinal cord injury, IL-16 plays a role in recruiting and activating inflammatory cells. Microglia that produce IL-16 migrate to the lesion site and other areas of significant neuronal damage [78]. Following neuroinflammation, it is suggested that IL-16 microglia are one of the first cells to respond [80]. In addition, macrophages with IL-16 remained present at the injury site for up to thirty days post injury, indicating long-term IL-16 function [78]. One study found that expression of IL-16 in microglia and macrophages is induced by the IL-12 p40 homodimer through IL-12Rβ1, but not IL-12 p70 [80]. Overall, the ability of IL-16 to quickly recruit microglia/macrophages to the lesion site following SCI results in increased neuronal damage and microvessel clustering [78].
2.6 Interleukin-10 family cytokines
Members of the IL-10 family of cytokines that have been studied after SCI include, IL-10, IL-19, IL-20, and IL-22 [81]. IL-10 is an anti-inflammatory cytokine that is produced by monocytes, B cells, dendritic cells, natural killer cells, and T cells [82]. In leukocytes, IL-10 acts on both innate and adaptive immune cells with a wide range of immunomodulatory activities that suppress proliferation, cytokine secretion, and costimulatory molecule expression of proinflammatory immune cells. The IL-10 receptor consists of heterotetramer complex made of two IL-10R1 molecules, encoded by the IL10ra gene, and two IL-10R2 molecules, encoded by the IL10rb gene (Figure 1) [83]. IL-10 downregulates several pro-inflammatory cytokines and inflammatory species [11]. In addition, IL-10 can affect T cell and natural killer cell function indirectly and directly through connection with monocytes and macrophages. The overall impact of IL-10 is determined by the timing and site of its production, which are both affected by which cells are making IL-10. Since IL-10 production by one cell type affects the ability of other cells to make IL-10, IL-10-producing cells show potential to regulate each other [82].
Following SCI, IL-10 downregulates pro-inflammatory molecules IL-1β, IL-2, IL-6, TNF-α, IFN-γ, matrix metalloproteinase-9, nitric oxide synthase, myeloperoxidase, and reactive oxygen species. IL-10 also provides trophic support to neurons through downregulation of pro-apoptotic factors cytochrome c, caspase 3, and Bax, as well as upregulation of anti-apoptotic factors B cell lymphoma 2 (Bcl-2) and Bcl-2-associated X, B-cell lymphoma-extra large (Bcl-xl) (Figure 1) [11]. There have been several studies performed to test IL-10’s therapeutic value as a treatment for SCI. Although these studies used a variety of different systemic and local methods to administer IL-10 after SCI, the majority of results showed strong positive effects from the IL-10. These positive effects after SCI include a reduction in pro-inflammatory molecules, macrophages expressing more antigens characteristic of an anti-inflammatory M2 phenotype, reduced lesion size, and an improvement in hind limb function [11, 84].
IL-19 is produced by monocytes and microglia, and binds to the IL-20 receptor complex, which consists of IL-20R1 and IL-20R2 chains [85]. Activated microglia upregulate IL-19 and express the IL-20 receptor complex [86]. It has also been shown that ablation of IL-19 in activated microglia increased the production of pro-inflammatory cytokines IL-6 and TNF-α, which demonstrates that IL-19 is predominately an anti-inflammatory cytokine in the central nervous system [86].
After SCI in mice, IL-19, IL-20R1 and IL-20R2 are upregulated [87]. In a series of four different experiments, mice with spinal cord injuries were treated with IL-19 [87]. As a result, Th2 cytokine synthesis was promoted, which polarized spinal microglial cells to an M2 phenotype. This helped resolve the inflammation, preserving myelin, neurons, and neuronal function. Overall, IL-19 attenuated macrophage accumulation, reduced protein levels of TNF-α and CCl2, promoted Th2 response and M2 macrophage activation, promoted angiogenesis by upregulating VEGF, upregulated HO-1 expression, and decreased oxidative stress in the injured region [87].
IL-20 is a proinflammatory cytokine that is predominately produced by monocytes and skin keratinocytes. IL-20 signals through both the IL-20R1/IL-20R2 heterodimer complex and the receptor complex composed of IL-22R1 and IL-20R2 [85]. Following spinal cord injury, IL-20 and its receptors are expressed in neurons, astrocytes, oligodendrocytes, and microglia in large amounts. IL-20 upregulates glial fibrillary acidic protein (GFAP), TGF-β1, TNF-α, MCP-1, and IL-6 expression, which stimulates astrocyte reactivation and migration [88]. As a result, glial scar border formation is enhanced. Moreover, IL-20 inhibits neuron outgrowth through upregulation of Sema3A/NRP-1 in PC-12 cells [88]. The overall result is irreversible neuronal loss and glial scar formation post-SCI. In vivo, anti-IL-20 mAb reduces the IL-20 inflammatory response, which improves motor and sensory functions, spinal cord tissue preservation, and reduces glial scar formation [88].
2.7 Interleukin-12 family cytokines
The IL-12 family is comprised of 4 members, IL-12, IL-23, IL-27 and IL-35 and each member is composed of α-subunit with a helical structure similar to type 1 cytokines and a β-subunit structurally related to the extracellular regions of Type 1 cytokine receptors [89]. However from this family of 4 cytokines, only the pro-inflammatory cytokine IL-12 has been assessed after SCI. IL-12 is produced by dendritic cells, macrophages, monocytes, neutrophils, microglia cells, and B cells [90]. The IL-12 receptor is made up of IL-12Rβ1 and IL-12Rβ2 chains [91]. IL-12 is a heterodimeric molecule, p70, formed from p40 and p35 chains. IL-12p70 is considered to be the biologically active cytokine that expresses nitric oxide synthase and TNF-α in microglia and macrophages. In T cells, p70 interacts with both IL-12Rβ1 and IL-12Rβ2. However, p70 treatment results in IL-16 mRNA inhibition due to inability to induce IL-16 promoter [80].
Yaguchi et al., administered IL-12 after SCI in mice and observed an increase in the number of activated macrophages and dendritic cells surrounding the lesion site and an increase in the expression of brain-derived neurotrophic factor adjacent to the injury. After IL-12 treatment, immunohistochemical analyses revealed that de novo neurogenesis and remyelination occurred. The mice treated with IL-12 also had a significant improvement in hind limb function [92].
2.8 Interleukin-17 family cytokines
IL-17 cytokines play important roles in both innate and adaptive immunity. IL-17A to IL-17F are highly conserved at the C terminus, and contain five spatially conserved cysteine residues that mediate dimerization [93, 94]. IL-17A and IL-17E have been identified and studied for the roles they play after SCI.
IL-17A is an important cytokine in regard to protective mechanisms against infectious diseases and inflammatory pathology within the immune system [95]. IL-17A is secreted by a multitude of cells including T cells, dendritic cells, and macrophages among others and binds to the A and C subunits of the IL-17 receptor to initiate signaling [95]. After SCI in rats, IL-17A is upregulated as early as 1 hour after injury, peaks at 24 hours, and remains above normal levels for at least 72 hours after injury [45]. This upregulation of IL-17 does appear to play a degenerative role on SCI recovery after a study was conducted using IL-17 knockout mice. IL-17 knockout mice showed increased locomotor function and decreased lesion size after SCI, which suggests that IL-17 expression regulates secondary degeneration of the neural tissue at the lesion site [96]. Recruitment of immune cells such as B cells, neutrophils, and dendritic cells were downregulated at 6 weeks following SCI [96].
Interleukin-25, also known as Interleukin-17E, is in the IL-17 family and binds to the heterodimer complex of IL-17A and IL-17-B receptor subunits. IL-25 has primarily been understood as a systemic type-2 inflammatory mediator that triggers significant helper T-cell expression and proinflammatory cytokine suppression, however its response following spinal cord injury is largely unknown. IL-25 is primarily derived from epithelial cells and macrophages in response to infection or inflammation and contributes to type-2 helper T cell (Th-2) activation [97]. Th2 cells are responsible for the release of anti-inflammatory cytokines IL-4, IL-5, and IL-13 which play a role in neural protection and regeneration against inflammation and neurotoxins [97].
The trafficking mechanism and inflammatory response of IL-25 post-SCI remains relatively unclear, but local injection of IL-25 into the lesion site post-SCI yields interesting and contradictory results. The local administration of IL-25 following spinal cord injury in 10-week old mice results in decreased locomotor function, an increase in lesion size, and neuronal demyelination which contradicts the systemic immune response upon an IL-25 presence [97]. Interestingly, the systemic administration of IL-25 show ineffective results in regard to improved functional mobility following spinal cord injury. Microglia and astrocytes survival are also unaffected upon injection of IL-25 suggesting that IL-25 indirectly activates inflammatory molecules associated with these immune events [97]. These results raise questions about the precise role of IL-25 after SCI and possible therapeutic interventions using IL-25.
3. Conclusions
Although significant progress has been made in terms of spinal stabilization and medical care of patients after SCI, there has not been much progress made in terms of treatments for SCI to retain or regain the function that is lost. In order to design treatments for SCI, a better understanding of the inflammation process is crucial. As outlined in this chapter ILs are an intricate player in inflammation after SCI. For some of these ILs, there timeline of involvement and roles they play in inflammation has been defined. However, there is still much more research that needs to be completed to understand the roles many of these ILs play. Along with understanding the current ILs, there will assuredly be more signaling cues discovered that are involved after SCI.
Could inflammation be modulated to retain or regain a significant amount of function after SCI? This is a fundamental question that needs to be addressed. As highlighted in rodent models, such as what is observed in IL-17 knockout mice or treatments with anti-inflammatory cytokines, modulating inflammation is a promising approach for treating SCI. However it is important to realize that all variables including age, sex, level of injury, and force to cause the trauma, are controlled in these rodent models, and thus treating human SCI will be more challenging. These facts highlight the essential need to conduct more research on inflammation after SCI.
\n',keywords:"interleukins, spinal cord injury, inflammation, macrophages, microglia",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/75585.pdf",chapterXML:"https://mts.intechopen.com/source/xml/75585.xml",downloadPdfUrl:"/chapter/pdf-download/75585",previewPdfUrl:"/chapter/pdf-preview/75585",totalDownloads:250,totalViews:0,totalCrossrefCites:0,totalDimensionsCites:1,totalAltmetricsMentions:0,impactScore:1,impactScorePercentile:70,impactScoreQuartile:3,hasAltmetrics:0,dateSubmitted:"November 5th 2020",dateReviewed:"January 29th 2021",datePrePublished:"March 9th 2021",datePublished:"July 14th 2021",dateFinished:"March 7th 2021",readingETA:"0",abstract:"In skin wound healing the injured tissue goes through a normal progression, inflammation subsides and remodeling occurs. However after spinal cord injury inflammation persists and there is less progression into a regenerative/rebuilding phase. This inflammatory process after spinal cord injury is orchestrated by many cell types and numerous cytokines. Although there are several positive effects of inflammation after spinal cord injury, such as the removal of debris, the substantial upregulation of immune cells has been shown to contribute to neural degeneration. Several chemokines and cytokines including many interleukins are involved in guiding these immune cells to the lesion. While there are many inflammatory cytokines acting on these immune cells after SCI, there are also several anti-inflammatory interleukins that have shown beneficial effects in reducing inflammation. After SCI in a rat model, interleukin-10 and interleukin-19 have been shown to downregulate the synthesis of pro-inflammatory species including interleukin-1β and tumor necrosis factor-α, which resulted in a significant improvement in rat hind limb function. Also, interleukin-4 and interleukin-13 are related anti-inflammatory cytokines that regulate many aspects of inflammation and have also been shown to induce alternative macrophage activation. The differing and complex roles interleukins play, highlight their importance on the inflammation that persists after spinal cord injury. Here we review both the positive effects and negative effects that interleukins have during the multifaceted inflammation process following spinal cord injury.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/75585",risUrl:"/chapter/ris/75585",book:{id:"10585",slug:"interleukins-the-immune-and-non-immune-systems-related-cytokines"},signatures:"Daniel J. Hellenbrand, Rylie M. Roddick, Sophia M. Mauney, Ryan T. Elder, Carolyn N. Morehouse and Amgad S. Hanna",authors:[{id:"338503",title:"M.Sc.",name:"Daniel J.",middleName:null,surname:"Hellenbrand",fullName:"Daniel J. Hellenbrand",slug:"daniel-j.-hellenbrand",email:"hellenbrand@neurosurgery.wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null},{id:"345800",title:"Ms.",name:"Carolyn N.",middleName:null,surname:"Morehouse",fullName:"Carolyn N. Morehouse",slug:"carolyn-n.-morehouse",email:"cmorehouse@wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"University of Wisconsin–Madison",institutionURL:null,country:{name:"United States of America"}}},{id:"345802",title:"Ms.",name:"Rylie M.",middleName:null,surname:"Roddik",fullName:"Rylie M. Roddik",slug:"rylie-m.-roddik",email:"rroddik@wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"University of Wisconsin–Madison",institutionURL:null,country:{name:"United States of America"}}},{id:"345805",title:"Ms.",name:"Sophia M.",middleName:null,surname:"Mauney",fullName:"Sophia M. Mauney",slug:"sophia-m.-mauney",email:"smauney@wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"University of Wisconsin–Madison",institutionURL:null,country:{name:"United States of America"}}},{id:"345806",title:"Mr.",name:"Ryan T.",middleName:null,surname:"Elder",fullName:"Ryan T. Elder",slug:"ryan-t.-elder",email:"rtelder@wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"University of Wisconsin–Madison",institutionURL:null,country:{name:"United States of America"}}},{id:"345807",title:"Dr.",name:"Amgad S",middleName:null,surname:"Hanna",fullName:"Amgad S Hanna",slug:"amgad-s-hanna",email:"hanna@neurosurgery.wisc.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"University of Wisconsin–Madison",institutionURL:null,country:{name:"United States of America"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Interleukins involved in inflammation after SCI",level:"1"},{id:"sec_2_2",title:"2.1 Interleukin-1 family cytokines",level:"2"},{id:"sec_3_2",title:"2.2 Interleukin-2 family cytokines",level:"2"},{id:"sec_4_2",title:"2.3 β common chain cytokines IL-3, and IL-5",level:"2"},{id:"sec_5_2",title:"2.4 IL-6 and IL-11",level:"2"},{id:"sec_6_2",title:"2.5 Interleukin-8 and interleukin-16",level:"2"},{id:"sec_7_2",title:"2.6 Interleukin-10 family cytokines",level:"2"},{id:"sec_8_2",title:"2.7 Interleukin-12 family cytokines",level:"2"},{id:"sec_9_2",title:"2.8 Interleukin-17 family cytokines",level:"2"},{id:"sec_11",title:"3. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'‘National Spinal Cord Injury Statistical Center, Facts and Figures at a Glance’, (2020)'},{id:"B2",body:'McKeon R. J., Schreiber R. C., Rudge J. 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Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
'},{corresp:null,contributorFullName:"Rylie M. Roddick",address:null,affiliation:'
Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
'},{corresp:null,contributorFullName:"Sophia M. Mauney",address:null,affiliation:'
Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
'},{corresp:null,contributorFullName:"Ryan T. Elder",address:null,affiliation:'
Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
'},{corresp:null,contributorFullName:"Carolyn N. Morehouse",address:null,affiliation:'
Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
'},{corresp:"yes",contributorFullName:"Amgad S. Hanna",address:"hanna@neurosurgery.wisc.edu",affiliation:'
Department of Neurological Surgery, University of Wisconsin, Madison, WI, USA
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\n
1. Introduction
\n
According to the Big Bang theory, the universe is expanding and cooling. During its expansion, the spontaneous breaks of fundamental symmetries led the universe to undergo a series of phase transitions. In high-energy physics models, the formation of topological defects, caused by transitions, such as domain walls, monopoles, and cosmic strings, among others, is predicted to occur according to the reference [1, 2].
\n
The cosmic string is among the most studied types of topological defects, although recent observations of cosmic background radiation have discarded it as the primary source for primordial density perturbations. Such a defect still serves as one of the contributions of this disturbance. This type of defect also serves as a possible source for explaining a considerable number of astrophysical effects, such as: bursts of gamma rays, where the energy scale of the string in which the symmetry is broken, on an energy scale of the order of 1014 GeV, explains the rate, duration, and fluency of gamma ray bursts [3]; high-frequency gravitational wave emissions, which have as a consequence of these emissions the stochastic set of gravitational waves generated by a cosmological network of non-Gaussian loops [4]; and the generation of high-energy cosmic rays [5]. The cosmic rays of high-energy particles may have originated during the process of collapse and/or annihilation of topological defects associated with the great unification theories.
\n
In condensed matter physics, it is well known that superconductors almost completely exclude any external magnetic field if it is less than a critical value (Meissner effect) [6]. However, for type 2 superconducting, which are formed by materials in which the transition to the superconducting state is gradual, in the presence of an intermediate state, if the external field is increased to a certain value greater than the critical value, such field. This superconductor passes through a magnetic flux tube form. These phenomena are called magnetic flux vortices which, in turn, are quantized.
\n
The possibility of the theoretical existence of such vortices was first demonstrated by Abrikosov [7]. He showed that these naturally occur as solutions to the Ginsburg-Landau theory of superconductivity in the presence of an external magnetic field. Following this theory, the existence of such objects was verified experimentally, and many of their properties were rigorously investigated in [6]. Some years later, Nielsen and Olesen [8] showed, starting from the relativistic field theory model with spontaneous break of symmetry, more specifically of the Abelian Higgs model interacting with a field of gauge, that this system presents solutions with cylindrical symmetry carrying a magnetic flux. These configurations correspond to vortex solutions.
\n
The analysis of the influence of this system on space-time geometry was performed by Garfinkle [9] and Laguna [10]. In their works, the authors coupled the energy-momentum tensor, associated to the Nielsen-Olesen model, with the Einstein field equations. In this sense, they have shown that the vortex has an internal structure characterized by the nonzero magnetic flux that runs along it, the extent of which is determined by the energy scale at which the symmetry is broken. Two scale lengths appear naturally, one related to the extent of the magnetic flux which, in turn, is proportional to the inverse of the vector field mass, mv, east field, which acquires mass due to the Higgs mechanism; and the other associated with the inverse of the scalar field mass, ms, the latter, as a measure of the point where the scalar field decreases to its vacuum value. Moreover, the authors also analyzed the geometry of space-time and verified that asymptotically the surface perpendicular to the vortex corresponds to Minkowski’s space-time minus a slice, resulting in a space with an angular deficit.
\n
A special vortex solution satisfying the Bogomolny-Prasad-Sommerfield (BPS) boundary [11, 12] shows the masses of the scalar field and of the same caliber field, that is, ms = mv. For this case, Linet [13] was able to find an exact solution for the metric tensor, which is determined in terms of the energy density of the cosmic string. In this limit, the surface perpendicular to the line of the solution of vortex has a conical structure and, the space-time surrounding, corresponds to the space-time of an idealized cosmic string.
\n
At great distances, the space-time generated by a cosmic string has, in its origin and in the orthogonal plane to the disposition of this object, a conical topology with a planar angle deficit proportional to the linear density of mass of this cosmic string. In quantum field theory, the nontrivial topology of this object induces non-vanish vacuum expected values for physical observables. These vacuum polarization effects can be interpreted as a modification in the quantum levels of the lower energy state of a theory. In quantum field theory, induced by a conic structure, they were the targets of many works published. For example, we can observe several published works, taking into account the case for scalar fields [14, 15, 16, 17, 18, 19] and fermionic fields [20, 21, 22] interacting with vector fields. Another induced physical observable, due to the presence of this defect, is the current and charge density, which will serve as the source for Maxwell’s equations. Such an object considering fermionic fields is seen in [23, 24, 25, 26].
\n
\n
\n
2. The general relativity and the space-time
\n
The general relativity theory is a geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. It is a set of hypotheses that generalizes Newton’s special relativity and the universal gravitation law providing a unified description of gravity as a geometric property of the space-time. In particular, the “curvature of space-time” is directly related to the energy and moment of any matter and radiation present. The relation is specified by Einstein’s field equations, a system of partial differential equations.
\n
All geometric information about the space-time would be contained in this mathematical object called, formally, metric tensor, \n\n\ng\nμν\n\n\n. In other words, the distribution of matter and energy tells how the geometry of space-time [27] must be. The equation proposed by Einstein for the theory of General Relativity is given by the expression below
Here, \n\n\nR\nμν\n\n\n is the Ricci tensor that is obtained from the Riemann tensor, \n\nR\n=\n\ng\nμν\n\n\nR\nμν\n\n\n is the scalar of curvature, and \n\n\nT\nμν\n\n\n is the energy-momentum tensor. In order to introduce the idea of the metric structure of the space-time, we will briefly review the necessary basic concepts, such as inertial frame and interval of events [27].
\n
Let us suppose that an inertial frame S is described in Cartesian coordinates (t, x, y, z). In this frame, we have the line element ds being infinitesimal and having its own time interval (event) given by
But if we consider a non-inertial reference system, S′, for example, the line element will not be given, in general, by the sum of the squares of the coordinate differentials. In this case, for a better understanding, let us consider an event in a rotating frame, around the z axis, whose angular frequency of rotation is \n\nω\n\n. Let (t′, x′, y′, z′) be the coordinates of this new S′ referential. The relation between both reference frames may be illustrated by Figure 1.
\n
Figure 1.
The relation between S and S′ reference frame with angular velocity \n\nω\n\n around the z = z′ axis.
\n
The general coordinate transformations between the both reference frames S and S′ are given as follow,
We see, therefore, that the line element is not only the sum or difference of the squares of the differential coordinates.
\n
Looking to the Eq. (2), we identify that \n\nd\n\ns\n2\n\n=\n\nη\nμν\n\nd\n\nx\nμ\n\nd\n\nx\nν\n\n\n, where we have the metric signature given by \n\n\nη\nμν\n\n=\n\n1\n\n−\n1\n\n\n−\n1\n\n\n−\n1\n\n\n\n being the four-vector position \n\n\nx\nμ\n\n=\n\nt\n\n−\n\nr\n→\n\n\n\n\n. On the other hand, looking into Eq. (6), when non-inertial coordinate systems are used, the line element will include terms that are products of the different coordinate differentials. So, we can write the line element as follows
Now, \n\n\ng\nμν\n\n\nx\n\n\n represents a set of ten functions of the space and time coordinates and it is symmetric, i.e., \n\n\ng\nμν\n\n\nx\n\n=\n\ng\nνμ\n\n\nx\n\n\n. The system described by Eq. (7) is called “curved system” and corresponds to an accelerated reference system. The functions \n\n\ng\nμν\n\n\nx\n\n\n contain all the geometric properties of the space-time. For the case where we deal with inertial frames, we just have \n\n\ng\nμν\n\n\nx\n\n=\n\nη\nμν\n\n\n.
\n
Einstein showed that accelerated referential are equivalent to gravitational fields so that gravitational effects will be described by the metric tensor, \n\n\ng\nμν\n\n\nx\n\n\n. In this case, the gravitation can be understood as a deviation in the metric of the space-time plane. Moreover, this metric is not fixed arbitrarily but will depend on the local distribution of matter.
\n
In fact, this equivalence is verified only locally. In a non-inertial system, given a metric \n\n\ng\nμν\n\n\nx\n\n\n, we can always reduce it globally to the Galileo form, Eq. (2), by means of a suitable coordinate transformation. On the other hand, a gravitational field cannot be eliminated globally by a coordinate transformation, and the metric can only be reduced to the flat form (Minkowski) only in a very small finite region of the space, i.e., locally. When such a situation occurs, the space-time is called pseudo-Riemannian space-time.
\n
\n
\n
3. Cosmic strings
\n
It is believed that fluctuations that gave rise to the large-scale structures of the Universe must have a primordial origin, that is, they are associated with the first moments after the Big Bang. The existing theories for structure formation in the Universe fall into two categories.
\n
One of them based on amplification of quantum fluctuations in a scalar field during inflation. The other one based on a phase transition with symmetry breaking in the primordial universe that gives rise to the formation of topological defects.
\n
Seen from the moment of creation, the Universe goes through phase successions. The transitions between the first of these phases occur when the Universe is dominated by a quantum gravitation whose exact contours are unknown but during which the interactions are thought to be unified and characterized by a high degree of symmetry. These transitions imply symmetry breaks and can have important implications including the formation of topological defects such as the formation of cosmic strings or initiation of a period of exponential inflation.
\n
A cosmic string is an object that can be obtained from an infinitely concentrated distribution of matter, with linear density of mass \n\nμ\n\n [2]. In the case of a certain distribution being located on the z-axis, the energy-momentum tensor, in cylindrical coordinates, is given by
Here, \n\n\nδ\n\n2\n\n\n\n\nr\n→\n\n\n\n is a two-dimensional Dirac delta function. Geometrically, a topological defect can be characterized by a space-time whose metric associated with this defect has the corresponding Riemann-Christoffel tensor null at all points, except for the defect, i.e., the space-time has conical singularity. In other words, it may be characterized by a bending tensor, which is proportional to a delta function supported on the defect.
\n
We want that the Eq. (8) generates a geometry with cylindrical symmetry. For that, our goal is to find a solution to Einstein’s equations describing the gravitational field of an ideal cosmic string with linear mass density \n\nμ\n\n along the z-axis. In this sense, the string will have no dependence over time, so it is a temporal invariant. We will also admit a symmetry of the string in relation to the azimuth angle, and finally that it remains invariant by boosts. Thus, the most general line element, in cylindrical coordinates, which exhibits such symmetry and maintains invariance by boosts transformations along the z-axis, is given by
Using Eq. (1), taking into account the metric tensor given in Eq. (9), we can calculate the Christoffel symbols and obtain a set of non-linear differential equations given by
Redefining the angular coordinate in Eq. (14), where we use the substitution \n\n\nϕ\n′\n\n=\nϕ\n/\nq\n\n with \n\n\nq\n\n−\n1\n\n\n=\n\n\n1\n−\n4\nμ\n\n\n\n, we have
where the angular coordinate varies in the range \n\n\n0\n\n\n2\nπ\n\nq\n\n\n\n, so that space-time is now locally flat except for \n\nr\n=\n0\n\n, which means except under the defect. This line element, from a global point of view, corresponds to Minkowski’s space-time minus one piece subtended by the angle \n\n8\nπμ\n\n. The quantity \n\nμ\n\n has great importance in string theory since it characterizes the intensity of the gravitational interaction and its value obtained from the Great Unification Theories is comprised in the order of 10−6 [28, 29]. Then, space-time generated by a cosmic string has the shape of a cone in the perpendicular plane to the string. Being flat itself, it satisfies Einstein’s equations in every region where \n\n\nT\nν\nβ\n\n=\n0\n\n.
\n
The effect of the string is therefore to introduce a deficit in the azimuthal angle given by \n\nΔ\nϕ\n=\n8\nπμ\n\n, generating in the surface (t, z) = constants, a conical geometry instead of a flat geometry, which will be pointed in the limit of the string internal structure going to zero. In this case, the corresponding space-time is conic and best described in cylindrical coordinates due to the symmetry of the problem. The geometry described above has many interesting features, such as:
Absence of Newtonian gravitational potential although this does not imply the absence of gravitational effects, that is, a particle placed in the presence of a cosmic string will not be attracted to it, whatever the order of magnitude of the mass density of the string, which is quite different from that predicted by Newton’s gravitational string of matter; in other words, the cosmic strings have zero gravitational potential [30].
It can act as a gravitational lens as shown in Figure 2, that is, due to the conic nature of space-time around the cosmic string, double images of objects located behind the string can be formed in relation to an observer [2].
Gravitational analog of the Aharonov-Bohm effect, due to the movement of test particles in space-time of cosmic strings through the study of geodesics [31].
Electrostatic self-interaction [13] that arises due to the gravitational field inducing a curvature in space-time, and this curvature causes distortions in the field lines of the electrostatic potential generated by a charged particle, causing this particle to undergo a finite force upon itself.
\n
Figure 2.
Representation of the light way coming from the infinity and “curving” due to the presence of a cosmic string.
\n
\n
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4. The Higgs mechanism
\n
Most of the symmetries observed in nature are not exact. For example, Isospin is not an exact symmetry of nature, because the proton and the neutron do not have the same mass. One way to study symmetry breaks in field theory with symmetry breaking is to introduce the Lagrangian terms with small coefficients that explicitly perform the break. In this section, we will be interested in a symmetry breaking which the Lagrangian is symmetric under the action of a group of transformations but the state of less energy is not.
\n
To understand how spontaneous symmetry breaking appears in many Abelian field theories, we will start considering the simple case, that is, the Lagrangian for a complex scalar field given by
where \n\nV\n\n\nφ\n\n\n=\n\nμ\n2\n\nφ\n\nφ\n∗\n\n+\nλ\n\n\n\n\nφ\n∗\n\nφ\n\n\n2\n\n\n, being \n\nλ\n\n the self-coupling constant. To this theory, making the transformation over the scalar field is as follows
As we may see, these transformations under the fields keep the Lagrangian unchanged. The transformations over the fields and their derivatives that do not depend on the point are named global gauge transformation.
\n
On the other hand, let us consider that the parameter \n\nα\n\n now depends on the point, it means, \n\nα\n≡\nα\n\nx\n\n→\nU\n\nx\n\n=\n\ne\n\niqα\n\nx\n\n\n\n\n. These kinds of transformation are called local gauge transformation.
\n
This way the transformation over the derivatives, Eq. (18), becomes
As we can see, the field derivative does not transform as the field itself. The second term that appears in Eq. (20) turns the Lagrangian as not invariant by these transformations over the fields. This way, to turn this theory unchanged by transformations where the parameter now depends on the point, we have to add new fields called “compensating fields,” \n\n\nA\nν\n\n\nx\n\n\n. Doing this we also have to redefine the derivative concept, and this way, we have
In Eq. (21), we have the covariant derivative. Now, under transformations over the fields, the fields derivative will transform itself like the own fields, which means
Hence, the total Lagrangian will change by the addiction of the dynamic of these “compensating fields” and its dynamic is given by the term \n\nL\n\n\nA\nν\n\n\n\n where we have only \n\n\nA\nν\n\n\n interacting among itself, this way we get
Note that \n\n\nF\nμν\n\n=\n\n∂\nμ\n\n\nA\nν\n\n−\n\n∂\nν\n\n\nA\nμ\n\n\n is the Maxwell electromagnetic tensor, and the “compensating field” is the four-vector potential of the electromagnetism, and this way, the parameter q is the electron charge. In Eq. (23), we have a U(1) invariant theory that couples photons with the charged matter. This theory is the known quantum electrodynamics theory.
\n
In general, the Higgs-Kibble mechanism is a process that generates mass for the gauge fields in this theory. Taking into account Eq. (23) with the parameters \n\nλ\n>\n0\n\n and \n\n\nμ\n2\n\n<\n0\n\n, this theory presents the spontaneous symmetry breaking. In this case, there exist a “ring” of degenerated vacuum states given by the minimal potential. This “ring” of degenerated vacuum values is parameterized as
The term \n\n\nA\nν\n\n\nA\nν\n\n\n that appears in Eq. (28) shows that the gauge field now acquires mass. Besides that we also can see in Eq. (28) that a massive scalar field, \n\nη\n\n, with mass \n\n\nm\nη\n2\n\n=\n2\nλ\n\nv\n2\n\n\n and a Goldstone scalar field appear. However, the Goldstone scalar field does not present physical relevance and may be reabsorbed through a gauge field redefinition. Taking the gauge field redefinition given by
The \n\n\nB\nν\n\n\n field presents mass \n\n\nm\nB\n\n=\nqv\n\n, non-vanishing.
\n
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4.1 Topological defects
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Topological defects are stable configurations of matter formed during phase transitions in the primordial universe. As already mentioned, during the early phases of the Universe, the material components are in physical states characterized by high degrees of symmetry and it is thought that the interactions will be unified. The cooling of the Universe, due to expansion, promotes the conditions for some of these symmetries to break, it is said, spontaneously.
\n
This happens in much the same way as a pencil which, standing vertically and only resting on its sharp beak, drops down on a flat, oriented surface in any direction. The symmetry of rotation that exists around the axis of the pencil vanishes and, furthermore, the point where the tip was supported separates all possible positions from the topped pencil and is said to be a topological defect. (A classic example of a break in symmetry is the ferromagnetic transitions in Landau theory.) According to the types of symmetries that are broken, various types of topological defects may form, including walls, cosmic strings, monopoles, and textures. The type of defect formed is determined by the symmetry properties of the material and the nature of the phase transition.
\n
To describe the idealized cosmic strings, i.e., static cosmic strings with infinite matter distribution along the z-axis and whose internal structure may be negligible, we will use the Nielsen and Olesen model. In this sense, by coupling the energy-momentum tensor associated with this theory to the Einstein field equations of general relativity, we study the influence of this model on space-time geometry. In fact, Laguna [10] and Garfinkle [9] did this, and in their works, they had shown that the space-time generated by the Nielsen-Olesen model was equivalent to space-time generated by a cosmic string. Thus, for a better understanding of the nature of a cosmic string, it is necessary to understand a little about models in field theory with spontaneous break of symmetry, as with the model proposed by Nielsen and Olesen.
\n
Domain walls are two-dimensional objects that form when a discrete symmetry is broken during a phase transition. A network of walls effectively divides the Universe into several “cells.” This type of defect has some very peculiar properties, one being that the gravitational field of a wall is repulsive rather than attractive. These objects may be represented as follow in Figure 3.
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Figure 3.
Domain walls associated with models where there is more than a minimum.
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Cosmic strings are one-dimensional objects that form when an axial or cylindrical symmetry is broken. They are very thin and can extend along the visible Universe. These objects may be represented as follow in Figure 4.
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Figure 4.
Cosmic strings associated with models in which a set of minimums is not connected.
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Monopoles have dimension zero, that is, are punctual, and form when a spherical symmetry is broken. In field theory with non-abelian gauge symmetriy broken may appear defects like magnetic monopole. These objects may be represented as follow in Figure 5.
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Figure 5.
Representation of a magnetic monopole defect. They are expected to be supermassive and have a magnetic charge.
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Whenever there is the possibility that cosmic strings or other topological defects form in a cosmological phase transition, they actually form. This circumstance had been first pointed out by Kibble, and therefore, in a cosmological context, the process of the formation of defects became to be known as the “Kibble mechanism” [1].
\n
One fact regarding the universe inflation period is that the causal effects in the early universe can only propagate at the speed of light c. This means that in the instant t, regions of the Universe separated more than a distance d = ct cannot know anything about each other. In a phase transition with symmetry breaking, different regions of the Universe will fall into different minimum potentials. This way, we actually think that topological defects are precisely the “boundaries” between these regions corresponding to different minimum potentials and their formation is thus an inevitable consequence of the phase transition.
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4.2 Vortex model in field theory
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The model proposed by Nielsen and Olesen for Abelian vortices, in the context of general relativity, generates a geometric structure similar to that of a cosmic string. In this sense, this object is a strong candidate to describe mathematically the cosmic strings; that is, they are strong candidates for the sources for this type of defect. However, Nielsen and Olesen, starting from a relativistic theory of fields, in 1973, have shown that it is possible to obtain solutions of vortices [8] starting from the Lagrangian density of the Abelian Higgs model, which is expressed by
Note that \n\n\nD\nν\n\n=\n\n∂\nν\n\n+\nie\n\nA\nν\n\n\n is the covariant derivative, \n\n\nF\nβν\n\n=\n\n∂\nβ\n\n\nA\nν\n\n−\n\n∂\nν\n\n\nA\nβ\n\n\n is the electromagnetism Maxwell’s tensor, and \n\nλ\n\n\n\nφ\n\nφ\n∗\n\n\n\n2\n\n\n is the auto-interaction term; when this term is put, this theory starts to present a infinity degenerated vacuum, i.e., the theory has infinite states of lower energy, which satisfies the condition \n\n\n\nφ\n\n2\n\n=\n\nm\n2\n\n/\n\n\n2\nλ\n\n\n\n. This way, for a particular choice vacuum configuration \n\nφ\n=\n\n\n\nm\n2\n\n\n2\nλ\n\n\n\n\n, the local gauge symmetry is broken.
\n
It is known that the action for this theory is written as
For a vortex in the z-direction, the components associated with the vector potential, in the Cartesian coordinate system, are \n\n\nA\nμ\n\n=\n\n0\n\nA\nx\n\n\nA\ny\n\n0\n\n\n. For this configuration, the component of the tensor \n\n\nF\nβν\n\n\n that interests us is \n\n\nF\n12\n\n\n, because from it we can calculate the flux that passes through the plane \n\n\nx\ny\n\n\n. Parametrizing the Higgs field by \n\nφ\n=\n\nφ\n\nexp\n\niχ\n\n\n, the flux, \n\nΦ\n\n, passing through an area bounded by a closed curve \n\nC\n\n, is given by
Here, we use, in Eq. (38), the fact that the line integral is carried out on the closed curve C, very far from the magnetic flux and that \n\n\nj\nμ\n\n=\n0\n\n. The equations of motion presented in Eqs. (36) and (37) are coupled differential equations in first order that are hard to find solutions. However, the standard procedure to solve these equations, at least numerically, is to assume the following cylindrical ansatz, with symmetry along the z-axis for the fields [8]
There exist no analytical solutions to these equations. On the other hand, we can find many vortex properties by general and numerical considerations under both equations. From the general point of view, it is possible to show that these equations present solutions as asymptotically well-defined. For points closer to its nucleus, we have \n\nf\n\nr\n\n≈\nA\n\nr\n\n→\n0\n\n. For points pretty distant from the vortex nucleus, it is observed that the functions \n\nf\n\nr\n\n\n and \n\nA\n\nr\n\n\n may be approximated in first order to
By using computational methods we can solve numerically Eqs. (40) and (41), and in Figure 6, we can see their behavior.
\n
Figure 6.
H(r) and \n\nφ\n\nr\n\n\n represent, respectively, the behavior of the magnetic field and the scalar field.
\n
From Figure 6, we can see that two mass scale come up, first of them is \n\n\nm\ns\n\n=\n\n2\n\nm\n\n that is related with the mass of the scalar field dislocated; it means \n\n\nφ\n′\n\n=\nφ\n−\nm\n/\n\nλ\n\n\n. The second one is related with the photon mass, \n\n\nm\nv\n\n=\nqm\n/\n\nλ\n\n\n, remember that the photon acquires mass because of the Higgs mechanism. Note that two length scales also appear in Figure 6. The first one \n\nδ\n=\n1\n/\n\nm\nv\n\n\n is related with the range of the electromagnetic field. The second latter, ξ = 1/ms, is related with the space scale for the Higgs field arrive its own vacuum value.
\n
In the literature Eqs. (23) and (24) form a system of coupled-equations and this system do not have exact solutions, but asymptotically we may solve these equations. The solutions that present finite linear density of energy, follow reference [32], are given by
On the other hand, Garfinkle [9], in 1985, studied the gravitational effects associated with the vortices of Nielsen and Olesen. For this purpose, he used the energy tensor, \n\n\nT\nβν\n\n\n, obtained from the Lagrangian of the Abelian Higgs model, Eq. (16). In the context of the general relativity, he used this tensor as source of the Einstein equations. In this case, a static metric, with cylindrical symmetry, can be written as
Given the metric, Eq. (44), solving the Einstein field equations for the energy-momentum tensor of Nielsen and Olesen, Garfinkle had found, as in flat space-time, symmetrically cylindrical static solutions which he represented as vortices. It also showed that, asymptotically, the space-time around a vortex become the Minkowski space-time minus a slice corresponding that one shown in Figure 2. This means that, asymptotically, the vortex can be seen as a cosmic string containing a magnetic field around it.
\n
\n
\n
\n
5. Conclusions
\n
Throughout this work, we introduced some reasons why cosmic string-like topological defects have been studied in energy physics and condensed matter. In fact the quantum effects on the fields of matter are caused due to the non-trivial topology of these objects giving rise to polarization effects. By understanding the vacuum as a state of lower energy, the effects of vacuum polarization can be understood as changes in the scale of this lower energy. Such effects in quantum field theory are seen by calculating the vacuum expected values, VEV, of certain observables, such as the induced current density [23] and the energy-momentum tensor of the matter fields [19] induced. These observables serve as sources for the Maxwell equations in the case of induced current density and for the Einstein equations in the case of the energy-momentum tensor. In the latter case, the source of the Einstein equations no longer consists of the classical energy-momentum tensor, \n\n\nT\nμν\n\n\n, but rather the energy-momentum quantizer, \n\n\n\nT\nμν\n\n\n\n, which will result in certain fixes in the metric tensor [33].
\n
We have also seen that in an inertial frame, the space-time is described by the Minkowski metric, Eq. (1), which consists of a singular and diagonal metric. However, when we move to accelerated frames, the metric becomes point dependent, consisting of a set of ten space-time coordinate functions, containing all information about the geometry of the range. In this way, we can see that accelerated frames are equivalent to gravitational fields, so that gravitational effects can be described by the metric tensor, \n\n\ng\nμν\n\n\n\nx\n\n\n. Thus, the gravitation may be understood as a deviation in the metric of the flat space-time. Moreover, this metric is not fixed arbitrarily but will depend on the distribution of local matter.
\n
Furthermore, the cosmic string is an object whose density of matter is infinitely concentrated in a line whose mass density is \n\nμ\n\n. With this object, which can be described by the energy-momentum tensor given in Eq. (7), the deformation caused in the space-time is conical and the metric described by this density of matter is given by Eq. (15), which consists of a Minkowskian metric with cylindrical symmetry, less than a slice equal to \n\n8\nπμ\n\n, which corresponds to the planar angle deficit orthogonal to the axis of symmetry of the cosmic string.
\n
Finally, we have seen that such idealized objects can be described through the Abelian vortices models proposed by Nielsen and Olesen. They showed that by the abelian Higgs model, Eq. (32), assuming a cylindrical ansatz, Eq. (39), It is possible the obtaining a set of two coupled second order differential equation, as it was showed in Eqs. (40) and (41), although they do not have a closed analytic form, but that may be obtained numerical and asymptotic solutions, Eq. (27). In this way, it is observed that two length scales appear naturally from this theory. One associated with the inverse of the mass of the scalar field, \n\nξ\n≡\n1\n/\n\nm\ns\n\n\n, and the other one related to the inverse of the mass of the vector field, \n\nδ\n≡\n1\n/\n\nm\nv\n\n\n, which acquires mass due to the mechanism of Higgs. Also in the scope of the Abelian vortices, Linet [13] and Garfinkle [9], starting from the energy-momentum tensor associated to the Nielsen and Olesen model as the source of the Einstein field equations, they obtained a metric associated to this model, and they found a metric described by a cosmic string. The internal structure of this object is delimited by the scale of energy in which the Higgs field decays to its vacuum value.
\n
\n
Acknowledgments
\n
I would like to thank Colégio de Aplicação for the technical and logistical support. I also thank the Coordenador de Educação Básica of the CAp. I thank Cassia for the emotional support that comforted me when I needed.
\n
Conflict of interest
The authors declare no conflict of interest.
\n',keywords:"cosmic string, curved space-time, relativity, field theory",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/69434.pdf",chapterXML:"https://mts.intechopen.com/source/xml/69434.xml",downloadPdfUrl:"/chapter/pdf-download/69434",previewPdfUrl:"/chapter/pdf-preview/69434",totalDownloads:761,totalViews:0,totalCrossrefCites:0,dateSubmitted:"September 12th 2018",dateReviewed:"April 28th 2019",datePrePublished:"October 8th 2019",datePublished:"January 22nd 2020",dateFinished:"October 8th 2019",readingETA:"0",abstract:"Due to the wide range of applications and effects of the Abelian vortex model of Nielsen and Olesen in the many areas of physics, ranging from condensed matter to astrophysical effects, some work in the literature is necessary to approach this topic in a succinct form that the undergraduate student in both physics and related areas has the possibility to know and understand. The mechanisms associated with this vortex model indicate him as a strong candidate for the source for the topological defects proposed by Vilenkin.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/69434",risUrl:"/chapter/ris/69434",signatures:"Mikael Souto Maior de Sousa and Anderson Alves de Lima",book:{id:"7357",type:"book",title:"New Ideas Concerning Black Holes and the Universe",subtitle:null,fullTitle:"New Ideas Concerning Black Holes and the Universe",slug:"new-ideas-concerning-black-holes-and-the-universe",publishedDate:"January 22nd 2020",bookSignature:"Eugene Tatum",coverURL:"https://cdn.intechopen.com/books/images_new/7357.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-83968-542-2",printIsbn:"978-1-83968-541-5",pdfIsbn:"978-1-83968-543-9",isAvailableForWebshopOrdering:!0,editors:[{id:"261441",title:"Dr.",name:"Eugene",middleName:"Terry",surname:"Tatum",slug:"eugene-tatum",fullName:"Eugene Tatum"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"274390",title:"Dr.",name:"Mikael Souto",middleName:null,surname:"Maior De Sousa",fullName:"Mikael Souto Maior De Sousa",slug:"mikael-souto-maior-de-sousa",email:"mikael.souto@ufrr.br",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"Universidade Federal de Roraima",institutionURL:null,country:{name:"Brazil"}}},{id:"284103",title:"Dr.",name:"Anderson",middleName:null,surname:"Alves De Lima",fullName:"Anderson Alves De Lima",slug:"anderson-alves-de-lima",email:"anderson.lima@ufcg.edu.br",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. The general relativity and the space-time",level:"1"},{id:"sec_3",title:"3. Cosmic strings",level:"1"},{id:"sec_4",title:"4. The Higgs mechanism",level:"1"},{id:"sec_4_2",title:"4.1 Topological defects",level:"2"},{id:"sec_5_2",title:"4.2 Vortex model in field theory",level:"2"},{id:"sec_7",title:"5. Conclusions",level:"1"},{id:"sec_8",title:"Acknowledgments",level:"1"},{id:"sec_11",title:"Conflict of interest",level:"1"}],chapterReferences:[{id:"B1",body:'Kibble TWB. Topology of cosmic domains and strings Journal of Physics A. 1976;9:1387. DOI: 10.1088/0305-4470/9/8/029/pdf\n'},{id:"B2",body:'Vilenkin A, Shellard EPS. Cosmic String and Other Topological Defects. Cambridge: Cambridge University Press; 1994\n'},{id:"B3",body:'Berezinski V, Hnatyk B, Vilenkin A. Physical Review D. 2001;64:043004. DOI: 10.1103/PhysRevD.64.043004\n'},{id:"B4",body:'Damour T, Vilenkin A. Physical Review Letters. 2000;85:3761. 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Cambridge: Cambridge University Press; 1990. p. 542\n'},{id:"B30",body:'Hooft G. Communications in Mathematical Physics. 1988;117:685. DOI: 10.1007/BF01218392\n'},{id:"B31",body:'Dowker JS. Nuovo Cimento. 1967;52:129. DOI: 10.1007%2FBF02710657\n'},{id:"B32",body:'Ma W, Pagels H. Physical Review C. 1978;36:137. DOI: 10.1016/0370-1573(78)90208-9\n'},{id:"B33",body:'Birrell ND, Davies PCW. Quantum Fields in Curved Space. Cambridge: Cambridge University Press; 1982\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Mikael Souto Maior de Sousa",address:"mikael.souto@ufrr.br",affiliation:'
Colégio de Aplicação, UFRR, Brazil
'},{corresp:null,contributorFullName:"Anderson Alves de Lima",address:null,affiliation:'
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IntechOpen’s Academic Editors and Authors have received funding for their work through many well-known funders, including: the European Commission, Bill and Melinda Gates Foundation, Wellcome Trust, Chinese Academy of Sciences, Natural Science Foundation of China (NSFC), CGIAR Consortium of International Agricultural Research Centers, National Institute of Health (NIH), National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Institute of Standards and Technology (NIST), German Research Foundation (DFG), Research Councils United Kingdom (RCUK), Oswaldo Cruz Foundation, Austrian Science Fund (FWF), Foundation for Science and Technology (FCT), Australian Research Council (ARC).
Open Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
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In order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
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Please note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at funders@intechopen.com
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Please be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
Open Access publication costs can often be designated directly in the grants or in specific budgets allocated for that purpose. Many of the most important funding organisations encourage, and even request, that the projects they fund are made available at no cost to the wider public. IntechOpen strives to maintain excellent relationships with these funders and ensures compliance with mandates.
\n\n
In order to help Authors identify appropriate funding agencies and institutions, we have created a list, based on extensive research on various OA resources (including ROARMAP and SHERPA/JULIET) of organizations that have funds available. Before consulting our list we encourage you to petition your own institution or organization for Open Access funds or check the specifications of your grant with your funder to ascertain if publication costs are included. Where you are in receipt of a grant you should clarify:
\n\n
\n\t
Does your institution already have a budget for covering Open Access publication costs?
\n\t
Does your grant list Open Access publication fees as legitimate direct/indirect costs?
\n
\n\n
If you are associated with any of the institutions in our list below, you can apply to receive OA publication funds by following the instructions provided in the links. Please consult the Open Access policies or grant Terms and Conditions of any institution with which you are linked to explore ways to cover your publication costs (also accessible by clicking on the link in their title).
\n\n
Please note that this list is not a definitive one and is updated regularly. To suggest possible modifications or the inclusion of your institution/funder, please contact us at funders@intechopen.com
\n\n
Please be aware that you must be a member, or grantee, of the institutions/funders listed in order to apply for their Open Access publication funds.
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The motor of the society is the industry and the research of this topic has to be empowered in order to increase and improve the quality of our lives.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/22.jpg",keywords:"Machine Learning, Intelligence Algorithms, Data Science, Artificial Intelligence, Applications on Applied Intelligence"},{id:"23",title:"Computational Neuroscience",scope:"Computational neuroscience focuses on biologically realistic abstractions and models validated and solved through computational simulations to understand principles for the development, structure, physiology, and ability of the nervous system. This topic is dedicated to biologically plausible descriptions and computational models - at various abstraction levels - of neurons and neural systems. This includes, but is not limited to: single-neuron modeling, sensory processing, motor control, memory, and synaptic plasticity, attention, identification, categorization, discrimination, learning, development, axonal patterning, guidance, neural architecture, behaviors, and dynamics of networks, cognition and the neuroscientific basis of consciousness. Particularly interesting are models of various types of more compound functions and abilities, various and more general fundamental principles (e.g., regarding architecture, organization, learning, development, etc.) found at various spatial and temporal levels.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/23.jpg",keywords:"Single-Neuron Modeling, Sensory Processing, Motor Control, Memory and Synaptic Pasticity, Attention, Identification, Categorization, Discrimination, Learning, Development, Axonal Patterning and Guidance, Neural Architecture, Behaviours and Dynamics of Networks, Cognition and the Neuroscientific Basis of Consciousness"},{id:"24",title:"Computer Vision",scope:"The scope of this topic is to disseminate the recent advances in the rapidly growing field of computer vision from both the theoretical and practical points of view. Novel computational algorithms for image analysis, scene understanding, biometrics, deep learning and their software or hardware implementations for natural and medical images, robotics, VR/AR, applications are some research directions relevant to this topic.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/24.jpg",keywords:"Image Analysis, Scene Understanding, Biometrics, Deep Learning, Software Implementation, Hardware Implementation, Natural Images, Medical Images, Robotics, VR/AR"},{id:"25",title:"Evolutionary Computation",scope:"Evolutionary computing is a paradigm that has grown dramatically in recent years. This group of bio-inspired metaheuristics solves multiple optimization problems by applying the metaphor of natural selection. It so far has solved problems such as resource allocation, routing, schedule planning, and engineering design. Moreover, in the field of machine learning, evolutionary computation has carved out a significant niche both in the generation of learning models and in the automatic design and optimization of hyperparameters in deep learning models. This collection aims to include quality volumes on various topics related to evolutionary algorithms and, alternatively, other metaheuristics of interest inspired by nature. For example, some of the issues of interest could be the following: Advances in evolutionary computation (Genetic algorithms, Genetic programming, Bio-inspired metaheuristics, Hybrid metaheuristics, Parallel ECs); Applications of evolutionary algorithms (Machine learning and Data Mining with EAs, Search-Based Software Engineering, Scheduling, and Planning Applications, Smart Transport Applications, Applications to Games, Image Analysis, Signal Processing and Pattern Recognition, Applications to Sustainability).",coverUrl:"https://cdn.intechopen.com/series_topics/covers/25.jpg",keywords:"Genetic Algorithms, Genetic Programming, Evolutionary Programming, Evolution Strategies, Hybrid Algorithms, Bioinspired Metaheuristics, Ant Colony Optimization, Evolutionary Learning, Hyperparameter Optimization"},{id:"26",title:"Machine Learning and Data Mining",scope:"The scope of machine learning and data mining is immense and is growing every day. 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We welcome chapters presenting research on the many applications of multi-agent studies including, but not limited to, the following key areas: machine learning for multi-agent systems; modeling swarms robots and flocks of UAVs with multi-agent systems; decision science and multi-agent systems; software engineering for and with multi-agent systems; tools and technologies of multi-agent systems.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/27.jpg",keywords:"Collaborative Intelligence, Learning, Distributed Control System, Swarm Robotics, Decision Science, Software Engineering"}],annualVolumeBook:{},thematicCollection:[],selectedSeries:{title:"Artificial Intelligence",id:"14"},selectedSubseries:null},seriesLanding:{item:null},libraryRecommendation:{success:null,errors:{},institutions:[]},route:{name:"ofsBook.detail",path:"/welcome/6dcb071a2e978694b6b1cb9c20afc1a3",hash:"",query:{},params:{hash:"6dcb071a2e978694b6b1cb9c20afc1a3"},fullPath:"/welcome/6dcb071a2e978694b6b1cb9c20afc1a3",meta:{},from:{name:null,path:"/",hash:"",query:{},params:{},fullPath:"/",meta:{}}}},function(){var e;(e=document.currentScript||document.scripts[document.scripts.length-1]).parentNode.removeChild(e)}()