\r\n\tThe science of aquifer study is no more in isolation. The cross cutting knowledge fields of GIS, Satellite Imagery, Electro-magnetism, Porous Media Flows, Dispersion and Monitoring, high speed and large data computing, etc have provided great impetus to study and research on aquifers. Even though volumes of literature is available, yet any further advancement of knowledge in the field of aquifers would always be welcome. This book aims and endeavors to fill up this vacuum, partially or to whatever extent is possible.
",isbn:"978-1-83962-302-8",printIsbn:"978-1-83962-301-1",pdfIsbn:"978-1-83962-303-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"5b13aa76c9209e22274018bd78cab538",bookSignature:"Dr. Muhammad Salik Javaid and Dr. Aftab Sadiq",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8976.jpg",keywords:"Groundwater Contamination, Rock structure , Mineralogy, Aquifer Zones, Aquifer Porosity, Aquifer Recharge, Artificial Recharge, Injection Wells, Aquifer Depletion, Transboundary Aquifers, International Water Laws, Cooperative Conservation Concepts",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 23rd 2019",dateEndSecondStepPublish:"October 14th 2019",dateEndThirdStepPublish:"December 13th 2019",dateEndFourthStepPublish:"March 2nd 2020",dateEndFifthStepPublish:"May 1st 2020",remainingDaysToSecondStep:"2 months",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,editors:[{id:"98883",title:"Dr.",name:"Muhammad Salik",middleName:null,surname:"Javaid",slug:"muhammad-salik-javaid",fullName:"Muhammad Salik Javaid",profilePictureURL:"https://mts.intechopen.com/storage/users/98883/images/system/98883.jpeg",biography:"Dr. Muhammad Salik Javaid has a long meritorious career interacting with hydrology, hydraulics and water resources as an engineering student, a registered professional engineer, a researcher and as university teaching professor. For over three decades he has worked as hydraulics engineer, a disaster risk consultant, and water resources expert in Pakistan and abroad in Corps of Engineers, Earthquake Reconstruction and Rehabilitation Authority (ERRA), Frontier Works Organization (FWO) and Design & Consultancy Department (DD&C). \r\nHis undergraduate engineering education is from Military College of Engineering (MCE). He is a graduate of Georgia Tech, Atlanta, USA where he earned his Masters and Doctoral degrees in Civil Engineering. He has been on the faculty of National University of Sciences & Technology (NUST), University of Lahore, and Abasyn University Islamabad, teaching undergraduate and graduate level courses related to hydrology and hydraulics.",institutionString:"Abasyn University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Abasyn University",institutionURL:null,country:{name:"Pakistan"}}}],coeditorOne:{id:"304163",title:"Dr.",name:"Aftab",middleName:null,surname:"Sadiq",slug:"aftab-sadiq",fullName:"Aftab Sadiq",profilePictureURL:"https://mts.intechopen.com/storage/users/304163/images/system/304163.jpg",biography:"Dr. Aftab Sadiq is a Professor of Civil Engineering at University of Wah, Pakistan. He received BSc (Civil Engg) from Military College of Engineering, Risalpur, Pakistan in 1981, and MS and PhD degrees from Georgia Institute of Technology, Atlanta, Georgia, USA in 1992 and 1994. His field of specialization is “Open Channel Flows” and his research work is focused on “Clear Water Scour around Bridge Abutments in Compound Channels”. He has also served on the faculty of National University of Sciences and Technology, Pakistan, and Air University, Islamabad, Pakistan. He has taught courses in fluid mechanics, open channel flows, hydraulic engineering and water resources engineering. Professor Aftab Sadiq has served on “Governmental Review Boards” and as a consultant to various civil engineering design, consultancy and project implementation organizations. 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1. Introduction
\n
Chronic obstructive pulmonary diseases (COPD), asthma and lung transplantation have been, by far, the respiratory diseases or conditions more studied, in terms of telemedicine. However, the interest of telehealth providers in new areas also related to neurologic conditions, such as neuromuscular diseases in need of home noninvasive ventilation (NIV) due to chronic respiratory failure, or sleep-related breathing disorders, has arisen in recent years.
\n
Existing evidence reveals promising results regarding reliability and validity of measures across all pulmonary conditions, and patients usually show a positive attitude toward telecare technologies. Other positive effects, for instance, detection of complications, better disease control, immediate feedback, and adequate medication use, have also been addressed [1]. Yet, there is still somewhat decreased adherence within time, possibly secondary to poor health status, time conflicts, device problems, and lack of ability to operate the system [2]. Furthermore, there is no solid evidence about the utilization of healthcare resources, as well as cost-effectiveness, paramount scenarios to advocate in favor of this new way of approaching chronic respiratory patients.
\n
In the following section, current evidence apropos specific respiratory diseases (COPD, asthma, lung transplantation, neuromuscular diseases, and SRBD) will be disclosed, focusing on the positive results, along with the pitfalls found so far.
\n
1.1. Telemedicine
\n
Telemedicine (TM) has several definitions and all of them emphasize the role of telemedicine to enable the completion of the medical act at distance (Table 1) [3–5]. Norrit et al. define TM as a scientific area that uses information and communication technologies (ICT) to share medical information [6]. Thanks to ICT development, TM clinical opportunities are increasing. The information provided by TM programs can be useful for diagnosis and treatment of several diseases, as well as for enhancing their follow-up.
The delivery of health care services, where distance is a critical factor, by all health care professionals using information and communication technologies for the exchange of valid information for diagnosis, treatment and prevention of disease and injuries, research and evaluation, and for the continuing education of health care providers, all in the interests of advancing the health of individuals and their communities.
Telemedicine is the use of medical information exchanged from one site to another via electronic communications to improve a patient’s clinical health status. Telemedicine includes a growing variety of applications and services using two-way video, email, smart phones, wireless tools, and other forms of telecommunications technology.
Telemedicine is conceived of as an integrated system of health-care delivery that employs telecommunications and computer technology as a substitute for face-to-face contact between provider and client.
\n
\n\n
Table 1.
Telemedicine’s definitions.
WHO: World Health Organization; ATA: American Telemedicine Association, Ref: Reference.
\n
Historically, Dr. Graham Bell performed the first TM experience, when he used the telephone calling for help when he was sick. Also, in 1923, Sahlgrenska University (Gothenburg) used the Morse code to provide medical advice. TM programs were funded by the privacy industries in 1990 for the first time, and in 1993, the first telemedicine symposium was celebrated. Over 50 years, TM has been used for different programs such as: monitored surgeries, remote assistance in rural zones of Arizona, or vital signs monitoring of astronauts in space, just like Bashur et al. demonstrated [7]. In fact, aerospace technology development has been one of the most important factors in TM evolution. In 1976, the Hermes satellite was put into orbit with the main objective of improving communications in remote areas of Canada. Since then, the Western Ontario University has been using it for telemonitoring of vital signs, sharing medical information between hospitals and, finally, sharing radiographies [8]. Moreover, the National Aeronautics and Space Administration (NASA) also has used TM to give medical assistance if a disaster takes place.
\n
Generally speaking, TM applications could be classified into three groups: (a) normal clinical activity (teleconsult, telediagnosis, teletreatment, etc.), (b) remote assistance, and (c) administration labors and patient management.
\n
1.1.1. Clinical activity
\n
Almost all studies are aimed for telemonitoring patients or sharing medical data, where this medical act at distance needs a TM platform and a clinical response. We could classify the clinical response into two groups: synchronic or asynchronic response (Figure 1). The main difference is the time to response [9]. While in the first group, the clinical response is immediate and allows performing a live medical act, the second group clinical response is deferred (minutes or few hours). Asynchronic response is useful in telepatologhy or teleradiology, or in other telediagnosis programs.
\n
Figure 1.
Telemedicine classification.
\n
\n
1.1.2. Remote assistance
\n
In this group, several medical actions are included such as online records for consulting previous medical charts, establishing a direct communication between patients and physicians, or teleconference between primary and specialized care doctors, useful for discussing difficult cases and take decisions for complex patients (terminal disease, multiple comorbidities, social exclusion, impossibility to attend the hospital, etc.).
\n
\n
1.1.3. Patients’ management
\n
Nowadays, patients manage their medical events via Internet more often, and their doctors can use the same way to give medical recommendations (rehabilitation, nutritional care, tobacco information, or health life recommendations). Obviously, TM is a helpful tool for health care personnel as well. In this case, TM is used to access scientific information or as a type of communication for multicentric and international clinical trials.
\n
\n
\n
1.2. Telemedicine: barriers and benefits
\n
According to the Europe Institute of Technologies findings, only 14.2% of citizens had used the Internet to solve their health related doubts. The more frequent searches regarding these issues were: disease description, clinical trials, medical literature, or patients’ disease associations (Table 2).
\n
Table 2.
Search topics by patients and healthcare professionals.
\n
There are several studies that have showed important barriers for applying TM programs. Segrelles-Calvo et al. suggested that healthcare policy, lacking studies about economic burden and cost-effectiveness of TM, no laws regarding the handling of information in TM programs and the resistance to change “usual medicine conception,” are some causes that explain slow TM implantation [10]. According to the concept of “resistant to change usual care,” Mira-Solves et al. presented the results of the ValCrònic program [11], in which authors discussed the causes to leave a TM program. The main reasons were: (1) difficulty to use the devices, (2) complex measures, (3) nonadherence with TM program, (4) technical problems, and (5) caregivers preferences.
\n
Another important barrier not well studied is the opinion of health professionals toward TM programs. Telemedicine collects a lot of information and their belief is that TM increases workload. However, this belief is not displayed in scientific studies. Jódar-Sánchez et al. [12] showed indeed that a specialized nurse could solve most of the clinical urgencies detected, where only 8 of 40 cases needed a pneumologist intervention. Similar results were published by Vitacca et al. [13] reporting that in 63% of alerts, these could be resolved only by a nurse, and in the rest of them both physician and nurse gave the clinical response. As conclusion, it seems that there are external factors acting as barriers in the TM implantation, and further works are required to establish them. Motulsky et al. [14] and Cresswell et al. [15] pooled those external factors in three groups: (1) healthcare institutions policy, (2) the urge of guidelines about TM, and (3) the need of specific formation and educational resources.
\n
Telemedicine offers four fundamental benefits [4]:
\n
Improved access: Telemedicine has been used to bring healthcare services to patients in distant locations.
Cost efficiencies: Telemedicine reduces the number of hospitalizations and the cost related to these events. Telemedicine program reduce patient displacement to Hospital and reduced travel times.
Improved quality: Studies have consistently shown that the quality of healthcare services delivered via telemedicine is as good as those given in traditional in-person consultations.
Patient demand: The greatest impact of telemedicine is on the patient, their family and their community. Telemedicine could reduce travel time and related stresses for the patient. Almost all studies have shown that patient and caregiver’s satisfaction is very high.
\n
\n
1.3. Telemedicine platforms
\n
In general, there is a common objective in telemedicine programs; however, there are several platforms in which TM could be offered. Telemedicine platforms are related to ICT. The most common scheme in telemedicine (Figure 2) is the one that includes devices to measure different vital signs or questionnaires, in order to perform a teleconsultation or to send educational resources to patients. Those measures could be made by the patients, anywhere and anytime. Clinical information is sent to a call center or a health professional by different means (telephone, Internet, etc.), and the clinical response is made according to all information regarding.
\n
Some of the ICT used in telemedicine platform are as follows:
\n
Videoconference. Possibly this ICT was one of the most important technological advances as a telemedicine platform. Mahmud et al. [16] made a follow-up platform of patients with chronic diseases (heart failure, COPD, cerebrovascular disease). In seven cases, the number of emergency department visits and hospitalizations were reduced, and the authors did not found complications in the use of the videoconference platform. These results were confirmed in 2000 by Johnston et al. [17] and by Nakamura et al. [18]. Johnston determined a reduction of 17% of home visits as well as a 27% reduction of costs in the telemedicine group. Moreover, Nakamura reported an improvement of daily activities in the telemedicine group. Recent studies have used videoconference to improve adherence to a telerehabilitation program [19], to follow-up patients with bipolar disorder [20] or to monitoring tuberculosis therapy compliance [21], among other topics. According to these studies, in our view the videoconference is a remarkable technology, facilitating the follow-up of patients to improve their adherence to treatment.
\n
Figure 2.
Telemedicine platform.
\n
Telephone. Mainly, studies have focused in the telephone as a device to follow-up of patients but Balas et al. [22] described five possible actions that we could also do via telephone: (1) follow-up, (2) videoconsultation due to interactive telephone, (3) telephonic reminders of taking a medicine or doing an exercise, (4) calling health professionals if case of clinical deterioration, and (5) clinical investigation.
\n
E-mail. Email is a rather quick tool for the patients to communicate with health professionals, making it easier for the latter to perform questionnaires so any given doubt of the patient or caregiver could be cleared up.
\n
\n
\n
2. Chronic obstructive pulmonary diseases
\n
It is now consensually agreed that an estimated number of 328 million people have COPD worldwide, that is, 168 million men and 160 million women. Moreover, COPD causes the death of 2.9 million people annually and it is projected to be the third cause of mortality by 2020 [23]. Whereas the three most important factors in individual patients that determine the economic and social costs of COPD are disease severity, presence of frequent exacerbations of disease and the presence of comorbidities, which are common (30–57%) in COPD patients [24], the current short-term and long-term strategies to reduce the burden of COPD comprise the triad of smoking cessation, minimizing acute exacerbations and management and prevention of comorbidities [25].
\n
Hence, a high priority should be given to interventions aimed at delaying the progression of disease, preventing exacerbations and reducing the risk of comorbidities in order to alleviate the clinical and economic burden of COPD in Western countries [26]. Among these interventions, telemedicine has shown some promising results although no conclusive evidence has been accomplished. The effects of telemedicine in COPD have been addressed in previous systematic reviews [27, 28]; however, their conclusions are not consistent since the types of tested interventions have been rather heterogeneous. These interventions range from simple telephone or video interviews to daily telemonitoring of physiological parameters or symptoms data, and that is why comparativeness of one study to the other does not come along easily.
\n
So far, there is moderate evidence of the benefit of telemedicine in COPD, in terms of increasing quality of life and reducing hospital admissions. Basically, the problem has been that in previous years the studies included in systematic reviews were underpowered, had heterogeneous populations and had lack of detailed intervention descriptions and of the care processes that accompanied telemonitoring [29]. Another issue is the clinical scenario where patients are usually recruited. For instance, telemedicine can be offered to those patients prone to exacerbations that are in stable condition [30], or right after admission regardless of the number of previous exacerbations or FEV1 obstruction severity [31].
\n
Regarding telemonitoring (understood as retrieving periodically clinical data such as oxygen saturation, heart rate, symptoms, etc.), recent data including randomized clinical trials of good quality are now available; however, some of them are still underpowered. In terms of hospital admissions, one of the latest systematic reviews on the matter, which included eight studies with 486 patients randomized to home telemonitoring or usual care, determined a significant lower risk of hospitalizations in the telemonitoring group. However, healthcare utilization in general was similar in both groups, since it was not clear whether the utilization was due to respiratory events specifically, and the lower range of compliance to telemonitoring reported by some studies may have influenced the ability of detecting clinical deterioration [32]. Moreover, even between this data retrieved on a daily basis there were different clinical features measured, which end up inevitability in being quite difficult to integrate quantitative variables because of missing or noncomparative data. Thus, the extrapolation of these results to the general population should be carried out with absolute caution. The usual problem with these systematic reviews is that, due to the heterogeneity of outcomes and the way the studies have assessed them, it is troublesome to determine the true effect of telemonitoring on COPD patients. For instance, adding a closer approach to patients with videoconsultations to the usual telemonitoring, which would be ideal in order to obtain higher rates of compliance or reduction of the use of healthcare resources in general, failed to demonstrate differences in hospital admissions or time to first admission or all-cause hospital admissions [33].
\n
Detection and management of COPD exacerbations in early stages is an important step in order to reduce hospital admissions and the consequent increase of quality of life and reduction of health costs in general. So far, telemedicine has proven to be a useful tool to achieve this.
\n
Physical activity, one of the strong mortality predictors in COPD patients, if not the strongest, has not been properly issued. Although no conclusive evidence of telemedicine benefit exists on this regard, the use of telehealthcare may lead to increased physical activity level [34]. A recent study that evaluated the feasibility of a telerehabilitation program compared to a regular outpatient program, showed an increase of physical activity measured by steps/day in the telerehabilitation group, with acceptable rates of satisfaction with the service, although no differences were found when the 6-minute walking test, dyspnea measured by the Medical Research Council or quality of life measured by the St. George’s Respiratory Questionnaire were compared [35].
\n
The cost-effectiveness of telemedicine in COPD is yet to be determined. In fact, a recent study carried out in the United Kingdom, which recruited 3230 patients where both at baseline and follow-up participants with COPD made up the largest telehealth intervention group, showed that costs of self-reported service use, combined with telehealth intervention costs, were greater for the group randomized to telehealth in addition to standard care than for the group randomized to usual care alone [36]. However, the validity of this conclusion may be biased for two reasons. First, the trial recruiters had foreknowledge of the allocation groups in many cases [37], and second, its transferability to other healthcare systems was not taken in consideration since the trial did not include all community and healthcare resources. Thus, a recent Danish trial (TeleCare North) will determine the real benefit of telemedicine in COPD in terms of health-related quality of life and the incremental cost-effectiveness ratio through a large-scale, pragmatic, cluster-randomized trial with nested economic evaluation [38].
\n
Quality of life, a paramount feature in COPD and a strong predictor of mortality, has been analyzed irregularly. Once again, the instruments used to determine the health related quality of life vary greatly among the telemedicine studies (i.e., Chronic Respiratory Disease Questionnaire, Chronic Respiratory Questionnaire, St. George’s Respiratory Questionnaire (SGRQ), Clinical COPD Questionnaire, EURO-QOL-5D Questionnaire, Medical Outcome Study Short-Form 36 Questionnaire), so comparative data is deficient. Overall, no significant differences have been found between a home telemonitoring group and the usual care group [32].
\n
The aim of telemedicine toward COPD patients should be to keep this population outside the hospital or the emergency rooms. Although there is evidence that this aim has been achieved in some studies, we are still in need of larger clinical trials which include a rigorous cost-effectiveness analysis in terms of use of healthcare resources separated by respiratory diseases or not, quality of life, and mortality. Furthermore, a 6- or 12-month follow-up is insufficient to determine conclusive differences in favor of telemedicine.
\n
\n
3. Asthma
\n
Asthma is a worldwide disease affecting 300 million of people, and its economic and social costs are mostly related to emergency visits and hospital admissions. Self-monitoring of symptoms and peak flow, following a written action plan and attending regular visits to their physician, have demonstrated to improve asthma control [39], and that is why approaches through telemedicine have been done to increase its control and follow-up. It has been hypothesized that providing self-monitoring tools such as easy-to-use handheld electronic monitoring devices or symptom questionnaires, patients can gain insight into their level of asthma control which gives them suggestions for subsequent treatment adjustment [40]. This is why telemedicine for asthma appears to be a promising tool to achieve this so wished for self-control and management of the disease.
\n
However, there are some pitfalls regarding telemedicine for asthma. If noncomparative data due to the different sort of interventions is a main issue for COPD, the problem is probably more serious for asthma. One of the most relevant systematic reviews in the matter included 21 studies, of which nine consisted in telephone calls, two in videoconferences, two in using the Internet, one in short text messaging, one in a combination of short text and Internet, and six more using other networked communications. This study demonstrated no improvement of quality of life and even a nonsignificant increase of emergency room visits in the telemedicine group, although a significant reduction of hospitalizations was observed [41]. However, some authors have stated some concerns about these meta-analysis conclusions. First of all, there were only few examples of a comprehensive telemanagement approach in asthma (defined as a treatment plan, self-monitoring of lung function by FEV1 and asthma control with feedback and e-communication with a professional to support this self-management), and second, patients in the control strategies often received an enhanced form of usual care, which makes it difficult to draw final conclusions on the effectiveness of telemanagement in asthma [40]. A more recent meta-analysis of 20 trials involving 10,406 asthmatic patients where common outcomes employed were healthcare utilization, quality of life and symptoms, concluded that the median effect of telemedicine was weakly positive, and that there were not differences between the types of interventions (telemonitoring, routine voice contact or videoconferencing). But the problem with this positive effect is that a publication bias exists due to the tendency of more positive results reported in earlier studies, which contained heterogeneous outcomes measurement and assessment [42].
\n
Regarding cost-effectiveness we are still in need of studies addressing the topic specifically, situation that withholds the use of telemedicine for asthma unquestionably. Probably the only evidence of cost-effectiveness of Internet-based self-management compared with usual care, showed no significant differences during a follow-up of one year. However, this study had several limitations, acknowledge by the authors. First, the quality adjusted life year estimates were calculated out of only two measurements throughout one year. Second, patients were inevitable conscious of the allocated group, which may have influenced their utility ratings. And third, the economic evaluation was limited to one year only [43]. Regarding a specific feature of telemedicine, another study showed that telephone consultations led by experienced nurses enabled a greater proportion of asthma patients to be reviewed at no additional cost to the health service, although these findings should not be extrapolated as a thorough cost-effectiveness analysis, compared to the comprehensive telemanagement as explained before [44, 45].
\n
Despite the similar moderate evidence either for asthma or COPD, there are some differences when telehealthcare main purposes are compared between the two diseases. While in COPD telemedicine aims to reduce exacerbations or their early detection in order to avoid emergency rooms visits or hospital admissions, in asthma these objectives are usually directed at assuring a better symptoms self-control and adherence to treatment, considering that undertreatment is the most common problem in European asthmatic subjects [46], and its usual presentation at early stages of life. A fitter control of asthma has been reported possibly secondary to the opportunity of register symptoms continually, thus, the patient obtained a more accurate picture of his disease severity and complied to treatment with a closer and efficient self-monitoring. However, this severity awareness led to an increased number of unscheduled visits and a harmful consumption of inhaled corticosteroids, which increased their adverse effects [47]. In a similar fashion, another study revealed that 43 patients under a mobile telephone interactive self-control system and compared with a control group, presented significantly higher mean daily dosage of either inhaled or systemic corticosteroids during the study period. Nonetheless, this system also demonstrated fewer unscheduled visits to the emergency department; higher peak expiratory flows at 4, 5, and 6 moths; higher FEV1 at 6 months; and better quality of life at 3 months after inclusion [48].
\n
Compliance to new technologies is a relevant feature of telemedicine since not all of public health systems can afford them, and there are still underprivileged groups who are not familiar to these sorts of interventions. It seems that telemedicine for asthma is feasible, although when compared to a web based self-management, patients presented higher rates of adherence to the classic paper based strategies of self-control of symptoms and action plans, though other critical feature such as lung function data was not reliable when the patient wrote it down on his own [49].
\n
In the pediatric population there is also lacking evidence of telemedicine benefit. Telemonitoring of lung function on daily home spirometry in 44 children with professional feedback did not reduce the frequency of exacerbations significantly when compared to conventional treatment, nor the number of unscheduled visits, FEV1, quality of life or use of inhaled corticosteroids [50]. This finding could be explained by the fact that a highly variable peak expiratory flow and FEV1 values at time of symptoms and a complete overlap in distributions between symptoms-free days and at times of symptoms [51], and also by the underpowered nature of the study.
\n
In conclusion, even though telemedicine for asthma seems to be a useful and promising tool for empowering the asthmatic patients in order to guarantee the self-control of the disease, the evidence of its benefit is still unclear. The short follow-ups, the heterogeneity of subjects and the insufficient evidence of its cost-effectiveness, are paramount aspects that restrain the use of telemedicine for asthmatic patients. We advocate for the tailoring treatment to the individual needs as the cornerstone of telehealthcare, although more studies are called for so the real effect of this new technologies can be elucidated.]
\n
\n
4. Sleep-related breathing disorders and obstructive sleep apnea
\n
Speaking of sleep-related breathing disorders, obstructive sleep apnea (OSA) is a prevalent disease that affects approximately 6–7% of global population, although these figures probably underestimate the real OSA prevalence. OSA is a sleep disorder in wich breathing repeatedly stops and starts, which lead to hypoxemia, subsequent arousals, sleep fragmentation, thus, a poor sleep quality in general. The main symptom is excessive daytime sleepiness, and is now acknowledge as an independent cardiovascular risk factor, increasing the probability of presenting hypertension, coronary artery disease, congestive cardiac failure, and stroke [52]. Attended full in-lab polysomnography (PSG) is the gold standard for OSA diagnosis, an expensive test that demands plenty of time as well as fully trained technicians, and that is why simplified sleep data recollection systems have been approved by the scientific societies for patients with high or low pretest probability of OSA, in order to reduce the waiting list for PSG [53]. Despite the increase of accredited sleep units, the demand of sleep studies has also increased over the years considering the prevalence of the disease. Therefore, waiting lists remain long [54]. Finally, continuous positive airway pressure (CPAP) is by far the recommended treatment for symptomatic or severe OSA, and it is known to reduce cardiovascular death and non-fatal cardiovascular events [55], however, adherence to treatment has been a troublesome factor in such a way that the first year of long-term treatment usually between 25 and 30% of patients drop out the device [56]. Having said this, there have been some efforts to reduce the long waiting lists and increase the rates of CPAP adherence through telemedicine.
\n
Regarding OSA diagnosis, the evidence of telemedicine usefulness is limited. So far, the American Academy of Sleep Medicine has classified the sleep recording devices into four categories. Full-attended in-lab PSG would be type 1; comprehensive portable unattended PSG with a minimum of seven channels (including electroencephalogram, electrooculogram, chin electromyogram, electrocardiogram or heart rate, airflow, respiratory effort, and oxygen saturation) corresponds to type 2; type 3 comprises modified portable systems with a minimum of four channels monitored, including ventilation or airflow (at least two channels or respiratory movement, or respiratory movement and airflow), heart rate or electrocardiogram, and oxygen saturation comprise; and finally type 4 includes continuous single or dual bioparameters with one or two channels, typically including oxygen saturation or airflow [57]. Despite the limitations of sensor losses that lead to technically inadequate recordings, the inability to assess sleep time duration or the distinction of apneas (central or obstructive), and the vast heterogeneity of sensors and recorders, the studies have confirmed the overall usefulness of type 3 devices, especially if they focus on the outcome which results in earlier access to treatment for the patient, specially those at high-risk of OSA. An alternative to type 3 devices is the home-polysomnography (H-PSG), which enables the home centered care for patients and a complete sleep evaluation allowing the possibility of diagnosing a large panel of sleep disorders. Thus, this H-PSG intends to perform as well as a full-attended PSG though in an unattended surrounding, without continuous supervision. A technician hooks-up the device, and this factor limits the wide us of this technique [58]. Since the loss of data is still a big issue with type 2 or 3 devices, potential future developments include the use of assistive technology and telemedicine to allow real-time remote monitoring.
\n
To enhance the quality of H-PSG signal, real-time telematics data transmission has been tested generating successful and high-fidelity recordings through a cell phone for an easily deployed home monitor device [59], and a failure rate of 11% of telemonitored in-hospital unattended PSG compared to a 23% failure for unattended H-PSG was observed in another study [60]. Moreover, a pilot study, where 90% of recordings were of excellent quality, consisted in a wireless device to obtain real-time remote supervision of H-PSG from the sleep lab [61]. With this amount of evidence, it seems telemedicine for sleep studies recordings is feasible and may be an important step to reduce the failure rates of home devices; however, there are important barriers for implementing telemedicine for sleep studies regularly. Telemonitoring devices are complex as well as their software; hence, incompatibility problems with other computer programs should be expected. Furthermore, the cost-effectiveness of these systems is yet to be determined considering the fact that the home must be equipped with a computer and Internet connection, along with high specifications for computer programs. However, investigations using integrated circuits available on the market (mobile telephony) have been conducted to simplify access to these technologies [62]. Last but not least, there are also problems related to privacy protection and security of medical data transmission [58]. An ongoing telehealth out-of-laboratory “Fast Track for Sleep Apnea” program for veterans has been reported, that has helped to relieve clinical load at the central sleep program, improved local access to sleep care, and improved patient satisfaction with health care for sleep-related breathing disorders. Nonetheless, the following challenges have been acknowledged so far: the programs needed to be properly integrated with other data management systems and data storage devices must be interfaced with computers attached to the VA server; data loss; and maintaining quality control using metrics [63]. Either way, further research is required to determine the role of telemedicine in sleep-related breathing disorders diagnosis, especially for OSA.
\n
CPAP has shown to wipe out the adverse effect of severe OSA, especially those effects related to cardiovascular diseases. However, the rates of adherence to CPAP are still far of being acceptable. That is way any measure to achieve CPAP adherence is needed, and new approaches such as telemedicine seems to be feasible and cost-effective. Compliance to CPAP is a complex process that involves the participation of the device itself, family support, physicians, health care personal, sleep unit, and government politics [64]. So far, low-quality evidence justifies the use of supportive interventions added to the usual clinical practice to increase CPAP adherence [65] and, similar to previous items, more clinical trials are called for to clear up the role of these interventions, where telemedicine is included. Earlier works presented contradictory results. A statistically significant higher adherence was found in a telemedicine-guided naïve to CPAP patients recently diagnosed with OSA along with greater satisfaction, concluding that telehealth might be cost-effective for CPAP adherence management [66]; while no differences were found in hours of CPAP use, functional status or client satisfaction in another study [67]. It is worth to mention that these two studies followed the patients for a 12-week and 30 days period, respectively. More recent clinical trials have added some light to the subject. A 12-month telemedicine intervention resulted in a median CPAP usage that was 0.9 h/night higher than that of an attention control group after 6 months, and 2.0 h/night higher after 12 months in a clinical trial including 250 patients, although the median adherence of all patients was low, with 19% of patients refusing the use of CPAP at all [68]. Another clinical trial of 75 patients, showed higher rates of adherence to CPAP after 3 months of telemedicine intervention, which was determined as a significant predictor of adherence, apart from age and sleepiness symptoms measured by the Epworth Sleepiness Scale [69]. Finally, although no difference in hours of CPAP use was found in a study including 139 OSA patients, telemedicine showed to be more cost-effective than the usual face-to-face management, with travel costs and lost work time being the most important sources of savings [70].
\n
Improvement in case detection and the resulting higher healthcare demand has not been accompanied by any real improvement in OSA management. In addition, health resources assigned to OSA and its treatment have been found to be inadequate [71]. Telemedicine is an appealing approach that needs to be explored and taken into consideration in order to obtain a diagnosis and follow-up of sleep-related breathing disorders in a more timely fashion, which would help to achieve the desirable management of these diseases.
\n
\n
5. Lung transplantation
\n
[Lung transplantation is offered for a great variety on respiratory diseases that have reached their end-stage, where no other treatment would obtain a reasonable survival. They are complex patients who are in need of aggressive immunosuppressive treatment for a lifetime that exposes them to opportunistic infections; so numerous complications are often taking place. By far, the major problem for every lung transplant patient is the allograft dysfunction, either acute or chronic (basically in its form of bronchiolitis obstructive syndrome). Allograft dysfunction is characterized for a functional decline of the implant, which is usually measured by FEV1 [72], and daily home spirometry has been shown to lead to earlier detection and staging of bronchiolitis obstructive syndrome when compared with standard pulmonary function testing [73]. Concerning the need of retrieving daily spirometric data, telemedicine has been studied as a feasible instrument, making some interesting progress conducive to a more efficient follow-up of patients and the prompt recognition of a possible complication.
\n
Earlier works determined the telemonitored spirometry as feasible, valid, reliable, and repeatable, when compared to the regular in-clinic functional testing [74–76]. Although these studies were clearly underpowered due to the small samples included. While on earlier works the objective is to determine the technical aspects of collecting acceptable spirometries, recent works have carried out clinical trials to demonstrate that a computerized rule-based decision support algorithm for nursing triage of potential acute bronchopulmonary events is effective [72, 77], or the identification of these events taking decision rules developed using wavelet analysis of declines in spirometry and increases in respiratory symptoms [78]. In conclusion, the evidence of the increase of quality of life and reduction of hospital admissions seems fairly positive, though we are still in need of more studies [79] and the training process for both medical staff and patients needs to be thorough [80] A different approach was revised by another study where telemedicine was employed in a clinical trial for lung transplant candidates, and clinical outcome measures were monitoring adherence and level of communication (for monitor acceptability and utilization), hospital length of stay after transplantation and survival at 4 months. However, no significant differences in clinical outcomes between groups were determined [81].
\n
Similar to the previous three respiratory conditions, telemedicine for lung transplant patients is feasible. Still and all, no cost-effectiveness has been demonstrated, thus, larger clinical trials are required to establish the position of these new techniques in lung transplantation.
\n
\n
6. Conclusions
\n
Telemedicine is a helpful tool to improve chronic respiratory patient management. Almost all results shows reduction in Emergency visits and the number of hospitalizations but despite of these results its implementation is troublesome and with different kind of factors relationship with this slowly development. Most users report that the difficult to use the devices or technology platform is the most important factor related to refuse telemedicine by users. We need to work to improve its implementation through educational programs to healthcare professionals and patients.
\n
\n\n',keywords:"COPD, eHealth, home telemonitoring, telemedicine, telemedicine platforms",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/51952.pdf",chapterXML:"https://mts.intechopen.com/source/xml/51952.xml",downloadPdfUrl:"/chapter/pdf-download/51952",previewPdfUrl:"/chapter/pdf-preview/51952",totalDownloads:833,totalViews:290,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"October 28th 2015",dateReviewed:"June 27th 2016",datePrePublished:null,datePublished:"August 31st 2016",readingETA:"0",abstract:"Telemedicine programs are widely used in respiratory diseases, more often in patients with chronic obstructive pulmonary diseases (COPD). Telemedicine platforms use several devices to measure vital signs such as heart rate, respiratory rate, pulsioximetry or blood pressure between others. It is not unusual that patients could do questionnaires about clinical situation or communicate with their nurses via telephone, video-calling and/or Skype. The majority of results has been positive, with reduction in the number of emergency visits, hospitalizations and noninvasive ventilations. Despite their promising results, telemedicine programs/platforms are slow to implement. In this chapter, we reviewed some of the factors related to telemedicine implementation such as patients’ adherence, impact of telemedicine design and professionals' resistance to change between others.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/51952",risUrl:"/chapter/ris/51952",book:{slug:"mobile-health-technologies-theories-and-applications"},signatures:"Gonzalo Segrelles-Calvo and Daniel López-Padilla",authors:[{id:"180563",title:"Dr.",name:"Gonzalo",middleName:null,surname:"Segrelles",fullName:"Gonzalo Segrelles",slug:"gonzalo-segrelles",email:"gsegrelles@hotmail.com",position:null,institution:{name:"King Juan Carlos University",institutionURL:null,country:{name:"Spain"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_1_2",title:"1.1. Telemedicine",level:"2"},{id:"sec_1_3",title:"1.1.1. Clinical activity",level:"3"},{id:"sec_2_3",title:"1.1.2. Remote assistance",level:"3"},{id:"sec_3_3",title:"1.1.3. Patients’ management",level:"3"},{id:"sec_5_2",title:"1.2. Telemedicine: barriers and benefits",level:"2"},{id:"sec_6_2",title:"1.3. Telemedicine platforms",level:"2"},{id:"sec_8",title:"2. Chronic obstructive pulmonary diseases",level:"1"},{id:"sec_9",title:"3. Asthma",level:"1"},{id:"sec_10",title:"4. Sleep-related breathing disorders and obstructive sleep apnea",level:"1"},{id:"sec_11",title:"5. Lung transplantation",level:"1"},{id:"sec_12",title:"6. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Jaana M, Paré G, Sicotte C. Home telemonitoring for respiratory conditions: a systematic review. Am J Manag Care. 2009;15:313–20.'},{id:"B2",body:'Sabati N, Snyder M, Edin-Stibbe C, Lindgren B, Finkelstein S. 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Practice parameters for the use of portable monitoring devices in the investigation of suspected obstructive sleep apnea in adults. Sleep. 2003;26:907–13.'},{id:"B58",body:'Bruyneel M, Ninane V. Unattended home-based polysomnography for sleep disordered breathing: current concepts and perspectives. Sleep Med Rev. 2014;18:341–7. doi: 10.1016/j.smrv.2013.12.002.'},{id:"B59",body:'Kayyali HA, Weimer S, Frederick C, Martin C, Basa D, Juguilon JA, Jugilioni F. Remotely attended home monitoring of sleep disorders. Telemed J E Health. 2008;14:371–4. doi: 10.1089/tmj.2007.0058.'},{id:"B60",body:'Gagnadoux F, Pelletier-Fleury N, Philippe C, Rakotonanahary D, Fleury B. Home unattended vs hospital telemonitored polysomnography in suspected obstructive sleep apnea syndrome: a randomized crossover trial. Chest. 2002;121:753e8.'},{id:"B61",body:'Bruyneel M, Van den Broecke S, Libert W, Ninane V. Real-time attended home-polysomnography with telematic data transmission. Int J Med Inform. 2013;82:696e701.'},{id:"B62",body:'Dellaca R, Montserrat JM, Govoni L, Pedotti A, Navajas D, Farré R. Telemetric CPAP titration at home in patients with sleep apnea-hypopnea syndrome. Sleep Med. 2011;12:153e7.'},{id:"B63",body:'Hirshkowitz M, Sharafkhaneh A. A telemedicine program for diagnosis and management of sleep-disordered breathing: the fast-track for sleep apnea tele-sleep program. Semin Respir Crit Care Med. 2014;35:560–70. doi: 10.1055/s-0034-1390069.'},{id:"B64",body:'Shapiro GK, Shapiro CM. Factors that influence CPAP adherence: an overview. Sleep Breath. 2010;14:323–35.'},{id:"B65",body:'Wozniak DR, Lasserson TJ, Smith I. Educational, supportive and behavioural interventions to improve usage of continuous positive airway pressure machines in adults with obstructive sleep apnoea. Cochrane Database Syst Rev. 2014;1:CD007736. doi: 10.1002/14651858.CD007736.pub2.'},{id:"B66",body:'Smith CE, Dauz ER, Clements F, Puno FN, Cook D, Doolittle G, Leeds W. Telehealth services to improve nonadherence: a placebo-controlled study. Telemed J E Health. 2006;12:289–96.'},{id:"B67",body:'Taylor Y, Eliasson A, Andrada T, Kristo D, Howard R. The role of telemedicine in CPAP compliance for patients with obstructive sleep apnea syndrome. Sleep Breath. 2006;10:132–8.'},{id:"B68",body:'Sparrow D, Aloia M, Demolles DA, Gottlieb DJ. A telemedicine intervention to improve adherence to continuous positive airway pressure: a randomised controlled trial. Thorax. 2010;65:1061–6. doi: 10.1136/thx.2009.133215.'},{id:"B69",body:'Fox N, Hirsch-Allen AJ, Goodfellow E, Wenner J, Fleetham J, Ryan CF, Kwiatkowska M, Ayas NT. The impact of a telemedicine monitoring system on positive airway pressure adherence in patients with obstructive sleep apnea: a randomized controlled trial. Sleep. 2012;35:477–81. doi: 10.5665/sleep.1728.'},{id:"B70",body:'Isetta V, Negrín MA, Monasterio C, Masa JF, Feu N, Álvarez A, Campos-Rodriguez F, Ruiz C, Abad J, Vázquez-Polo FJ, Farré R, Galdeano M, Lloberes P, Embid C, de la Peña M, Puertas J, Dalmases M, Salord N, Corral J, Jurado B, León C, Egea C, Muñoz A, Parra O, Cambrodi R, Martel-Escobar M, Arqué M, Montserrat JM; SPANISH SLEEP NETWORK. A Bayesian cost-effectiveness analysis of a telemedicine-based strategy for the management of sleep apnoea: a multicentre randomised controlled trial. Thorax. 2015;70:1054–61. doi: 10.1136/thoraxjnl-2015-207032.'},{id:"B71",body:'Rotenberg B, George C, Sullivan K, Wong E. Wait times for sleep apnea care in Ontario: a multidisciplinary assessment. Can Respir J. 2010;17:170–4.'},{id:"B72",body:'Finkelstein SM, Scudiero A, Lindgren B, Snyder M, Hertz MI. Decision support for the triage of lung transplant recipients on the basis of home-monitoring spirometry and symptom reporting. Heart Lung. 2005;34:201–8.'},{id:"B73",body:'Robson KS, West AJ. Improving survival outcomes in lung transplant recipients through early detection of bronchiolitis obliterans: daily home spirometry versus standard pulmonary function testing. Can J Respir Ther. 2014;50:17–22.'},{id:"B74",body:'Finkelstein SM, Snyder M, Edin-Stibbe C, Chlan L, Prasad B, Dutta P, Lindgren B, Wielinski C, Hertz MI. Monitoring progress after lung transplantation from home-patient adherence. J Med Eng Technol. 1996;20:203–10.'},{id:"B75",body:'Lindgren BR, Finkelstein SM, Prasad B, Dutta P, Killoren T, Scherber J, Stibbe CL, Snyder M, Hertz MI. Determination of reliability and validity in home monitoring data of pulmonary function tests following lung transplantation. Res Nurs Health. 1997;20:539–50.'},{id:"B76",body:'Wagner FM, Weber A, Park JW, Schiemanck S, Tugtekin SM, Gulielmos V, Schüler S. New telemetric system for daily pulmonary function surveillance of lung transplant recipients. Ann Thorac Surg. 1999;68:2033–8.'},{id:"B77",body:'Finkelstein SM, Lindgren BR, Robiner W, Lindquist R, Hertz M, Carlin BP, VanWormer A. A randomized controlled trial comparing health and quality of life of lung transplant recipients following nurse and computer-based triage utilizing home spirometry monitoring. Telemed J E Health. 2013;19:897–903. doi: 10.1089/tmj.2013.0049.'},{id:"B78",body:'Wang W, Finkelstein SM, Hertz MI. Automatic event detection in lung transplant recipients based on home monitoring of spirometry and symptoms. Telemed J E Health. 2013;19:658–63. doi: 10.1089/tmj.2012.0290.'},{id:"B79",body:'Fadaizadeh L, Najafizadeh K, Shafaghi S, Hosseini MS, Ghoroghi A. Using home spirometry for follow up of lung transplant recipients: “A Pilot Study”. Tanaffos. 2013;12:64–9.'},{id:"B80",body:'Fadaizadeh L, Najafizadeh K, Shajareh E, Shafaghi S, Hosseini M, Heydari G. Home spirometry: assessment of patient compliance and satisfaction and its impact on early diagnosis of pulmonary symptoms in post-lung transplantation patients. J Telemed Telecare. 2016;22:127–31'},{id:"B81",body:'Mullan B, Snyder M, Lindgren B, Finkelstein SM, Hertz MI. Home monitoring for lung transplant candidates. Prog Transplant. 2003;13:176–82.'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Gonzalo Segrelles-Calvo",address:"gsegrelles@hotmail.com",affiliation:'
Pneumology Department, University Hospital Rey Juan Carlos, Mostoles, Spain
Pneumology Department, University Hospital Gregorio Maranon, Madrid, Spain
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1. Introduction
Nowadays, one of the most innovative procedures to improve communications is the random scattering of microwave or radio signals that may enhance the amount of information that can be transmitted over a channel. This fact, from a mathematical point of view, is due to the growth of the phase space available for that channel, which provides a more rich mathematical base to define every single signal. In many recent papers, a common subject is the use of a broad range of base functions to span each signal. The hope is that every single collision of the initial signals will be scattered and reaches another phase space region providing additional information, but the increase of phase space involves a more complicated set of describing functions. A multiple scattering of the obstacles enlarges the effective aperture in a time-reversed process for acoustic or electromagnetic signals when they are placed in random manner.
Another current tool is time reversal, or phase conjugation in the frequency domain, where a source at one location transmits sound or electromagnetic waves, which are received at another place, time reversed (or phase conjugated), and retransmitted. The effect is to eliminate noise pollution.
Despite the existence of the mentioned resources and others like multiple-input multiple-output (MIMO), many problems survive, but fortunately, we have proposed some additional ways to improve the broadcasting by diminishing the information loss. Some of our results are based on communication theory and others in the mathematical properties of particular integral equations and their solutions.
Through the present chapter, we introduce for convenience a hypothetical discrete system in order to write finite matrices. But we can certainly extend the validity of our expressions as we will see, even for both discrete and continuum systems provided the involved potentials fulfill very general conditions not discussed in the present work.
In the same manner, because the formalism we have developed for the study of time reversibility refers to acoustic systems, we recall that the scalar wave equation for acoustic signals can be written as:
E1
We now describe the quantities appearing in Eq. (1), represents the mass density and the compressibility of the propagation medium, while is the acoustic signal.
Because the wave equation is of second order in time, we can talk about time reversibility, and then allows solutions, which travel toward the future or the past. An efficient time reversal requires to ensure that the system be ergodic, making possible that the signal may travel both senses in time. To improve focusing, we must describe the signal propagation towards the future or past by means of equations of the same type [18, 22, 27] that is both directions inhomogeneous or both homogeneous. Linearity permits that a signal traveling toward the past can be written with the aid of the integral equation:
frT−t=f∘rT−t+∫V∫−∞∞U∗r′G∘∗r′rT−t′tfr′T−t′dt′dV′E2
In Eq. (2), G∘∗r′rT−t′t is the free Green function, U∗r′ depicts the complex dispersion coefficients, and frT−t is the returning signal that has traveled toward the past. The inhomogeneous term f∘rT−t is known as a sink term and makes both the outgoing and returning equations inhomogeneous integral equations. In Eq. (2), the parameter represents the time during which the outgoing signal (the one traveling toward the future) is being considered and recording. It is observed experimentally [9] that the time-reversed signal has a definition of a 14th of , the wavelength of the used signal for acoustic signals but this is also true for electromagnetic waves. On several experiments [9, 10], Lerosey, de Rosny, Tourin, and Fink have shown that when such a source term is included, the apparent cross section is increased in two ways: first, the multiple scattering also multiplies the available phase space so when the time is reversed, the information is increased, and second, in the electromagnetic case, the sink term stimulates and triggers the braking of the confinement of the evanescent waves that also raise the information and in consequence the definition to level of about λ14. In acoustics, the sink term consists in the operation of the source in reverse order; in the electromagnetic case, the sink term can be implemented with a crest of fine wires around the antennas.
2. Recovering the matrix equations
As we have said above and considering that from a strictly mathematical point of view, both the acoustic and electromagnetic waves achieve the same wave equation type (with a vector version in the electromagnetic case). Then, we can regain, without further ado, the vector matrix formalism [1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14] which generalizes the discrete scalar time reversal acoustic model and includes an original model for discrete broadcasting systems that we have called the plasma sandwich model (PSM) [8, 16, 17, 18] and we put some associated parameters appeared on it into the named vector matrix formalism (VMF) [8, 20, 24]. But we must underline that is the resonant behavior the one must be considered for increasing efficiency on communications and to achieve extraordinary resolution. To this end, we remember that a three-dimensional version of Eq. (1) can be written as the Fourier transform of an integral generalized homogeneous Fredholm’s equation (GHFE) [21, 22, 23, 24] for resonances, and does not matter if for acoustic or electromagnetic ones. To analyze the resonant behavior, we must eliminate the inhomogeneous term so we can write the following algebraic equation satisfied by the Fourier transform of the resonant waves:
E3
where the kernel is the product of the Fourier transform of the free Green function with the interaction U (without loss of generality we can suppose that U does not depend on ), so this can be written explicitly as:
1−ηRωG∘ωUnmwRnω=0E4
At this point, we must say that we could obtain a transfer matrix description [16, 17, 18] instead Eq. (4), but our last equation represents the core of the VMF version. The fact is there are important differences between the two formalisms; for example, VMF makes the time-reversal process easy. Of course, we are moving over a frequency domain and not over a time-dependent one, the former the appropriate in agreement with information theory applications. And certainly, the most important difference is that VMF formalism includes the concept of the resonant solutions.
3. Introducing the PSM parameters
One of the methods we have proposed is based on experiments executed by Xiang-kun Kong, Shao-bin Liu, Hai-feng Zhang, Bo-rui Bian, Hai-ming Li et al. [8] in which they put three layers of plasma joined and alternated with one of them magnetized in the core and the other two unmagnetized in the extremes of the device; when this plasma sandwich is submitted to an external electric potential, it is observed that for a range of values of the external potential, the refraction index is negative [15, 19]. When we analyzed those experiments, we conclude that for this range of the electric potential, the plasma sandwich brakes the confinement of the evanescent waves as occurs in a left-hand material and we proposed a model named the plasma sandwich model for the behavior of the propagation media. Depending on the particular conditions of the propagation media, that is, depending of the values of the plasma sandwich parameters, and for particular conditions of the external electric potential, the propagation media may behave like the plasma sandwich and acquire a negative refraction index. In this section, we introduce the PSM parameters and find the resonant frequencies for a specific problem, underlying that resonant frequencies can be used only to associate an interval of frequencies of a real signal to a device that could be an antenna and not to a single emitted frequency by them; this is because resonant waves are released evanescent waves that vanish in the resource sites and not precisely information carriers. The frequency bands we can build from the resonant frequencies can be considered as convenient highways for the transit of information. Every kernel depends on the response of the media in circumstances that can vary for different time intervals. In this manner, we present an example very easy to work but in which is not relevant the particular behavior of the signal we used to get it. Next, we can find the resonant frequencies for an academic example. First, we choose an appropriate discrete kernel , for convenience; in this particular kernel, we do not take into account the three components of the electromagnetic field (usually represented for the indices n and m). However, we propose a system constituted by two emitting antennas. One possible may be written [1, 3, 4, 5, 6, 7]:
E5
In kernel (5), we have introduced the plasma sandwich model (PSM) parameter , which is defined as:
E6
Definition (6) involves with the physical meaning of the wave number of an incident beam that interacts with the magnetic and electric fields in a way that the whole kernel is the expressed in Eq. (5); is the average thickness of a plasma-magnetized layer that generates this interaction; parameter is the average value for the plasma frequency in the magnetized plasma layer which can be written in terms of the local electron concentration in the layer as:
E7
In this definition, is the electron concentration, is the electronic charge, and is the permittivity of vacuum.
It is possible to note that any change in the parameter values gives different broadcasting conditions [5]. PSM suggests that there is not a single stationary set of iterated layers but a bunch of sets evolving in time and in consequence with different effects for each frequency. We must remember that the equation to solve is Eq. (3) where,
Kmn∘r\'rω=0ifr\'=rUnmr\'Gωnm∘r\'rifr\'≠rE8
The last two ubiquitous conditions to achieve resonance are the vanishing of Fredholm’s determinant for Eq. (4), and that Fredholm’s eigenvalue λ equals to 1 [6, 11, 22, 23]. The last two conditions give us the expected resonant frequencies for the system constituted by two antennas dependent on the PSM parameters. Now, we must remember that resonances have a special behavior that can be represented by a complex frequency:
E9
The transformation of the evanescent waves for traveling ones is due precisely to the imaginary part In addition, the relation between and the wave number is:
The abbreviated components of the matrix in (11) are explicitly
E12
and
E13
In Eqs. (12) and (13), we have used the following definitions:
E14
E15
E16
E17
To have an image of the solutions of Eq. (11) (see Figure 1), we can make and those are the real and imaginary parts of , and fix the value for the plasma frequency so we have the following image:
We obtain for the particular conditions:
E18
E19
The solutions (resonances):
E20
E21
In this case only, is properly a resonance and has not physical meaning but maintain their orthogonality properties.
4. Communication theory measurement of information loss
Because we have now a wide vision of the loss of information and we know that this is the reason that the images are not perfect, we can use the results of Shannon, Nyquist, Wiener, Hartley, Hopf [25, 26, 27, 28, 29], and other authors that have formulated a measure of the loss of information in communication systems. We support our mathematical results on related works [6, 11, 24, 26, 28], which give us a solid theoretical frame to our present and future papers. Indeed, because the capacity of a channel and entropy are very close concepts, we can use some of the results we have cited above to answer the problem for TRT and LHM.
Basically, we recall two theorems:
Theorem I.
If the signal and noise are independent and the received signal is the sum of the transmitted signal and the noise, then the rate of transmission is:
E22
This means that the rate of transmission is the entropy of the received signal less the entropy of the noise. The channel capacity is:
E23
Theorem II.
The capacity of a channel of band Θ perturbed by white thermal noise power when the average transmitter power is limited to is given by:
C=ΘlogP+NNE24
In this expression, P is the average power of the transmitted signal and N is the average noise power.
From these two theorems, we make our proposal for a channel where we have lost information in three ways. That is, we have limitations on the maximum frequency Θ (band), the presence of different classes of noise, and on a limited time T available for a time-reversal process. Then, defining a joint average for the power , the channel capacity is:
CT=ΘlogP+QnTQnTE25
This remains equal to zero when . The very significant feature of this proposal is the explicit dependence on , in both the joint average power and the channel capacity, as opposed to the conventional treatment of the signal time duration that is considered as a limit process which tends to infinity. This is a consequence of the explicit form of the Fourier transform of the time-reversed Green function that changes with a factor , so even if we are not forced to do so, we can think of it as a parameter that defines the channel. We can think of an arbitrary channel but, when we use it to reverse any signal in time, we follow a different process depending on the time we decide to fit. Then, we can label the channel with each as a different one and of course with a different capacity with those corresponding to other values of . Because of the arguments expressed previously in this work, we can use this measure to the same extent on LHM, ATR, and TRT. For a related discussion of the equivalence of the time-reversal methods and the employment of left-hand materials, we can see ref. [30], and for the use of time reversal on antennas, we can see also ref. [16].
5. An academic example
In order to give an insight into information measurement applied to TR, let us propose that our system behaves like a filter. So, in this particular example, we have no loss if we select t < T. We also propose that we have a signal like [12]:
sin2πΘt2πΘtE26
And, that we have instead of the incoming signal in Eq. (15) another like [10]
12sin2πΘtπΘt2E27
The input function Eq. (26) is a sample of a more general function generated by the sum of a series of shifted functions
asin2πΘt2πΘtE28
where a, the amplitude of the sample is no greater than (S is the peak allowed transmitter power).
The channel capacity would be [23] approximately (provided that SN is small)
CT=ΘlogS+QnTQnTE29
In the time-reversal process, we have shown that for each Fourier component, we should add a complex exponential factor dependent on T. But we know now that the tool is the same and that only the numerical value of channel capacity CT changes. We see how in practice the time-reversal parameter T appears explicitly but also that when we cut the time duration of reversed signal, it is possible to consider them as an additive contribution to . But the form of Eq. (25) suggests a generalized measure of a blend or mix channel capacity when sharing the same band W and differ only by the recording time
CT1,T2,⋯,Tn=ΘlogS+QnT1T2⋯TnQnT1T2⋯TnE30
The fact that we are using the same band but different cutting limits also suggests that we can design an appropriate filter that can distinguish between signals according to the recording time that is we can superpose signals with the same frequency range but with different recording times. In a previous work, we have sketched a filter, but now we give a better-defined device, so we propose (see Figure 2) as a hint to get the filter, the following steps for both the transmitter and the receiver:
Figure 1.
Image of the solutions of Eq. (11) when the related equation is 987.93(x2-y2–106) = y (106-2x).
Figure 2.
Flow chart for a proposal device. This can emit and read the blended messages with recording times beneath to the unique band .
Figure 3.
The former radio broadcasting procedure: modulated amplitude. Image given by Pérez-Martinez [31].
5.1 Transmitter
First, increase the n frequencies on the unique entrance band (that is centered in frequency ) incoming from the inverse of , then the n new top frequencies are used to create n transformed signals with the rule suggested by communication theory and these last signals enter a blender. Then, the mixed signal is taken by a band generator and projected in Q new bands centered at the frequencies (each corresponds to a resonant frequency). Finally, each band enters this signal transmitter.
5.2 Receiver
The traveling signals enter the mirror band amplifier, so called because it knows that there are resonant frequencies and then can create (or separate the signal in Q resonant bands) sub-bands and amplify the signal in each band (at this moment, each band carries a piece of the original n different signals); after this, the signals are blended and then sending to a secondary mirror band generator which knows that there are n recording times and because of that it can create n bands with the higher central frequencies (these last signals could be amplitude-modulated signals) and distribute the blended signal among them. Then, every signal on each band enters a frequency dimmer (the inverse operation performed by the frequency elevators in the transmitter), so we retrieve the n original signals corresponding to the unique band . For example, in Section 3, we have that the total number of resonances is , and the two resonant frequencies are and .
At this point, it is important to say that the key point on the use of the proposed device is the build of information packs described in another place in order to diminish mutual interference between different signals.
6. Error in time reversing and a related theorem
Based on the equivalence of the TRT and the properties of the Green function, we can trust that any discussion about the interaction of metamaterials with electromagnetic field can be done through this function and simultaneously observe the effect of a time reversal. For this reason, we can now describe the error in terms of the Green function by the hypothesis that LHM can be put to test by forward and backward in time signals and read the results with two points of view: first, the direct effect of the loss of information because of the limited record time T or second, how the negative refraction index helps to preserve information. Now, we can review our previous results and generalize using the kernels, so we can characterize the capacity of a channel in many different circumstances. So, we have made use of the analogies [30] between the TRT and the employment of LHM to propose that we can express the capacity of any of these negative refraction index materials in the same terms or procedures as those of TRT. Also, we can propose an identical description for the channel capacity that is Eq. (24) and its generalization Eqs. (25) and (30). Then, the matrix formalism for discrete systems can be used to characterize the channel capacity of transmission of information in a process of time reversibility using the Fourier transforms of the Green functions (properly we use the kernels with the interaction matrix ) forward and backward. That is, by the first step, the signal transforms like (in the following equations I and F stand for initial and final places):
E31
then in the second step, it returns to the initial place by means of the operation.
E32
Then, the complete signal trip would be:
E33
So that by defining the error in the time-reversing process by:
E34
We can write this like:
E35
or
E36
Eq. (36) is a corollary that shows explicitly the role of both the forward and backward Fourier transforms of the Green function (we have done on Eq. (8) for convenience and also for the complete kernels and ). Eq. (36) is very clear about the origin of the errors because we can see, for example, that in the case that the forward and backward Green functions are mathematically one the transpose conjugated of the other for a perfect time reversal (when acting the first on a column vector and on a row vector the other), we get that the error is zero and that the error increases as the differences of both functions also increase. In a very special case, we can then propose that and only differ by the factor or when the only source of error is the recording time , so that we obtain from Eq. (36) that:
E37
In Eq. (37), the function has the form of the Fourier transform of the Green function but with the argument translated by an amount equal to the recording time that appears explicitly in Eq. (19) that is the Fourier transform of:
E38
But with the time running backward, so, as we will show in a moment, if T is very short, the error will be very huge. On the contrary, if the time goes to infinity, the error will go to zero. Resuming, the new Eqs. (33)–(38), make possible a characterization of the lost information in left-hand materials not only for microwave range, but also for visible frequencies because we have extended recently the time-reversal techniques (see ref. [3, 12]).
and because the kernel of the Fourier transform of the generalized inhomogeneous Fredholm’s equation (GIFE) satisfies the following integral equations:
E41
E42
While Eq. (41) exactly represents the problem with a finite recording time T, Eq. (42) represents a hypothetical problem in which the recording time is infinite.
Then, we can suppose that the two kernels in Eq. (40) represent the real and the hypothetical problem described above. Of course, we see that if real conditions approximate the ideal ones, the error is clearly zero. But we can factorize the interaction matrix in Eq. (43):
E44
But Eq. (44) says clearly that the error does not depend on the form of the interaction, only depends on the recording time T. Even we have supposed that the only source of error was the recording time, we do not suppose any particular behavior for the interaction. So, we have enunciated and proved a theorem:
Theorem III.
In the time-reversal problem and for left-hand material conditions, the normalized error:
E45
is independent of the explicit form of the interaction provided the last is isotropic.
Returning to the time representation, for the time-dependent retarded isotropic (remember that in the following expression, the indices m and n indicates components of the field and can be omitted), free Green function related to , we can write explicitly.
E46
and for the advanced time-dependent free Green function related to :
E47
That is the recording time appears explicitly in the advanced Green function and we can show that its value makes possible to blend many signals on the same channel without interference. It is important to note that for resonances, the relevant Green functions are precisely the free ones and not the complete ones as we can see in Eqs. (5) and (6).
7. Information packs
In this section, we present the support and the definition of the information packs that are required for the adequate performance of the device shown in Section 6 and that by him constitute a method to improve the broadcasting efficiency. To this end, we must remember that on communication theory [9, 10] are defined the so-called ensembles of functions dependent on time. One of their properties is really a group one from the mathematical point of view and lies in that any ensemble transforms into another member of the same ensemble when we change the function at any certain amount of time. To illustrate this property, we shift by an amount t1 the argument of all the members of the ensemble defined as follows:
Fθt=sint+θE48
where θ is distributed uniformly from 0 to 2π.
Then, we have:
E49
where φ is distributed uniformly from 0 to 2π.
Then, each function has changed individually, but the ensemble as a whole is invariant under the transformation. Also, if we apply the operator T which gives for each member
Sαt=TFαtE50
It implies that
Sαt+t1=TFαt+t1E51
It is possible to prove that if T is an invariant operator and the input ensemble Fαt is stationary, the output ensemble Sαt is also stationary. Now, for communication purposes, the operator T, which could be a modulation process, is not invariant because of the phase carrier that gives certain time structure, but if the translations are multiples of the periods of the carrier, then the modulation will be invariant. At this stage, it is important to remember that Wiener [6] has pointed out that if a device is linear as well as invariant (in the sense of the last definition), then the Fourier analysis is the appropriate mathematical tool for dealing with the problem. Now, suppose in addition that we are interested on functions that are limited to the band from 0 to Θ cycles per second, then we have the following theorem [10]:
Let Ft contain no frequencies over Θ. Then:
Ft=∑−∞∞Xnsinπ2Θt−nπ2Θt−nE52
where,
Xn=Fn2WE53
In this expansion, Ft is represented as a sum of orthogonal (basis) functions. The coefficients Xn of the various terms can be considered as coordinates in an infinite dimensional “functions space.” We will take the last theorem (Eqs. (52) and (53)) as a very suggestive rule to consider the recently obtained resonant frequencies. If we use physical arguments about the reasons of the presence of a resonance, we can be sure that channels available for broadcasting are also limited in number. Indeed, in a recent paper, we have generalized the procedure for electromagnetic scalar and vector potentials [30] and we have established that we can use either the electromagnetic field or the potentials for obtaining the resonances and also for the use of the recording time as a resource to optimize communications. And now, we can build information packs (IP) that are functions, which represent a part of the signal we want to send with the minimum loss of information. The resultant expression is:
Fet=∑−∞∞Xn,esinπ2ωet−nπ2ωet−nE54
where,
Xn,e=Fen2ωeE55
Every ωe allows us to build a decomposition like (54) but we expect that only a few terms are necessary for a well representation of Fet. Next, we send separately each Fet by its own device and it is all we need for broadcasting. To receive the signal, we need a separate device for each ωe.
A very important feature is that because of the properties of the modulation process stated in Eqs. (50) and (51), we can recover, for any arbitrary signal, the behavior under spectral representation and under separated pack representation. So we can either talk about Fet in Eq. (54) as the representation of some element of the basis function for the spectral representation or directly as the e component of an arbitrary signal St=TFt. Now, we recall the two resonances founded in another work [3]:
ω1=π4d+ω0E56
and
ω2=3π4d+ω0E57
Suppose that St is the signal
St=sinπ2Θtπ2ΘtE58
Then, we have the first pack:
S1t=∑−∞∞Xn,1sinπ2ω1t−nπ2ω1t−nE59
with
Xn,1=Sn2ω1E60
And, we have the second pack
S2t=∑−∞∞Xn,2sinπ2ω2t−nπ2ω2t−nE61
with
Xn,2=Sn2ω2E62
We can see that if Θ=ω1, the only coordinate distinct to zero is X0,1=1 and if Θ=ω2, only survives the term X0,2=1. So, we remark self-consistency of the method.
Even VMF has a broad application on the microwave range, maybe it would be more useful to apply for larger frequencies. But even the great technological boom, there is not any device that could manipulate visible light at length as happens with microwaves. Whatever we can recall some of the basic early ideas on radio broadcasting when the option was sending information by means of modulating the wave’s amplitude as appears in Figure 3. However, we can take our definition of information packs and put it in a modulated visible-light signal taking the enveloping of the signal we name the wrapping signal (WS) as the information that can be injected inside Eq. (54). Technically, we rewrite Eqs. (50) and (51) in the form:
Hβt=ΩSβtE63
It implies that
Hβt+t1=ΩSβt+t1E64
Now, the operator Ω is a generic operator like T but acting over the ensemble Sβt. Some care must be taken when reading the WS information, because the translations stated in Eqs. (63) and (64) were multiples of the periods of the carrier, and then as we said above, the modulation will be invariant. The resonant frequencies will be obtained by the same procedure.
In order to complete the methodology, we recall the concept of group velocity cgt and construct this inherent quotient between them and the enveloping frequency ωg which results in the wave number κg, so we associate them with the resonance frequencies in a similar form as we styled with microwaves, but now these last signals come from the measured properties of the Green’s function associated with the modulated signal. In this way, in Eq. (54), we put directly the WS first for a non modulated beam:
Se\'t=∑−∞∞Xn,e\'sinπ2ωe\'t−nπ2ωe\'t−nE65
in which the coefficients are given by:
Xn,e\'=Se\'n2ωe\'E66
The signal Se\'t in (65) can be viewed as the representation of some element of the new basis functions or as the e\' component of an arbitrary amplitude-modulated signal He\'t. Now, we can give an example where we use the same values for the resonances on Eqs. (56) and (57) and where we propose an arbitrary amplitude modulated or WS (for a modulated visible light beam) signal given as follows:
Ht=acosΘAt+δE67
In Eq. (67), ΘA=Θp±Θm is an arbitrary frequency, and in a same manner, a and δ are preconceived constants but otherwise arbitrary.
With these preliminaries, we can build the first IP:
As we said above, the resonances must come also for the WS. By this procedure, we have enlarged the scope of the formalism we named vector-matrix or VMF [1, 2, 3].
In order to complete our example, we put explicit values of the resonances for the two visible light IP:
H1t=∑−∞∞Xn,1sinπ2π4d+ω0t−nπ2π4d+ω0t−nE74
And explicitly
Xn,1=acosΘAn2π4d+ω0+δE75
For the second IP
H2t=∑−∞∞Xn,2sinπ23π4d+ω0t−nπ23π4d+ω0t−nE76
in which
Xn,2=acosΘAn23π4d+ω0+δE77
8. Conclusions
In Eqs. (25), (29), (30), (34)–(40), we have shown that it is possible to use an operator language and the properties of the Green function to define the capacity of a channel, the loss of information, and finally, the error in the time-reversal process. Therefore, we can use our results to describe the behavior of LHM interacting with electromagnetic field whether forward or backward in time. Thanks to our interpretation of a resonance in the broadcasting problem with the left-hand material conditions, and the application of the model PSM, we make up a broadcasting system that has the power for distinguishes between signals according to their recording time, and allows to superpose signals in the same frequency range having different recording times with the minor loss because of resonance technology; to this end, we have presented a detailed support and definition of the information packs (IP) and the possibility of application for visible light. In addition, we have enunciated and proved a theorem (theorem III) that establishes: for the TRT and LHM, the normalized error is independent of the particular behavior of the interaction. Summarizing, we give a complete recipe for optimizing communications efficiency.
\n',keywords:"wireless communications, optimal broadcasting, information packs, negative refraction index, communication theory, wave propagation through plasma",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/66166.pdf",chapterXML:"https://mts.intechopen.com/source/xml/66166.xml",downloadPdfUrl:"/chapter/pdf-download/66166",previewPdfUrl:"/chapter/pdf-preview/66166",totalDownloads:149,totalViews:0,totalCrossrefCites:0,dateSubmitted:"October 9th 2018",dateReviewed:"February 4th 2019",datePrePublished:"March 15th 2019",datePublished:"October 30th 2019",readingETA:"0",abstract:"This chapter is devoted to review a set of new technologies that we have developed and to show how they can improve the process of broadcasting in two principal ways: that is, one of these avoiding the loss of transmission signals due to abrupt changes in sign of the diffraction index and the other, preventing the mutual perturbation between signals generating information leak. In this manner, we propose the join of several of the mentioned technologies to get an optimum efficiency on the process of broadcasting communications showing the theoretical foundations and discussing some experiments that bring us to create the plasma sandwich model and others. Despite our very innovative technology, we underline that a complete recipe must include other currently in use like multiple-input multiple-output (MIMO) simultaneously. We include some mathematical proofs and also give an academic example.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/66166",risUrl:"/chapter/ris/66166",signatures:"Juan Manuel Velazquez Arcos, Ricardo Teodoro Paez Hernandez, Tomas David Navarrete Gonzalez and Jaime Granados Samaniego",book:{id:"8723",title:"Telecommunication Systems",subtitle:"Principles and Applications of Wireless-Optical Technologies",fullTitle:"Telecommunication Systems - Principles and Applications of Wireless-Optical Technologies",slug:"telecommunication-systems-principles-and-applications-of-wireless-optical-technologies",publishedDate:"October 30th 2019",bookSignature:"Isiaka A. Alimi, Paulo P. Monteiro and António L. Teixeira",coverURL:"https://cdn.intechopen.com/books/images_new/8723.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"208236",title:"Dr.",name:"Isiaka A.",middleName:null,surname:"Alimi",slug:"isiaka-a.-alimi",fullName:"Isiaka A. Alimi"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"96912",title:"Dr.",name:"Ricardo Teodoro",middleName:null,surname:"Paez Hernandez",fullName:"Ricardo Teodoro Paez Hernandez",slug:"ricardo-teodoro-paez-hernandez",email:"phrt@correo.azc.uam.mx",position:null,institution:{name:"Universidad Autónoma Metropolitana",institutionURL:null,country:{name:"Mexico"}}},{id:"114776",title:"Dr.",name:"Juan Manuel",middleName:null,surname:"Velazquez Arcos",fullName:"Juan Manuel Velazquez Arcos",slug:"juan-manuel-velazquez-arcos",email:"jmva@correo.azc.uam.mx",position:null,institution:{name:"Universidad Autónoma Metropolitana",institutionURL:null,country:{name:"Mexico"}}},{id:"179014",title:"MSc.",name:"Jaime",middleName:null,surname:"Granados Samaniego",fullName:"Jaime Granados Samaniego",slug:"jaime-granados-samaniego",email:"jgs3112@yahoo.com",position:null,institution:null},{id:"291342",title:"MSc.",name:"Tomas David",middleName:null,surname:"Navarrete Gonzalez",fullName:"Tomas David Navarrete Gonzalez",slug:"tomas-david-navarrete-gonzalez",email:"ngtd@azc.uam.mx",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Recovering the matrix equations",level:"1"},{id:"sec_3",title:"3. Introducing the PSM parameters",level:"1"},{id:"sec_4",title:"4. Communication theory measurement of information loss",level:"1"},{id:"sec_5",title:"5. An academic example",level:"1"},{id:"sec_5_2",title:"5.1 Transmitter",level:"2"},{id:"sec_6_2",title:"5.2 Receiver",level:"2"},{id:"sec_8",title:"6. Error in time reversing and a related theorem",level:"1"},{id:"sec_9",title:"7. Information packs",level:"1"},{id:"sec_10",title:"8. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Velázquez-Arcos JM, Granados-Samaniego J. Wave propagation under confinement break. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE). 2016;11(2. Ver. I):42-48. e-ISSN: 2278-2834, p-ISSN: 2278-8735. Available from: www.iosrjournals.org'},{id:"B2",body:'Velázquez-Arcos JM, Granados-Samaniego J, Vargas CA. 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Journal of Applied Physics. 2003;93:3906'},{id:"B19",body:'Hernández-Bautista F, Vargas CA, Velázquez-Arcos JM. Negative refractive index in split ring resonators. Revista Mexicana de Fisica. 2013;59(1):139-144. ISSN: 0035-00IX'},{id:"B20",body:'Velázquez-Arcos JM. Nanotechnology can be helped by a new Technology for Electromagnetic Waves. Nanoscience and Nanotechnology. 2012;2(5):139-143. DOI: 10.5923/j.nn.20120205.02'},{id:"B21",body:'de la Madrid R. The decay widths, the decay constants, and the branching fractions of a resonant state. Nuclear Physics A. 2015;940:297-310'},{id:"B22",body:'Velázquez-Arcos JM, Vargas CA, Fernández-Chapou JL, Salas-Brito AL. On computing the trace of the kernel of the homogeneous Fredholm’s equation. Journal of Mathematical Physics. 2008;49:103508. DOI: 10.1063/1.3003062'},{id:"B23",body:'de la Madrid R. The rigged Hilbert space approach to the Gamow states. Journal of Mathematical Physics. 2012;53(10):102113. DOI: 10.1063/1.4758925'},{id:"B24",body:'Velázquez-Arcos JM. Fredholm’s equation and Fourier transform on discrete electromagnetic systems. IJRRAS. 2012;11(3):456-469. Available from: www.arpapress.com/Volumes/Vol11Issue3/IJRRAS_11_3_11.pdf'},{id:"B25",body:'Shannon CE. A mathematical theory of communication. The Bell System Technical Journal. 1948;27:379-423, 623-656'},{id:"B26",body:'Nyquist H. Certain factors affecting telegraph speed. Bell System Technical Journal. 1924:324. Certain Topics in Telegraph Transmission Theory, A.I.E.E. Trans., vol. 47, April 1928, pp. 617'},{id:"B27",body:'Hartley RVL. The Interpolation, Extrapolation and Smoothing of Stationary Time Series, NDRC Report. New York-London: Wiley; 1949'},{id:"B28",body:'Wiener N. The Ergodic theorem. Duke Mathematical Journal. 1939;5:1-18'},{id:"B29",body:'Hopf E. On causality statistics and probability. 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UK Research and Innovation (former Research Councils UK (RCUK) - including AHRC, BBSRC, ESRC, EPSRC, MRC, NERC, STFC.) Processing charges for books/book chapters can be covered through RCUK block grants which are allocated to most universities in the UK, which then handle the OA publication funding requests. It is at the discretion of the university whether it will approve the request.)
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