Calculation parameters.
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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\r\n\tOrganic synthesis has always been one of the central topics of research for the scientific community in the academic laboratories and industrial world. Many striking journal articles and remarkable reviews and books have been published in the past year describing the practicability and applications of the subject demonstrating the importance of organic synthesis. In the present book, we will be putting together the topics in organic synthesis which may include but not limited to, (1) the basic terms and concepts, (2) various organic reactions including reduction, oxidation, addition, elimination, rearrangements, and cycloadditions, (3) Total Synthesis of Natural products, (4) transition metal catalysts, organocatalysts, enzymes and biotransformations, (5) applications in medicinal chemistry and drug design and development, (6) purification methods and characterization techniques, etc. To set a limit and to increase the scope of the book, author(s) are encouraged to send the chapters that include selected examples with practical applications and good yielding reactions reported within the past decade. Older topics with significant findings or their essence to prepare the foundation may be included in the chapter are welcomed as well.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"f3bbbd989d0896f142d317ccb8abcc35",bookSignature:"Dr. Prashant S Deore",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8807.jpg",keywords:"Natural Product Synthesis, Organic Reaction Mechanism, Stereoselective synthesis, Chirality, C-H Functionalization, Cross-Coupling Reactions, Heterogeneous Catalysis, Homogeneous Catalysis, Green Synthesis, Green Solvents and Reagents, Bioorganic synthesis, Click Chemistry",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"December 10th 2018",dateEndSecondStepPublish:"January 14th 2019",dateEndThirdStepPublish:"March 15th 2019",dateEndFourthStepPublish:"May 20th 2019",dateEndFifthStepPublish:"July 19th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"251769",title:"Dr.",name:"Prashant",middleName:"S",surname:"Deore",slug:"prashant-deore",fullName:"Prashant Deore",profilePictureURL:"https://mts.intechopen.com/storage/users/251769/images/system/251769.png",biography:"Dr. Prashant S. Deore was born in India. He received a Master’s degree in organic chemistry from Pune University in 2007. In the same year, he qualified with the SET and CSIR-NET (JRF) and joined in the group of Prof. Narshinha P. Argade for the doctoral studies in National Chemical Laboratory, India. In 2014, he awarded with a Ph. D. in Chemistry and was a recipient of the 2nd prize in “2014 Eli Lilly and Company Asia Outstanding Thesis Awards”. In July 2014 he moved to Canada and joined as a postdoctoral researcher in the group of Prof. Richard Manderville at the University of Guelph, Canada. Presently, Dr. Deore is working on the collaborative project between the University of Guelph and Aterica health Inc., and providing consulting to the company. His research interest includes organic synthesis, fluorescent probes development, nucleic acid synthesis and modifications, and aptasensor development for proteins and food toxins.",institutionString:"University of Guelph",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"8",title:"Chemistry",slug:"chemistry"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"270935",firstName:"Rozmari",lastName:"Marijan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/270935/images/7974_n.png",email:"rozmari@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{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:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],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:"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:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],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. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"63026",title:"Vertical Natural Vibration Modes of Ballasted Railway Track",doi:"10.5772/intechopen.79738",slug:"vertical-natural-vibration-modes-of-ballasted-railway-track",body:'\nA ballasted track is characterized by its structure, with a ballast layer sandwiched between sleepers and a roadbed, which greatly reduces impact loads generated by dynamic rolling—contact interaction between the wheels and rails. However, this benefit has an adverse effect: The ballasted tracks are structurally prone to deteriorate over time. They absolutely require periodic maintenance work and repair. Recently, many attempts were made to improve the ballasted track structure. For example, many types of elastic and/or viscoelastic structural members, such as rail pads, under-sleeper pads and under-ballast mats, were attempted to reduce ballast degradation [1, 2, 3]. In one experimental investigation, the sleeper’s vibration characteristics, including the dynamic effects of sleeper/ballast interactions, were investigated through a modal analysis to predict the railway track’s dynamic response [4]. Dynamic wheel/rail interactions, which significantly contribute to impact vibration and noise, were also investigated for rail and wheel surface defects in field measurements and numerical simulations [5, 6, 7, 8]. When considering the future of the railway management, it is impossible to disregard the necessity for frequent maintenance that is dependent upon manual aid. Therefore, the need exists to improve maintenance methods for the ballasted track based on findings from empirical and numerical investigations of the dynamic response characteristics and deterioration factors of the ballast layer.
\nRunning trains cause dynamic loads mainly through two mechanisms [9, 10]. One is the dynamic load from passing axle loads as a train passes. The related frequency characteristics, which depend on the number of axles passing per unit of time, are limited to low frequencies of only several Hertz to approximately 30 Hz. The other mechanism is the impact load that is generated dynamically by the rolling contact mechanism between the wheels and rails. The ballast layer transmits this sharp pulse-shaped impact load superimposed on the low-frequency loads from passing axles. This waveform, when transformed into a frequency domain, exhibits numerous vibration components with broadband characteristics that extend from low frequencies to several kilohertz. That is to say, dynamic response measurements of the ballasted track require high-precision measurements of vibration components ranging broadly from several Hertz to several kilohertz. Outputs of sensor would be degraded by noise of tens of millivolts deriving from the inductive currents of high-voltage overhead cables in conventional field measurements, which necessitated the use of a low-pass filter to alleviate that interference. Ensuring the measurement accuracy of high-frequency vibration components exceeding 50–100 Hz was impossible under such conditions. For that reason, no comprehensive discussion of these components has been reported in the literature to date.
\nThis chapter gives accurate field measurements of the dynamic responses of the ballasted track with a train passage at a sampling frequency of 10 kHz without low-pass filters, using special sensing sleepers and sensing stones produced by the authors [11, 12]. Using the measurement effects, the analysis can be done with a focal point on propagation characteristics of dynamic loads inside the ballast layer and vertical natural modes of the ballast layer. Moreover, the author conducted a free fall-weight impact loading test on a full-scale mock-up of a ballasted track to ascertain the response motions of the ballast layer, with high rapidity and with high accuracy, in the high-frequency region immediately after the impact load was used [13]. Furthermore, using a direct solver MUMPS [14, 15, 16, 17] corresponding to large-scale parallel computing of a distributed memory type, according to finite element transient response analysis FrontISTR [18] and Advance/FrontSTR [19] based on a fine ballast aggregate model, both the elastic natural vibration mode and the rigid-body bounce natural vibration mode of the granular ballasted layer are simulated numerically.
\nIn general, a dynamic load propagates as an elastic wave through the interior of an object, consequently inducing the natural vibration modes specific to the object, which can be applied to the ballasted track composed of the ballast aggregate. Although the ballast layer is a discontinuous structure, it presumably has natural vibration modes that are specific to the ballasted track. Figure 1 shows some characteristics of the principal natural vibratory motions in the vertical direction of the ballast layer [20]. One characteristic is the rigid-body bounce natural vibration mode. Another is the elastic shrinkage natural vibration mode. The ballasted track structure represents a single degree of freedom system that includes sleepers, rails and other components which constitute the track structure mass, along with the ballast layer and roadbed which constitute the spring rigidity component. In the bounce natural vibration mode, this single degree of freedom system moves vertically and rigidly under a train’s dynamic load. The ballast layer acts as an elastic one-directional spring in the vertical direction. Rigid-body natural vibration modes of six kinds exist: They are translational and rotational along each of the three axes. In both the dynamic loads applied to the ballast layer and in the responses of the ballast layer, the translational vibration components in the vertical direction are predominant.
\nPrincipal vertical natural vibration motions of the ballast layer. (a) Rigid-body bounce mode, (b) elastic shrinkage mode.
Therefore, this research specifically examines the translational bounce behaviour in the vertical direction. According to the dynamics, the natural frequency of the first-order rigid-body bounce mode f1 is given theoretically as \n
The elastic vibration mode is the motion by which the whole ballast layer shrinks and stretches vertically as an elastic body. This natural vibration mode is considered not to occur in a normal-state ballast layer but to occur when the ballast layer is under high confining pressure generated by the train’s weight applied to the layer. To date, no report of the relevant literature has described a study conducted to capture this mode, that is, ballast motion in the frequency domain related to this mode. Moreover, on a real track, natural vibration that entails bending deformation and torsional deformation of the members occurs. According to the physical theory related to standing waves on the railway track, the natural frequency of the elastic first-order vibration mode f1 is given theoretically as \n
The author built a full-scale mock-up of the ballasted track structure and investigated natural vibration characteristics of the ballasted track by performing an experimental modal analysis based on impulse excitation tests.
\nFigure 2 shows the profile/plane of the mock-up and the sensor positions [22, 23, 24]. To build the full-scale mock-up, the author employed new ballast using hard andesite, which complies with the same standard for the real track. They were compacted sufficiently. Type 3 prestressed concrete (PC) monoblock sleepers were used for the mock-up. They are used widely for the metre-gauge (1067 mm-wide) railway lines that are conventionally used for Japan Railway Companies. For the prevention of interference of vibration effects of the concrete frame, urethane foam panels were sandwiched between the mock-up and the outer concrete frame. The author installed acceleration sensors on the mock-up and the concrete frame, vibrated the mock-up and ensured that the vibrations were sufficiently isolated to assess the vibration-insulating properties. The author conducted tests by hitting the end of the sleeper laterally, longitudinally and vertically with an impulse hammer to make it vibrate. Test records included measurements of the acceleration responses: 22 sleeper locations and several ballast layer locations. From those data the accelerance was calculated: the transfer functions of the acceleration responses to the excitation force in the frequency domain. Then experimental modal analysis was conducted considering the location relations of the measuring points. As a result, for the ballasted track, the author was able to identify the natural vibration frequencies and their modal shapes between the low-frequency domain and 1 kHz.
\nOverview of full-scale vibration test.
Figure 3 presents the natural vibration frequencies and the specific modal shapes of the ballasted track that were acquired from the test results [22, 23, 24]. Although there are rigid-body vibration modes of six types as described above, the figure shows only the rigid-body translational mode in the vertical direction. It also shows that the vertical and translational rigid-body vibration is generated at 98 Hz, which agrees well with earlier reported research results. Furthermore, six types of dominant natural vibration mode entailing the bending and torsional deformations of sleepers are identified as shown in the same figure. Nevertheless, the author was unable to capture any vertical elastic natural vibration mode of the ballast layer in this test. That is true probably because the elastic vibration modes of the whole ballast layer would occur only when the ballast layer continuity is sufficiently satisfied according to the train loads on the ballast layer.
\nMode shapes of natural vibration acquired from test results.
Dynamic responses were measured on an actual ballasted track of a main conventional railway line in Japan to identify the dominant natural vibration modes of the ballasted track. The track structure at the measurement site, consisting of continuous welded rail weighing 60 kg/m and type 3 PC sleepers, was designed based on the Japanese standard [25], which allows a running speed higher than 130 km/h. The measurement site was located on a solid embankment in a straight section. For spacing between the sleepers, 41–42 sleepers are positioned over a distance of 25 m. The author chose a straight section with satisfied track conditions, based on measurement data from an inspection car. The ballast layer at the measurement site is made of new andesite hard stones with clear-cut edges. The ballast layer is approx. 30 cm thick.
\nFigure 4 presents an overview of sensor positions. Details of the measurements are described in earlier reports of the literature [26, 27]. This article specifically examines the measured responses for a passenger train moving at approx. 120 km/h (sampling frequency is 10 kHz). The sleeper vibration acceleration and the ballast vibration acceleration were measured using piezoelectric triaxial acceleration sensors: 10 mV/G sensitivity, 500 G measurement range and 2–10,000 Hz frequency range within 5% deviation. The ratio of noise to the maximum measurable acceleration is approximately 0.002%. The acceleration sensor also offers an appropriate level of performance to enable measurement for the determination of load characteristics in a high-frequency domain. The following analyses were conducted by obtaining linear amplitude spectra by application of fast Fourier transformation of the time history response waveforms in response to vibration accelerations, with smoothing at a 20 Hz bandwidth.
\nMeasuring sensor positions.
Figure 5 shows a special sensing sleeper designed to assess the dynamic load distribution on the sleeper bottom, for a wide frequency range from a low frequency of 0.01 Hz up to a high frequency of several tens of kilohertz. The sensing unit comprises a type 3 PC sleeper fitted with many ultra-thin-type impact load sensors. Attached to the sleeper’s whole undersurface is a solid mass comprising 75 impact load sensors (25 pieces × 3 rows). Each impact load sensor has a main body and cover members. The main body including a piezoelectric film has solid cover plates on both surfaces. The cover plates (8 cm × 8 cm) transmit impact load to the main body in cases of impact loads of a running train, thereby preventing sensor breakage [12, 27]. Each sensor can measure a load up to a maximum of 10 kN. The sensor has thin metal plates attached to both sides of a thin piezo-film. The structure, which resembles that of a condenser, has no internal resistance. For that reason, no current is induced by noise sources, even in the electromagnetically high-tension environment that prevails during train operation. This feature enables high-quality load measurement. Both terminals output a charge that is proportional to the impact load, but digitization of the charge output is extremely difficult. For that reason, the charge from the sensor is usually converted into a voltage by integrating the electric circuit attached to a sensor output terminal (charge amplifier). For that purpose, an impedance transformation circuit with extra-high impedance, ultra-low noise and differential input-type operational amplifiers (OP-amps) can be used for the instrumentation preamplifier. Moreover, this sensor has good reactivity. Because the output voltage can be as high as several tens of volts, the ratio of noise to the maximum measuring load is as low as 0.003%. The sensor can measure load characteristics at high frequencies.
\nOverview of sensing sleeper.
Figure 6 shows the acceleration amplitude spectrum and the displacement amplitude spectrum of the ballast gravel at 10 cm depth. The acceleration spectrum shows that components at frequencies higher than 100 Hz as well as the low-frequency components contribute greatly to the ballast response. These high-frequency vibration components are attributable to the sharp pulse-shaped impact loads induced by the dynamic mechanisms between the wheels and rails.
\nAcceleration and displacement amplitude spectra of the ballast (measured).
When particularly addressing the ballast displacement, its amplitude is extremely small in the high-frequency domain. For instance, the displacement amplitude is only 1/1000 μm at a frequency of approx. 800 Hz, which is equivalent to the natural frequency of the ballasted track entailing the third mode of the vertical bending of the sleeper. Therefore, the vibration components in the high-frequency domain are not transmitted by rigid-body vibrations around the centre of gravity of the ballast gravel, but the dynamic loads are transmitted through the elastic undulation propagation because of the local and minute deformation behaviour and sliding behaviour at the tips of the edges of contact points between the ballast stones. However, the displacement amplitude in the low-frequency domain from several Hertz to 20 Hz is several thousand times higher than those in the high-frequency domain. Consequently, the loads in the low-frequency domain are transmitted mainly through rotational and translational rigid-body vibrations of the individual ballast gravel particles. This figure also depicts peak profiles of responses related to the natural vibration modes of the ballasted track explained in the preceding paragraph. These curves identify the rigid-body resonance mode of the ballast layer around 100 Hz and indicate another large peak profile at around 300 Hz. From the full-scale experiment presented in Figure 3, the rigid-body natural vibration mode of the ballasted track appears at 98 Hz.
\nFigure 7 shows the relation between the two-dimensional distribution of the vertical loading on the bottom surface of the sleeper and the normalized vertical displacement of the sleeper in cases of two frequencies (110 and 310 Hz), which give the peak profiles of the response curves. In the figures, θ denotes the relative phase angles with reference to vertical motion at the centre of the sleeper. In the distribution maps, red denotes the positive load (compression). Blue shows the negative load (tension). Regarding the sleeper motion, the downward direction indicates the downward behaviour of the sleeper. The upward direction indicates the upward behaviour of the sleeper. Panels (a) and (b) show that the sleeper repeats a vertical periodic movement at these frequencies, entailing bending deformation of the sleeper at high frequencies, in synchronization with the phase angles.
\nDistribution of vertical loading at the bottom of the sensing sleeper and normalized displacement at the top of the sleeper (measured).
The author repeatedly performed drop-weight impact loading tests using a full-scale mock-up of the ballasted track, dropping a steel weight from a given height and applying impact loads having a sharp pulse shape directly to the track structure. Figure 8(a) presents an overview of the test device. Figure 8(b) depicts the positions of sensors used for the measurements. The test setup consists of a 30 cm-thick ballast layer built with new andesite ballast gravel on a concrete roadbed. A track structure was built using three pieces of type 3 PC sleepers and two pieces of rails weighing 60 kg/m. The steel weight frame, positioned over the sleeper at the centre, was dropped repeatedly from the given height to apply impact loads to the track structure. Measured data for the magnitude of the impact loads, the vertical displacement of the sleepers and the acceleration responses of sleepers and ballast were recorded by sampling the data at 10 kHz or 20 kHz. This chapter presents a discussion of the measurement results of the displacement responses of the sleepers [9, 13].
\nOverview of impact loading test. (a) Drop-weight impact test device, (b) sensor positions.
Figure 9(a) shows the time history response of the centre sleeper’s vertical displacement after impact loading. This average curve shows results obtained from about 4000 loading tests, excluding initial loading of the first 1000 iterations. The downward displacement in the chart shows the ballast layer compression. The upward displacement represents extension of the ballast layer. Figure 9(b) especially depicts data obtained at the moment immediately after loading. The average value of the impact load on the ballast through the left and right rails was 217 kN. The figure shows that because of the compression applied by an impact load, the ballast layer instantaneously deforms elastically. The compression produces maximum downward displacement of 0.178 mm in 0.71 ms. Subsequently, it returns to the preloading position in 1.1 ms. Results show that only about 1 ms is necessary for the ballast layer compression and restoration. Displacement responses of the sleeper and load during that time include few vibration components at low frequencies.
\nVertical displacement of sleepers immediately after impact loading. (a) Sleeper displacement, (b) close-up of displacement.
Following the compression and restoration motions of the ballast layer, sleeper-jumping occurs. The average jumping speed is approximately 1.71 times as high as the average of the compression speed. Their initial speed can be approximately 12.1 times faster than the average compression speed. The jumping height of the sleeper reaches 5.1 mm in 24.4 ms. The sleeper returns to the initial position within 46.7 ms after loading. The jumping behaviour during unloading includes no high-frequency vibration component. Most of the vibration comprises low-frequency components. The author posits that the cause of sleeper-jumping is the abrupt release of the strain energy stored in the ballast.
\nFigure 9, as described, presents the vertical displacement of the sleeper. Presumably, similar behaviour occurs in the upper part of the ballast layer immediately under the sleepers, which means that the motion under impact loading is extremely slight. The compression and restoration behaviours are high-frequency responses that last for a very short time: about 1 ms. Therefore, high-frequency vibration components are dominant in ballast responses under loading. However, ballast motions during unloading are induced mainly by low-frequency vibration components that cause large displacement and which last longer.
\nThree-dimensional shape measurement was performed to ascertain three-dimensional vertex coordinates of more than 4000 ballast gravel pieces. Based on the measured coordinates, each shape was expressed using a polyhedral rigid-body discrete element model and was converted into aggregate, with the same size and the same shape, of the tetrahedron secondary elastic finite elements. Details of the measurements were presented in an earlier report [28]. Figure 10 presents some exemplary images of a ballast gravel piece and its numerical discrete element and finite element models. Regarding the finite element models, a sufficiently fine mesh size of 1 cm was adopted to support the precise representation of natural frequencies of individual ballast gravel up to several 10 kHz.
\nExemplary pictures of existing ballasts and the digitized models. (a) Ballast, (b) DEM model, (c) FEM model.
Regarding the physical properties of the ballast, density ρ = 2700 (kg/m3), Young’s modulus E = 30 (GPa), Poisson’s ratio ν = 0.2 and structural damping parameter η = 0.01 are adopted. The ballast gravel density was the laboratory experimental value obtained from specific gravity tests. The Young’s moduli and Poisson’s ratio were referred or derived from previous reports of the literature. Regarding the structural damping coefficient, the author adopted general values of a concrete structure.
\nFigure 11 presents a procedure for the creation of the ballast aggregate using both discrete element and finite element modeling. First, about 100 pieces of the ballast polyhedron discrete element models with different shapes and sizes were placed randomly in the air above rectangular box frames of 20 cm width and length. The gravel was then dropped freely with gravity and was compressed vertically with a loading plate using discrete element software. Next, all individual polyhedron discrete element models were converted into assemblages consisting of the small finite tetrahedron second-order elastic solid elements and split into 1 cm meshes with geometry and contact point information maintained. Each polyhedron discrete element model was divided into approximately 1000 tetrahedron finite elements. The finished rectangular block model has 20 cm width and length, with 17 cm height, and has more than 90,000 tetrahedron finite elements.
\nCompaction and modeling of the ballast aggregate with MPCs.
For this procedure, the contact points were mutually connected through multipoint constraints (MPCs), which connected the nodes of elements in three axial directions related to the contact pair of blocks at each contact point. The provided contact-connectivity exhibited no expansion or contraction because it was several tens of thousands of times harder than that of ballast pieces. Accordingly, the spring functions around the contact points were represented by the elastic deformation of the ballast angularities, which were composed of the assemblages of several tetrahedron finite elements adjacent to the contact points.
\nFigures 12 and 13 present a finite element model of a type 3 PC monoblock sleeper developed by the authors [24] and consisting of 51,146 nodes and 51,944 solid elements. The sleeper model can make a precise representation of all natural frequencies described above, with their response values up to 1 kHz within 5% deviation. Its physical weight is 161.40 kg. Its volume is 0.0677 m3.
\nModel of a type 3 PC sleeper.
Model of a type 3 PC sleeper. (a) Side view, (b) top view, (c) end face and reinforce bars.
A large-scale finite element model was constructed with multipoint constraints (MPCs) by assembling 48 units of the rectangular unit block models of the ballast described above and the type 3 PC sleeper model. Figure 14 presents finished analysis model and its domain segmentation for large-scale parallel computing by the finite element programming code of FrontISTR. The model consists of 7.05 million nodes and 4.15 million second-order solid elements. The degrees of freedom of the model exceed 21 million. By adopting the finite element analysis using the precise model of the ballast layer having a complicated structure, it is possible to reproduce phenomena such as stress concentration and wave propagation within the ballast layer rapidly, easily and exactly. The entire model is divided into 24 sub-domains to introduce the direct solver MUMPS corresponding to the parallel computing of a distributed memory type. By applying the finite element normal-mode analysis by FrontISTR, a set of normal modes related to the ballast aggregate and sleeper system is obtained. Specifications related to the various parameters of each model are presented in Table 1.
\nAssembly of ballasted track model and domain segmentation for large-scale parallel computing.
Item | \nYoung’s modulus (GPa) | \nPoisson’s ratio | \nDensity (kg/m3) | \n
---|---|---|---|
Ballast | \n30 | \n0.200 | \n2700 | \n
Concrete | \n45 | \n0.167 | \n2350 | \n
Steel | \n210 | \n0.290 | \n7820 | \n
Calculation parameters.
The time history response waveforms were calculated numerically by inputting the measured loading waveforms to the top surface of a sleeper model when a passenger train moved over the top surface of the previously described ballasted track model.
\nFigure 15 displays the actual waveforms of vertical loading (measured in cross-sectional area of 14 cm width and 18 cm length on the bottom surface of the rails) applied by the first axles of a lead coach bogie when the passenger train moved through the test section at about 120 km/h [26, 27].
\nMeasured rail seat loads.
The figure shows that the axles passed immediately above the sleeper centre at around 55 ms. Finite element analysis shows that the measured time history waveforms are uniformly input to all nodal points located within the bottom area of the rails on the top surface of the sleeper model. The calculation time interval is set at Δt = 0.1 (ms). The total calculation steps are 800.
\nFigure 16 portrays the distribution of the response nodal displacement of the ballast aggregate and the sleeper system at t = 55.0 (ms) when the load peaks appeared as the first axle of the lead coach bogie that passed above the sleeper centre. It is apparent that the dynamic displacement induced by a passing train on the ballast is not distributed uniformly throughout the ballast aggregate and the sleeper. Significant displacement is concentrated locally around the rail positions. Analytical results demonstrate that 30 μm maximum downward displacement occurred.
\nDistribution of nodal displacement (t = 55.0 ms).
Figure 17 depicts the time history waveforms of response of the von Mises stress on the cross-section inside the gravel angle acting on three contact points, each with some angularity, of the ballast gravel placed at different depths below the loading point of the left rail location. As the figure shows, the stresses in the gravel increase gradually, alternately repeating the minute upward (compression) and downward (tension) motions at a frequency of approximately 300 Hz, according to the inputted loads. In this case, the maximum stresses of approximately 50 MPa after elapsed time of about 45–53 ms are observed near the ballast surface beneath the sleeper bottom. It is apparent that the rise in the peak response value becomes gentler as the measurement point becomes increasingly distant (i.e. deeper) from the loading point. A tendency exists for waveforms to become smoother along with the steep decrease in high-frequency vibration included in the wave. Although the investigation reported here involves elastic body analysis without the use of any constitutive equation, the diminishing trend of energy inside the ballast is reproduced closely by simulating the ballast aggregate structure in detail. Results show that the ballast aggregate structure featuring angular parts has the mechanism of energy attenuation.
\nTime history of on Mises stress.
Figure 18 portrays linear amplitude spectra of response of the von Mises stress on the cross-section inside the gravel angle acting at different depths below the loading point of the left rail, as obtained by conducting fast Fourier transformation of these time history response waveforms and smoothing them at a 20 Hz bandwidth. As the figure shows, these spectra curves identify the first-order elastic vibration resonance mode of the ballast layer at around 337 Hz, where the whole ballast layer stretches vertically as an elastic body.
\nResponse spectrum of the von Mises stress.
To detect the exact frequency of the elastic vibration mode of the ballast layer, the author conducted a numerical experiment (simulation), which simulates the impulse loading experiment using a transient response analysis of the previously described large-scale sleeper-ballast aggregate model.
\nFigure 19 shows the amplitude spectra of response of the vertical displacement of the sleeper by application of a 0.1 ms square waveform of impulse loading. Impulse loading to the left and right rails totals 100 kN. Results of the numerical experiment of the impact loading indicate that the rigid-body natural vibration mode occurs at around 310 Hz. Results show that the analytical natural frequency of the elastic vibration mode of the ballast layer more or less coincides with the measured one described above and that the frequency corresponds to three times the value of the measured natural frequency of the rigid-body mode.
\nResponse spectrum of vertical displacement regarding impulse loading.
To examine the dominant rigid-body resonance motion around 100 Hz, this chapter presents a description of the large-scale finite element transient response analysis of the ballasted track using nonlinear contact springs (i.e. tensionless springs) in place of the MPCs. Results of the drop-weight tests described above suggest that the jumping motion of the ballasted track, the rigid-body bounce mode, will cause large displacement. Therefore, regarding the previously described large-scale finite element model of the ballasted track, information of the contact points between the ballast pieces and the sleeper nodes is modeled with nonlinear contact springs, that is, with tensionless contact. Table 2 presents parameters of calculations related to contact points. In this analysis, the tension spring factors are set at 1/100,000 values of the compression spring factors.
\nItem | \nCompression spring factor (GN/m) | \nTension spring factor (GN/m) | \n
---|---|---|
Ballast-ballast | \n30 | \n0.0003 | \n
Sleeper-ballast | \n10 | \n0.0001 | \n
Calculation parameters related to contact points.
With finite element analysis, the measured waveforms of the rail seat load were inputted to the top surface of the sleeper model using tensionless springs. Figure 20 presents the nodal displacement distribution of the ballast aggregate and the sleeper system at t = 55.0 ms when load peaks appeared immediately after the first axle of the lead coach bogie passed above the sleeper centre.
\nDistribution of nodal displacement (t = 55.0 ms).
Figure 21 depicts time history waveforms of the response of the von Mises stress on the cross-section inside the angular part of the gravel under the left rail. As the figure shows, considerable stresses of approximately 57 MPa are obtained near the surface of the ballast layer under the sleeper bottom. In the figure, in general, the positive motion denotes compression and downward behaviour. Negative motion denotes tension and upward behaviour.
\nTime history response of the von Mises stress.
Figure 22 displays the linear amplitude spectra of response of von Mises stress, on the cross-section inside the gravel angle acting at different depths below the loading point of the left rail, which are obtained by conducting fast Fourier transformation of these time history response waveforms and by smoothing them at 20 Hz bandwidth. As the figure shows, these spectral curves identify the first-order elastic vibration resonance mode of the ballast layer at around 337 Hz, where the entire ballast layer stretches vertically as an elastic body.
\nSpectra of von Mises stress.
Figure 23 presents the time history of response of the vertical displacement at the left edge of the sleeper immediately after the 0.1 ms square impulse loading waveforms of 100 kN. In this figure, the downward displacement shows the downward motion of the sleeper (i.e. ballast layer compression); the upward displacement represents the upward motion of sleeper (i.e. ballast layer extension). According to the figure, when an impact load is applied, the ballast layer instantaneously deforms elastically because of compression. It then returns to the preloading position. Consequently, it takes only about 1 ms for the ballast layer to be compressed and restored. Following compression and restoration of the ballast layer, sleeper-jumping occurs. The cause of this sleeper-jumping is the strain energy stored in the ballast under the compression procedure and its abrupt release.
\nTime history response of sleeper displacement.
Figure 24 presents amplitude spectra of the vertical displacement of the sleeper. Results indicate that rigid-body natural vibration occurs at around 120 Hz. The value is approximately 10–20% larger than the experimental one and is almost one-third of the elastic natural vibration frequency. Large-scale finite element analysis by tensionless analysis reveals that rigid-body natural vibration mode occurs at almost one-third of the elastic natural vibration frequency.
\nResponse spectrum of vertical displacement related to impulse loading.
Figure 25 presents time history waveforms of response of the von Mises stress on the cross-section inside the angular part of the gravel where the maximum response stress occurs. This analysis shows that strong stresses up to 80 MPa can be observed in tetrahedral elements near the contact part, whereas the average maximum pressure on the ballast surface is 74 kPa. The stress acting on the angular part is approximately 1100 times greater than the average value of the loading stress on the ballast surface. Assuming that the unconfined compressive strength is 60 MPa at the angular part of the ballast gravel, the application of a dynamic load of 55 kPa or more to the surface of the ballast layer under the bottom surface of the sleeper would cause minute fracturing or breakage around the angular part of the ballast gravel, where the stress will converge.
\nTime history response waveforms of the von Mises stress.
Figure 26 presents results of measurements indicating the maximum values for all sensors (measured in a cross-sectional square area with 8 cm sides on the whole bottom surface of the sleeper, total: 75 pieces, 25 units × 3 rows) as the passenger train passed. The figure also shows a threshold line of 55 kPa at which breakage will occur in the angular part of the ballast gravel. Minute breakage might occur at points within the ballast layer where the stress converges if the measured value exceeds this line. As the figure shows, this limit was exceeded in 40 out of the 75 sensors; the ratio of exceeding the threshold is 53%. The results indicate that the degradation of the ballast layer might occur at any time under the effects of regular train passage. Further experimentation and analysis must be conducted to clarify this issue.
\nDistribution of the maximum load acting during passage of a passenger train.
According to the results, when information related to the contact points between the sleeper bottom and ballast pieces is modeled with MPCs, numerically obtained results show that the vertical elastic natural vibration mode of the ballast layer occurred at about 310 Hz. However, when the contact point is modeled with nonlinear contact springs, i.e. with tensionless contact, the rigid-body natural vibration mode is found numerically as approximately 120 Hz. The analytical result coincides to a considerable degree with those obtained using in situ measurements and full-scale experiments. Accordingly, the natural mode which is expected to occur when an impact load is applied is determined mainly by the contact condition on the sleeper bottom.
\nAs shown in Figure 5 presented earlier, the amplitude of displacement of the ballast gravel decreases in inverse proportion to the squares of the frequency, according to the physical theory. Therefore, the occurrence of the rigid-body natural vibration at one-third of the elastic natural vibration frequency is expected to induce nine times larger amplitude of displacement within the composite structure of the ballasted track than in the case of the elastic natural frequency. The occurrence of the rigid-body natural vibration is expected to contribute greatly to the progress of the ballast deterioration. In theory, improvement of the contact condition between the sleeper bottom and the boundary region of the ballast layer might reduce the amplitude of displacement to one-ninth at most compared with that in the current status of the ballasted track. Moreover, measurements of the ratio of the rigid-body natural vibration and the elastic vibration at the site are expected to contribute to quantitative evaluation of the ballasted track condition.
\nFigure 27 presents the structural damping coefficient on the sleeper bottom in the vertical direction for a 30 cm-thick ballast layer, as identified by the experimental model analysis using full-scale mock-ups of the ballasted track and precise finite element analysis according to an earlier report of the literature [24]. As the figure shows, the structural damping factor of the ballasted layer has extremely strong dependence on the frequency. The ballast layer, in the high-frequency domain over 200 Hz, provides extremely high damping functions for reducing the impact energy. However, the ballast layer is almost non-resistant to the wave components of dynamic loads in the low-frequency domain. The load components in the low-frequency domain will be reduced only slightly unless the ballast aggregate is fully constrained by an appropriate amount of uniform pressure from the surrounding area. To reduce the ballast degradation based on these mechanisms, improvement of the contact condition of the boundary region adjacent to the sleeper bottom in the ballast layer contributes to restraint of the occurrence of the rigid-body natural vibration modes at low frequencies.
\nStructural damping coefficient in the vertical direction for a 30 cm-thick ballast layer.
As described in this chapter, although the results are limited to the ballasted track of metre-gauge railway lines in Japan, the author dealt with natural vibration modes of the ballast layer, which will engender the phenomena of ballast deterioration, based on precise field measurement, full-scale experiments and large-scale numerical analyses based on high-performance parallel computing. These results can be summarized as described below.
Impact loads imposed by running trains induce natural vibration modes within the ballast layer that are specific to the structure and which consequently propagate within the ballast layer through the natural vibration modes. Natural vibration modes play an important role in ballast layer deterioration.
According to drop-weight impact loading test, the high-frequency vibration components are dominant in the ballast responses under loading. The ballast motions during unloading are induced mainly by low-frequency vibration components that cause large displacement and which last longer.
Analytical results indicate that the stress acting on the angular part of the ballast gravel is approximately 1100 times greater than the average loading stress on the ballast surface under the sleeper bottom. Minute fracturing or breakage around locations where the stress acting on the angular part of the ballast gravel converges will occur at any time because of the effects of regular train passage.
Normal frequencies of the vertical elastic vibration mode are detected numerically at around 310 Hz. The rigid-body bounce mode of the ballast layer occurs at almost one-third of the frequency of the elastic vibration mode. These analytical normal frequencies coincide closely with the measured ones.
The occurrence of rigid-body modes of the ballast layers plays an important role in the progress of ballast deterioration. The improvement of the contact condition near the sleeper bottom is expected to contribute to reduction of the displacement amplitude of ballast gravel. That will reduce the ballast degradation.
The combined structure, which consists of the ballast layer and sleepers, vibrates in synchrony with resonance motions induced by the impulse waves. Improvement of contact conditions near the sleeper bottom is expected to contribute to reduce the displacement amplitude of the ballast gravel and to reduce ballast degradation.
Neurofeedback [1, 2] is a smart biofeedback platform which provides real-time feedback to individuals about their neurophysiological signals in order to achieve brain activity associated with therapeutic benefit. Brain activity of an individual is measured continuously using an EEG system during the course of neurofeedback training and parameters describing neurophysiological signals such as alpha power or peak alpha frequency are calculated in real-time [3]. These calculated features of ongoing brain activity are then presented to the individual either in an audio or visual form [3]. The idea behind this is that through repeated provision of such feedback, the individual gains an awareness of their current brain state and can identify different mental strategies which help them achieve the desired brain state [4]. Once the individual identifies strategies which work for them, they can keep practicing them over the course of multiple sessions with the final aim of being able to implement these strategies independent of a neurofeedback session.
Neurofeedback has already been investigated extensively for the management of several neuropsychiatric conditions [5] such as Attention Deficit Hyperactivity Disorder (ADHD) [6], depression and anxiety [7], cognition [8] and stroke rehabilitation [9] for example. Being able to target brain signals through neurofeedback can be of great benefit in conditions such as chronic pain. This is because the perception of chronic pain depends on how multiple regions of the brain process the ascending pain signals [10, 11]. Such central processing of incoming pain signals has been shown to be different in chronic pain patients compared to healthy participants by a number of studies [12, 13, 14]. Considering the brain plays such an important in the development and maintenance of chronic pain state, being able to target changes in the neurophysiological signal which reflect such brain activity using a novel therapy such as neurofeedback is of great interest.
The field of neurofeedback therapy for chronic pain is rapidly developing. Several studies have been performed on a range of medical conditions over the last decade [15]. The current studies are highly heterogenous with a number of variations in neurofeedback protocol and delivery [15, 16]. This chapter aims to give an overview of the neurophysiological changes observed in chronic pain and how these have been targeted by different neurofeedback studies. We also discuss the different aspects of neurofeedback protocols which have been used so far and the outcomes of these studies in terms of reduction in pain and pain associated symptoms.
Our understanding of the neuroscience underlying pain has evolved significantly over time. Neural pathways involved in pain perception have been shown in Figure 1. One of the earliest theories explaining pain was the “specificity theory” (Figure 1: Red pathway). According to this theory, pain is experienced when an injury to a particular part of the body leads to signals being relayed via nociceptive neurons to the “pain center” [17]. The brain was considered to be a “passive recipient of sensory information” [17].
Neural pathways underlying pain perception proposed by different pain theories.
One of the landmark theories which was highly influential in changing this prior understanding of pain was the Gate Control Theory by Melzack and Wall (1965) [18] (Figure 1: Blue pathway). This theory proposed that several neurons in the spinal cord, such as large fibers carrying touch and vibration sensations as well as interneurons in substantia gelatinosa of the dorsal horn, modulate the incoming signals from the site of pain, thereby influencing the final signal which is transmitted to the brain for processing.
Since then, advances in neuroimaging has revealed that in addition to neural pathways in the spinal cord, several cortical structures are also involved in modulating pain perception [19, 20] (Figure 1: Purple pathway). Some of the areas which have been reported to be involved include anterior cingulate gyrus, somatosensory cortex, insular cortex, thalamus and prefrontal cortex [19]. These findings suggest that there is not a single “pain centre”. Instead, pain is processed by a “pain matrix” connecting different parts of the brain, thereby, reinforcing the idea that pain perception is a result of several sensory, affective and cognitive processes [10, 11]. Therefore, pain experienced by an individual is an integration of the current information about the painful sensory stimulation and prior information from previous experiences which influence the emotions, anxiety, attention and expectations of the individual about the pain [21].
Different areas of the cortex constituting the pain matrix project onto the hypothalamus and amygdala, which then give rise to both descending inhibitory pathways and descending facilitatory pathways [21, 22]. These descending pathways directly project onto the dorsal horn of the spinal cord where gating of pain is occurring, therefore, influence the signals which are relayed up the ascending pathways [21, 22]. This process is known as top-down modulation of pain [23].
In summary, the pain perceived by an individual is an integration of how different parts of the cortex process the ascending pain signals as well as how the activity of these cortical and subcortical structures influence the ascending pain signals via descending pathways [17, 21, 24]. With the discovery of these higher-order processes which influence pain perception, several neuromodulatory therapies such as neurofeedback (NFB), hypnosis and meditation, have been explored with the potential of controlling pain by influencing this supraspinal cortical processing of pain [25].
Generally, the EEG oscillations are categorized based on their frequency into theta (4–7 Hz), alpha (8–12 Hz), low beta or beta1 (15–20 Hz) and high beta or beta2 (22–30 Hz) [26, 27, 28, 29]. Another oscillation which is widely investigated in the field of neuromodulation is sensorimotor rhythm (SMR). SMR refers to oscillations in the 12–15 Hz range which appear in spindle-like pattern over the sensorimotor cortex during idling of the motor cortex [30, 31]. Motor execution or motor imagery which activates the motor cortex leads to a decrease in the SMR activity [31].
Each of these brain rhythms is associated with a specific cognitive state. For instance, whilst alpha waves have been associated with a relaxed state, beta waves are associated with wakefulness and a state of engagement in task. Theta waves have been associated with drowsiness [27, 32].
Patients with chronic pain have differences in their resting-state brain (EEG) oscillations from healthy individuals. An example of a chronic pain condition which has been extensively investigated for identification of EEG correlates of chronic pain has been spinal cord injury (SCI). A study by Sarnthein et al. [12] showed that SCI patients with central neuropathic pain had increased activity of theta and beta oscillations compared to healthy individuals. These findings were confirmed by another study [13] which observed similar increases in theta and beta activity, but in addition, also identified lower levels of alpha activity in this patient population. This association between chronic pain and EEG changes was further strengthened when Jensen et al. [33] demonstrated that even within a group of patients with spinal cord injury, individuals with central neuropathic pain had higher theta and lower alpha activity than patients with spinal cord injury but no chronic pain.
These patterns of EEG have also been reported in other chronic pain conditions. For instance, patients with migraine have higher theta and delta power compared to healthy controls [14]. Patients with fibromyalgia have been shown to have higher theta activity with sources estimated to be in the left dorsolateral prefrontal and orbitofrontal cortex, higher beta and gamma activity with sources estimated to be in the insular, primary motor and primary and secondary somatosensory cortices and slowing of the dominant alpha peak [34].
Identification of such neurophysiological correlates of chronic pain is important as it not only provides the necessary feedback signal to increase voluntary control in therapies such as neurofeedback, but also allows monitoring the efficacy of the therapy in modulating the neurophysiological processes targeted by the therapy.
There are two key modalities which have been used to provide neurofeedback – EEG neurofeedback and fMRI neurofeedback. Whilst EEG neurofeedback provides feedback based on the neurophysiological signals recorded through an EEG system, fMRI neurofeedback provides feedback based on the degree of activation of a particular region of the brain detected using fMRI imaging in real time [35]. Hence it is inevitable that there is some lag between the activation and signal detection in fMRI neurofeedback which happens almost instantaneously in EEG neurofeedback [35].
Evidence regarding efficacy of fMRI neurofeedback in pain is limited understandably due to the increased difficulties and expenses associated with this form. The common region of interest which has been targeted in fMRI studies has been rostral anterior cingulate gyrus (rACC), whereby increased activity of rACC, measured through detecting an increase in blood oxygen level dependent signal from the region, has been associated with pain reduction [36, 37]. However, these studies have been severely limited in terms of number of sessions [37, 38], therefore the full benefit of the neurofeedback which occurs over the course of several sessions has not been explored yet in fMRI neurofeedback for chronic pain.
A number of brain rhythms have been targeted by EEG neurofeedback in order to increase resilience to pain (Table 1). The commonly targeted rhythms include theta (4–7 Hz), alpha (8–13 Hz), beta (14–30 Hz) and sensorimotor (12–15 Hz over the sensorimotor area) [17]. However, the change desired in each of these rhythms varies. Whilst pain reduction has been associated with an increase in the power of alpha and sensorimotor rhythms, contrastingly, a decrease in theta and beta rhythms have been associated with pain relief [17]. However, very few studies target these signals in isolation [20, 39]. More often studies target multiple signals at the same time, whereby patients are either shown each rhythm individually at the same time or they are shown feedback based on the ratio of two such signals [40, 41, 42, 43].
Brain rhythm | Frequency | Desired change |
---|---|---|
Theta | 4–7 Hz | Decrease in power |
Alpha | 8–13 Hz | Increase in power |
Beta | 14–30 Hz | Decrease in power |
Sensorimotor rhythm | 12–15 Hz Over sensorimotor cortex | Increase in power |
Neurofeedback targets [17].
In general, neurofeedback sessions tend to be 30–45 minutes long and patients are offered 20–40 sessions [15]. The frequency of these sessions ranges from one to five times a week, but studies which administered more frequent sessions have reported greater pain relief. Commonly used electrodes for providing feedback include C3, C4, Cz, T3, T4, FP1, P3 and P4 [15].
Feedback has been provided in a range of ways. Auditory feedback has been mainly in the form of changing volume of sound, whereby, achievement of signal has been associated with an increase in the volume heard [44]. Visual feedback used has been more varied (Figure 2). Some studies use simple bars to show the feedback, whereby the height of the bar is proportional to the intensity of the signal [45]. Other studies have changed the color of the bar on achievement of signal such that when the threshold is met, the color turns green, otherwise it remains red [43]. Some studies have tried to engage the users through the idea of games whereby the width of a river increases as the intensity of signal increases for instance [41, 46]. Therefore, feedback has been provided in a range of ways. Another form of stimulation which can be explored in the context of neurofeedback is tactile stimulation. Some studies have even combined two forms of stimuli such as visual and auditory whereby patient is shown an angry and shouting patient [36]. In order to calm the patient, the individual has to achieve the desired changes in the brain rhythms.
Schematic representation of visual stimulus provided in different neurofeedback studies.
Several neurofeedback studies have shown pain reduction following neurofeedback. Key randomized controlled trials in the field have been summarized in Table 2. Reduction in pain has been reported across several pain conditions such as Fibromyalgia [27, 29, 36, 41], Central Neuropathic Pain in Paraplegic patients [28, 43, 47, 48, 49], Traumatic Brain Injury [39, 50], Chemotherapy-Induced Peripheral Neuropathy [51], Primary Headache [52], Complex Regional Pain Syndrome Type I [53], Post-Herpetic Neuralgia [37] and chronic lower back pain [54]. There is a wide range of pain reduction reported which can range from an average of 6–82% reduction in pain intensity [15]. A recent systematic review published showed that ten out of twenty-one studies published in the field reported a pain reduction of greater than 30% which is considered to be clinically significant reduction [15].
Study | Chronic pain condition | Target brain oscillation | % Pain reduction | Pain associated symptoms reported to improve following NFB |
---|---|---|---|---|
Goldway et al. (2019) [36] | Fibromyalgia | ↓Amygdala activation (fMRI) | 7% | REM latency Sleep quality |
Prinsloo et al. (2018) [50] | Chemotherapy-induced peripheral neuropathy | ↑Alpha ↓Beta | 45% | Fatigue Cancer-related symptoms Physical functioning Quality of life |
Guan et al. (2015) [37] | Post-herpetic Neuralgia | ↓rACC activity (fMRI) | 64% | None studied |
Farahani et al. (2014) [45] | Primary headache | ↑SMR ↓Theta ↓Beta | 19% | None studied |
Caro et al. (2011) [29] | Fibromyalgia | ↑SMR ↓Theta ↓Beta | 39% | Fatigue |
Kayiran et al. (2010) [40] | Fibromyalgia | ↑SMR ↓Theta ↓Beta | 82% | Fatigue Depression Anxiety Social functioning Physical functioning |
Randomized controlled trials investigating role of neurofeedback in chronic pain conditions.
Such variability in the degree of pain reduction could be due to a number of aspects of the neurofeedback protocol ranging from number of sessions, frequency of sessions, target frequencies and electrodes used for feedback, for example. The neurofeedback studies conducted so far have been highly variable on more than one of these aspects [15, 16], making comparison of results across studies impossible. Therefore, it is difficult to determine which of these parameters is responsible for the difference or how to best optimize each of these aspects of the training.
Most of the neurofeedback studies have measured changes in pain immediately following neurofeedback [39, 43, 52, 55, 56]. Furthermore, pain reduction has been reported to be sustained even at follow up of 3–6 months after completion of neurofeedback training [28, 36, 41, 49, 50, 51, 54]. However, these studies do not report whether the corresponding change in brain rhythm which were measured following completion of training were also sustained at long-term follow-up. We do not know the length of time for which the effect of neurofeedback on brain rhythms is sustained. Interestingly, one study reported that although pain reduction did not occur immediately following completion of the training course, there was improvement in pain at follow-up [36]. This could suggest that perhaps NFB could lead to changes in the underlying brain networks which occurs over a longer period of time but can be sustained for longer duration. These results provide the preliminary evidence for potential of neurofeedback for providing analgesia in chronic pain.
It has been shown that neurofeedback not only leads to reduction in pain but leads to improvement in a number of pain associated symptoms such as depression [27, 39, 41, 54, 57, 58, 59, 60], anxiety [27, 41, 54, 57, 59], fatigue [27, 29, 41, 49, 51], and sleep [36, 39, 49, 50, 51, 57]. These symptoms have been known to co-exist with pain in chronic pain conditions and also known to exacerbate the individual’s pain on a day-to-day basis [61, 62, 63]. Therefore, by being able to target these symptoms along with pain, neurofeedback has the potential to holistically improve the well-being of these individuals. A summary of different symptoms which have been shown to improve following neurofeedback have been shown in Figure 3.
Schematic representation of pain and pain associated symptoms in chronic pain syndromes.
Current neurofeedback studies have a number of limitations. There are currently only seven controlled trials in the field [29, 41, 47, 51, 52, 64, 65], of which only one trial is of high quality [65]. Most of the trials lack appropriate blinding as the control group are often patients on other pain medications [29, 66]. This makes the blinding of patient difficult and could lead to patient’s belief in treatment affecting the results. Only two studies have implemented sham neurofeedback [36, 37].
The best sham treatment to offer is debatable. One would argue that patients could be shown the feedback signal from another region of the brain. But this might not be best as it might be the case that another region which is used for feedback might be the undiscovered part of the pain matrix. Another way to provide sham feedback would be to show the individual the recording from another participant or their own recording in a reverse order. Whilst this might be a true sham condition as the feedback shown to the individual would be independent of the individual’s brain activity, it might mean that the patients find no relief of symptoms and discover that it is a sham treatment. Either way, such sham neurofeedback needs to be implemented by more studies in order to truly understand whether the pain reduction reported in these individuals is due to underlying changes in neuronal networks.
Whilst we have learnt a lot about neurofeedback over the past decade, there is still a lot which is unknown about this technique. Neurofeedback differs from other neuromodulatory techniques such entrainment and transcranial magnetic stimulation in that neurofeedback involves active involvement of the individuals in changing the brain oscillations, as opposed to passive reception of stimulation [5]. We do not know which of these is a more efficient technique to alter brain oscillations yet. Furthermore, it is also unknown what mental strategies in particular are associated with changes in brain oscillations seen in the studies so far. Some of the common instructions given to patients undergoing training involve asking them to stay relaxed, imagining happy moments, revisiting happy memories and thinking about favorite family member or friends. However, none of the studies so far document which of these strategies actual work for the patients. Therefore, further qualitative studies are required to see what patients have been using to actively change their brain oscillations during neurofeedback in order to provide more focused instructions to patients undergoing training. Furthermore, studies should aim to analyze the correlation between neurophysiological signal and pain reduction rather than solely focusing on the behavioral outcomes [29, 41, 47, 51, 52, 64, 65]. Establishing such correlation between behavioral change and changes in neurophysiological signal is key to understanding whether the pain relief is truly due to neurofeedback.
In addition to this, there is also a possibility that once the patients have been able to identify the mental strategy which allows them to achieve the desired brain state and practice in the neurofeedback setting for a number a sessions, they might be able to implement such mental strategies without the ongoing EEG signal feedback. It is not clear if this possible or how long it might take for an individual to become independent of the EEG feedback and still receive pain relief.
The current neurofeedback studies are highly heterogenous. It is unclear which brain regions, oscillations, feedback form or training length is required to optimize the improvement in pain. More studies are required comparing one aspect of the neurofeedback training program at once in order to determine which of these parameters provide the most therapeutic benefit.
Another area of uncertainty is the efficacy of neurofeedback in different pain conditions. Studies so far have shown that all chronic pain condition report pain reduction to some degree following neurofeedback. However, it is not known whether neurofeedback is better for some chronic pain conditions than others. It might be the case that neuronal changes seen following neurofeedback is linked to central sensitization only, in which case several chronic pain conditions may benefit from it equally as many pain conditions have this as the underlying pathology. However, we do not know whether it is equally as good at treating nociceptive pain as seen in conditions such as arthritis.
Furthermore, the role that neurofeedback will play in pain management in the future is not clear [16]. It is not clear whether it has the true potential to substitute pharmacological agents completely. It might be the case that it might reduce the escalation of opioid usage in this patient cohort. Hence further studies are needed to determine the maximum potential of this form of therapy.
In general, neurofeedback is well tolerated with a minority of patients experiencing mild adverse events. These adverse events are often self-limiting and tend to be controlled by decreasing the frequency of training [43, 48]. Adverse events seen in neurofeedback studies seem to be more common in certain patient groups than others. For instance, some individuals with spinal cord injury and central neuropathic pain have reported some hypersensitivity of soles of the feet due to recovery of proprioception or spasms of the lower limb, [28, 48]. Patients with traumatic brain injury have reported an increase in nausea and the intensity of their headaches [39, 67]. It is difficult to confirm that these side-effects are due to NFB as these reported symptoms are often seen in these conditions irrespective of provision of neurofeedback therapy. Overall, NFB is safe and well-tolerated in majority of patients in most clinical studies.
Neurofeedback has also been delivered in the home setting by a few recent studies [43, 48]. This can be achieved through the use of a headset which records activity from one single electrode, such as C4 [43, 48] or FP1 [39] and makes use of an app on tablets to analyze and showcase feedback to the individual [28, 48]. Such systems have been implemented in patients with central neuropathic pain [43, 48] as well as traumatic brain injury [39]. Patients could practice neurofeedback for 5- or 10-minutes sessions as and when they wanted.
These studies have shown some promising results. With further expansion of this technology, it might be possible for individuals to benefit from neurofeedback at their home as and when required as patients have on average used neurofeedback 3–40 times over the course of 2–3 months in these studies [43, 48]. Two of these studies have reported around 33% reduction in pain [43, 48] whereas one of them reported 16% reduction in pain [39] on average in participants who tried these home-based systems.
One of these studies also performed qualitative research on user experience following such home-based systems [43]. Overall, it was reported that the patient satisfaction score was high when measured using QUESB (Quebec User Evaluation of Satisfaction Questionnaire). According to the patients, the key factors which affected the frequency of their use of the home-based device were their health state, availability of free time and their intensity of pain. Patients also put effectiveness, ease of use and comfort as their main priority when using any such home-based device. Hence whilst the current home-based technology used in this study showed that it could record the data with decent quality, it also highlighted that patients wanted technology which was able to provide neurofeedback wirelessly using headset and smart device as well as collect information from the scalp without the use of gel to connect electrodes.
Being able to do this on a regular basis would also increase the efficacy of the therapy and patients might be able to use neurofeedback in addition to or instead of commonly used pharmacological agents which are associated with significant adverse effect profiles. Therefore, home-based neurofeedback can act as a novel treatment option to provide pain relief to patients with much fewer side effects than current pharmacological agents [68].
Neurofeedback is a newly emerging technique which can be used to achieve brain states associated with increased resilience to pain. The results so far have been very promising not only in terms of improvement in chronic pain, where as many as half of the studies in the field have shown clinically significant reduction in clinical pain following neurofeedback, but also in terms of improvement in pain associated symptoms such as fatigue, depression, anxiety and sleep which have also been reported to improve with neurofeedback. Being able to target all of these co-morbidities holistically using neurofeedback is key for the overall improvement in the well-being of chronic pain patients because these factors are often interlinked and aggravate each other.
There is still a lot of work that needs to be done. Different aspects of training protocols, such as target signal, number of sessions, length of sessions and scalp region of interest, need to be optimized in order to identify parameters which lead not only to successful modulation of the brain activity but also a corresponding change in pain signals. Currently, it is not clear what neurofeedback protocol brings about maximum pain relief for patients.
Furthermore, identification of mental strategies which enable individuals to reach therapeutic brain states is also required, with the aim being that eventually individuals will be able to practice these strategies independent of the feedback system after an initial course of training sessions. Whilst, there is a lot of work to do, the results so far have been promising, opening window of opportunity to manage a number of chronic pain conditions at low cost and without the side effects associated with the currently available pharmacological agents.
The authors have no conflict of interest to declare.
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\\n\\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
\\n\\nIn the case of Retraction or removal of the Work, the publisher will be under no obligation to refund the APC.
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\n\n3. CORRECTIONS
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\n\n4. FINAL REMARKS
\n\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
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