Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
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This achievement solidifies IntechOpen’s place as a pioneer in Open Access publishing and the home to some of the most relevant scientific research available through Open Access.
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We are so proud to have worked with so many bright minds throughout the years who have helped us spread knowledge through the power of Open Access and we look forward to continuing to support some of the greatest thinkers of our day.
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Thank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
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\n'}],latestNews:[{slug:"intechopen-supports-asapbio-s-new-initiative-publish-your-reviews-20220729",title:"IntechOpen Supports ASAPbio’s New Initiative Publish Your Reviews"},{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"}]},book:{item:{type:"book",id:"9715",leadTitle:null,fullTitle:"Botany - Recent Advances and Applications",title:"Botany",subtitle:"Recent Advances and Applications",reviewType:"peer-reviewed",abstract:"This book integrates knowledge of plant biotechnology, plant physiology, and the environment. It presents new information about soil organic carbon sequestration using plant species (tropical grasses) that have potential in climate change mitigation. It also presents scientific knowledge on the multipurpose role of microRNA (miRNA), focusing mainly on stress tolerance in crop plants. Chapters discuss uses, methods, and advantages of recombinant DNA technology and novel plant biotechnology applications for plant-based vaccines. This volume brings together knowledge about non-edible plants seeds as potential sources of biodiesel production to mitigate the global energy crisis.",isbn:"978-1-83969-259-8",printIsbn:"978-1-83969-258-1",pdfIsbn:"978-1-83969-260-4",doi:"10.5772/intechopen.87519",price:119,priceEur:129,priceUsd:155,slug:"botany-recent-advances-and-applications",numberOfPages:118,isOpenForSubmission:!1,isInWos:null,isInBkci:!1,hash:"3e59225e9e029129a60fe724004b8d24",bookSignature:"Bimal Kumar Ghimire",publishedDate:"November 24th 2021",coverURL:"https://cdn.intechopen.com/books/images_new/9715.jpg",numberOfDownloads:1064,numberOfWosCitations:1,numberOfCrossrefCitations:2,numberOfCrossrefCitationsByBook:0,numberOfDimensionsCitations:3,numberOfDimensionsCitationsByBook:0,hasAltmetrics:0,numberOfTotalCitations:6,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 3rd 2020",dateEndSecondStepPublish:"December 3rd 2020",dateEndThirdStepPublish:"February 1st 2021",dateEndFourthStepPublish:"April 22nd 2021",dateEndFifthStepPublish:"June 21st 2021",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6",editedByType:"Edited by",kuFlag:!1,featuredMarkup:null,editors:[{id:"94560",title:"Prof.",name:"Bimal Kumar",middleName:null,surname:"Ghimire",slug:"bimal-kumar-ghimire",fullName:"Bimal Kumar Ghimire",profilePictureURL:"https://mts.intechopen.com/storage/users/94560/images/system/94560.jpg",biography:"Dr. Bimal Kumar Ghimire is currently an assistant professor\nin the Department of Crop Science, College of Sanghuh Life\nScience, Konkuk University, Seoul, South Korea. He received his\nMS in Botany (major in Cytogenetics) from North Bengal University, India. He obtained his Ph.D. in Agriculture Science from\nKangwon National University, South Korea, in 2008. Subsequently, he joined the Department of Botany, Sikkim University,\nIndia, as an assistant professor. He has published more than 100 articles in peer-reviewed journals and books. He has edited and written several books and contributed chapters on different aspects of plant sciences including light sources generally\nused in controlled agriculture, genetic transformation, and secondary metabolites\nof medicinal plants. His research interests and experience include plant anatomy,\ngenetic diversity in bioenergy crops, allyl compounds, tissues and cell culture, bioreactor culture, and genetic transformation of important medicinal plants.",institutionString:"Konkuk University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Konkuk University",institutionURL:null,country:{name:"Korea, South"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"41",title:"Plant Biology",slug:"agricultural-and-biological-sciences-plant-biology"}],chapters:[{id:"76724",title:"Insights into Metabolic Engineering of the Biosynthesis of Glycine Betaine and Melatonin to Improve Plant Abiotic Stress Tolerance",doi:"10.5772/intechopen.97770",slug:"insights-into-metabolic-engineering-of-the-biosynthesis-of-glycine-betaine-and-melatonin-to-improve-",totalDownloads:92,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,abstract:"Metabolic engineering in plant can be describe as a tool using molecular biological technologies which promotes enzymatic reactions that can enhance the biosynthesis of existing compounds such as glycine betaine (GB) in plant species that are able to accumulate GB, or produce news compounds like GB in non-accumulators plants. Moreover we can include to these definition, the mediation in the degradation of diverse compounds in plant organism. For decades, one of the most popular ideas in metabolic engineering literature is the idea that the improvement of gly betaine or melatonin accumulation in plant under environmental stress can be the main window to ameliorate stress tolerance in diverse plant species. A challenging problem in this domain is the integration of different molecular technologies like transgenesis, enzyme kinetics, promoter analysis, biochemistry and genetics, protein sorting, cloning or comparative physiology to reach that objective. A large number of approaches have been developed over the last few decades in metabolic engineering to overcome this problem. Therefore, we examine some previous work and propose some understanding about the use of metabolic engineering in plant stress tolerance. Moreover, this chapter will focus on melatonin (Hormone) and gly betaine (Osmolyte) biosynthesis pathways in engineering stress resistance.",signatures:"Cisse El Hadji Malick, Miao Ling-Feng, Li Da-Dong and Yang Fan",downloadPdfUrl:"/chapter/pdf-download/76724",previewPdfUrl:"/chapter/pdf-preview/76724",authors:[{id:"339797",title:"Ph.D.",name:"El Hadji Malick",surname:"CISSE",slug:"el-hadji-malick-cisse",fullName:"El Hadji Malick CISSE"},{id:"350806",title:"Prof.",name:"Fan",surname:"Yang",slug:"fan-yang",fullName:"Fan Yang"},{id:"350807",title:"Dr.",name:"Da-Dong",surname:"Li",slug:"da-dong-li",fullName:"Da-Dong Li"},{id:"350808",title:"Dr.",name:"Ling-Feng",surname:"Miao",slug:"ling-feng-miao",fullName:"Ling-Feng Miao"}],corrections:null},{id:"76960",title:"Soil Carbon Storage Potential of Tropical Grasses: A Review",doi:"10.5772/intechopen.97835",slug:"soil-carbon-storage-potential-of-tropical-grasses-a-review",totalDownloads:190,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:1,abstract:"Environmental degradation and climate change are key current threats to world agriculture and food security and human–induced changes have been significant driving forces of this global environmental change. An important component is land degradation which results in a diminished soil organic carbon (SOC) stock with concomitant loss of soil condition and function. Land management to improve soil organic matter content, condition and productivity is therefore a key strategy to safeguard agricultural production, food supply and environmental quality. Soil organic carbon sequestration through the use of plant species with high photosynthetic efficiency, deep roots and high biomass production is one important strategy to achieve this. Tropical pastures, which are adapted to a wide range of environmental conditions have particular potential in this regard and have been used extensively for land rehabilitation. Tropical pastures also have advantages over trees for biomass and carbon accumulation due to their rapid establishment, suitability for annual harvest, continual and rapid growth rates. In addition, tropical pastures have the potential for SOC storage in subsoil horizons due to their deep root systems and can be used as biomass energy crops, which could further promote their use as a climate change mitigation option. Here we aimed to review current knowledge regarding the SOC storage potential of tropical grasses worldwide and identified knowledge gaps and current research needs for the use of tropical grasses in agricultural production system.",signatures:"Bezaye Gorfu Tessema, Heiko Daniel, Zenebe Adimassu and Brian Wilson",downloadPdfUrl:"/chapter/pdf-download/76960",previewPdfUrl:"/chapter/pdf-preview/76960",authors:[{id:"339641",title:"Dr.",name:"Bezaye",surname:"Tessema",slug:"bezaye-tessema",fullName:"Bezaye Tessema"},{id:"339732",title:"Prof.",name:"Brian",surname:"Wilson",slug:"brian-wilson",fullName:"Brian Wilson"},{id:"339733",title:"Prof.",name:"Heiko",surname:"Daniel",slug:"heiko-daniel",fullName:"Heiko Daniel"},{id:"339734",title:"Dr.",name:"Zenebe",surname:"Adimassu",slug:"zenebe-adimassu",fullName:"Zenebe Adimassu"}],corrections:null},{id:"76358",title:"Optimization and Characterization of Novel and Non-Edible Seed Oil Sources for Biodiesel Production",doi:"10.5772/intechopen.97496",slug:"optimization-and-characterization-of-novel-and-non-edible-seed-oil-sources-for-biodiesel-production",totalDownloads:260,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,abstract:"Biodiesel mainly comes from edible oil, and there is little research on its yield from non-edible sources with low-cost oil. It is paramount to investigate the non-edible oil resources which may lead to advance the commercial feasibility of biodiesel and cost effectiveness as well as resolve the food issues. This chapter describes four novel non-edible seed oil sources comprising Koelreuteria paniculata, Rhus typhina, Acacia farnesiana and Albizzia julibrissin for biodiesel production. We aimed to optimize different reaction parameters for oil extraction, alkali-catalyzed transesterification process for maximal biodiesel production and finally evaluate its compatibility with mineral diesel. The optimization factors in transesterification included the molar ratio of methanol to oil, reaction time, stirring intensity, catalyst concentration and temperature. Two methods have been described including Soxhlet and mechanical for extraction of seed oil. The synthesized esters were evaluated and characterized through the nuclear magnetic resonance (NMR; 1H and 13C), Fourier transform infrared (FT-IR) and gas chromatography–mass spectrometry (GC–MS) and the total conversion of crude oil to fatty acid methyl esters (FAMEs) were established. The inductively coupled plasma-optical emission spectrometry (ICP-OES) and Elemental Analyzer (EA) were used for evaluation of elemental concentration. The physico-chemical characterizations of the biodiesel, i.e., flash point, pour point, cloud point, and density were within the American Society for Testing and Materials (ASTM; D6751) and European Standards ((EN14214). Koelreuteria paniculata produced highest biodiesel oil content by Soxhlet extraction (28–30%) followed by the Albizzia julibrissin (19–24%), Acacia farnesiana (23%), Rhus typhina (20–22%). The density ranged from 0.83–0.87 @ 15°C (g/cm3) and the kinematic viscosity ranged from 3.75–6.3 (mm2/s) among all the plant sources. Koelreuteria paniculata had highest Na (5456.2), Cr (1246.8), Ni (658.36), and Al (346.87) elemental concentrations (μg/g) than other plant sources. The elemental percent of C, H, N, and O of biodiesel ranged from 72.54–76.86, 11.25–13.34, 1.97–2.73, and 9.86–12, respectively. In conclusion, these non-edible plant seeds offer a cheap source of renewable energy and can be easily grown on barren and wastelands and contribute to efficient biodiesel production to mitigate the energy crisis.",signatures:"Inam Ullah Khan and Syed Aftab Hussain Shah",downloadPdfUrl:"/chapter/pdf-download/76358",previewPdfUrl:"/chapter/pdf-preview/76358",authors:[{id:"336759",title:"Dr.",name:"Syed Aftab Hussain",surname:"Shah",slug:"syed-aftab-hussain-shah",fullName:"Syed Aftab Hussain Shah"},{id:"345660",title:"Dr.",name:"Inam Ullah",surname:"Khan",slug:"inam-ullah-khan",fullName:"Inam Ullah Khan"}],corrections:null},{id:"76930",title:"Plant-based Vaccines: The Future of Preventive Healthcare?",doi:"10.5772/intechopen.97861",slug:"plant-based-vaccines-the-future-of-preventive-healthcare-",totalDownloads:332,totalCrossrefCites:2,totalDimensionsCites:2,hasAltmetrics:0,abstract:"Infectious diseases threatened humankind countless times through history, when knowledge on microorganisms was absent and medical capabilities were limited. Pandemics and outbreaks caused death of millions, brought empires to their knees and even wiped some ancient civilizations. In “modern” days, despite of improved medical application, sanitary precautions and effective medicines, infectious diseases are still cause of more than 54% of total mortality in developing countries. Millions of people are protected from the infectious diseases annually as a result of mass immunization campaigns. Nevertheless, novel diseases as COVID-19, MERS-CoV, avian influenza, Ebola, Zika and possible future infections require dynamic vaccine research and investment. Along with all the advantages of vaccines, there are several limitations regarding cost, biosafety/biosecurity, storage, distribution, degradation topics. Plant-based vaccine production for humans and animals has been under serious consideration to overcome some of these limitations. Nowadays, plant biotechnology brought new insight to vaccines research through gene transfer strategies to plants and improvements in amount, isolation and purification and addition of adjuvant for production of recombinant vaccine antigens in plants. Recombinant vaccines can undeniably offer us new standards and legal regulations to be introduced for the development, approval, authorization, licensing, distribution and marketing of such vaccines. The aim of this chapter is to exploit uses, methods and advantages of recombinant DNA technology and novel plant biotechnology applications for plant-based vaccine research in respect to existing infectious diseases.",signatures:"Sinan Meriç, Tamer Gümüş and Alp Ayan",downloadPdfUrl:"/chapter/pdf-download/76930",previewPdfUrl:"/chapter/pdf-preview/76930",authors:[{id:"147364",title:"Prof.",name:"Çimen",surname:"Atak",slug:"cimen-atak",fullName:"Çimen Atak"},{id:"191695",title:"Dr.",name:"Alp",surname:"Ayan",slug:"alp-ayan",fullName:"Alp Ayan"},{id:"191696",title:"Dr.",name:"Sinan",surname:"Meriç",slug:"sinan-meric",fullName:"Sinan Meriç"},{id:"333168",title:"MSc.",name:"Tamer",surname:"Gümüş",slug:"tamer-gumus",fullName:"Tamer Gümüş"}],corrections:null},{id:"77085",title:"microRNA Utilization as a Potential Tool for Stress Tolerance in Plants",doi:"10.5772/intechopen.97480",slug:"microrna-utilization-as-a-potential-tool-for-stress-tolerance-in-plants",totalDownloads:190,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,abstract:"This chapter describe the possibilities of MicroRNAs (miRNAs) in crop plants gene expression regulation in different metabolic pathways. Several current researches have shown different environmental stresses induce abnormal expression of miRNA, thus signifying that miRNAs may be an appropriate tool for genetical improvement in plant for stress tolerance. These miRNAs mainly control gene expression through translational inhibition. Generally, stress induce miRNAs-based inhibition of their target mRNAs, however, positive transcription factors accumulated and become more active after mRNA inhibition. Initially, researchers were mainly focused on miRNA identification, appropriate to specific or multiple environmental condition, expression profiling and recognize their roles in stress tolerance. Transformed miRNA expression studied in some plant species for better understanding of plant development and stress tolerance such as heavy metal, salinity, temperature, drought and nutrient deficiency. All these findings indicate that miRNAs act as a potential tool for genetic engineering and to enhance stress tolerance in crop plants.",signatures:"Jyoti Rani",downloadPdfUrl:"/chapter/pdf-download/77085",previewPdfUrl:"/chapter/pdf-preview/77085",authors:[{id:"339029",title:"Assistant Prof.",name:"Jyoti",surname:"Rani",slug:"jyoti-rani",fullName:"Jyoti Rani"}],corrections:null}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},subseries:null,tags:null},relatedBooks:[{type:"book",id:"6277",title:"Physical Methods for Stimulation of Plant and Mushroom Development",subtitle:null,isOpenForSubmission:!1,hash:"33dff71e3489403e273057ae36bd0dbd",slug:"physical-methods-for-stimulation-of-plant-and-mushroom-development",bookSignature:"Mohamed El-Esawi",coverURL:"https://cdn.intechopen.com/books/images_new/6277.jpg",editedByType:"Edited by",editors:[{id:"191770",title:"Dr.",name:"Mohamed A.",surname:"El-Esawi",slug:"mohamed-a.-el-esawi",fullName:"Mohamed A. 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\r\n\tThe book will shed the light on the basic principles of infrared (IR) spectrophotometry and its environmental, industrial, and pharmaceutical applications. \r\n\tEnvironmental applications will deal with water, and wastewater treatments, characterization of different sorbents, and waste removers, contaminants detection in water, and waste management. \r\n\tIndustrial applications will focus on the analysis of paint, paper, pharmaceutical, and sugar industries and the applicability of infrared spectroscopy in these fields.
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\r\n\tDrug analysis, food and dietary supplements testing and analysis, and natural products analysis will be discussed as parts of the pharmaceutical applications of infrared spectroscopy.
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1. Introduction
Gastroesophageal reflux disease (GERD) is a chronic condition in which patients suffer troublesome symptoms and/or complications as the reflux of stomach contents occurs. GERD is a common disease worldwide with the range of an estimated prevalence of 18.1–27.8% in North America, 8.8–25.9% in Europe, 2.5–7.8% in East Asia, 8.7–33.1% in the Middle East, 11.6% in Australia, and 23.0% in South America [1]. It causes significant morbidity, considerable decrease of quality of life, and high costs of exams and treatment derived from repeated visits to the doctor.
The patients with GERD suffer from typical symptoms, such as heartburn and regurgitation, as well as other atypical symptoms including chest pain, cough, asthma, and hoarseness. With the usage of proton pump inhibitors (PPIs) in the clinic, a dramatic improvement in symptom resolution and life quality, as well as in mucosal healing, is expected.
However, the treatment of GERD fails in a proportion of patients despite the high efficacy of PPIs. This situation is referred as to refractory GERD symptoms. What is worse, it is getting more and more common in clinical practices. In this chapter, we will discuss about this difficult situation, emphasizing on diagnosis and treatment, combined with suggested management of these patients.
2. Definition of refractory GERD symptom
The definition of “refractory GERD” has traditionally been described as a group of varying symptom presentations related to GERD, which persists even though the patients accepted the standard daily PPI therapy for at least 12 weeks. Some researchers referred to a failure to achieve satisfactory symptomatic response, for example, less than 50% improvement of relief of symptoms and life quality, to once-daily PPI to be classified as “refractory GERD” or “refractory reflux symptoms” [2]. The continued symptoms must be to a degree that impairs quality of life, and symptoms must be “reflux-related,” which are supposed to be influenced by sex, age, ethnicity, social status, comorbidity, and cultural background. However, there is a controversy of the PPI dose for the definition of “refractory GERD.” Some investigators prefer that inadequate response to twice-daily PPI treatment as refractory disease [3]. Moreover, the patient’s remaining symptoms are subjective to and dependent on the patient’s expectations of the therapy. It needs more clinical practice and further researches to supplement the definition in the future.
3. Causes of refractory GERD symptom
There are some underlying causes of refractory GERD. Firstly, poor compliance and adherence should be excluded before further evaluation is pursued. There are some key points of medication administration for patients, such as taking PPIs at the optimal 30–60 minutes prior to meal; avoiding discontinued PPIs without doctors’ instruction even though the symptoms are relieved; receiving enough information about PPIs therapy. These points are initial important considerations for resolving the refractory GERD. Then, other disorders with GERD-like symptoms, such as esophageal disorders and functional gastrointestinal disorders, should be considered in the differential diagnosis of patients with persistent symptoms (Figure 1).
Figure 1.
Causes of refractory GERD symptom.
Additionally, obesity and overeating are other common factors associated with PPI failure in patients initially diagnosed with GERD.
4. Diagnosis of refractory GERD symptom
4.1 Symptom evaluation
The first important step is to identify the actual nature of the persisting symptoms. It can help a physician to choose the correct equipment for the next step of diagnosis. The typical symptoms of GERD are heartburn and regurgitation, which can be recognized by the GerdQ questionnaire. It is a revision of the Reflux Disease Questionnaire (RDQ) with positive predictor questions about heartburn and regurgitation as well as negative predictors about epigastric pain and nausea. It is reported that there is a sensitivity of 65% and specificity of 71% with GerdQ, which is close to the efficiency done by the clinical judgment of gastroenterologists [4]. However, presenting regurgitation should also be differentiated to gastroparesis or rumination syndrome. Except that, the physician should be aware of the proportion of patients with the atypical symptoms, such as retrosternal discomfort and pain, cough, asthma, hoarseness, throat discomfort, foreign body sensation in throat, globus sensation, belching, dysphagia, and epigastric pain and epigastric discomfort.
A recent study shows that there is about half of patients with atypical symptom, combined or uncombined with typical symptom [5]. In short, it is essential to figure out which symptoms respond and which do not respond to PPI therapy. More detailed questioning about symptom often help clarify the cause for a patient’s persistent symptoms. Especially, the patients with atypical symptom might have poor response to PPI therapy because there are probably other causes or diseases that overlapped GERD.
4.2 Endoscopy
Upper endoscopy should be taken principally to exclude non-reflux esophageal disorders and other gastric diseases and to check whether erosive esophagitis exists, which can provide evidence of ongoing acid reflux. However, endoscopy is of limited value for diagnosis of refractory GERD symptom. It is because that most patients have normal endoscopy. The potential reasons are that most patients with refractory GERD symptom have other esophageal motility problem; they have non-erosive reflux disease (NERD); or PPIs they taken has healed the mucosal injury.
4.3 Esophageal manometry
All patients with refractory GERD symptom are strongly recommended to undergo esophageal manometry. The purpose mainly is to find esophageal motor disorders, for example, achalasia, weak peristalsis, hypertensive esophageal dysmotility, diffuse esophageal spasm (DES), hiatus hernias (HH), high UES pressure, and abnormal lower esophageal sphincter (LES) pressure. Secondly, but more important, esophageal manometry is applied for identifying the accurate location of LES in order to place reflux monitoring pH sensors.
4.4 Ambulatory monitoring for reflux
There are two methods for esophageal reflux monitoring, called as On-PPI and Off-PPI. In off-PPI (7 days after cessation of PPI), the presence of abnormal acid reflux and/or positive symptom-reflux relationship can be confirmed. The relevant parameter to be observed is esophageal acid exposure, which is the proportion of time (in minutes or percentage of time) spent below pH 4, as well as correlation between symptoms and reflux events (symptom index (SI) and/or symptom association probability (SAP)). Positive symptom association with normal esophageal acid exposure is considered hypersensitive esophagus (HE), reflecting an underlying visceral hypersensitivity. For on-PPI reflux monitoring, impedance-pH monitoring should reasonably be proposed as the preferred investigation. It can detect nonacid reflux during the PPI therapy period, which is one of causes for persistent GERD symptom. It also can figure out whether acid reflux is controlled or not by the treatment (Table 1).
Nonerosive reflux disease (NERD)
No mucosal break Normal esophageal acid exposure
Hypersensitive esophagus (HE)
No mucosal break Normal esophageal acid exposure SI > 50%, SAP > 95%
Functional heartburn (FH)
Heartburn refractory to PPIs, no mucosal break, normal esophageal acid exposure SI < 50%, SAP < 95%
Table 1.
Diagnosis based on endoscopy, esophageal manometry, and ambulatory monitoring for reflux.
4.5 Assessment and evaluation for psychological status
Psychological disorders such as hysteria, anxiety, and distress should also be evaluated in patients with refractory symptoms. Weak correlation of symptoms with acid reflux events might indicate a high level of anxiety and hysteria as compared with patients who demonstrate a close correlation between symptoms and acid reflux event [6]. Anxiety and depression have been shown to increase reflux symptoms reported in population-based studies. A study has reported that patients who did not respond to PPI treatment were suffered from more psychosocial problem [7].
5. Management of refractory GERD symptom
5.1 Lifestyle modifications
Weight loss, head of bed elevation, and avoiding late-night meals, which have been shown as effective interventions for GERD, have not been demonstrated yet equally useful in patients with refractory reflux symptoms. The value of lifestyle modifications in patients with refractory symptoms lies in avoidance of specific lifestyle activities that have been identified by patients or physicians to trigger symptoms. A low-bulk and low-fat diet along with small but more frequent meals should surely be recommended.
5.2 Medicine
Increasing the PPI dose or to change to an alternative PPI improved the symptom in some patients [8]. However, this dosing strategy should be used for a short time period (2–3 months) and should be tapered if it does not result in improvement of symptoms. The addition of an H2RA at bedtime was shown to significantly reduce the duration of nocturnal acid breakthrough (NAB) pain modulators. Transient lower esophageal sphincter relaxation (TLESR) reducers can be considered for patients with abnormal frequency of nonacid reflux. The drugs that can reduce the number of reflux events regardless of their acidity are theoretically desirable because of the potential for weakly acidic or bile reflux to cause symptoms. Nevertheless, high-quality controlled trials are needed to demonstrate its efficacy in patients with refractory symptoms.
Visceral pain modulator therapy has been another option for patients with an acid-hypersensitive esophagus or functional heartburn. A randomized, placebo-controlled trial has demonstrated citalopram 20 mg/day to be of symptomatic benefit in patients with acid-hypersensitive esophagus and refractory GERD symptoms [9].
5.3 Endoscopic therapy
Stretta procedure and EsophyX transoral incisionless fundoplication are two antireflux endoscopic devices which are clinically available. The Stretta procedure showed clinical improvement of esophageal symptoms and a decrease in PPI use but no significant effect on esophageal acid exposure [10]. EsophyX offers a less invasive alternative to laparoscopic fundoplication for PPI-dependent GERD patients, which still needs further studies to demonstrate its efficiency.
5.4 Antireflux surgery
Comparing with patients with adequate PPI symptom control, antireflux surgery might have a less favorable clinical outcome for the patients with refractory GERD symptom. Normal acid exposure and the presence of atypical reflux symptoms and persisting symptoms despite PPI therapy are predictors of a poor postoperative outcome. It is important to confirm pathological reflux before considering antireflux surgery if there is no proven esophagitis. Summarily, surgery can be a valuable option in patients with typical reflux symptoms with inadequate response to PPIs, provided abnormal esophageal acid exposure and/or positive symptom association analysis in off-PPI test [11].
5.5 Psychological treatment
According to a recent research, perceptions of reflux symptoms are associated with psychosocial distress in these patients with refractory GERD symptom who have normal impedance-pH results. Furthermore, patient-reported symptom severity is associated with physiological differences, as opposed to psychosocial factors [11]. In these patients with psychological disorders, treatment-targeted psychosocial abnormality may improve patient response to PPI therapy [2]. Psychological treatment should be a potential consideration in the case of the patients without other identifiable causes. In many clinical experiences, psychological disorders may be an underlying etiology in many patients with refractory symptoms (Figure 2).
Figure 2.
Diagnostic and treatment algorithm for patients with refractory GERD symptom.
\n',keywords:"gastroesophageal reflux disease (GERD), refractory proton pump inhibitor (PPI) symptoms, high-resolution manometry (HRM), impedance-pH monitoring, refractory reflux symptoms",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/63508.pdf",chapterXML:"https://mts.intechopen.com/source/xml/63508.xml",downloadPdfUrl:"/chapter/pdf-download/63508",previewPdfUrl:"/chapter/pdf-preview/63508",totalDownloads:1367,totalViews:224,totalCrossrefCites:0,totalDimensionsCites:0,totalAltmetricsMentions:0,introChapter:null,impactScore:0,impactScorePercentile:36,impactScoreQuartile:2,hasAltmetrics:0,dateSubmitted:"March 12th 2018",dateReviewed:"August 8th 2018",datePrePublished:"December 19th 2018",datePublished:"April 3rd 2019",dateFinished:"September 11th 2018",readingETA:"0",abstract:"Gastroesophageal reflux disease (GERD) is a chronic condition in which patients suffer troublesome symptoms and/or complications as the reflux of stomach contents occurs. GERD is a common disease worldwide with the range of estimated prevalence 18.1–27.8% in North America, 8.8–25.9% in Europe, 2.5–7.8% in East Asia, 8.7–33.1% in the Middle East, 11.6% in Australia and 23.0% in South America. It causes significant morbidity, considerable decrease of quality of life and high costs of exams and treatment derived from repeated visit doctor. The patients with GERD suffer from typical symptoms such as heartburn and regurgitation, as well as other atypical symptoms including chest pain, cough, asthma, and hoarseness. With the usage of pump inhibitors (PPIs) in clinic, a dramatic improvement in symptom resolution and life quality, as well as in mucosal healing is expected. However, the treatment of GERD fails in a proportion of patients despite the high efficacy of PPIs. This situation is getting more and more common in clinical practices. In this chapter, we will discuss about this difficult situation, emphasizing diagnosis and treatment, combined with suggested management of these patients.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/63508",risUrl:"/chapter/ris/63508",book:{id:"7104",slug:"gastroesophageal-reflux-disease-theory-and-research"},signatures:"Xia Chen and Fei Wang",authors:[{id:"250058",title:"Dr.",name:"Xia",middleName:null,surname:"Chen",fullName:"Xia Chen",slug:"xia-chen",email:"xiac6686@gmail.com",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. Definition of refractory GERD symptom",level:"1"},{id:"sec_3",title:"3. Causes of refractory GERD symptom",level:"1"},{id:"sec_4",title:"4. Diagnosis of refractory GERD symptom",level:"1"},{id:"sec_4_2",title:"4.1 Symptom evaluation",level:"2"},{id:"sec_5_2",title:"4.2 Endoscopy",level:"2"},{id:"sec_6_2",title:"4.3 Esophageal manometry",level:"2"},{id:"sec_7_2",title:"4.4 Ambulatory monitoring for reflux",level:"2"},{id:"sec_8_2",title:"4.5 Assessment and evaluation for psychological status",level:"2"},{id:"sec_10",title:"5. Management of refractory GERD symptom",level:"1"},{id:"sec_10_2",title:"5.1 Lifestyle modifications",level:"2"},{id:"sec_11_2",title:"5.2 Medicine",level:"2"},{id:"sec_12_2",title:"5.3 Endoscopic therapy",level:"2"},{id:"sec_13_2",title:"5.4 Antireflux surgery",level:"2"},{id:"sec_14_2",title:"5.5 Psychological treatment",level:"2"}],chapterReferences:[{id:"B1",body:'El-Serag HB, Sweet S, Winchester CC, Dent J. Update on the epidemiology of gastro-oesophageal reflux disease: A systematic review. Gut. 2014;63:871-880'},{id:"B2",body:'Sifrim D, Zerbib F. Diagnosis and management of patients with reflux symptoms refractory to proton pump inhibitors. Gut. 2012;61:1340-1354'},{id:"B3",body:'Martinez SD, Malagon IB, Garewal HS, Cui H, Fass R. Nonerosive reflux disease (NERD)—Acid reflux and symptom patterns. Alimentary Pharmacology & Therapeutics. 2003;17:537-545'},{id:"B4",body:'Jones R, Junghard O, Dent J, Vakil N, Halling K, Wernersson B, et al. Development of the GerdQ, a tool for the diagnosis and management of gastro-oesophageal reflux disease in primary care. Alimentary Pharmacology & Therapeutics. 2009;30:1030-1038'},{id:"B5",body:'Wang F, Li P, Ji GZ, Miao L, Fan Z, You S, et al. An analysis of 342 patients with refractory gastroesophageal reflux disease symptoms using questionnaires, high-resolution manometry, and impedance-pH monitoring. Medicine. 2017;96(5):e5906'},{id:"B6",body:'Becher A, El-Serag H. Systematic review: The association between symptomatic response to proton pump inhibitors and health-related quality of life in patients with gastro-oesophageal reflux disease. Alimentary Pharmacology & Therapeutics. 2011;34:618-627'},{id:"B7",body:'Chen X, Li P, Wang F, Ji G, Miao L, You S. Psychological results of 438 patients with persisting gastroesophageal reflux disease symptoms by symptom checklist 90-revised questionnaire. Euroasian Journal of Hepato-Gastroenterology. 2017;7:117-121'},{id:"B8",body:'Fass R, Sontag SJ, Traxler B, Sostek M. Treatment of patients with persistent heartburn symptoms: A double-blind, randomized trial. Clinical Gastroenterology and Hepatology. 2006;4:50-56'},{id:"B9",body:'Viazis N, Keyoglou A, Kanellopoulos AK, Karamanolis G, Vlachogiannakos J, Triantafyllou K, et al. Selective serotonin reuptake inhibitors for the treatment of hypersensitive esophagus: A randomized, double-blind, placebo-controlled study. The American Journal of Gastroenterology. 2012;107:1662-1667'},{id:"B10",body:'Arts J, Sifrim D, Rutgeerts P, Lerut A, Janssens J, Tack J. Influence of radiofrequency energy delivery at the gastroesophageal junction (the Stretta procedure) on symptoms, acid exposure, and esophageal sensitivity to acid perfusion in gastroesophageal reflux disease. Digestive Diseases and Sciences. 2007;52:2170-2177'},{id:"B11",body:'Yadlapati R, Tye M, Keefer L, Kahrilas PJ, Pandolfino JE. Psychosocial distress and quality of life impairment are associated with symptom severity in PPI non-responders with normal impedance-pH profiles. The American Journal of Gastroenterology. 2018;113:31-38'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Xia Chen",address:"xiac6686@gmail.com",affiliation:'
Medical Center for Digestive Diseases, The Second Affiliated Hospital of Nanjing Medical University, Nanjing, China
Medical Center for Digestive Diseases, The Second Affiliated Hospital of Nanjing Medical University, Nanjing, China
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\n
1. Introduction
\n
As it is emphasized in [1, 2], the tasks of analysis and synthesis of control processes occurring in dynamic systems of different physical nature, operating in conditions of substantial plant parametric uncertainty, including the engineering ones, are currently the most urgent and challenging within the framework of the control theory. Among these tasks, one could mention the problem of flux control for the electric motor vector control systems operating in uncertainty because the flux control quality strongly affects the electromagnetic torque and speed control quality, and thus the drive power efficiency. For this reason, of great importance are the tasks of stability investigation and parametric synthesis of robust control systems (their characteristic polynomials) for the plants which parameters vary within the given or unknown intervals of values.
\n
In the area of investigation and synthesis of dynamic system characteristic polynomials, there exists a lot of approaches and methods. For the first time, the necessary and sufficient conditions for systems up to the 3-rd order were formulated by James Maxwell in 1868. Later appeared the stability criteria of Routh–Hurwitz, Mikhajlov, Nyquist, and Bode, which made it possible to check stability of the systems of order n. The frequency Nyquist criterion was the first one that could be used for synthesis by estimation of the system degree of stability. Among the modern methods of synthesis [1, 2] together with the frequency ones, the root locus and state-space methods could be listed. In his book [1], Jurgen Ackermann gives, in particular, the algebraic approach to uncertainty considering different, including the nonlinear, types of the coefficient functions and generating stability regions in the parameter space of real physical parameters of the system (polynomial). The main results in the area of the frequency approach to analysis and synthesis of robust dynamic (control) systems are given in [3], where the stability of uncertain polynomials, including interval ones, is also considered.
\n
The methods for analysis and synthesis of polynomial families represent a separate group. One of the most effective solutions for the task of interval polynomial family investigation within the algebraic approach has been proposed by Kharitonov [4], where in the general case, the task of polynomial stability analysis is reduced to consideration of only four specific polynomials of the whole family with constant coefficients. In [3, 5], the frequency criteria of Hurwitz robust stability are considered, which allow to define the coefficient perturbation sweep for the nominally stable polynomial and various types of uncertainties. Hurwitz robust stability is also investigated in [6, 7, 8, 9, 10]. In [6], the maximal deviation intervals of perturbed Hurwitz polynomial coefficients assuring strict Hurwitz property are determined on the basis of the algebraic method worked out using Kharitonov’s polynomials [4]. The similar task is solved in [7] but using the Hermite-Biler theorem, which allows to reduce twice the power of investigated polynomial. The way for calculation of perturbed polynomial coefficients’ maximal limit values that guarantee sector stability is given in [8]. The linear dependence of coefficient perturbation is considered by Bartlett, et al. for a class of polynomial families generated by convex polytopes in the coefficient space [9]. Here the so-called edge theorem was proved assuring derivation of the stability analysis task to investigation of root location for the finite number of the parametric families. The edge theorem allows to analyze both stability and quality characteristics of the family. A combination of the stochastic and worst-case approaches to the problem of uncertainty is proposed in [10]. It certainly widens the scope of types of treatable uncertainties and reduces conservatism. However, it works properly only in the cases permitting an arbitrarily small probability of specification violation. Thus, to the specific extent, it still bears the drawbacks of the stochastic approach to control, which guarantees only the “average” performance.
\n
An analog of Kharitonov theorem [11] was formulated for the unstable interval polynomials’ homogeneous classes of equivalence. Criteria of existence of such classes of equivalence were obtained. Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional-integral-derivative (PID) controller is proposed in paper [12] to carry out design for different plants that contain perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial or not. Time-delay systems involving multiple imaginary roots (MIRs) and their stability analysis, which becomes much more complicated than that in the case with only simple imaginary roots, are treated in [13]. For a class of time-delay systems, it was proved that the invariance between the multiple imaginary roots and the simple imaginary roots holds for any multiplicity as well as for the degenerate cases. In paper [14], monic complex polynomials are identified with the sets of their roots instead of being identified with the vectors of their coefficients. A proof is given that the space of Hurwitz polynomials of degree n with positive (resp. negative) coefficients is contractible and also that the space of monic (Schur or Hurwitz) aperiodic polynomials is contractible. A computational method to verify the stability of a convex combination of polynomials is considered in [15] and aimed at the robust stability analysis of a linear system. A simple algebraic test (a matrix inequality) for the stability of the segment of polynomials determined by the given two Hurwitz stable polynomials is proposed. Kučera gives a survey [16] where he navigates the area of the polynomial approach in the control system design technique. Such areas as parameterization of stabilizing controllers, called Youla–Kučera parameterization, are explained; the results on reference tracking, disturbance elimination, pole placement, deadbeat control, robust stabilization, and some others are described.
\n
Of great interest are the problems of ensuring system stability and quality being solved in the modern statements of the problem [2] as tasks of guaranteeing system robustness, which could be solved by application of the root locus approach. The basic benefit of this approach is that its application itself, by its nature, implies parametric variations (i.e., uncertainty). The root locus approach is a powerful method used for the system synthesis [2] and is notable for its descriptiveness ensuring both calculation of the system robust parameters’ values and possibility of detailed overview of the dynamic properties variation changes, the system response to uncertainties that is particularly important when investigating systems with uncertain and in particular interval parameters.
\n
Root locus approach to the problem is considered in [17, 18, 19, 20, 21, 22, 23]. Paper [17] gives a solution for a compensator synthesis on the basis of the root locus method application. The task of a stable characteristic polynomial synthesis for the interval dynamic system (IDS) by setting up coefficients of the given (initial) unstable one for the case of location of its root locus initial point (where the variable parameter is equal to zero) family within the left half-plane is solved in [21], where the stability is attained via simple setting up the interval of the free term variation.
\n
The above analyzed literature covers various approaches to the uncertainty treatment. However, most of the theoretical works are focused on the tasks of robust stability analysis. The methods for synthesis are not that widely represented, often suffer from complexity and in most cases are enough narrow, which means that they certainly provide instruments for system synthesis, but they are mostly “closed on themselves,” which means that they do not provide the complete picture in the sense of showing up what is happening “under cover,” which is especially important for the qualitative robust system (polynomials) synthesis. The root locus approach is rarely applied even though it represents the dynamic picture of the system response to uncertainties in the most comprehensive way and thus seems to be the most suitable one to deal with uncertainties.
\n
As for polynomial families, the root locus approach gives us the transparent picture of root dynamics making it possible to see as if from the inside, for example, what subfamilies constitute the whole family of uncertain polynomials in terms of their configuration and stability or some other dynamic indicators bearing significant information about the system behavior and thus leading the way for its investigation and synthesis.
\n
In this work, the root locus methods are described for calculating intervals of uncertainty for coefficients of the given (initial) stable or unstable polynomial with coefficients subject to perturbations, which ensure its robust stability. The proposed methods are based on introduction and application of the notions “extended root locus,” “diagram of the root locus parameter function values distribution along the stability bound” and can be used for both synthesis of interval stable polynomials by setting up (adjusting) the unstable ones and analysis of the polynomial behavior under coefficient perturbations. The influence of every coefficient upon the polynomial behavior could be observed.
\n
The work further develops results represented in the papers of Anderson [22] and Kharitonov [4] where they consider the issues of analysis and synthesis of robust interval polynomial families.
where aj are given (initial) values of real polynomial coefficients, j = 1, 2, …, n.
\n
In the event of coefficient perturbations, a vector of coefficients of (1), a = (a1, …, an-1, an), belongs to some connected set A ⊂ Rn, a ∈ A; n is a degree of the polynomial (integer value); s is a complex variable, s = σ + iω.
\n
Suppose that coefficients of (1) vary within the following intervals:
where \n\n\n\na\n¯\n\nj\n\n\n and \n\n\n\na\n¯\n\nj\n\n\n are the minimal and maximal limit values of closed interval (2) of coefficients aj variation correspondingly. Polynomial (1) can be both, non-Hurwitz or Hurwitz one.
\n
After substituting s = σ + iω, write the root locus and parameter equations [18] correspondingly:
\n\nv\n\nσ\nω\n\n=\n0\n,\nand\nE3
\n
\n\n\na\nn\n\n=\nu\n\nσ\nω\n\n,\nE4
\n
where u(σ,ω) and v(σ,ω) are the real functions of two independent variables σ and ω.
\n
The root locus method represents a powerful and effective tool for stable and qualitative polynomial synthesis and analysis. However, as it is known, this method allows to consider polynomials with only a single variable coefficient (parameter) and cannot be applied in the cases when all coefficients are uncertain. Therefore, the task is to generalize the root locus method for the cases when the number of variable coefficients is arbitrary and thus to solve the problem of investigation of the uncertain polynomial dynamics and working out methods for synthesis of the robustly stable uncertain (interval) polynomial by setting up the given polynomial (non-Hurwitz or Hurwitz) with constant/variable coefficients and determining intervals of all its coefficients (stability intervals) assuring its robust stability.
\n
\n
\n
3. Root locus portraits of uncertain polynomials
\n
Definition 1. The algebraic equation coefficient or the parameter of the dynamic system, described by this algebraic equation, which is being varied in a definite way for generating the root locus, when it is assumed that all the rest coefficients (parameters) are constant, is called the root locus parameter or free parameter.
\n
If the root locus parameter is aj, it is named the root locus relative to parameter (coefficient) aj.
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Definition 2. The root locus relative to the algebraic equation free term is called the free root locus.
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Definition 3. Points, where the root locus branches begin and where the root locus parameter is equal to zero are called the root locus initial points.
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Definition 4. The family P of root loci of interval polynomial (1) with coefficients varying within (2) name as the interval polynomial root locus portrait (interval polynomial root locus) or interval dynamic system root locus portrait (interval dynamic system root locus).
\n
Let us along with the parameter an vary also parameter an-1 of (1). Thus, we generate a (free) root locus field Fk (k = 1. 2, …) in the plane s of system roots, which could also be named a two-parameter root locus field or a (interval) root locus subfamily. Parameter an-1 used for the field generation is named a root locus field parameter.
\n
It is evident that the root locus Eq. (3) represents also the equation of level lines of the free root locus field Fk. Root locus portrait P is then represented by the family of root locus fields,
that represents the infinite set of root locus fields and therefore possesses their properties, and from the mathematical point of view, all root locus fields of P feature the same qualities. Therefore, the portrait P can be investigated as a single root locus field Fk.
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Hereinafter the term “root locus” is used in the sense of “Teodorchik – Ewans free root locus” [18].
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4. Polynomial analysis and synthesis based on the extended root locus
i–sequential number of the polynomial in (6), which is equal to its degree, \n\ni\n=\n\n\n1\n,\nn\n\n¯\n\n\n; aj—coefficients, \n\nj\n=\n\n\n1\n,\ni\n\n¯\n\n\n.
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Every polynomial (8) of (i−1) degree is generated from the i-degree polynomial supposed that ai = 0. Polynomials of (6) have common coefficients, but not common roots.
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Definition 5. System of polynomials (6) name as the extension of polynomial(1) or extended polynomial.
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Definition 6. Complete set of extension (6) root loci name as the extended root loci of (1).
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Extension En of polynomial gn(s) could be represented by the finite set of polynomials,
\n\n\nE\nn\n\n=\n\n\n\ng\ni\n\n\ns\n\n\n\n.\nE9
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Statement 1. In case of variation of any coefficient aj,\n\nj\n=\n\n\n1\n,\n\n\ni\n−\n1\n\n\n\n¯\n\n\n, of polynomial gi(s) (7) within the specific interval, \n\n\n\na\n¯\n\nj\n\n\n ≤ aj ≤ \n\n\n\na\n¯\n\nj\n\n\n, every initial point of its free root locus (excluding the point located at the origin) moves along its unique trajectory, representing itself one of the branches of polynomial gi−1(s) (8) root locus, generated relative to this coefficient, and its current position is determined at a point corresponding to the current value of aj.
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Proof. As at initial points of polynomial (6) free root locus the free term aj is equal to zero, it is evident that (8) represents the equation of initial points of the free root locus of (6), that is, when varying aj\n\n\n\nj\n=\n\n\n1\n,\n\n\ni\n−\n1\n\n\n\n¯\n\n\n\n\n, the root locus of (8) relative to aj represents the geometric place of initial points of the root locus of (7). Therefore, every initial point of the free root locus of (7) at fixed aj coincides in the complex plane s with one of the polynomial (8) roots at the given value of aj. It is evident, that while varying aj, this root (and hence, this initial point) moves in the complex plane s, generating one of the (i – 1) branches (trajectories) of the root loci of (8) relative to aj. Thus, the statement has been proved.
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Definition 7. Name gi−1(s) (8) as the originative polynomial relative to gi(s) (7) and the root locus of (8)—the originative root locus of polynomial (7) free root loci.
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Every (i−1)-th polynomial of (6) is the originative one relative to i-th polynomial (6).
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Consequence 1. In case of continuous variation of the polynomial gi(s) coefficient aj, \n\nj\n=\n\n\n1\n,\n\n\nn\n−\n1\n\n\n\n¯\n\n\n, every branch of this polynomial root locus, initiated at the specific initial point, migrates continuously along the corresponding branch of the originative root locus relative to aj-1, being the trajectory of this initial point, correspondingly in direction of increase or decrease of the originative root loci parameter aj.
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Consequence 2. If polynomial gi-1(s) being the originative one for the polynomial gi(s) is asymptotically stable, all initial points of polynomial gi(s) free root locus, excluding zero one, are located in the left half-plane s:
where \n\n\ns\nμ\ni\n\n\n—roots of gi(s); \n\n\np\nμ\ni\n\n\n—initial points of polynomial gi(s) free root locus; μ—root (initial point) sequential number, \n\nμ\n=\n\n\n1\n,\ni\n−\n1\n\n¯\n\n\n.
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Further in the text, polynomial gi-1(s) free root locus is referred to as the originative one relative to that of gi(s) and gi(s) free root locus—as the originated one relative to that of gi-1(s).
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Statement 1 is illustrated by Figures 1 and 2. Initial points here are designated by signs “x” (crosses) and letters “p” with the lower indexes, designating the point sequential numbers, and upper indexes, designating the sequential numbers of the corresponding root locus. The root locus sequential number is indicated by a digit next to its corresponding branch.
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Figure 1.
Polynomial (1) root locus portrait (field) at n = 3, 5 ≤ а2 ≤ 45: (a) originated portrait and (b) originated portrait combined with its originative root locus (n = 2).
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Figure 2.
Free root locus portrait (field) for polynomial g4(s) = s4 + 10 s3 + 35 s2 + a3s + a4, 100 ≤ а3 ≤ 5 combined with its originative root locus (n = 3).
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4.2 Synthesis of stable interval polynomials based on the extended root locus
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Consider Eq. (3) in the sense of four following possible cases: n is uneven, (n – 1)/2 is even/uneven, n is even, and n/2 is even/uneven. The root locus parameter equations (as it is in the general form see (4)) are composed in the same way.
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Specify the set \n\n\nA\ni\n+\n\n\n of ai values at the cross points of polynomial (7) root locus positive branches with axis ω:
where \n\n\nn\ni\n+\n\n\n is a number of cross points.
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Statement 2. If all initial points of polynomial (7) root locus, excluding a single one at the origin, are located in the left half-plane s, and this polynomial is asymptotically stabile, when the following condition holds:
\n\n0\n<\n\na\ni\n\n<\ninf\n\nA\ni\n+\n\n.\nE13
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Proof. Based on the root locus properties [2, 18] and expressions (10) and (11), it can be stated, that provided all initial points of polynomial (7) root locus are located in the left half-plane s (excluding the initial point at the origin), the specific number ni of root locus branches (ni = i − 2 when i is even and ni = i − 1 when i is uneven), initiating at these points, cross the stability bound iω striving along the asymptotes directed to the right half-plane. As the rest of the root locus branches does not cross the stability bound, they are completely stable. For positive branches, crossing the stability bound, specify the set
of intervals \n\n\nS\nil\n\n\n of values ai within the segments from the initial point \n\n\np\nil\n\n\n (where ai = 0) of every branch up to its cross point with axis iω. Thus, the maximal possible interval of ai values, ensuring stability of (6), is equal to
For the 4-th degree polynomial represented in Figure 2, the interval \n\n\nS\n\ni\nmax\n\n\n=\n\n0\n\n\na\n4\n\n\nt\n\n\n\n\n.
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Theorem 1. For ensuring asymptotic stability of regular or interval polynomial (1), it is enough to.
find among polynomials of extension (6), the stable polynomial of degree i = k being the closest one to n;
set up sequentially every coefficient aj of (1), beginning with aj = ak + 1, within interval (k + 1) < j ≤ n by setting up the free term ai of the corresponding i-th polynomial of extension (5) as per condition (13) assuming i = j.
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Proof. If polynomial gi(s) = gk(s) is stable, then on the basis of Consequence 2 of Statement 1 (expressions (10) and (11)), the stability of gi+1(s) can be ensured by simple application of condition (13). Thus, stability of all polynomials gi(s) is sequentially ensured beginning with the polynomial of degree i = k + 1 up to the polynomial of degree i = n inclusive, that is, for \n\ni\n=\n\n\n\n\nk\n+\n1\n\n\n,\nn\n\n¯\n\n\n. Thus, Theorem 1 has been proved.
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An algorithm for the robustly stable regular or interval polynomial synthesis is given below.
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Step 1. Composing the extension En(6) of the given initial nominal polynomial gn(s) (1).
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Step 2. Sequential check for stability of the extension polynomials, beginning with the polynomial of degree n, until finding the stable polynomial of degree i = k.
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In case of synthesis of the whole interval polynomial, begin the procedure with the 1-st degree polynomial, i = k = 1, specifying interval of a1 according to the appropriate requirements or arbitrarily.
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Step 3. Transfer to the polynomial of the next higher degree, i = k + 1.
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Step 4. Calculating coordinates \n\n\nω\n\ni\nl\n\n+\n\n\n of cross points of the polynomial gi(s) free root locus positive branches with the axis iω by solving its appropriate root locus Eq. (3).
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Cross points \n\n\nω\n\ni\nl\n\n+\n\n\n generate on the axis iω a so-called “crossing domain” \n\n\nW\ni\n+\n\n\n:
\n\n\nω\n\ni\nl\n\n+\n\n∈\n\nW\ni\n+\n\nE16
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Properties of this domain and behavior of the interval root locus portrait at the stability bound iω have been investigated in [18]. On the basis of the fact, that every function of (3) represents continuous differentiable function (steadily increasing/decreasing function), it has been found in [18] that for ensuring stability of the whole interval family, it is required to calculate the parameter \n\n\na\ni\n\n=\n\na\n\ni\nl\n\n+\n\n\n(13) values at only two extreme “dominating points”:
by solving the corresponding Eq. (3) after substituting preliminarily into this equation, the appropriate combination [18] of the limit values of each coefficient, from a1 to ai−1, which have been calculated already in this algorithm when generating the originative polynomial gi−1(s). For finding two coordinates (17), two different combinations of coefficients should be substituted into the root locus equation and thus two different equations should be solved.
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Step 5. Determining the value of \n\ninf\n\nA\ni\n+\n\n\n(12) for polynomial gi(s) by calculating minimal values \n\n\na\n\'\n\n=\n\na\n\ni\n\nmin\n\n\n\'\n\'\n\n\n\n\n\nω\ni\n+\n\nmin\n\n\n\n and \n\n\na\n\n\'\n\'\n\n\n=\n\n\na\ni\n+\n\nmin\n\n\n\n\nω\ni\n+\n\nmax\n\n\n\n of coefficient ai correspondingly at points \n\n\n\nω\ni\n+\n\nmin\n\n\n and \n\n\n\nω\ni\n+\n\nmax\n\n\n solving twice Eq. (4) for polynomial gi(s) at the stability bound:
\n\n\na\ni\n\n=\nu\n\nω\n\n,\nE18
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after substituting previously into (18) the corresponding combinations of coefficients (from a1 to ai−1) [18]. Thus,
where \n\n\n\na\n¯\n\ni\n\n\n is the upper limit of ai variation interval. The required interval (13) is: \n\n0\n<\n\na\ni\n\n<\n\n\na\n¯\n\ni\n\n.\n\n
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Step 6. If the last polynomial of extension (6), that is, that of degree n, has been already processed (i = n), the calculation is considered finished. Otherwise proceed to step 3.
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4.3 Example
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Synthesis of the interval polynomial of the 3-rd degree.
Step 2. As coefficients of polynomials (21.1) and (21.2) are positive, then both families of these polynomials are asymptotically stable (i = k = 2), and therefore, on the basis of Consequence 2 of Statement 1, the root loci family of (21.3) initial points is located in the left half-pane. Thus, for making stable, the polynomial (21.3) uses Statement 2 and Theorem 1.
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Step 3. Transfer to the polynomial of the next higher degree, i = 2 + 1 = 3.
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Step 4. Calculating coordinates (16) of the “dominating points” for polynomial g3(s). For this purpose, consider the appropriate root locus (3) and parameter (18) equations:
\n\n\nω\n3\n\n–\n\na\n2\n\nω\n=\n0\n,\nE22
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and parameter function (18) at the stability bound:
On the basis of (23) and (24), it can be stated that the character of parameter (23) distribution along the axis σ is steadily increasing and the single extreme point is located at the origin. Thus, there exists the only one extreme point:
5.1 Crossing region of the polynomial root locus portrait
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Functions (29) and (30) imply properties of analyticity and continuity and, thus, the points where axis iω is crossed by the branches of the root locus family P(5), given the condition.
\n\n0\n<\n\nа\nj\n\n<\n+\n∞\n,\nE31
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constitute on the stability boundary, axis iω, a specific crossing region, \n\n\nD\nω\nP\n\n\n.
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Definition 8. The region at the asymptotic stability boundary iω of the interval system root locus portrait P, described by characteristic polynomial (26), where the given portrait parameter function (30) values family is located, name the crossing region\n\n\nD\nω\nP\n\n\n of the root locus portrait P.
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The region \n\n\nD\nω\nP\n\n\n is a continuous one and, thus, each root locus field Fk(5) and each branch \n\n\nb\nki\n\n,\n\ni\n=\n1\n,\n2\n,\n…\n\n of the field root loci generate specific subregions, correspondingly subregion \n\n\n\nD\nω\nF\n\nk\n\n\n and continuous subregion \n\n\n\nD\nω\nb\n\ni\n\n\n, within the above specified region \n\n\nD\nω\nP\n\n\n.
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Over the symmetry of the portrait hereinafter, the only upper half-plane s is considered.
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5.2 Majorant and minorant of the extremum region
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Obtain the extremum parameter function values within \n\n\n\nD\nω\nF\n\nk\n\n⊂\n\nD\nω\nP\n\n\n. To do so, it is necessary to carry out investigation of this function for extremum. It is evident that the majorant parameter function (majorant) can be obtained through rewriting Eq. (30):
Evidently, for n = 4, Eqs. (32) and (35) are the majorant and the minorant for the whole portrait.
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Definition 9. Extremum region\n\n\nD\nω\ne\n\n\n of the interval system root locus portrait described by the characteristic polynomial (26) is a region [0, \n\n\nω\n\ne\nmax\n\n\n\n] at the system asymptotic stability boundary iω where the given portrait parameter function (30) extremum values, \n\n\n\n\na\n4\n\ne\n\nmax\n\n\n(34) and \n\n\n\n\na\n4\n\ne\n\nmin\n\n\n(36), family is located provided all coefficients аj vary within limits (31).
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5.3 Diagram of the parameter function distribution along the stability boundary
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Figure 3 represents the character (diagram) of the parameter function (30) distribution along the boundary of stability by its majorant (32) and minorant (35). For better understanding and descriptiveness, the diagram in Figure 3 is shown by strait lines, although it constitutes curves. Region \n\n\nD\nω\nP\n\n\n constitutes three subregions (see Figure 3):
Dω+ where the parameter function is getting increased (increase region);
Dω− where the parameter function is getting decreased (decrease region);
Dωс where increase and decrease regions combine (mixed region).
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Figure 3.
A diagram for distribution of the interval system root locus portrait parameter function along the asymptotic stability boundary.
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Analyze the region Zω with the interval \n\n\n\nz\n\'\n\n\nz\n\n\'\n\'\n\n\n\n⊆\n\nZ\nω\n\n\n where the initial points of the root locus portrait migrate through the stability boundary to the right half-plane. In the diagram, zero points z’, z” are mapped by points z1, z2.
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Within interval [0, z’], covering completely region Dω+ and partly region Dωc (\n\n\n\nD\nω\n\n+\n\n⊂\n\n0\n\nz\n\'\n\n\n\n, \n\n\n0\n\nz\n\'\n\n\n∩\n\n\nD\nω\n\nc\n\n\n), only the positive branches cross the stability boundary, and here the whole family Z of initial points is located in the left half-plane L,
\n\nZ\n⊂\nL\n.\nE37
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But specific pieces of the positive branches are situated within the right half-plane. For this reason, in some cases, the unstable polynomials could have been found within the whole family (26). However, there certainly could always be found the intervals (27) of stability where the whole family is stable. Name the interval [0, z’] the system stability region.
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The interval [z’, z”] covers some piece of the region Dωс and some of the region Dω−,\n\n\n\nz\n\'\n\n\nz\n\n\'\n\'\n\n\n\n∩\n\n\nD\nω\n\nc\n\n\n, \n\n\n\nz\n\'\n\n\nz\n\n\'\n\'\n\n\n\n∩\n\n\nD\nω\n\n−\n\n\n. In this case, axis iω is crossed by combination of both positive and negative branches, and the root locus portrait certainly includes a series of initial points, and thus the whole branches, that have migrated over the boundary to the right half-plane. Therefore, this case always gives us the family (26) that includes combination of stable and unstable polynomials. Name the interval [z’, z”] the system instability region.
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If the interval [z”, ∞] completely belongs to the region Dω−,
\n\n\nz\n″\n∞\n\n⊂\n\n\nD\nω\n\n−\n\n,\nE38
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only the negative branches cross the stability boundary iω, and the family Z together with the corresponding positive branches are located in the right half-pane,
\n\nZ\n⊂\nR\n.\nE39
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No stable polynomial could be found in (26). This region name the system complete instability region.
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5.4 Real crossing region of the portrait
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Specify the region \n\n\nD\nω\nR\n\n\n where the branches of the given real root locus portrait cross the stability boundary. To find its limits, consider Eq. (29) and determine the values of its roots. When \n\nω\n>\n0\n\n.
where \n\n\nω\nmax\n\n\n, \n\n\nω\nmin\n\n\n represent the real crossing region.
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Definition 10. The region [\n\n\nω\nmin\n\n\n,\n\n\nω\nmax\n\n\n] at the stability boundary iω, where the polynomial (26) root locus portrait branches migrate through to the right half-plane, name the real crossing region\n\n\nD\nω\nR\n\n\n of the system root locus portrait:
5.5 Graphic-analytical stability conditions for interval polynomials
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Define below three possible ways of the real crossing region location and the corresponding stability conditions.
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5.5.1 Real crossing region belongs to the increase region Dω+
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\n\n\nD\nω\nR\n\n⊂\n\n\nD\nω\n\n+\n\n.\nE42
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In this case \n\n\nω\nmax\n\n<\n\nω\n\ne\nmin\n\n\n\n.
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Statement 3. When the dynamic system root locus portrait, described by polynomial (26), satisfies relationship (42), the whole family Z of the portrait initial points is located in the left half-plane L,
\n\nZ\n⊂\nL\n.\nE43
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Then, define the set S of the root locus portrait Р branches’ intervals si:
The following statement can be formulated on the basis of expressions (42) and (47).
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Statement 4. The dynamic system, described by the interval characteristic polynomial family (26) and satisfying expression (42), is asymptotically stable if
Definition 11. One or more stable polynomials with constant coefficients within the family (26) that guarantee stability of the whole family name the dominating polynomials.
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From Statement 4 and the previous conclusions, the following stability condition goes.
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Stability condition 1. The asymptotic stability of the interval system family, described by the root locus portrait Р(5) satisfying expression (42), is guaranteed if polynomial
of the family is stable. Polynomial (49) represents the dominating one.
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Stability is verified using the Stability condition 1. The polynomial parameters are calculated with application of the Statement 4.
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5.5.2 Real crossing region belongs to the decrease region Dω−
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\n\n\nD\nω\nR\n\n⊂\n\n\nD\nω\n\n−\n\n.\nE50
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It happens in case if \n\n\nω\nmin\n\n≥\n\nω\n\ne\nmax\n\n\n\n.
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The above made conclusions allow to formulate the following statement.
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Statement 5. If the interval system root locus portrait P satisfies condition (50), the whole family Z of its initial points satisfies Eq. (39), and the system is asymptotically unstable.
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5.5.3 Real crossing region completely or partially belongs to the mixed region Dωс
We have this when the following conditions are not satisfied: \n\n\nω\nmax\n\n<\n\nω\n\ne\nmin\n\n\n\n, \n\n\nω\nmin\n\n≥\n\nω\n\ne\nmax\n\n\n\n.
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For this case
\n\nP\n=\n\nP\n+\n\n+\n\nP\n−\n\n,\nE52
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We have already discussed the increase part of (52), when P− = ∅. Hence, this section considers the decrease part, P−. Consider first the family Z of the root locus portrait P−.
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Statement 6. If condition (51) holds, family Z of initial points of the dynamic system root locus portrait, described by characteristic polynomial (26), can be located in both left half-plane L and right half-plane R, that is, the following options of Z location may take place:
As options (54)–(57) deliberately indicate instability of the system in whole, consider below only option (53) of the system poles location,
\n\n\nω\nmax\n\n<\nω\n\n\nz\n′\n\n\n,\nE58
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where ω(z′) is coordinate ω at point z′ (Figure 3).
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In this case proceed just as in (44)–(47) but only substituting ωmax instead of ωmin.
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Statement 7. The asymptotic stability of the dynamic system, described by polynomial family (26) and satisfying expression (51), is ensured when the following condition holds:
From condition (59) follows that the system asymptotic stability for part Р− of portrait (52), provided that condition (53) holds, is defined by the value of \n\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\n. Therefore, for checking stability of Р−(52), it is enough to check the only one following dominating polynomial of (26):
Because in this case, the portrait represents the compound one (52), check the stability by checking both polynomials, (49) and (60).
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Stability condition 2. If the interval dynamic system root locus portrait Р(52), describing the family of characteristic polynomials (26), satisfies expression (51), the system asymptotic stability is ensured when the following dominating polynomials
From the results obtained above also goes that in case (51) the system asymptotic stability can be verified by only a single polynomial of (26) having constant coefficients. The equation to choose depends of condition (49) verification results. If the verification shows that \n\nmin\n\n\n\n\na\n¯\n\n4\n\n\n\nω\nmin\n\n\n\n\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\n\n=\n\n\na\n¯\n\n4\n\n\n\nω\nmin\n\n\n\n, then Eq. (61) is applied for the stability check. If it shows that \n\nmin\n\n\n\n\na\n¯\n\n4\n\n\n\nω\nmin\n\n\n\n\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\n\n=\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\n, then the stability is verified by (62).
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To determine the coefficients of (26), ensuring satisfaction of expressions (53) and (58), Eqs. (30) and (31) are applied. Thus, coefficients а1 and а3 must satisfy the inequality:
To verify the system stability, the stability conditions 1 and 2 are used. For calculation of the system (polynomial) parameters, expressions (48), (49) and (63) are used.
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Polynomial stability could be estimated graphically directly from the plots (see Figures 3 and 4).
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Figure 4.
Dynamics of the interval system root locus portrait at the asymptotic stability boundary.
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5.6 Example
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Coefficients of the given polynomial (26): \n\n\na\n1\n\n∈\n\n\n5\n\n\n10\n\n\n,\n\n\na\n2\n\n∈\n\n\n5\n\n\n10\n\n\n,\n\n\na\n3\n\n∈\n\n\n5\n\n\n10\n\n\n,\n\n\na\n4\n\n∈\n\n\n5\n\n\n10\n\n\n.\n\n
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Extremum region: \n\n\nD\nω\ne\n\n\n: ωe min = 3,16; ωe max = 5,92; a4e min = 100,04; a4e max = 1223,96.
In Figure 4, the above indicated regions are shown. The points, corresponding to the dominating polynomials (61), (62), are designated by r’ and r”. The real crossing region in this case completely covers the extremum region, \n\n\nD\nω\ne\n\n⊂\n\nD\nω\nR\n\n,\n\n\n\nr\n\'\n\n\nr\n\n\'\n\'\n\n\n\n⊆\n\nD\nω\nR\n\n\n.
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It is evident that the given polynomial family in whole is unstable. Within region Zω = [z’, z”], there exist poles that have migrated to the right half-plane (see (54)), which is confirmed by the negative value of the parameter \n\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\nI.
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Dominating polynomials of the family are the following:
Polynomials stability check shows that polynomial (6), which root loci crosses the stability boundary at point \n\n\n\na\n¯\n\n4\n\n\n\nω\nmin\n\n\n\n, is stable, and polynomial (66), which root loci crosses the stability boundary at point \n\n\n\na\n¯\n\n4\n\n\n\nω\nmax\n\n\n\n, has two roots with positive real parts.
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Extraction of the stable polynomial subfamily of the given unstable family:
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The stable root locus family, satisfying conditions (58) and (59), should cross the stability boundary within the region bounded by interval [r’, z’] as in this case all initial points of the root locus family are located in the left half-plane (53) (see Section 5.5).
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To calculate the maximal value of а3 that defines the stable subfamily within the given root locus portrait, apply formula (63):
As per stability condition 2, the root locus portrait subfamily having new modified values of а3 and а4 (\n\n\n\na\n¯\n\n3\n\n=\n80\n\n,\n\n\n\na\n¯\n\n4\n\n=\n60\n\n) is asymptotically stable.
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6. Conclusions and future developments
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A method has been worked out for synthesis of asymptotically stable regular or interval polynomial from the given Hurwitz or non-Hurwitz source polynomial with constant/interval coefficients by setting up coefficients of the given one. The root locus approach is used. The task is solved by introduction of notions of the “extended polynomial” (“generalized polynomial”) and the polynomial “extended root locus,” which allows to obtain a descriptive picture of the polynomial root dynamics under coefficient variations and to disclose on this basis the cause of instability. The intervals of uncertainty for each coefficient being set up are specified along the root locus branches.
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The above described method based on the “extended root locus” notion is new and allows to extend the application sphere of the root locus method, which is traditionally considered to be the method of system synthesis by only a single parameter (coefficient) variation and with only one variable parameter (coefficient), in both directions: system synthesis by many parameter variations and system synthesis with many parameter variations.
\n
Investigation of the fourth power dynamic system behavior in conditions of the interval parameter variations has also been carried out on the basis of root locus portraits and introduction of the notion of the “diagram of the root locus parameter function values distribution along the stability bound.” Behavior regularities for interval system root locus portraits at the stability boundary have been formulated. On this basis, the stability conditions have been derived, and graphic-analytical method has been worked out for calculating intervals of parameter variation ensuring the system robust stability.
\n
In continuation of the results of Anderson [22] and Kharitonov [4] in this work, it is proved that for the 4th power interval system family asymptotic stability analysis, it is enough to use the only one polynomial of this kind. It is also shown, how to find and extract the stable families from the unstable ones.
\n
The above discussed topic is certainly worth further investigation in the light of continuous progress of both theory and technology. When speaking of the practical implementations, it could be noted that most of the control system synthesis tasks, especially those in the area of robust control, are currently still being solved in a somewhat “local domestic” way, when a designer each time tries to invent a solution to be suitable for the specific application experiencing the lack of more generalized methods. Besides this, a great deal of existing robust control methods share and suffer complexity. In this connection, further in-depth investigation of the uncertain polynomials’ root locus portraits seems helpful, especially the analysis of its composition in terms of configurations variety, constituting subfamilies, placement of various root domains within the prescribed regions in the complex plane and, of course, dynamics. They also could be distinguished for their undoubted descriptiveness.
\n
Polynomial equation approach in the design technique [16], and root locus technique in particular, is descriptive, clear, and easy to use and computerize and thus could be helpful in many application areas including the areas of industry, biology, medicine, etc. It can be used for proper parameterization of robust drive controllers, for example, in the area of railway traffic control, in particular for the cases of tackling the problems of breaking and skidding.
\n
\n
Acknowledgments
\n
The author acknowledges the support of this work by the Belarusian Republican Foundation for Fundamental Research.
\n
\n',keywords:"polynomial, dynamic system, uncertainty, stability, robustness, root locus portrait, extended root locus, root locus parameter function",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/65970.pdf",chapterXML:"https://mts.intechopen.com/source/xml/65970.xml",downloadPdfUrl:"/chapter/pdf-download/65970",previewPdfUrl:"/chapter/pdf-preview/65970",totalDownloads:920,totalViews:74,totalCrossrefCites:0,dateSubmitted:"July 26th 2018",dateReviewed:"December 20th 2018",datePrePublished:"March 5th 2019",datePublished:"May 2nd 2019",dateFinished:"March 4th 2019",readingETA:"0",abstract:"The root locus method is proposed in the chapter for searching intervals of uncertainty for coefficients of the given (source) polynomial with constant or interval coefficients under perturbations, which ensures its robust stability regardless of whether the given polynomial is Hurwitz or not. The method is based on introduction and application of the “extended root locus” notion. Polynomial adjustment is performed by setting up each one of its coefficients separately and sequentially and determining permissible values of coefficient variation intervals (intervals of uncertainty). The effect of each coefficient variation upon the polynomial root dynamics (behavior) is considered and analyzed separately, and this influence could be observed in the root locus portraits. Root locus method is thus generalized to the cases when the number of polynomial variable coefficients is arbitrary. The root locus parameter distribution diagram along the asymptotic stability bound is introduced and applied for observing the roots behavior regularities. On this basis, the stability conditions are derived, and analytical and graphic-analytical methods are worked out for calculating intervals of variation for the 4th order polynomial family parameters ensuring its robust stability. It also allows to extract Hurwitz subfamilies from the non-Hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/65970",risUrl:"/chapter/ris/65970",signatures:"Nesenchuk Alla",book:{id:"8599",type:"book",title:"Polynomials",subtitle:"Theory and Application",fullTitle:"Polynomials - Theory and Application",slug:"polynomials-theory-and-application",publishedDate:"May 2nd 2019",bookSignature:"Cheon Seoung Ryoo",coverURL:"https://cdn.intechopen.com/books/images_new/8599.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-83880-270-7",printIsbn:"978-1-83880-269-1",pdfIsbn:"978-1-83880-639-2",isAvailableForWebshopOrdering:!0,editors:[{id:"230100",title:"Prof.",name:"Cheon Seoung",middleName:null,surname:"Ryoo",slug:"cheon-seoung-ryoo",fullName:"Cheon Seoung Ryoo"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. The problem formulation",level:"1"},{id:"sec_3",title:"3. Root locus portraits of uncertain polynomials",level:"1"},{id:"sec_4",title:"4. Polynomial analysis and synthesis based on the extended root locus",level:"1"},{id:"sec_4_2",title:"4.1 Extended root locus",level:"2"},{id:"sec_5_2",title:"4.2 Synthesis of stable interval polynomials based on the extended root locus",level:"2"},{id:"sec_6_2",title:"4.3 Example",level:"2"},{id:"sec_8",title:"5. Investigation of behavior at the stability bound and synthesis of interval polynomial families: root locus parameter function distribution diagram",level:"1"},{id:"sec_8_2",title:"5.1 Crossing region of the polynomial root locus portrait",level:"2"},{id:"sec_9_2",title:"5.2 Majorant and minorant of the extremum region",level:"2"},{id:"sec_10_2",title:"5.3 Diagram of the parameter function distribution along the stability boundary",level:"2"},{id:"sec_11_2",title:"5.4 Real crossing region of the portrait",level:"2"},{id:"sec_12_2",title:"5.5 Graphic-analytical stability conditions for interval polynomials",level:"2"},{id:"sec_12_3",title:"5.5.1 Real crossing region belongs to the increase region Dω+",level:"3"},{id:"sec_13_3",title:"5.5.2 Real crossing region belongs to the decrease region Dω−",level:"3"},{id:"sec_14_3",title:"5.5.3 Real crossing region completely or partially belongs to the mixed region Dωс",level:"3"},{id:"sec_16_2",title:"5.6 Example",level:"2"},{id:"sec_18",title:"6. Conclusions and future developments",level:"1"},{id:"sec_19",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Ackermann J. Robust Control: The Parameter Space Approach. 2nd ed. London: Springer Verlag; 2002. 483 p. ISBN 1-85233-514-9\n'},{id:"B2",body:'Dorf R, Bishop R. Modern Control Systems. 12th ed. N.Y.: Prentice Hall; 2011. 1084 p. ISBN-13:978-0-13-6024583\n'},{id:"B3",body:'Polyak B, Scherbakov P. Robust stability and control [in Russian]. Nauka. 2002. 303 p. ISBN 5-02-002561-5\n'},{id:"B4",body:'Kharitonov V. About asymptotic stability of equilibrium of the linear differential equations systems family [in Russian]. Differential Equations. 1978;XIV:2086-2088. ISSN 0374-0641\n'},{id:"B5",body:'Tsypkin Y. Robust stability of relay control systems [in Russian]. Doklady Mathematics. 1995;340:751-753. ISSN 0869-5652\n'},{id:"B6",body:'Barmish B. Invariance of the strict hurwitz property for polynomials with perturbed coefficients. IEEE Transactions on Automatic Control. 1984;2:935-936. ISSN 0018-9286\n'},{id:"B7",body:'Soh Y. Strict hurwitz property of polynomials under coefficient perturbations. IEEE Transactions on Automatic Control. 1989;34:629-632. ISSN 0018-9286\n'},{id:"B8",body:'Soh Y. Maximal perturbation bounds for perturbed polynomials with roots in the left-sector. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1994;41:281-285. ISSN 1549-8328\n'},{id:"B9",body:'Bartlett A, Hollot C, Lin H. Root location of an entire polytope of polynomials in suffices to check the edges. Mathematics of Control, Signals, and Systems. 1987;1:61-71. ISSN 0932-4194\n'},{id:"B10",body:'Tempo R, Calafiori C, Dabbene F. Randomized Algorithms for Analysis and Control of Uncertain Systems with Applications. London: Springer-Verlag; 2013. 357 p. ISBN 978-1-4471-4609-4\n'},{id:"B11",body:'Dikusar V, Zelenkov G, Zubov N. Criteria of existence of homogeneous classes of equivalence for unstable interval polynomials [in Russian]. Doklady Mathematics. 2009;3:322-324. ISSN 0869-5652\n'},{id:"B12",body:'Li X, Yu H, Yuan M, Wang J. Design of robust optimal proportional-integral-derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters’ perturbations circumstance. IET Control Theory & Applications. 2010;4:2427-2440. DOI: 10.1049/iet-cta.2009.0508\n'},{id:"B13",body:'Lia X, Niculescub S, Celac A, Wanga H, Caia T. Invariance properties for a class of quasipolynomials. Automatica. 2014;50:890-895. ISSN 0005-1098\n'},{id:"B14",body:'Aguirre-Hernández B, Cisneros-Molina J, Frías-Armenta M. Polynomials in control theory parameterized by their roots. International Journal of Mathematics and Mathematical Sciences. 2012. ID 595076:19 pages. DOI: 10.1155/6396\n'},{id:"B15",body:'Aguirre B, Suárez R. Algebraic test for the Hurwitz stability of a given segment of polynomials. Boletín de la Sociedad Matemática Mexicana: Tercera Serie. 2006;12:261-275, ISSN 1405-213X\n'},{id:"B16",body:'Kučera V. Polynomial control: Past, present, and future. International Journal of Robust and Nonlinear Control. 2007;17:682-705. ISSN 1049-8923\n'},{id:"B17",body:'Barmish B, Tempo R. The robust root locus. Automatica. 1993;26:183-192. ISSN 0005-1098\n'},{id:"B18",body:'Nesenchuk A. Analysis and Synthesis of Robust Dynamic Systems on the Basis of Root Locus Approach [in Russian]. Minsk: UIIP NAS of Belarus; 2005. 234p. ISBN 985-6744-18-0\n'},{id:"B19",body:'Nesenchuk A. Parametric synthesis of qualitative robust control systems using root locus fields. In: In Proceedings of the 15th Triennial World Congress of IFAC; 21–26 July 2003. Barselona, Spain. London: Elsevier Science Ltd.; 2003. pp. 331-335. ISBN 008044220X\n'},{id:"B20",body:'Nesenchuk A, Nesenchuk V. Industrial robot control system parametric design on the base of methods for uncertain systems robustness. In: Cubero S, editor. Industrial Robotics: Theory, Modeling and Control. Mammendorf: PlV pro literatur Verlag Robert Mayer-Scholz; 2007. pp. 895-926. ISBN 3-86611-285-8. ch33. ISBN 3-86611-285-8\n'},{id:"B21",body:'Nesenchuk A. Parametric synthesis of interval control systems using root loci of Kharitonov’s polynomials. In: Proceedings of the European Control Conference (ECC\'99); 31 August-03 September 1999; Karlsruhe, Germany. 1999. 1 electronic. opt. disc (CD-ROM). ID 123, 6 p\n'},{id:"B22",body:'Anderson B. On robust Hurwitz polynomials. IEEE Transactions on Automatic Control. 1987;32:909-913. ISSN 0018-9286\n'},{id:"B23",body:'Nesenchuk А. A method for synthesis of robust interval polynomials using the extended root locus. In: Proceedings of the American Control Conference (ACC\'2017); 24–26 May 2017. Seattle, USA: Seattle: IEEE; 2017. pp. 1715-1720. ISBN 978-1-5386-5426\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Nesenchuk Alla",address:"anes@newman.bas-net.by",affiliation:'
United Institute of Informatics Problems of the Belarusian National Academy of Sciences, Minsk, Belarus
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My method of translating this into day to day in clinical practice is non-exhaustible and my habit of exchanging knowledge and expertise with others in those fields is the code and secret of success.",institutionString:null,institution:{name:"Majmaah University",country:{name:"Saudi Arabia"}}},{id:"313277",title:"Dr.",name:"Bartłomiej",middleName:null,surname:"Płaczek",slug:"bartlomiej-placzek",fullName:"Bartłomiej Płaczek",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/313277/images/system/313277.jpg",biography:"Bartłomiej Płaczek, MSc (2002), Ph.D. (2005), Habilitation (2016), is a professor at the University of Silesia, Institute of Computer Science, Poland, and an expert from the National Centre for Research and Development. His research interests include sensor networks, smart sensors, intelligent systems, and image processing with applications in healthcare and medicine. 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After positions as a lecturer at the University of Port Elizabeth, he accepted a position as Associate Professor at the University of Pretoria, South Africa.\r\n\r\nIn 1992, he motivates the concept of 'television and computer-based education” as means to reach large student numbers with only the best of teaching expertise and publishes an article on the concept in the SA Journal of Higher Education of 1993 (and later in 2003). The University of Pretoria subsequently approved a series of test projects on the concept with outreach to Mamelodi and Eerste Rust in 1993. In 1994, the University established a 'Unit for Telematic Education ' as a support section for multiple faculties at the University of Pretoria. In subsequent years, the concept of 'telematic education” subsequently becomes well established in academic circles in South Africa, grew in popularity, and is adopted by many universities and colleges throughout South Africa as a medium of enhancing education and training, as a method to reaching out to far out communities, and as a means to enhance study from the home environment.\r\n\r\nProfessor Snyman in subsequent years pursued research in semiconductor physics, semiconductor devices, microelectronics, and optoelectronics.\r\n\r\nIn 2000 he joined the TUT as a full professor. Here served for a period as head of the Department of Electronic Engineering. Here he makes contributions to solar energy development, microwave and optoelectronic device development, silicon photonics, as well as contributions to new mobile telecommunication systems and network planning in SA.\r\n\r\nCurrently, he teaches electronics and telecommunications at the TUT to audiences ranging from first-year students to Ph.D. level.\r\n\r\nFor his research in the field of 'Silicon Photonics” since 1990, he has published (as author and co-author) about thirty internationally reviewed articles in scientific journals, contributed to more than forty international conferences, about 25 South African provisional patents (as inventor and co-inventor), 8 PCT international patent applications until now. Of these, two USA patents applications, two European Patents, two Korean patents, and ten SA patents have been granted. A further 4 USA patents, 5 European patents, 3 Korean patents, 3 Chinese patents, and 3 Japanese patents are currently under consideration.\r\n\r\nRecently he has also published an extensive scholarly chapter in an internet open access book on 'Integrating Microphotonic Systems and MOEMS into standard Silicon CMOS Integrated circuitry”.\r\n\r\nFurthermore, Professor Snyman recently steered a new initiative at the TUT by introducing a 'Laboratory for Innovative Electronic Systems ' at the Department of Electrical Engineering. The model of this laboratory or center is to primarily combine outputs as achieved by high-level research with lower-level system development and entrepreneurship in a technical university environment. Students are allocated to projects at different levels with PhDs and Master students allocated to the generation of new knowledge and new technologies, while students at the diploma and Baccalaureus level are allocated to electronic systems development with a direct and a near application for application in industry or the commercial and public sectors in South Africa.\r\n\r\nProfessor Snyman received the WIRSAM Award of 1983 and the WIRSAM Award in 1985 in South Africa for best research papers by a young scientist at two international conferences on electron microscopy in South Africa. He subsequently received the SA Microelectronics Award for the best dissertation emanating from studies executed at a South African university in the field of Physics and Microelectronics in South Africa in 1987. In October of 2011, Professor Snyman received the prestigious Institutional Award for 'Innovator of the Year” for 2010 at the Tshwane University of Technology, South Africa. This award was based on the number of patents recognized and granted by local and international institutions as well as for his contributions concerning innovation at the TUT.",institutionString:null,institution:{name:"University of South Africa",country:{name:"South Africa"}}},{id:"317279",title:"Mr.",name:"Ali",middleName:"Usama",surname:"Syed",slug:"ali-syed",fullName:"Ali Syed",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/317279/images/16024_n.png",biography:"A creative, talented, and innovative young professional who is dedicated, well organized, and capable research fellow with two years of experience in graduate-level research, published in engineering journals and book, with related expertise in Bio-robotics, equally passionate about the aesthetics of the mechanical and electronic system, obtained expertise in the use of MS Office, MATLAB, SolidWorks, LabVIEW, Proteus, Fusion 360, having a grasp on python, C++ and assembly language, possess proven ability in acquiring research grants, previous appointments with social and educational societies with experience in administration, current affiliations with IEEE and Web of Science, a confident presenter at conferences and teacher in classrooms, able to explain complex information to audiences of all levels.",institutionString:null,institution:{name:"Air University",country:{name:"Pakistan"}}},{id:"75526",title:"Ph.D.",name:"Zihni Onur",middleName:null,surname:"Uygun",slug:"zihni-onur-uygun",fullName:"Zihni Onur Uygun",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/75526/images/12_n.jpg",biography:"My undergraduate education and my Master of Science educations at Ege University and at Çanakkale Onsekiz Mart University have given me a firm foundation in Biochemistry, Analytical Chemistry, Biosensors, Bioelectronics, Physical Chemistry and Medicine. After obtaining my degree as a MSc in analytical chemistry, I started working as a research assistant in Ege University Medical Faculty in 2014. In parallel, I enrolled to the MSc program at the Department of Medical Biochemistry at Ege University to gain deeper knowledge on medical and biochemical sciences as well as clinical chemistry in 2014. In my PhD I deeply researched on biosensors and bioelectronics and finished in 2020. Now I have eleven SCI-Expanded Index published papers, 6 international book chapters, referee assignments for different SCIE journals, one international patent pending, several international awards, projects and bursaries. In parallel to my research assistant position at Ege University Medical Faculty, Department of Medical Biochemistry, in April 2016, I also founded a Start-Up Company (Denosens Biotechnology LTD) by the support of The Scientific and Technological Research Council of Turkey. Currently, I am also working as a CEO in Denosens Biotechnology. The main purposes of the company, which carries out R&D as a research center, are to develop new generation biosensors and sensors for both point-of-care diagnostics; such as glucose, lactate, cholesterol and cancer biomarker detections. My specific experimental and instrumental skills are Biochemistry, Biosensor, Analytical Chemistry, Electrochemistry, Mobile phone based point-of-care diagnostic device, POCTs and Patient interface designs, HPLC, Tandem Mass Spectrometry, Spectrophotometry, ELISA.",institutionString:null,institution:{name:"Ege University",country:{name:"Turkey"}}},{id:"267434",title:"Dr.",name:"Rohit",middleName:null,surname:"Raja",slug:"rohit-raja",fullName:"Rohit Raja",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/267434/images/system/267434.jpg",biography:"Dr. Rohit Raja received Ph.D. in Computer Science and Engineering from Dr. CVRAMAN University in 2016. His main research interest includes Face recognition and Identification, Digital Image Processing, Signal Processing, and Networking. Presently he is working as Associate Professor in IT Department, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur (CG), India. He has authored several Journal and Conference Papers. He has good Academics & Research experience in various areas of CSE and IT. He has filed and successfully published 27 Patents. He has received many time invitations to be a Guest at IEEE Conferences. He has published 100 research papers in various International/National Journals (including IEEE, Springer, etc.) and Proceedings of the reputed International/ National Conferences (including Springer and IEEE). He has been nominated to the board of editors/reviewers of many peer-reviewed and refereed Journals (including IEEE, Springer).",institutionString:"Guru Ghasidas Vishwavidyalaya",institution:{name:"Guru Ghasidas Vishwavidyalaya",country:{name:"India"}}},{id:"246502",title:"Dr.",name:"Jaya T.",middleName:"T",surname:"Varkey",slug:"jaya-t.-varkey",fullName:"Jaya T. Varkey",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/246502/images/11160_n.jpg",biography:"Jaya T. Varkey, PhD, graduated with a degree in Chemistry from Cochin University of Science and Technology, Kerala, India. She obtained a PhD in Chemistry from the School of Chemical Sciences, Mahatma Gandhi University, Kerala, India, and completed a post-doctoral fellowship at the University of Minnesota, USA. She is a research guide at Mahatma Gandhi University and Associate Professor in Chemistry, St. Teresa’s College, Kochi, Kerala, India.\nDr. Varkey received a National Young Scientist award from the Indian Science Congress (1995), a UGC Research award (2016–2018), an Indian National Science Academy (INSA) Visiting Scientist award (2018–2019), and a Best Innovative Faculty award from the All India Association for Christian Higher Education (AIACHE) (2019). She Hashas received the Sr. Mary Cecil prize for best research paper three times. She was also awarded a start-up to develop a tea bag water filter. \nDr. Varkey has published two international books and twenty-seven international journal publications. She is an editorial board member for five international journals.",institutionString:"St. Teresa’s College",institution:null},{id:"250668",title:"Dr.",name:"Ali",middleName:null,surname:"Nabipour Chakoli",slug:"ali-nabipour-chakoli",fullName:"Ali Nabipour Chakoli",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/250668/images/system/250668.jpg",biography:"Academic Qualification:\r\n•\tPhD in Materials Physics and Chemistry, From: Sep. 2006, to: Sep. 2010, School of Materials Science and Engineering, Harbin Institute of Technology, Thesis: Structure and Shape Memory Effect of Functionalized MWCNTs/poly (L-lactide-co-ε-caprolactone) Nanocomposites. Supervisor: Prof. Wei Cai,\r\n•\tM.Sc in Applied Physics, From: 1996, to: 1998, Faculty of Physics & Nuclear Science, Amirkabir Uni. of Technology, Tehran, Iran, Thesis: Determination of Boron in Micro alloy Steels with solid state nuclear track detectors by neutron induced auto radiography, Supervisors: Dr. M. Hosseini Ashrafi and Dr. A. Hosseini.\r\n•\tB.Sc. in Applied Physics, From: 1991, to: 1996, Faculty of Physics & Nuclear Science, Amirkabir Uni. of Technology, Tehran, Iran, Thesis: Design of shielding for Am-Be neutron sources for In Vivo neutron activation analysis, Supervisor: Dr. M. Hosseini Ashrafi.\r\n\r\nResearch Experiences:\r\n1.\tNanomaterials, Carbon Nanotubes, Graphene: Synthesis, Functionalization and Characterization,\r\n2.\tMWCNTs/Polymer Composites: Fabrication and Characterization, \r\n3.\tShape Memory Polymers, Biodegradable Polymers, ORC, Collagen,\r\n4.\tMaterials Analysis and Characterizations: TEM, SEM, XPS, FT-IR, Raman, DSC, DMA, TGA, XRD, GPC, Fluoroscopy, \r\n5.\tInteraction of Radiation with Mater, Nuclear Safety and Security, NDT(RT),\r\n6.\tRadiation Detectors, Calibration (SSDL),\r\n7.\tCompleted IAEA e-learning Courses:\r\nNuclear Security (15 Modules),\r\nNuclear Safety:\r\nTSA 2: Regulatory Protection in Occupational Exposure,\r\nTips & Tricks: Radiation Protection in Radiography,\r\nSafety and Quality in Radiotherapy,\r\nCourse on Sealed Radioactive Sources,\r\nCourse on Fundamentals of Environmental Remediation,\r\nCourse on Planning for Environmental Remediation,\r\nKnowledge Management Orientation Course,\r\nFood Irradiation - Technology, Applications and Good Practices,\r\nEmployment:\r\nFrom 2010 to now: Academic staff, Nuclear Science and Technology Research Institute, Kargar Shomali, Tehran, Iran, P.O. Box: 14395-836.\r\nFrom 1997 to 2006: Expert of Materials Analysis and Characterization. Research Center of Agriculture and Medicine. Rajaeeshahr, Karaj, Iran, P. O. Box: 31585-498.",institutionString:"Atomic Energy Organization of Iran",institution:{name:"Atomic Energy Organization of Iran",country:{name:"Iran"}}},{id:"248279",title:"Dr.",name:"Monika",middleName:"Elzbieta",surname:"Machoy",slug:"monika-machoy",fullName:"Monika Machoy",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/248279/images/system/248279.jpeg",biography:"Monika Elżbieta Machoy, MD, graduated with distinction from the Faculty of Medicine and Dentistry at the Pomeranian Medical University in 2009, defended her PhD thesis with summa cum laude in 2016 and is currently employed as a researcher at the Department of Orthodontics of the Pomeranian Medical University. She expanded her professional knowledge during a one-year scholarship program at the Ernst Moritz Arndt University in Greifswald, Germany and during a three-year internship at the Technical University in Dresden, Germany. She has been a speaker at numerous orthodontic conferences, among others, American Association of Orthodontics, European Orthodontic Symposium and numerous conferences of the Polish Orthodontic Society. She conducts research focusing on the effect of orthodontic treatment on dental and periodontal tissues and the causes of pain in orthodontic patients.",institutionString:"Pomeranian Medical University",institution:{name:"Pomeranian Medical University",country:{name:"Poland"}}},{id:"252743",title:"Prof.",name:"Aswini",middleName:"Kumar",surname:"Kar",slug:"aswini-kar",fullName:"Aswini Kar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/252743/images/10381_n.jpg",biography:"uploaded in cv",institutionString:null,institution:{name:"KIIT University",country:{name:"India"}}},{id:"204256",title:"Dr.",name:"Anil",middleName:"Kumar",surname:"Kumar Sahu",slug:"anil-kumar-sahu",fullName:"Anil Kumar Sahu",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/204256/images/14201_n.jpg",biography:"I have nearly 11 years of research and teaching experience. I have done my master degree from University Institute of Pharmacy, Pt. Ravi Shankar Shukla University, Raipur, Chhattisgarh India. I have published 16 review and research articles in international and national journals and published 4 chapters in IntechOpen, the world’s leading publisher of Open access books. I have presented many papers at national and international conferences. I have received research award from Indian Drug Manufacturers Association in year 2015. My research interest extends from novel lymphatic drug delivery systems, oral delivery system for herbal bioactive to formulation optimization.",institutionString:null,institution:{name:"Chhattisgarh Swami Vivekanand Technical University",country:{name:"India"}}},{id:"253468",title:"Dr.",name:"Mariusz",middleName:null,surname:"Marzec",slug:"mariusz-marzec",fullName:"Mariusz Marzec",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/253468/images/system/253468.png",biography:"An assistant professor at Department of Biomedical Computer Systems, at Institute of Computer Science, Silesian University in Katowice. Scientific interests: computer analysis and processing of images, biomedical images, databases and programming languages. He is an author and co-author of scientific publications covering analysis and processing of biomedical images and development of database systems.",institutionString:"University of Silesia",institution:{name:"University of Silesia",country:{name:"Poland"}}},{id:"212432",title:"Prof.",name:"Hadi",middleName:null,surname:"Mohammadi",slug:"hadi-mohammadi",fullName:"Hadi Mohammadi",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/212432/images/system/212432.jpeg",biography:"Dr. Hadi Mohammadi is a biomedical engineer with hands-on experience in the design and development of many engineering structures and medical devices through various projects that he has been involved in over the past twenty years. Dr. Mohammadi received his BSc. and MSc. degrees in Mechanical Engineering from Sharif University of Technology, Tehran, Iran, and his PhD. degree in Biomedical Engineering (biomaterials) from the University of Western Ontario. He was a postdoctoral trainee for almost four years at University of Calgary and Harvard Medical School. He is an industry innovator having created the technology to produce lifelike synthetic platforms that can be used for the simulation of almost all cardiovascular reconstructive surgeries. He’s been heavily involved in the design and development of cardiovascular devices and technology for the past 10 years. He is currently an Assistant Professor with the University of British Colombia, Canada.",institutionString:"University of British Columbia",institution:{name:"University of British Columbia",country:{name:"Canada"}}},{id:"254463",title:"Prof.",name:"Haisheng",middleName:null,surname:"Yang",slug:"haisheng-yang",fullName:"Haisheng Yang",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/254463/images/system/254463.jpeg",biography:"Haisheng Yang, Ph.D., Professor and Director of the Department of Biomedical Engineering, College of Life Science and Bioengineering, Beijing University of Technology. He received his Ph.D. degree in Mechanics/Biomechanics from Harbin Institute of Technology (jointly with University of California, Berkeley). Afterwards, he worked as a Postdoctoral Research Associate in the Purdue Musculoskeletal Biology and Mechanics Lab at the Department of Basic Medical Sciences, Purdue University, USA. He also conducted research in the Research Centre of Shriners Hospitals for Children-Canada at McGill University, Canada. Dr. Yang has over 10 years research experience in orthopaedic biomechanics and mechanobiology of bone adaptation and regeneration. He earned an award from Beijing Overseas Talents Aggregation program in 2017 and serves as Beijing Distinguished Professor.",institutionString:null,institution:{name:"Beijing University of Technology",country:{name:"China"}}},{id:"89721",title:"Dr.",name:"Mehmet",middleName:"Cuneyt",surname:"Ozmen",slug:"mehmet-ozmen",fullName:"Mehmet Ozmen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/89721/images/7289_n.jpg",biography:null,institutionString:null,institution:{name:"Gazi University",country:{name:"Turkey"}}},{id:"265335",title:"Mr.",name:"Stefan",middleName:"Radnev",surname:"Stefanov",slug:"stefan-stefanov",fullName:"Stefan Stefanov",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/265335/images/7562_n.jpg",biography:null,institutionString:null,institution:{name:"Medical University Plovdiv",country:{name:"Bulgaria"}}},{id:"242893",title:"Ph.D. Student",name:"Joaquim",middleName:null,surname:"De Moura",slug:"joaquim-de-moura",fullName:"Joaquim De Moura",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/242893/images/7133_n.jpg",biography:"Joaquim de Moura received his degree in Computer Engineering in 2014 from the University of A Coruña (Spain). In 2016, he received his M.Sc degree in Computer Engineering from the same university. He is currently pursuing his Ph.D degree in Computer Science in a collaborative project between ophthalmology centers in Galicia and the University of A Coruña. His research interests include computer vision, machine learning algorithms and analysis and medical imaging processing of various kinds.",institutionString:null,institution:{name:"University of A Coruña",country:{name:"Spain"}}},{id:"294334",title:"B.Sc.",name:"Marc",middleName:null,surname:"Bruggeman",slug:"marc-bruggeman",fullName:"Marc Bruggeman",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/294334/images/8242_n.jpg",biography:"Chemical engineer graduate, with a passion for material science and specific interest in polymers - their near infinite applications intrigue me. \n\nI plan to continue my scientific career in the field of polymeric biomaterials as I am fascinated by intelligent, bioactive and biomimetic materials for use in both consumer and medical applications.",institutionString:null,institution:null},{id:"255757",title:"Dr.",name:"Igor",middleName:"Victorovich",surname:"Lakhno",slug:"igor-lakhno",fullName:"Igor Lakhno",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/255757/images/system/255757.jpg",biography:"Igor Victorovich Lakhno was born in 1971 in Kharkiv (Ukraine). \nMD – 1994, Kharkiv National Medical Univesity.\nOb&Gyn; – 1997, master courses in Kharkiv Medical Academy of Postgraduate Education.\nPh.D. – 1999, Kharkiv National Medical Univesity.\nDSC – 2019, PL Shupik National Academy of Postgraduate Education \nProfessor – 2021, Department of Obstetrics and Gynecology of VN Karazin Kharkiv National University\nHead of Department – 2021, Department of Perinatology, Obstetrics and gynecology of Kharkiv Medical Academy of Postgraduate Education\nIgor Lakhno has been graduated from international training courses on reproductive medicine and family planning held at Debrecen University (Hungary) in 1997. Since 1998 Lakhno Igor has worked as an associate professor in the department of obstetrics and gynecology of VN Karazin National University and an associate professor of the perinatology, obstetrics, and gynecology department of Kharkiv Medical Academy of Postgraduate Education. Since June 2019 he’s been a professor in the department of obstetrics and gynecology of VN Karazin National University and a professor of the perinatology, obstetrics, and gynecology department. He’s affiliated with Kharkiv Medical Academy of Postgraduate Education as a Head of Department from November 2021. Igor Lakhno has participated in several international projects on fetal non-invasive electrocardiography (with Dr. J. A. Behar (Technion), Prof. D. Hoyer (Jena University), and José Alejandro Díaz Méndez (National Institute of Astrophysics, Optics, and Electronics, Mexico). He’s an author of about 200 printed works and there are 31 of them in Scopus or Web of Science databases. Igor Lakhno is a member of the Editorial Board of Reproductive Health of Woman, Emergency Medicine, and Technology Transfer Innovative Solutions in Medicine (Estonia). He is a medical Editor of “Z turbotoyu pro zhinku”. Igor Lakhno is a reviewer of the Journal of Obstetrics and Gynaecology (Taylor and Francis), British Journal of Obstetrics and Gynecology (Wiley), Informatics in Medicine Unlocked (Elsevier), The Journal of Obstetrics and Gynecology Research (Wiley), Endocrine, Metabolic & Immune Disorders-Drug Targets (Bentham Open), The Open Biomedical Engineering Journal (Bentham Open), etc. He’s defended a dissertation for a DSc degree “Pre-eclampsia: prediction, prevention, and treatment”. Three years ago Igor Lakhno has participated in a training course on innovative technologies in medical education at Lublin Medical University (Poland). Lakhno Igor has participated as a speaker in several international conferences and congresses (International Conference on Biological Oscillations April 10th-14th 2016, Lancaster, UK, The 9th conference of the European Study Group on Cardiovascular Oscillations). His main scientific interests: are obstetrics, women’s health, fetal medicine, and cardiovascular medicine. \nIgor Lakhno is a consultant at Kharkiv municipal perinatal center. He’s graduated from training courses on endoscopy in gynecology. He has 28 years of practical experience in the field.",institutionString:null,institution:null},{id:"244950",title:"Dr.",name:"Salvatore",middleName:null,surname:"Di Lauro",slug:"salvatore-di-lauro",fullName:"Salvatore Di Lauro",position:null,profilePictureURL:"https://intech-files.s3.amazonaws.com/0030O00002bSF1HQAW/ProfilePicture%202021-12-20%2014%3A54%3A14.482",biography:"Name:\n\tSALVATORE DI LAURO\nAddress:\n\tHospital Clínico Universitario Valladolid\nAvda Ramón y Cajal 3\n47005, Valladolid\nSpain\nPhone number: \nFax\nE-mail:\n\t+34 983420000 ext 292\n+34 983420084\nsadilauro@live.it\nDate and place of Birth:\nID Number\nMedical Licence \nLanguages\t09-05-1985. Villaricca (Italy)\n\nY1281863H\n474707061\nItalian (native language)\nSpanish (read, written, spoken)\nEnglish (read, written, spoken)\nPortuguese (read, spoken)\nFrench (read)\n\t\t\nCurrent position (title and company)\tDate (Year)\nVitreo-Retinal consultant in ophthalmology. Hospital Clinico Universitario Valladolid. Sacyl. National Health System.\nVitreo-Retinal consultant in ophthalmology. Instituto Oftalmologico Recoletas. Red Hospitalaria Recoletas. Private practise.\t2017-today\n\n2019-today\n\t\n\t\nEducation (High school, university and postgraduate training > 3 months)\tDate (Year)\nDegree in Medicine and Surgery. University of Neaples 'Federico II”\nResident in Opthalmology. Hospital Clinico Universitario Valladolid\nMaster in Vitreo-Retina. IOBA. University of Valladolid\nFellow of the European Board of Ophthalmology. Paris\nMaster in Research in Ophthalmology. University of Valladolid\t2003-2009\n2012-2016\n2016-2017\n2016\n2012-2013\n\t\nEmployments (company and positions)\tDate (Year)\nResident in Ophthalmology. Hospital Clinico Universitario Valladolid. Sacyl.\nFellow in Vitreo-Retina. IOBA. University of Valladolid\nVitreo-Retinal consultant in ophthalmology. Hospital Clinico Universitario Valladolid. Sacyl. National Health System.\nVitreo-Retinal consultant in ophthalmology. Instituto Oftalmologico Recoletas. Red Hospitalaria Recoletas. \n\t2012-2016\n2016-2017\n2017-today\n\n2019-Today\n\n\n\t\nClinical Research Experience (tasks and role)\tDate (Year)\nAssociated investigator\n\n' FIS PI20/00740: DESARROLLO DE UNA CALCULADORA DE RIESGO DE\nAPARICION DE RETINOPATIA DIABETICA BASADA EN TECNICAS DE IMAGEN MULTIMODAL EN PACIENTES DIABETICOS TIPO 1. Grant by: Ministerio de Ciencia e Innovacion \n\n' (BIO/VA23/14) Estudio clínico multicéntrico y prospectivo para validar dos\nbiomarcadores ubicados en los genes p53 y MDM2 en la predicción de los resultados funcionales de la cirugía del desprendimiento de retina regmatógeno. Grant by: Gerencia Regional de Salud de la Junta de Castilla y León.\n' Estudio multicéntrico, aleatorizado, con enmascaramiento doble, en 2 grupos\nparalelos y de 52 semanas de duración para comparar la eficacia, seguridad e inmunogenicidad de SOK583A1 respecto a Eylea® en pacientes con degeneración macular neovascular asociada a la edad' (CSOK583A12301; N.EUDRA: 2019-004838-41; FASE III). Grant by Hexal AG\n\n' Estudio de fase III, aleatorizado, doble ciego, con grupos paralelos, multicéntrico para comparar la eficacia y la seguridad de QL1205 frente a Lucentis® en pacientes con degeneración macular neovascular asociada a la edad. (EUDRACT: 2018-004486-13). Grant by Qilu Pharmaceutical Co\n\n' Estudio NEUTON: Ensayo clinico en fase IV para evaluar la eficacia de aflibercept en pacientes Naive con Edema MacUlar secundario a Oclusion de Vena CenTral de la Retina (OVCR) en regimen de tratamientO iNdividualizado Treat and Extend (TAE)”, (2014-000975-21). Grant by Fundacion Retinaplus\n\n' Evaluación de la seguridad y bioactividad de anillos de tensión capsular en conejo. Proyecto Procusens. Grant by AJL, S.A.\n\n'Estudio epidemiológico, prospectivo, multicéntrico y abierto\\npara valorar la frecuencia de la conjuntivitis adenovírica diagnosticada mediante el test AdenoPlus®\\nTest en pacientes enfermos de conjuntivitis aguda”\\n. National, multicenter study. Grant by: NICOX.\n\nEuropean multicentric trial: 'Evaluation of clinical outcomes following the use of Systane Hydration in patients with dry eye”. Study Phase 4. Grant by: Alcon Labs'\n\nVLPs Injection and Activation in a Rabbit Model of Uveal Melanoma. Grant by Aura Bioscience\n\nUpdating and characterization of a rabbit model of uveal melanoma. Grant by Aura Bioscience\n\nEnsayo clínico en fase IV para evaluar las variantes genéticas de la vía del VEGF como biomarcadores de eficacia del tratamiento con aflibercept en pacientes con degeneración macular asociada a la edad (DMAE) neovascular. Estudio BIOIMAGE. IMO-AFLI-2013-01\n\nEstudio In-Eye:Ensayo clínico en fase IV, abierto, aleatorizado, de 2 brazos,\nmulticçentrico y de 12 meses de duración, para evaluar la eficacia y seguridad de un régimen de PRN flexible individualizado de 'esperar y extender' versus un régimen PRN según criterios de estabilización mediante evaluaciones mensuales de inyecciones intravítreas de ranibizumab 0,5 mg en pacientes naive con neovascularización coriodea secunaria a la degeneración macular relacionada con la edad. CP: CRFB002AES03T\n\nTREND: Estudio Fase IIIb multicéntrico, randomizado, de 12 meses de\nseguimiento con evaluador de la agudeza visual enmascarado, para evaluar la eficacia y la seguridad de ranibizumab 0.5mg en un régimen de tratar y extender comparado con un régimen mensual, en pacientes con degeneración macular neovascular asociada a la edad. CP: CRFB002A2411 Código Eudra CT:\n2013-002626-23\n\n\n\nPublications\t\n\n2021\n\n\n\n\n2015\n\n\n\n\n2021\n\n\n\n\n\n2021\n\n\n\n\n2015\n\n\n\n\n2015\n\n\n2014\n\n\n\n\n2015-16\n\n\n\n2015\n\n\n2014\n\n\n2014\n\n\n\n\n2014\n\n\n\n\n\n\n\n2014\n\nJose Carlos Pastor; Jimena Rojas; Salvador Pastor-Idoate; Salvatore Di Lauro; Lucia Gonzalez-Buendia; Santiago Delgado-Tirado. Proliferative vitreoretinopathy: A new concept of disease pathogenesis and practical\nconsequences. Progress in Retinal and Eye Research. 51, pp. 125 - 155. 03/2016. DOI: 10.1016/j.preteyeres.2015.07.005\n\n\nLabrador-Velandia S; Alonso-Alonso ML; Di Lauro S; García-Gutierrez MT; Srivastava GK; Pastor JC; Fernandez-Bueno I. Mesenchymal stem cells provide paracrine neuroprotective resources that delay degeneration of co-cultured organotypic neuroretinal cultures.Experimental Eye Research. 185, 17/05/2019. DOI: 10.1016/j.exer.2019.05.011\n\nSalvatore Di Lauro; Maria Teresa Garcia Gutierrez; Ivan Fernandez Bueno. Quantification of pigment epithelium-derived factor (PEDF) in an ex vivo coculture of retinal pigment epithelium cells and neuroretina.\nJournal of Allbiosolution. 2019. ISSN 2605-3535\n\nSonia Labrador Velandia; Salvatore Di Lauro; Alonso-Alonso ML; Tabera Bartolomé S; Srivastava GK; Pastor JC; Fernandez-Bueno I. Biocompatibility of intravitreal injection of human mesenchymal stem cells in immunocompetent rabbits. Graefe's archive for clinical and experimental ophthalmology. 256 - 1, pp. 125 - 134. 01/2018. DOI: 10.1007/s00417-017-3842-3\n\n\nSalvatore Di Lauro, David Rodriguez-Crespo, Manuel J Gayoso, Maria T Garcia-Gutierrez, J Carlos Pastor, Girish K Srivastava, Ivan Fernandez-Bueno. A novel coculture model of porcine central neuroretina explants and retinal pigment epithelium cells. Molecular Vision. 2016 - 22, pp. 243 - 253. 01/2016.\n\nSalvatore Di Lauro. Classifications for Proliferative Vitreoretinopathy ({PVR}): An Analysis of Their Use in Publications over the Last 15 Years. Journal of Ophthalmology. 2016, pp. 1 - 6. 01/2016. DOI: 10.1155/2016/7807596\n\nSalvatore Di Lauro; Rosa Maria Coco; Rosa Maria Sanabria; Enrique Rodriguez de la Rua; Jose Carlos Pastor. Loss of Visual Acuity after Successful Surgery for Macula-On Rhegmatogenous Retinal Detachment in a Prospective Multicentre Study. Journal of Ophthalmology. 2015:821864, 2015. DOI: 10.1155/2015/821864\n\nIvan Fernandez-Bueno; Salvatore Di Lauro; Ivan Alvarez; Jose Carlos Lopez; Maria Teresa Garcia-Gutierrez; Itziar Fernandez; Eva Larra; Jose Carlos Pastor. Safety and Biocompatibility of a New High-Density Polyethylene-Based\nSpherical Integrated Porous Orbital Implant: An Experimental Study in Rabbits. Journal of Ophthalmology. 2015:904096, 2015. DOI: 10.1155/2015/904096\n\nPastor JC; Pastor-Idoate S; Rodríguez-Hernandez I; Rojas J; Fernandez I; Gonzalez-Buendia L; Di Lauro S; Gonzalez-Sarmiento R. Genetics of PVR and RD. Ophthalmologica. 232 - Suppl 1, pp. 28 - 29. 2014\n\nRodriguez-Crespo D; Di Lauro S; Singh AK; Garcia-Gutierrez MT; Garrosa M; Pastor JC; Fernandez-Bueno I; Srivastava GK. Triple-layered mixed co-culture model of RPE cells with neuroretina for evaluating the neuroprotective effects of adipose-MSCs. Cell Tissue Res. 358 - 3, pp. 705 - 716. 2014.\nDOI: 10.1007/s00441-014-1987-5\n\nCarlo De Werra; Salvatore Condurro; Salvatore Tramontano; Mario Perone; Ivana Donzelli; Salvatore Di Lauro; Massimo Di Giuseppe; Rosa Di Micco; Annalisa Pascariello; Antonio Pastore; Giorgio Diamantis; Giuseppe Galloro. Hydatid disease of the liver: thirty years of surgical experience.Chirurgia italiana. 59 - 5, pp. 611 - 636.\n(Italia): 2007. ISSN 0009-4773\n\nChapters in books\n\t\n' Salvador Pastor Idoate; Salvatore Di Lauro; Jose Carlos Pastor Jimeno. PVR: Pathogenesis, Histopathology and Classification. Proliferative Vitreoretinopathy with Small Gauge Vitrectomy. Springer, 2018. ISBN 978-3-319-78445-8\nDOI: 10.1007/978-3-319-78446-5_2. \n\n' Salvatore Di Lauro; Maria Isabel Lopez Galvez. Quistes vítreos en una mujer joven. Problemas diagnósticos en patología retinocoroidea. Sociedad Española de Retina-Vitreo. 2018.\n\n' Salvatore Di Lauro; Salvador Pastor Idoate; Jose Carlos Pastor Jimeno. iOCT in PVR management. OCT Applications in Opthalmology. pp. 1 - 8. INTECH, 2018. DOI: 10.5772/intechopen.78774.\n\n' Rosa Coco Martin; Salvatore Di Lauro; Salvador Pastor Idoate; Jose Carlos Pastor. amponadores, manipuladores y tinciones en la cirugía del traumatismo ocular.Trauma Ocular. Ponencia de la SEO 2018..\n\n' LOPEZ GALVEZ; DI LAURO; CRESPO. OCT angiografia y complicaciones retinianas de la diabetes. PONENCIA SEO 2021, CAPITULO 20. (España): 2021.\n\n' Múltiples desprendimientos neurosensoriales bilaterales en paciente joven. Enfermedades Degenerativas De Retina Y Coroides. SERV 04/2016. \n' González-Buendía L; Di Lauro S; Pastor-Idoate S; Pastor Jimeno JC. Vitreorretinopatía proliferante (VRP) e inflamación: LA INFLAMACIÓN in «INMUNOMODULADORES Y ANTIINFLAMATORIOS: MÁS ALLÁ DE LOS CORTICOIDES. 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