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Barely three months into the new year and we are happy to announce a monumental milestone reached - 150 million downloads.
\n\nThis 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.
\n\nWe 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.
\n\nThank you for making IntechOpen your place of learning, sharing, and discovery, and here’s to 150 million more!
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-partners-with-ehs-for-digital-advertising-representation-20210416",title:"IntechOpen Partners with EHS for Digital Advertising Representation"},{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"}]},book:{item:{type:"book",id:"4787",leadTitle:null,fullTitle:"Herbicides, Physiology of Action, and Safety",title:"Herbicides",subtitle:"Physiology of Action and Safety",reviewType:"peer-reviewed",abstract:"Herbicides are one of the most widely used groups of pesticides worldwide for controlling weedy species in agricultural and non-crop settings. 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Faecal Incontinence and Autoimmune Diseases",doi:null,correctionPDFUrl:"https://cdn.intechopen.com/pdfs/72604.pdf",downloadPdfUrl:"/chapter/pdf-download/72604",previewPdfUrl:"/chapter/pdf-preview/72604",totalDownloads:null,totalCrossrefCites:null,bibtexUrl:"/chapter/bibtex/72604",risUrl:"/chapter/ris/72604",chapter:{id:"69125",slug:"faecal-incontinence-and-autoimmune-diseases",signatures:"Batool Mutar Mahdi",dateSubmitted:"November 26th 2018",dateReviewed:"August 21st 2019",datePrePublished:"October 2nd 2019",datePublished:"April 29th 2020",book:{id:"7861",title:"Current Topics in Faecal Incontinence",subtitle:null,fullTitle:"Current Topics in Faecal Incontinence",slug:"current-topics-in-faecal-incontinence",publishedDate:"April 29th 2020",bookSignature:"John Camilleri-Brennan",coverURL:"https://cdn.intechopen.com/books/images_new/7861.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"169437",title:"Associate Prof.",name:"John",middleName:null,surname:"Camilleri-Brennan",slug:"john-camilleri-brennan",fullName:"John Camilleri-Brennan"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"77656",title:"Dr.",name:"Batool Mutar",middleName:null,surname:"Mahdi",fullName:"Batool Mutar Mahdi",slug:"batool-mutar-mahdi",email:"abas_susan@yahoo.com",position:null,institution:{name:"University of Baghdad",institutionURL:null,country:{name:"Iraq"}}}]}},chapter:{id:"69125",slug:"faecal-incontinence-and-autoimmune-diseases",signatures:"Batool Mutar Mahdi",dateSubmitted:"November 26th 2018",dateReviewed:"August 21st 2019",datePrePublished:"October 2nd 2019",datePublished:"April 29th 2020",book:{id:"7861",title:"Current Topics in Faecal Incontinence",subtitle:null,fullTitle:"Current Topics in Faecal Incontinence",slug:"current-topics-in-faecal-incontinence",publishedDate:"April 29th 2020",bookSignature:"John Camilleri-Brennan",coverURL:"https://cdn.intechopen.com/books/images_new/7861.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"169437",title:"Associate Prof.",name:"John",middleName:null,surname:"Camilleri-Brennan",slug:"john-camilleri-brennan",fullName:"John Camilleri-Brennan"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"77656",title:"Dr.",name:"Batool Mutar",middleName:null,surname:"Mahdi",fullName:"Batool Mutar Mahdi",slug:"batool-mutar-mahdi",email:"abas_susan@yahoo.com",position:null,institution:{name:"University of Baghdad",institutionURL:null,country:{name:"Iraq"}}}]},book:{id:"7861",title:"Current Topics in Faecal Incontinence",subtitle:null,fullTitle:"Current Topics in Faecal Incontinence",slug:"current-topics-in-faecal-incontinence",publishedDate:"April 29th 2020",bookSignature:"John Camilleri-Brennan",coverURL:"https://cdn.intechopen.com/books/images_new/7861.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"169437",title:"Associate Prof.",name:"John",middleName:null,surname:"Camilleri-Brennan",slug:"john-camilleri-brennan",fullName:"John Camilleri-Brennan"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},ofsBook:{item:{type:"book",id:"8535",leadTitle:null,title:"Public Diplomacy",subtitle:null,reviewType:"peer-reviewed",abstract:"
\r\n\tIn textbooks and manuals, diplomacy is often defined as "the science of foreign relations" and "the art of negotiation." This certainly makes a lot of sense. A balanced analysis of the global situation and the correct consideration of the balance of power in the international arena are essential for the development of truly scientific, deeply grounded recommendations in the field of foreign policy. It is necessary to carefully study historical trends, fully take into account the different directions and trends in international relations, to be able to seek and attract allies to desired side, to achieve the isolation of the most aggressive and hostile circles. One can really expect success only if diplomacy acts in principle and, at the same time, pragmatically and flexibly, avoids dogmatism and sectarianism, and is not afraid of compromises that ultimately benefit national interests. Hence, the importance of mastering a number of sciences: history of individual countries and international relations, international law, complex sciences related to the study of the world economy and the economies of individual countries, comparative political science and law, philosophy, psychology, and etc. In short, diplomacy should rely on the laws of social life and consider the findings of the relevant sciences.
\r\n\r\n\tThis book intends to provide the reader with a comprehensive understanding of the real essence of public diplomacy. Public diplomacy and related concepts such as ""strategic communication"" and ""national branding"" are a part of increasingly common public administration practices. It also represents an area of research with significant growth potential. The nation states have in various contexts recognized the need to communicate with foreign communities and to develop networks through various forms of interaction, including international communication, exchange programmes and cultural diplomacy. As a result, public diplomacy has become an effective tool of purposeful communication with the foreign public to promote short-term political goals, to develop long-term relations, and to address pressing issues of transnational politics. Nevertheless, there are big problems that lie behind the popularization of modern public diplomacy initiatives which will also be discussed in the book.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"ca82945156946b18f4e457ce91ac6643",bookSignature:"Dr. Galina V. Timofeeva and Ms. Alexandra Baranova",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8535.jpg",keywords:"Diplomatic Service, Cultural Diplomacy, Negotiation, Tools, Mechanisms, Actors, Official Diplomacy, Digital Diplomacy, Conflict Resolution, Intergovernmental Organizations, Cooperation",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 13th 2019",dateEndSecondStepPublish:"March 27th 2020",dateEndThirdStepPublish:"May 26th 2020",dateEndFourthStepPublish:"August 14th 2020",dateEndFifthStepPublish:"October 13th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"311522",title:"Dr.",name:"Galina",middleName:"V.",surname:"Timofeeva",slug:"galina-timofeeva",fullName:"Galina Timofeeva",profilePictureURL:"https://mts.intechopen.com/storage/users/311522/images/system/311522.jpg",biography:"Galina V. Timofeeva, PhD is a Professor at the Department of Economics and Public Diplomacy at the Institute of Public Service and Management of the Russian Presidential Academy of National Economy and Public Administration (RANEPA). Professor Timofeeva is an expert of the Higher Attestation Commission of the Ministry of Education and Science of the Russian Federation. She is also an expert and a scientific editor of the strategy of socio-economic development of the Republic of Abkhazia-2025, as well as the specialist at the Russian Foundation for Basic Research.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}}],coeditorOne:{id:"312195",title:"Ms.",name:"Alexandra",middleName:null,surname:"Baranova",slug:"alexandra-baranova",fullName:"Alexandra Baranova",profilePictureURL:"https://mts.intechopen.com/storage/users/no_image.jpg",biography:"Dr. Alexandra Baranova is a lecturer at the Russian Academy of National Economy and Public Administration. Her scientific interests include linguistic tools of public diplomacy, as well as the role of mass media in diplomatic processes.",institutionString:"Russian Presidential Academy of National Economy and Public Administration",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Russian Presidential Academy of National Economy and Public Administration",institutionURL:null,country:{name:"Russia"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"23",title:"Social Sciences",slug:"social-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247041",firstName:"Dolores",lastName:"Kuzelj",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247041/images/7108_n.jpg",email:"dolores@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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This mutation results from a single nucleotide change (GAT GTT) in the sixth codon of the first exon of the beta-globin gene, resulting in the substitution of glutamic acid to valine (HbS) [1]. When an individual inherits two sickle cell genes (one from each parent, Hb S/S), he or she is affected with sickle cell anemia. The Hb S/S mutation is the most common form of SCD, it accounts for 60–70% of SCD in the United States. Other forms result from a coinheritance of an HbS allele with another abnormal β-globin chain, HbC (Hb S/C) and from a β-thalassemia (Hb S/β+, Hb S/β0) being the most common among others. The mutation results in a beta chain of the hemoglobin molecule that is more hydrophobic compared to its normal counterpart (HbB) and is prone to polymerization during episodes of lower oxygen tension, hypothermia or many other stressors. A deoxygenated hemoglobin B (HbB) of patients with SCD will aggregate along its molecular axis leading to distortion of the cell membrane and giving it a sickle shape appearance. A hallmark of sickle cell disease is intermittent vaso-occlusive events (VOE) and chronic hemolytic anemia. VOE in acute and chronic pain as well as organ damage most notably to the bones, spleen, liver, brain, lungs, kidneys and joints [2].
\nSCD is a disease that is mostly present in persons of African, Mediterranean, Middle Eastern and Indian ancestry but has been found in individuals of any ethnic background. The prevalence of sickle cell trait, among African Americans in the United States, is 10%, or 3.5 million people, leading to the incidence of SCD among this ethnic group of approximately 1 in 365 live births. More than 100,000 individuals in the United States are estimated to suffer from SCD. In the United Kingdom, the prevalence is about 12,500 people. Globally, it is estimated that about 5–7% of the world’s population are carriers of the mutant hemoglobin gene [3, 4], most of which residing on the African continent. As a matter of fact, about 15 million Africans are affected by SCD, more than all other continents combined. And about 200–300,000 affected births per year occur on the African continent [4, 5], accounting for more than 75% of the SCD newborns worldwide. Globally, SCD is one the four most common autosomal recessive diseases along with cystic fibrosis, thalassemia and Tay-Sachs.
\nAlthough in some areas of the world, such as Western African countries, where new treatment modalities are not as widely accessible, SCD accounts for as many as 16% of deaths in children under 5 years old, the death rate has remarkably been reduced in the United States in recent times. In fact, many children did not live to adulthood about half a century ago. With the emergence of hydroxyurea, new born screening, newer and better antibiotics as well as the introduction of the pneumococcal vaccine, the lifespan for sickle cell individuals in the United States has increased substantially to 48 years old for female and 42 years old for male. As a matter of fact, the median survival age of patients with SCD living between 1910 and 1950 was below 20 years of age [6]. By 1980, 50% of children survived beyond 20 years of age; and by 2009, 85% of SCD affect patients did. In England, the trend for hospital admissions related to SCD has been on the rise; from 2001/2002 to 2009/2010, admissions with a diagnosis of SCD have risen by more than 50%.
\nThe management of SCD is complex and multidisciplinary. Supportive management includes regular follow-ups with the healthcare providers, adequate diet and sleep. Symptomatic management targets symptoms of the disease and include blood transfusions, pain management, antibiotics for infections among many other possible treatments. Preventive managements include vaccinations, avoidance of stressors that triggers crisis, hydroxyurea treatment, transfusion, etc. Abortive therapy is the attempt at preventing painful crisis from getting worse and leading to other complications. They include nitrous oxide and anti-adhesion factors. The ultimate goal is curative therapy, which can arise from stem cell transplantation, and gene therapy in the future. This chapter focuses solely on the pain management of patients with SCD and is divided into acute pain, chronic pain and neuropathic pain.
\nSickle cell related pain is classified into three categories: acute pain, chronic pain and neuropathic pain [7]. Acute pain is, by far, the most commonly encountered type of pain by healthcare providers and is the precursor of chronic and neuropathic pain. The pathophysiology of sickle cell pain is still not completely understood but is thought to be initiated by stress/deoxygenation leading to the polymerization of sickle Hb in the red blood cells (RBC) inside the micro and macro-vasculature. This causes the RBC to lose its deformability and adhere to together on the vascular endothelium that in turn gets activated. The latter participates in the recruitment of white blood cells (WBC), which further accentuates the existing vascular occlusion and facilitates tissue ischemia and damage. The activation of endothelial cells along with the tissue damage provokes the release of inflammatory mediators (including arachidonic acid, histamines, bradykinin, H+, K+, cytokines, serotonin, substance P, leukotrienes among others) [8, 9]. The combination of tissue damage and the resulting secondary inflammatory process generated is thought to be the cornerstone of the pain perceived during VOE. They convert chemical and mechanical energy into electrochemical impulse. The release of interleukin-1 activates the cyclo-oxygenase (COX) system that in turns converts arachidonic acid into prostaglandins E2 and I2. This inflammatory soup created interacts to permit and facilitate the transduction and transmission of the painful stimuli from the periphery the central nervous system via the nerve endings, spinal cord and the thalamus. Some of the mediators (Substance P and bradykinin) also cause vasodilatation and extravasation of fluid leading to focal edema and tenderness in the affected areas.
\nThe peripheral nociceptors involved in the painful cascade send their signals via fast acting A-delta and slow acting C fibers to the dorsal horn of the spinal cord by means of the dorsal root ganglion. From the dorsal horn of the spinal cord, the pain signals travel contralaterally through the spinothalamic tract to the thalamus that in turn has multiple interconnections with other systems such as the limbic system (mediator of memory and emotion), the reward system (mediator of pleasure and addiction) and the glia. The signals are then either facilitated or suppressed at the level of the spinal cord by different modulators. The N-methyl-D-aspartate (NMDA) receptor is probably the most important receptor involved in the facilitation of pain transmission. Other important modulators include endogenous endorphins, serotonin and norepinephrine. With knowledge of the implicated factors involved in sickle cell pain, better management can be made targeting the involved transmitters, receptors and modulators.
\nThe vaso-occlusive event (VOE) is the most common cause of morbidity in the patients with SCD [10]. VOE also account for the most common cause of hospital admissions and missed school days. Some data report that up to 95% of hospital admissions related to SCD are for acute painful crises [11, 12]. Multicellular aggregates leading to blood flow obstruction in small blood vessels, depriving downstream tissues of oxygen and nutrient constitute the painful pathway of VOE, which was described earlier in this chapter. Although VOE-related pain can affect any part of the body and often cause generalized pain, it more commonly presents as pain in the extremities in the pediatric population, as opposed to being more commonly seen as headache, chest pain, abdominal and back pain in older individuals [13]. The average duration of an acute pain crisis, based on hospital length of stay, is about 7 days [7]. Fever and leukocytosis typically accompany the patient’s presentation and the extent of WBC tends to correlate with the degree of pain [14, 15]. Also, the higher the level of Hb and hematocrit is, the more likely it is that a VOE will occur [9]. Even if leukocytosis associated with VOE does not necessarily signify an infectious process, careful evaluation should be undertaken, as these individuals are highly susceptible to pathogens. A careful and thorough history and physical examination should be undertaken. Inquiring about the onset, location, radiation, quality, relieving and aggravating factors associated with the current painful episode, any differences between the current episode and previous episodes, the presence of fever, transfusion history, medications, baseline hemoglobin level, and a thorough physical exam can assist in making a more definite diagnosis. Any atypical presentation should prompt further investigation (Table 1). The triggers of VOE can be physical, psychological, physiological and environmental among many. At any age group, a painful crisis typically begins with sudden onset of pain.
\n\n
| \n
Primary investigation upon initial presentation of a SCD patient in pain.
Management of SCD patient presenting to the ED with VOE.
Although most individuals with SCD presenting to the healthcare professional with VOE will exhibit different types complains as far as onset, location, quality and intensity of their pain, the painful crisis will typical last between 7 and 10 days and can be described as possessing four different phases: A prodromal phase, initial phase, established phase and resolving phase [16, 17, 18]. A prodromal phase lasts 1–2 days and consists of aches, numbness or paresthesia in the area that will subsequently become painful. Physical signs of the prodromal phase include loss of usual appearance of the eyes (loss of luster or yellowing of the eyes). Laboratory values are significant for a decrease in erythrocyte deformability and increase density of erythrocytes. The second phase, initial phase, also lasting 1–2 days, is characterized by an increase in pain level and laboratory findings such as decreased RBC deformability, increase in the number of dense cells, red cell distribution width (RDW), reticulocytosis, leukocytosis, and relative thrombocytopenia. The third phase, the established phase, is when the pain level is at its peak. The patient will show signs of frustration, depression, will tend to complain about hospital staff due to lack of appropriate treatment. Physical exam will show an elevated temperature, signs of inflammation, joint effusions. Laboratory signs will consist of elevated WBC, decreased Hb, and elevated reticulocyte count, elevated LDH, CPK and CRP. This phase is the longest for an average of about 4–5 days. The fourth and final phase, lasting 3 days on average, is the resolving phase; patients start showing signs of decreasing pain, RBC deformability increases, as well as fibrinogen, orosomucoid, ESR, platelets and plasma viscosity. The blood level of sickled RBC is decreased during the final phase. The increase in plasma viscosity leads to a hypercoagulable state that becomes a culprit for recurrence of another painful crisis. In fact, about 16% of hospital admissions because of VOE get readmitted with recurrence within 1 week of discharge [11, 19]. The reasons for readmissions include, but not limited to, withdrawal syndrome, premature discharge, inadequate pain management during hospital admission, development of tolerance to opioid medications, opioid-induced hyperalgesia (OIH). Analysis of children admitted to hospitals with VOE show that patients typically show a blunted response to pain relief after the fourth to sixth day of admission [20]. The reason for this phenomenon is unknown but could be related to OIH, tolerance or provider inexperience with prolonged VOE pain. This subset of patients is more likely to return to the hospital and get readmitted. Special attention should be paid to readmitted patient since these tend a have a higher morbidity and mortality rate. Also, care should be taken not to under treat patients in the resolving phase of the VOE; Even if the pain seems to subside during this phase, it is important to continue aggressive pain management, provide patients with appropriate discharge instructions to avoid overdose or withdrawal after discharge, arrange for appropriate follow-up.
\nThis table points out important factors to consider when doing a primary investigation of a SCD patient presenting to the ED in pain. It is important to perform a full assessment of the patient to rule out any serious adverse events that are commonly associated with SCD.
\nThe first time SCD was recognized as its own disease was in 1910 when a medical resident observed the sickle appearing cell under a microscope [21]. Since then, many more discoveries about the disease were made, and its treatment still remains a dynamic process with changes constantly occurring. The therapeutic research initially consisted of finding ways to prevent the blockage of small blood vessels by the sickles shape RBC [22]. It was not until the 1960s that pain was recognized as a major symptom in SCD. Among the first pharmacological approaches used to treat it figured papaverine and acetaminophen [23]. It was not until later that opioid medications were used for the treatment of SCD and now represents the cornerstone of treatment for acute painful crisis. Appropriate treatment of VOE crisis is crucial since the consequences associated with the latter are many. Those involve acute chest syndrome in about 50% of VOE-related hospitalization, acute multi-organ failure and sudden death [24, 25, 26]. Aborting the acute painful episode at the prodromal phase could potentially prevent or minimize tissue damage [16]. A wide range of treatment modalities exists for the treatment of acute sickle cell pain. Nonpharmacological approaches such as acupuncture, heat, ice, relaxation techniques and hypnosis but are not covered in detail in this chapter [9, 27, 28, 29, 30]. Pharmacological approaches for the treatment of VOE around the globe consist predominantly of opioid analgesic including full agonists, partial agonists, mixed agonists-antagonists, antagonists but also include opioid adjuvants as well as nonopioid analgesics such NSAIDs, acetaminophen and other adjuvants [9]. As previously mentioned, VOE is the most common presentation (up to 90%) of patients with SCD to the healthcare facilities (i.e., Emergency Department). The first step in management focuses on immediate pain control with fluids and analgesics as evidence exists demonstrating that rapid and efficient control of acute pain related to VOE reduces pain scores, length of hospital stay, improve patient satisfaction [28, 31], reduce hospitalization in patients with SCD and also a decrease in the development of chronic pain syndromes, which is commonly seen in the sickle cell population [9, 32].
\nHowever, managing the pain could be more difficult than anticipated by the healthcare provider, as the SCD patient’s pain management differs from that of the rest of the population. Indeed, the patient with sickle cell disease tends to be more tolerant to opioid medications then the rest of the population due to chronic administration, VOE pain can appear out of proportion for most providers and necessitates higher doses of narcotics which most emergency department providers are not accustom to administer. This underlines the reason why most patients with sickle cell disease report that their pain is undertreated in the emergency department and that the providers lack understanding and compassion [9, 33, 34, 35, 36, 37, 38]. Additionally, VOE-related pain more exaggerated than expected, every patient possesses his own unique sensation, perception and expression of pain.
\nIndicators of adequate VOE management consist, but not limited to, admission to the hospital (indicates poor pain control in the ED), readmission to the hospital (indicator that pain was not well controlled during hospital stay), length of stay (indicator of effective pain management during hospital stay), pain intensity felt during ED visit or hospitalization (different pain measurement assessment available), patient and parents satisfaction, increase or decrease in VOE/SCD-related complications (Table 2).
\n\n
| \n
Indicators of effective/ineffective VOE treatment.
The indicators of an effective treatment of SCD patients during their visit to the ED or admission to the hospital are shown here. Signs of ineffective treatment are admission from the ED to the hospital, readmission to the hospital after discharge, increased length of stay in the ED or the hospital, elevated pain assessment score, poor patient and/or parent satisfaction.
\nFacilities that have taken into account these indicators of effective VOE pain management have demonstrated benefice in rapid treatment of patients presenting to their healthcare facility with VOE with an individualized plan for each patient. An individualized plan results in decreased hospital admissions, readmissions, length of ED and hospitalization, substantial decrease in pain scores, increased patient and parent satisfaction. Although no single plan or approach is perfect for all patients, there are different algorithms that are available to the healthcare provider that serve as helpful guide for the patient presenting with VOE. Using an algorithm has shown to be simple, cost-effective and beneficial for the patient’s generalized well-being. Institutions that commonly encounter patients with VOE are encouraged to either follow an existing effective algorithm or create their own. Every patient presenting to the healthcare provider with VOE-related pain would require his or her own individualized treatment plan [39]. Our preferred algorithm is inspired by the American Pain Society and is detailed in the following paragraph.
\nThis figure outlines our guidelines for the recommendation of the treatment of VOE in the ED.
\nAlternatively, institution that do not typically encounter individuals with SCD and that do not have an algorithm in place for the management of a patient that presents to their healthcare facility for the first time should involve starting with the lowest dose for the shortest duration possible in order to control the symptoms if the pain is mild to moderate and the patient has not been opioid naïve [39]. If the pain is moderate to severe and the patient has previously attempted an opioid medication without relief, a higher dose of opioid is preferred. From that baseline, the physician should titrate the dose, and duration of the analgesic medications upwards until adequate pain relief is achieved. On the other hand, as discussed earlier, the patient who presents for a subsequent visit to the same healthcare facility should initially be restarted on the same analgesic regimen with which adequate pain relief was obtained in the previous visits for VOE crises.
\nWhenever initiating opioid analgesia, it is mandatory to monitor for respiratory and sedation status. Useful questionnaires such as the Richmond Agitation Sedation Scale (RASS), the visual analogue scale (VAS) exist for sedation and pain assessment respectively. Respiratory status is typically monitored by pulse oximetry and visual assessment although some institution advocate for continuous end-tidal carbon dioxide monitoring (EtCO2), especially when using high doses of opioids.
\nThe preferred and recommended primary pharmacological method to treat the VOE crises is the opioid analgesic route and the commonly used medications include codeine, morphine, hydromorphone, fentanyl, hydrocodone/acetaminophen, hydrocodone/ibuprofen, oxymorphone, oxycodone, methadone and diamorphine [9].
\nThe first opiate used for VOE in the ED was meperidine in the 1960s. At home, short-acting oxycodone with acetaminophen was the most often used home medication. Morphine sulfate then got FDA approval in the 1980s and became the opiate of choice for the management of VOE in the 1990s. Not only did morphine show improvement in pain management and decreased hospital admissions related to VOE, it also did not possess the feared seizure side effect related to the meperidine metabolites, Normeperidine. These metabolites reduce the seizure threshold and also accumulate in patient with renal insufficiency, a complication commonly seen in patients with SCD [40, 41, 42]. In today’s world though, as mentioned earlier, many different types of opioid are used effectively for the treatment of VOE-related pain but in the United States, intravenous hydromorphone is the drug most commonly used in the hospital setting and oral oxycodone as home prescription medications [43]. As a comparison, in the United Kingdom, intravenous morphine, diamorphine and oral oxycodone are the most commonly used pain medications for VOE pain.
\nOpioid agonists produce their effect by binding into μ receptors. The potency of a particular opioid is dependent on the binding affinity or strength with which that drug binds to its receptors and there is a great amount of variability of potency between different opiates. For example, hydromorphone is 5–7 as potent as morphine while sufentanyl is 500–1000 as potent as morphine. When an opiate binds to its receptors, it initiates a cascade of biochemical events that starts with activation of G-proteins, inhibition of adenylate cyclase activity and extrusion of K++ that result in hyperpolarisation of cell membranes, which delays or prevents the transmission of painful stimuli. Additionally, there exists a multitude of different receptors that each mediates the desired analgesic differently. Thus, the response to opioids depends not only on the type of opioid used, but also on the number and activity of the opioid receptors that a certain patient has. An opioid that binds a low number of receptors and has poor affinity, for example, is unlikely to produce effective analgesia in certain patients even if the dose is high. On the other hand, an opioid binding to an elevated number of receptors and with moderate or high binding affinity would provide effective analgesia even if used in small doses. This is part of the reason, among many others, why there is an immense variability to the pain response in patients with SCD. A dose considered an under treatment for a particular patient could overdose another patient.
\nUnfortunately, opioids are not without side effects. The long list of mild to moderate adverse effects includes pruritus, nausea, vomiting, constipation, urinary retention, seizures, hives and the notorious respiratory depression. As mentioned earlier, seizures are mostly associated with meperidine. Other opioids have also possessed a potential for albeit a lot smaller and thought to be derived from the neuroexcitation related to metabolite of the opiate. Opioid-induced pruritus is one of the most prevalent complications with the use of opioids and is typically well controlled by either hydroxyzine, diphenhydramine, low dose naloxone and, now recognized as the most effective treatment, nalbuphine. The more serious complications, some of which are very popular topic of debates in the world today include addiction, tolerance, withdrawal, physical dependence and pseudoaddiction. A condition feared by many providers in today’s world is addiction; a condition that is influenced by genetic, psychological and environmental factors that lead to compulsive use despite harm. Opiates are strong stimulants of the reward/pleasure system, increasing the level of dopamine in the system, which in turn enhances the desire to achieve the reward/pleasure. Addiction can ultimately lead to overdose and death. Tolerance, on the other hand, represents a state of adaptation in which exposure to the same amount of the drug results in a lower effect than previously obtained. Physical dependence also happens frequently and is the cause of the known withdrawal syndrome that manifests with abrupt cessation or an exaggerated reduction in the dose of opiate administered. Signs and symptoms of withdrawal include tremor, shakiness, anxiety, depression, lacrimation, rhinorrhea, fatigue, irritability, and diarrhea. Pseudoaddiction is very common in patients with SCD. It is a state, in which the patient appears to be seeking for excessive amount of medication, but is due to under-treatment of pain and resolves when the pain is treated properly. Opioid-induced hyperalgesia (OIH) results from chronic administration of opioid medications. A process that is not totally proven and well understood yet but is thought to result from a minor excitatory pathway that becomes magnified with chronic use of the opiates and, ultimately, becomes the dominant effect. The sites of pain from OIH are typically the same as the sites perceived during the VOE crisis, but the quality of the pain differs. It is more neuropathic in nature.
\nNonsteroidal anti-inflammatory drugs (NSAIDs) are the main adjuvant of opioid in today’s therapeutic guidelines of most healthcare facilities. Ketorolac tromethamine is the NSAID most commonly used for this purpose; it is commonly administered either intravenously or intramuscularly at a dose of 0.5 mg kg−1 for a maximum of 30 mg every 6 h for 5 days. NSAIDs partly inhibit the inflammatory cascade involved in VOE (see above). Although usually not sufficient to resolve a pain crisis as a sole treatment, it works synergistically with opioids. For moderate VOE pain, a single dose of 30 mg IV is typically sufficient. Opioids are limited by their propensity to cause gastritis and gastric bleeding. The drug should be used cautiously in patients with peptic ulcer disease or a history of gastrointestinal bleeding. NSAIDs can impair kidney function and accelerate the renal injury produced by sickle cell disease itself. For these reasons, many specialists avoid NSAIDs in patients with sickle cell disease.
\nKetamine is gaining a lot of popularity for the treatment of VOE refractory to opioids. A lot of institutions have integrated its use in their algorithm of VOE treatment and strong evidence exists regarding its efficacy as an adjuvant to opioids and NSAIDs. Ketamine is a noncompetitive antagonist at the
In addition to the acute crises, patients with SCD also suffer from chronic pain, which often times overlap with acute pain crises and create difficulty in designing a treatment plan. These individuals can find management of their pain very difficult and therefore change providers frequently, resulting in a higher degree of misdiagnosis and misperception of their pain. Identifying the presenting syndrome can help individualize a treatment plan and therefore understanding the signs and symptoms of chronic pain is crucial for aggressive and effective therapy.
\nChronic pain is generally defined as pain that is present for 3 or more months. As opposed to the acute pain, which is sharp and throbbing in nature with a sudden onset, chronic pain is often vague, deep, and achy there is present for a longer period. Approximately 5–10% of adult patients with sickle cell disease are affected with chronic pain [44]. However, a recent study from Pain in Sickle Cell Epidemiology Study reported the incidence of chronic pain in 29% of 292 adult patients [45]. These patients tend to be older and use more opioids [46]. The chronic pain is categorized into two types. The first type is objective and is due to visible signs such as leg ulcers and avascular necrosis which is associated with deep somatic pain. The second type is due to recurrent acute attacks of painful crises. Failure to treat these acute attacks can lead to chronic pain syndrome and resultant neuropathic pain. The exact pathophysiologic mechanism is not fully understood, however central component has been described in which the threshold for the perception of pain is lowered, resulting in pain from typically nonpainful stimuli (allodynia) and severe pain generated by mildly painful stimuli (hyperalgesia) (Figure 2).
\nDistribution of SCD patient with chronic pain.
This figure depicts the age distribution of SCD patient with chronic pain. As demonstrated by the figure, the larger proportion of SCD patients with chronic pain is between 20 and 29 years old.
\nAlthough the exact mechanism underlying the transition from acute to chronic pain is not fully understood, some contributing factors include chronic inflammation, organ damage, and opioid-induced hyperalgesia [47]. According to a study presented at the Annual Meeting of American Society of Hematology, patients with chronic pain (defined as >50% of days reported as painful crises collected over 6 months) tend to be older (41 vs. 32 years), use more opioids (11.45 mg/day vs. 2.92 mg/day), and have higher levels of mast cell activation [48].
\nOpioid-induced hyperalgesia is a state of sensitization caused by repetitive exposure to opioids resulting in paradoxical response to pain. Although there is no understanding or consensus on the biomolecular mechanism, it is believed to be secondary to neuroplastic changes in the central and peripheral nervous system [49]. Despite it being a controversial topic, patients with sickle cell disease with chronic pain do require increasingly higher dosage adjustments.
\nRecent research demonstrates clear evidence that chronic inflammation and mast cell activation plays a role in the chronic pain state of patients with sickle cell disease. Mast cells release the neuropeptide substance P, which promotes neurogenic inflammation and nociceptive activation [48]. Additionally, tryptase, a serine proteinase found within mast cells appears far more elevated in patients with chronic pain in sickle cell disease. This can help guide future therapy directed toward inhibition of mast cell activation, and implementation of medications such as Cromolyn. This can also help identify and diagnose patients with sickle crises who present to the emergency department and are sadly mistaken as drug seeking opportunists.
\nThe cornerstone to therapy involves recognition of the disease state and assessment of the pain intensity, which helps individualize therapy. Prevention of SCD pain is crucial by avoidance of precipitating factors (dehydration, infection, diuretics, altitude, acidosis, and hypoxia), as repetitive acute inflammation can result in chronic pain. The approach to pain management in patients with SCD with chronic pain is multidisciplinary, involving the use of pharmacologic analgesic drugs, nerve blocks, physical therapy, and cognitive behavioral therapy [46]. Discussion of hydroxyurea and other disease modifying therapies is appropriate. Close attention should be made to psychosocial issues including depression and social isolation [45].
\nMild chronic pain can be treated with acetaminophen or dihydrocodeine. In patients with liver failure, acetaminophen can be avoided and NSAIDS such as ibuprofen can be used, but should be used with caution in patients with borderline renal function or failure. In patients with moderate pain, consideration of slow release morphine with small amounts of rapid-release morphine for breakthrough pain is advised [46]. Alternatives to Morphine include hydromorphone, oxycodone, methadone, or transdermal fentanyl. Methadone in particular can be efficacious in patients with suspected opioid-induced hyperalgesia due to its N-methyl-D-aspartate (NMDA) antagonism and monoaminue uptake reuptake inhibition. In patients who cannot tolerate opioid side effects and have contraindications the prior listed opioid analgesics, tramadol, a selective Mu-receptor agonist and serotonin–norepinephrine reuptake inhibitor can be considered [44]. The goal of chronic pain management is to maximize the quality of life rather than short-term pain suppression [45]. Other adjuvants include partial opioid agonists such as buprenorphine, topical agents, corticosteroids, antihistamines, benzodiazepines, antidepressants, anticonvulsants, and phenothiazines.
\nIn patients with severe chronic pain, alternative procedures can be considered in addition to opioid therapy. For example, in a patient with deep somatic pain of avascular necrosis of the hip, an interventional nerve block could supply instant relief for 12 h, and potentially 72 h if the injectate is liposomal Bupivacaine [49, 50]. Physiotherapy can help strengthen muscle fibers and loosen stiff joints, preventing contractures and physical disability. Psychological support with cognitive behavioral therapy can help the patient cope with pain or deal with the mental agony and psychosocial stressors associated with sickle cell disease [46]. Adapting to cognitive skills can also help alter the perception of pain as negative thinking has been linked to higher pain scores. Massage therapy, relaxation techniques, and even self-prayer have been reported in published studies to help with chronic pain [51]. The American Pain Society strongly recommends psychological, behavioral and physical modalities as necessary complements to pharmacologic therapy, as a significant effect on pain scores and activities of daily living have been reported [52]. Orthopedic devices for back or leg support can be deployed to reduce chronic pain in the hips or back. Orthopedic surgery, such as total hip replacement should be deferred until the pain is no longer tolerable [46].
\nLastly, it important to note that patients with SCD are not immune to non-hemoglobinopathic pain. Excluding other disease processes is essential and misdiagnosis can be life threatening. Conditions that can mimic the chronic pain state include but are not limited to ischemic colitis, pancreatitis, bone marrow infarction, hepatobiliary disorders, and vertebral body necrosis [53].
\nIn addition to acute and chronic pain, a neuropathic component of pain plays a large and undiagnosed constituent of chronic disease. Data suggest that the development of neuropathic pain is responsible for the transition from acute to chronic pain with aging [54]. The general understanding is that multiple components of central sensitization and peripheral nerve injury are responsible. Types of neuropathic pain include peripheral neuropathic (caused by vaso-occlusive crises and neuropathies) and central neuropathic (caused by CNS damage, ictus, and central sensitization). Peripheral nerve injury and prostaglandin release can sensitize peripheral nerve endings and facilitate the transmission of pain along the A-delta and C fibers to the cerebral cortex [44]. The exact mechanism, however, is poorly understood, which hinders our progression toward achieving novel therapies.
\nNeuropathic pain from SCD occurs more commonly in older adults and females, which is hypothesized to be secondary to abnormalities in pain signaling pathways. These patients have extreme sensitivity to tactile touch (allodynia), increased pain from a normally painful stimulus (hyperalgesia) and extreme sensitivity to temperature [45]. Some studies demonstrate the prevalence to be approximately 20% of the chronic pain population. In a 2013 article published in Pediatric Blood and Cancer, 37% of patients with SCD were identified to have neuropathic pain and only 5% were reported to be taking a neuropathic pain drug (gabapentin), which highlights the lack of diagnosis and treatment [55]. Thus, appropriate screening tools such as the pain DETECT questionnaire could help identify patients with neuropathic pain and help initiate treatment.
\nAlthough no single treatment therapy exists, a multimodal pharmacologic approach can be instituted in patients diagnosed with neuropathic pain. Treatment may include tricyclic antidepressants (TCA, SSRI, SNRIs, MAOIs) or anticonvulsants (pregabalin, gabapentin), although there is no data supporting its use in patients with SCD [56]. With a better safety profile and less side effects than opioids, tramadol (a typical analgesic with weak opioid receptor agonism and SNRI activity) can act centrally and be helpful in treating neuropathic pain, but should be used with caution in patients with renal failure [57, 58].
\nUntil SCD can be fully cured (possibly with gene therapy), new and improved treatment modalities are necessary. The information currently available about SCD is that rapid and aggressive therapy at the first sign of a VOE help reduce the length of the event and even abort it. Currently, patients with VOE receive treatment 2–3 days after the onset of the prodromal signs [16]. Measurement should be made in the future to offer patients with SCD methods of treatment available at home such as opioids (IV or IM), supplemental oxygen, and rapid hydration methods. Anti-inflammatory agents and oral opioids represent the current home treatment modalities. Vasodilators also represent a fundamental therapeutic weapon for VOE, especially when used early. Administration of nitric oxide (NO) in the emergency department has shown to abort the crisis in some patients; however, no benefice was found when NO was used during the hospital stay [59, 60, 61]. Perhaps NO could be offer as a home medication and its use would be even earlier than it would be in the ED. Recently, reports have emerged of small doses of opioid antagonist in combination with an agonist enhanced the analgesic effect and delayed the development of tolerance [62]. Recent trials targeting the inhibition of the capsaicin receptor transient receptor potential vanillin 1 (TRPV1) showed promising results in relieving pain in patients with SCD [63].
\nAlthough many complications stem from SCD, leading to a significantly reduced lifespan, pain remains the most cardinal sign of the disease and is still inappropriately treated. The main explanations for the inadequate treatment are the providers’ lack of knowledge about the disease and its narcotic requirement, lack of institutional treatment protocol in place and lack of patient education. The most important factors about the treatment, to our knowledge, are rapid and aggressive treatment as soon as signs of VOE happen, adequate rehydration and oxygenation. The treatment modalities have evolved enormously since the discovery of the disease and hopes for future treatment are bright.
\nTo the entire staff of Advocate Illinois Masonic Medical Center, Dr. Arjang Khorasani, Dr. Kenneth Candido and Dr. Nick Knezevic, thank you for your continuous support through-out our work.
\nIn statistical physics only a few problems can be solved exactly. For complex problems, numerical methods can give exact results for problems that could only be solved in an approximate way. Numerical simulation can be a way to test the theory. The numerical results can be compared to the experimental results. The numerical simulation is placed between the fundamental and the experimental treatment; it has a quasi-experimental character (numerical experience). For problems of statistical physics, the most widely used simulation methods are the Monte Carlo method and the molecular dynamics method.
The first Monte Carlo simulation (MCS) was proposed by Metropolis et al. in 1953 [1]. The second Monte Carlo simulation was proposed by Wood and Parker in 1957 [2]. The obtained results were in good agreement with the experimental results of Bridgman [3] and those of Michels et al. [4]. In this method we attribute a series of initial positions chosen randomly to a system of N particles interacting through a defined potential. A sequence of particle configurations is generated by giving successive displacements to particles; we only retain configurations to ensure that the probability density is that of the chosen.
Molecular dynamics simulation (MDS) has been first introduced to simulate the behavior of fluids and solids at the molecular or atomic level. MDS was used for the first time by Alder and Wainwright in the late 1950s [5, 6] to study the interactions of hard spheres. The principle is the resolution of equations of motion for a hard sphere system in a simulation cell. The basic algorithm is Verlet’s algorithm [7].
In this chapter, we will present techniques of numerical simulations using the Monte Carlo method. We will present an application on the gas phase during plasma-enhanced chemical vapor deposition (PECVD) of thin films. The application concerns collisions between particles. Particles are in Brownian motion. Collisions, elastic or inelastic, are considered to be binary. Non-elastic collisions result in effective chemical reactions.
In Section 2, we cite some MCS and MDS works on PECVD processes. Section 3 presents general rules on numerical simulation methods. Section 4 presents how to simulate a physical problem using MCS? We present the Metropolis algorithm as a scheme to trait random configurations and different modules related to elaborate an MCS code. In Section 5, we apply the MCS on SiH4/H2 gas mixture during a PECVD process. Finally the conclusion summarizes the contents of the chapter.
The PECVD is the most widely used technique to produce hydrogenated amorphous silicon thin films (a-Si:H) for solar cells and for film transistors and electronic devices [8, 9]. Reactions during plasma deposition are complex and are not understood completely.
Gorbachev et al. [10, 11, 12] have developed a model that is based on chemical reactions and different processes in a PECVD reactor. The model takes into account the formation of SinHm oligomers (n ≤ 5). It presents a simulation of the growth of the films. Gorbachev et al. found that Si2H5 and Si3H7 strongly influence the growth of the film [11].
Valipa et al. [13] calculated the β reactivity of the SiH3 radical on a surface of a silicon lattice plane during the growth of a-Si:H using MDS. The mechanisms of physical and chemical interactions of low temperature plasmas with surfaces can be explored using MDS [14].
For a CH4/H2 mixture, Farouk et al. used the Monte Carlo method (PIC/MC); they calculated the ionization rate of the plasma and the deposition rate of the thin layer [15]. Rodgers et al. [16] have developed three-dimensional Monte Carlo simulations of diamond (100) surface CVD. Other works on MCS are in [17, 18, 19].
In our previous works [20, 21, 22, 23, 24], we were interested in the study of the gas phase and the interaction of plasmas with the surface, for SiH4/H2 and CH4/H2 gas mixtures during PECVD processes. The used numerical simulation techniques were MCS and MDS. To complete the studies, we used the fluid model [25].
The starting point of numerical simulation is a physical phenomenon; its purpose is to obtain useful physical results. Between these two points, several steps can be identified. These steps are general and they are applicable for MCS. The steps can be summarized as follows:
The physical phenomenon must be defined by the description of the dominant domain of physics. The main assumptions and simplifying approximations are necessary to understand the physical phenomenon and the design of the first model.
Mathematical model requires a mathematical formulation of the problem. It may be a problem of elements or discrete object or a problem of a continuous medium; it may be a spatiotemporal problem or frequency problem and may be a deterministic or probabilistic problem.
It would be interesting to know the mathematical equations that govern the phenomenon:
The forces between particles and elements
The potential interaction
The determination of a time scale
The determination of a length scale
Definition of constant magnitudes of motion and equilibrium magnitudes
Continuity equations, balance equations, transfer equations, etc.
The MCS technique has been chosen for this work; knowing its basic algorithm is necessary for elaborating the simulation. This step requires some actions:
Validation of the model on simple cases
Simulation calculation on complex phenomena
The MCS is based on a probabilistic process with a random choice of configurations and samples of the situation of the physical system. The two pedagogical examples most cited in the literature are the integration of a single variable function and Ising’s model of spin. In the following subsection, we define the integration of a single variable function. We introduce the Ising model at the end of Section 4.2.2.
Calculation of the definite integral for a function f(x) of a single variable x on domain {a, b} has been proposed (Figure 1):
The integral of a function f(x).
Let:
Let xi and yi be real random numbers (i = 1, 2,…, N), and let H be a real number greater than the f(x) for x belonging to the domain {a, b} (or x ∈ {a, b}).
Let r1 and r2 be two random numbers belonging to the domain {0, 1} according to a uniform distribution law. Generators (e.g., Ran, RANDOM, RANDUM, or other IMSL mathematical libraries) of random numbers can be used:
where xi and yi are random numbers (xi ∈ {a, b} and yi ∈ {0, H}).
The Monte Carlo (MC) method is based on a probabilistic process. Let N be the total number of cases chosen (possible cases). It is necessary to count the number of favorable cases (or the number of points below the curve y = f(x)); let yi ≤ f(xi)). The number of favorable cases is Nfav. When N➔∞, the value
An example [26] is the calculation of the value π by calculating the integral
We take a = 0.0, b = 1.0, and H = 1.0.
For different values of N, we show that the numerical solution tends to π = 4
Although this integral is simple, it shows the strength and simplicity of the method. The technique can be generalized for the integration of multivariate functions.
We note that integration by the MC method is based on:
The choice of
Each configuration chosen is either
For statistical physics problems, the probabilistic choice of configurations is not always deterministic; the favorable and unfavorable cases are not exclusive. According to the Metropolis algorithm [26, 27], the steps of the simulation are:
Choice of a simulation cell of adequate shape to the studied phenomena. The size of the simulation cell is related to a scale of length characteristic of the forces and interaction potential of the studied phenomenon. This cell may contain Npc particles (and/or elements).
Choice of an initial configuration that responds to some physical and thermodynamic properties. The total or internal energy of the system is Ei.
Infinitesimal random displacement of a particle (or element of the system) and calculation of the new internal energy of the system Ef. This displacement is related to the physical magnitudes: time scale and length scale.
If
If
If
Figure 2 shows how to choose between the selected configurations. Let
Configuration choice according to Metropolis scheme.
Numerical simulation using the MC method is a very important tool for the study of static properties. The basic algorithm is based on probability notions. Understanding of the distribution function and/or interaction potentials is the heart of the calculation.
In equilibrium statistical physics, the system has a certain probability that can be in any states. The probability of being in a state
where T is the absolute temperature and kB is called Boltzmann’s constant. It is conventional to denote the quantity (kBT)−1 by the symbol β. The normalizing factor Z, or partition function, is given by:
The average of a quantity Q fora system in equilibrium is:
The internal energy U, is given by:
which can be written in terms of a derivative of the partition function:
From thermodynamics we have expressions for the specific heat C, the entropy S, and the Helmholtz free energy F:
or
and
and
We can calculate other parameters affecting the system.
The Monte Carlo method is an excellent technique for estimating probabilities, and we can take advantage of this property in evaluating the results. The simplest and most popular model of a system of interacting variables in statistical physics is the Ising model. It consists of spins
The Ising model has been studied in one and two dimensions to obtain results of thermal properties, phase transition, and magnetic properties [26, 27, 28]. For chosen values of J and/or B, different steps may be taken for the calculations (simulation cell, initialization, configurations, boundary conditions, calculation algorithms). For any configuration, each spin takes the two possible directions. The detail of the calculation procedure is not the purpose of this chapter.
We give a system of N particles (atoms, molecules, ions or particles) placed in a cell of fixed volume, generally of cubic form. The initial positions may, depending on the case, be distributed randomly according to a certain law (uniform or otherwise) or have a given symmetry. In a fluid, a gas, or a plasma, the particles may have random positions in general; in a solid or surface, with a crystal structure, the particles take ordered positions. The choice of random initial positions allows great freedom on the choice of the number of particles in the cell.
At the first step, the particles are given velocities that are generally selected to have a zero total momentum. If the system is in thermodynamic equilibrium, the initial velocities will be randomly chosen according to a Maxwell-Boltzmann law. In the general case, the velocity distribution is according to the problem dealt with. All other phase properties can be initialized to the particles; the main thing is the conservation of the total quantities of the system.
The particles interact with each other according to chosen interaction potentials. Since the interaction potentials are specific for each “numerical experiment,” the main part of the work consists in calculating the interaction energies for each proposed configuration.
The choice of interaction potentials is directly related to the mathematical formulation of the problem according to the state of the medium: fluid, gas, plasma, or solid. It can be Lennard-Jones potential, Coulomb potential, Debye potential, Morse potential, Stillinger-Weber potential, Born-Mayer potential, Moliere potential, or others.
In general, two main boundary conditions are used: periodic boundary conditions (PBC) and minimum image convention (MIC) [29].
To minimize the surface effect, periodic boundary conditions (PBC) [30] are invariably imposed. The simulation cell is reproduced throughout the space to form an infinite mesh. We can simulate the properties of an infinite system. The particles that we follow are in the central cell; if a particle crosses a wall with a certain velocity, its image returns with the same velocity by the opposite wall. Under these conditions, the number of particles in the central cell, and consequently the density, is constant. These conditions also allow the conservation of the energy and the momentum of the system and do not introduce periodic effects (because of the interaction between particles).
According to the hypotheses and according to the geometry of the problem, other boundary conditions are proposed [26]. For example, in order to model thin films, the simulation cells are longitudinal and parallel to the film; one uses PBC in the directions parallel to the film. In the direction normal to the film, free edge boundary conditions can be used. In such cases, it may be appropriate to also include surface fields and surface interactions. In this way, one can study phenomena such as wetting, interface localization-delocalization transitions, surface-induced ordering and disordering, etc.
The core of the program includes calculating the potential energies of particle configuration and particle collisions. The interactions and collisions between particles can be elastic or inelastic; they can be binary or collective. For computation, the interaction energy of a particle with its neighbors is carried out by refocusing a base cell on the particle. This particle only interacts with particles in this region. This is called the “minimal image convention” (MIC) [1].
Generally, a RANDOM generator of real random numbers ri belonging to the domain {0, 1} (or ri ∈ {0, 1} is available. This distribution law is uniform.
To have a real random number xi belonging to the domain {a, b} (or
To have a real random number xi belonging to the domain {a, b} (or xi ∈ {a,b}) according to a formula (or law) of nonuniform distribution f(x), a histogram technique is used. Let Nm be the number of intervals. If the mesh is regular (Figure 3):
Random number selection according to f (x) distribution.
We define:
We define the sequence:
and the sequence:
Hence each real random number ri belongs to the domain {0, 1} (where ri ∈ {0, 1}) (according to the uniform law); this number belongs to the domain {rxj-1, rxj}. It corresponds to a random value xran of the domain {xj-1, xj}; this number satisfies the formula (or the law) of nonuniform distribution f(x).
This technique can be generalized for a nonuniform distribution law f(x) with an irregular mesh Δxi, or with tabular data f(xi) with
The technique can be generalized, too, for a discrete distribution law f(i) with
In the literature, the reader can find simple algorithms for the choice of random numbers of some simple functions (Gaussian, etc.).
It is necessary to find some parameters allowing the control of the smooth course of the evolution of the system. We must look for the constants of movement. For example for an isolated system, we have the conservation of the total energy and the quantity of matter.
By using the numerical simulation, it is possible to calculate many spatiotemporal quantities F(r,t). These quantities can be positions, speeds, kinetic moments, particle energies, concentrations, transport coefficients, etc. It would then be possible to calculate all other quantities related to F(r,t).
For the calculation of the averages, one can note the quantities on the space, on the time or on both. The histogram methods can be used. Static or dynamic distribution functions and spatial or temporal correlation functions can be calculated. It should be noted that the SMC is much more adequate for static properties because of the probabilistic choice of configurations.
Any calculated function or parameter F(r,t) can be used for another application in another calculation program.
In the MCS model discussed extensively in this chapter, it’s more about collisions between particles. It’s
Other MCS models, named
For statistical physics problem solving (such as thin film deposition problems), MCS models use experimental, numerical, or theoretical data from other methods and models. Models can be improved to
Schematic of a hybrid model of three modules used to study gas mixtures in the PECVD [
To solve statistical physics problems with evolutions as a function of time,
Other CVD and PECVD works on MCS are presented in Ref.s [15, 34, 35, 36, 37, 38]. They show how MCS methods can study properties of gas mixtures and properties of the growth of thin films.
In this section, we present an example of PP-MCS of collisions and reactions in gas phase of SiH4/H2 mixture used in PECVD process. Some paragraphs have been treated in previous works [21, 24].
We use a MCS to study collisions and chemical reactions in gas phase of SiH4/H2 mixture used in the PECVD process. In this phase, important reactions have been identified that contribute to the production and the consumption of hydrogen (H), silylene (SiH2), and silyl (SiH3). The hydrogen consumption reactions SiH4 + H → SiH3 + H2 and SiH3 + H → SiH2 + H2 are found to play a central role in deciding the distribution of hydrogen [39].The plasma chemistry indicates that H atoms and SiH3 radicals play an important role in the a-Si:H deposition process [40]. Experimentally, it is generally accepted that SiH3 radicals dominate a-Si:H and μc-Si film growth from SiH4 plasmas in the PECVD; it is the key precursor of a-Si:H deposition [41]. The proposed MCS allowed to get the ratio SiH2/SiH3 and mean value of densities of species. It provides information on SiH4 dissociation and on the production of SiH3, H, SiH2, and Si2H6 and other important parameters.
The plasma in the PECVD reactor is weakly ionized. For our study, the mixture gas contains 22% of SiH4 and 78% of H2; the pressure is 100 mtorr, the temperature of the gas ranges from 373 to 723 K, the electron temperature is about 2.5 eV, and the electron density is 3. 108 cm−3. The process is considered to be stationary. We take into account electrons and eight neutral species (SiH4, SiH3, SiH2, H, H2, Si2H6, Si2H5, SiH).
Symbol | Reactions | Kreac (cm3/s) |
---|---|---|
R1 | SiH4 + e→SiH3 + H+e | k1 = 3 × 10−11 [42] |
R2 | SiH4 + e→SiH2 + 2H + e | K2 = 1.5 × 10−10 [42] |
R3 | SiH4 + e→SiH + H + H2 + e | K3 = 9.34 × 10−12 [42] |
R4 | SiH4 + e→SiH2 + H2 + e | K4 = 7.19 × 10−12 [42] |
R5 | H2 + e→2H + e | K5 = 4.49 × 10−12 [42] |
R6 | Si2H6 + e→SiH3 + SiH2 + H + e | K6 = 3.72 × 10−10 [42] |
R7 | Si2H6 + e→SiH4 + SiH2 +e | K7 = 1.1 × 1010× (1.(1./(1. + (0.63 × P)))) [43] |
R8 | SiH4 + H→SiH3 + H2 | K8 = 2.8 × 10−11 × exp.(−1250/T) [44] |
R9 | SiH4 + SiH2→Si2H6 | K9 = 1.1 × 1010 × (1.−(1./(1. + (0.63 × P)))) [43] |
R10 | SiH3 + SiH3→SiH4 + SiH2 | K10 = 0.45 × 1.5 × 10−10 [44] |
R11 | SiH4 + Si2H5→SiH3 + Si2H6 | K11 = 5 × 10−13 [42] |
R12 | SiH3 + H→SiH2 + H2 | K12 = 2 × 10−11 [44] |
R13 | SiH3 + Si2H6→SiH4 + Si2H5 | K13 = 4 × 10−10 × exp. (−2500/T) [44] |
R14 | SiH2 + H→SiH + H2 | k14 = 2 × 10−11 [44] |
R15 | Si2H6 + H→Si2H5 + H2 | K15 = 0.66 × 2.4 × 10−10 × exp. (−1250/T) [43] |
R16 | Si2H6 + H→SiH4 + SiH3 | K16 = 0.34 × 2.4 × 10−10 × exp. (−1250/T) [44] |
R17 | SiH + H2→SiH3 | K17 = 2 × 10−12 [43] |
R18 | SiH2 + SiH3→Si2H5 | K18 = 3.77 × 10−13 [43] |
R19 | SiH2 + H2→SiH4 | K19 = 3 × 10−12 × (1. + (1./1. + (0.03 × P))) [43] |
R20 | 2SiH3→Si2H6 | K20 = 0.1 × 1.5 × 10−10 [43] |
R21 | SiH4 + SiH→Si2H5 | K21 = (1.−(1./(1. + (0.33 × P)))) × (6.9 × 10−10) [43] |
List of gas phase reactions and corresponding rate constants [24].
Let
And chemical reaction for the production of A is as:
Rate production and consumption for any species A are taken as:
The MCS is based on binary collisions at the microscopic level. Elastic collisions are between all particles, and inelastic collisions (or effective collisions) are those that result in a chemical reaction. A chemical reaction needs a collision involving at least two particles (atoms, ions, electrons, or molecules). According to kinetic theory, gases consist of particles in random motion. These particles are
Form of the simulation cell.
Let ni be the density of neutral spice
The chosen particle takes randomly three components of space in cell
Let ni and nj be the densities of species
According to the kinetic theory of gases, we have for an incident particle
where <sij> is the cross section of the particle
The mean free path
The time between two collisions τij is then:
For chemical effective reactions (inelastic collisions) between two reactive species
General rules of collision theory are applied:
The new velocities of the colliding particles are calculated using conservation of energy and momentum for elastic collisions.
Conservation of total energy as isolated system.
Movement of the center of mass and relative motion around the center of mass.
The reader can refer to some fundamental physics books that deal with general notions of collisions and corresponding parameters [45, 46, 47, 48].
The plasma in the PECVD reactor is weakly ionized. At low temperature, particles interact occasionally with each other and move under the effect of thermal agitation. In reality, only a small fraction of collisions are effective (result in a chemical reaction) [21].
In our MCS, after traveling a random walk given by a Gaussian distribution, the first chosen particle collides with a second particle (molecule, atom, radical, or electron). The last particle
where
The activation energy is given by:
where the pre-exponential factor is assumed to be the collision frequency factor and Kreac is the rate constant of the gas phase reaction.
The two colliding particles (e.g., the electron and SiH4 molecule) can interact by several reactions (R1, R2, R3, and R4 in Table 1); we choose randomly one of gas phase reactions occurring according to a,
where
All chemical systems go naturally toward states of minimum Gibbs free energy [21, 24]. A chemical reaction tends to occur in the direction of lower Gibbs free energy. To determine the direction of the reaction that is taking place, we use the old and new values of Kreac and the equilibrium constant with reactants and product concentrations. Each set of binary collisions can be related or converted into time. As cited in section (a), Table 1 gives gas phase reactions and corresponding rate constants used in this MCS.
To continue the simulation, after the elastic collision, particle
From Metropolis algorithm, the scheme of this MCS is as follows:
Choices of particle of spice
Choices of random collision with a spice j.
Study of collision type (elastic, inelastic). If the collision is elastic the particle i move with a new velocity and mean free path, and we return to step (b). If the collision is inelastic particles i and j give new particles i’ and j’, according to Metropolis scheme, and we return to step (a) or (b). Periodic boundary conditions are used to keep particles in the elementary cell.
At each step, we can note the different statistics.
Once the species are selected for the simulation model, an estimate of species densities should be made. Following the model of interaction and collisions between particles (binary, collective, etc.), a first choice of the minimum number Ni of particles of each species is made. A first estimate of the sizes (Lx, Ly, Lz) of the elementary cell is made.
The study of the types of interaction potentials and the calculation of the approximate values of the force ranges, the kinetic energies, the internal energies, and the energies of activation make it possible to correct the minimal numbers Ni of particles and the sizes (Lx, Ly, Lz) of the elementary cell.
Let kp be the number of a species, kp = 1,…, 9. The minimal numbers Qnp(kp) and the sizes (Lx, Ly, Lz) have to be discussed for statistical calculations.
For numerical programming, according to the programming language used and according to the size (or the computational capacity) of the computer, it is necessary to find a judicious choice of the tables of integer or real values and which values would be useful to save all during simulation. Let Ncol,m be the maximum number of elastic collisions per particle, and let Ncycle be the number of cycles to average the simulation calculations.
For this MCS, the numerical chosen values are in Table 2.
Cell dimensions and steps for collisions | Number of species Kp | Initial number of particles in cell | ||
---|---|---|---|---|
Lx (m) | 4.68 10−6 | 1 | Qnp(SiH4) | Qnp1 |
Ly (m) | 4.68 10−6 | 2 | Qnp(SiH3) | 10 |
Lz (m) | 20.0 10−3 | 3 | Qnp(SiH2) | 10 |
4 | Qnp(H) | 10 | ||
Ncol,m | 500 | 5 | Qnp(H2) | Qnp5 |
Ncycle internal cycle | 2000 | 6 | Qnp(Si2H6) | 10 |
Ncycle external cycle | 200,000 | 7 | Qnp(SiH) | 10 |
8 | Qnp(Si2H5) | 10 | ||
9 | Qnp(e) | Qnp9 |
Used quantities and parameters in calculations for the gas temperature Tg = 520 K.
For radicals (e.g., SiH3), particle numbers Qnp(k) are very small; we take Qnp(k) = 10. These numbers cannot take value 1 or 0, even if a species k is in trace form in the gas. The value 0 for a species k means that any other species k’ does not make a collision with the species k; and the value 1 means that we have no collisions between particles of the same species in the cell.
Qnp1, Qnp5, and Qnp9 are calculated from the volume of cell, the pressure, the temperature, and the total number of particles in the cell (Qnp1 = 0.81187824 * 109; Qnp5 = 0.20296956 * 109; Qnp9 = 131).
As we have chosen a stationary regime, we must reach the values and properties at equilibrium. The results of the simulation show this trend. In MCS, averaged values, distribution functions, autocorrelation functions, and correlation functions can be calculated. To ensure rapid convergence of calculations, it would be useful to look for statistically symmetric (or stationary or unsteady) parameters [26, 50].
As an example for our MCS calculation, we have:
The number of Si2H6, SiH, and Si2H5 particles reaching the surface is negligible.
Let Ns,i and Ns, H2 be the densities of a species
Let Ns,i be the density of a species
The reactions begin with the dissociation (consumption) of H2 and SiH4 by R5, R1, and R2 reactions.
The production of SiH3 is done by R8, and then there is production of SiH2 by R12.
The reaction R2: SiH4 + e → SiH2 + 2H + e plays the central role in SiH4 dissociation by electron impact [24]. This result is compatible with [39].
The second important chemical reaction in the SiH4 dissociation is R1: SiH4 + e → SiH3 + H + e [24]. This result is compatible with that of Perkins et al. [51] and that of Doyle et al. [52].
Type | H2 | SiH4 | H | SiH3 | SiH2 |
---|---|---|---|---|---|
Ns,i/Ns, H2 | 1 | 0.23 | 1.67 10−4 | 8.60 10−5 | 9.86 10−6 |
Ratios Ns,i/Ns, H2 of particles reaching the surface compared to H2.
Type | SiH4 | SiH3 | SiH2 |
---|---|---|---|
6.695 10−6 | 7.965 10−6 | 775 10−6 |
Ratios Ns,i/Nv,i of particles reaching the surface compared to volume.
MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.
We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.
A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].
Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.
The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.
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