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Author: William Schiesser
Publisher: CRC Press
ISBN: 1000509982
Category : Mathematics
Languages : en
Pages : 165
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Book Description
Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.
Author: William Schiesser
Publisher: CRC Press
ISBN: 1000509982
Category : Mathematics
Languages : en
Pages : 165
Get Book Here
Book Description
Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.
Author: William Schiesser
Publisher: CRC Press
ISBN: 1000509958
Category : Mathematics
Languages : en
Pages : 196
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Book Description
Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.
Author: William Schiesser
Publisher: CRC Press
ISBN: 9781003243052
Category : Mathematics
Languages : en
Pages : 188
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Book Description
Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.
Author: Ronald E Mickens
Publisher: World Scientific
ISBN: 981122255X
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Author: Dumitru Baleanu
Publisher: Springer Science & Business Media
ISBN: 1461404576
Category : Technology & Engineering
Languages : en
Pages : 302
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Book Description
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.
Author: Sanjay Gupta
Publisher: Simon and Schuster
ISBN: 1501166751
Category : Psychology
Languages : en
Pages : 336
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Book Description
Keep your brain young, healthy, and sharp with this science-driven guide to protecting your mind from decline by neurosurgeon and CNN chief medical correspondent Dr. Sanjay Gupta. Throughout our life, we look for ways to keep our minds sharp and effortlessly productive. Now, globetrotting neurosurgeon Dr. Sanjay Gupta offers “the book all of us need, young and old” (Walter Isaacson, #1 New York Times bestselling author of The Code Breaker) with insights from top scientists all over the world, whose cutting-edge research can help you heighten and protect brain function and maintain cognitive health at any age. Keep Sharp debunks common myths about aging and mental decline, explores whether there’s a “best” diet or exercise regimen for the brain, and explains whether it’s healthier to play video games that test memory and processing speed, or to engage in more social interaction. Discover what we can learn from “super-brained” people who are in their eighties and nineties with no signs of slowing down—and whether there are truly any benefits to drugs, supplements, and vitamins. Dr. Gupta also addresses brain disease, particularly Alzheimer’s, answers all your questions about the signs and symptoms, and shows how to ward against it and stay healthy while caring for a partner in cognitive decline. He likewise provides you with a personalized twelve-week program featuring practical strategies to strengthen your brain every day. Keep Sharp is the “must-read owner’s manual” (Arianna Huffington) you’ll need to keep your brain young and healthy regardless of your age!
Author: Institute of Medicine
Publisher: National Academies Press
ISBN: 0309316928
Category : Medical
Languages : en
Pages : 251
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Book Description
Myalgic encephalomyelitis (ME) and chronic fatigue syndrome (CFS) are serious, debilitating conditions that affect millions of people in the United States and around the world. ME/CFS can cause significant impairment and disability. Despite substantial efforts by researchers to better understand ME/CFS, there is no known cause or effective treatment. Diagnosing the disease remains a challenge, and patients often struggle with their illness for years before an identification is made. Some health care providers have been skeptical about the serious physiological - rather than psychological - nature of the illness. Once diagnosed, patients often complain of receiving hostility from their health care provider as well as being subjected to treatment strategies that exacerbate their symptoms. Beyond Myalgic Encephalomyelitis/Chronic Fatigue Syndrome proposes new diagnostic clinical criteria for ME/CFS and a new term for the illness - systemic exertion intolerance disease(SEID). According to this report, the term myalgic encephalomyelitis does not accurately describe this illness, and the term chronic fatigue syndrome can result in trivialization and stigmatization for patients afflicted with this illness. Beyond Myalgic Encephalomyelitis/Chronic Fatigue Syndrome stresses that SEID is a medical - not a psychiatric or psychological - illness. This report lists the major symptoms of SEID and recommends a diagnostic process.One of the report's most important conclusions is that a thorough history, physical examination, and targeted work-up are necessary and often sufficient for diagnosis. The new criteria will allow a large percentage of undiagnosed patients to receive an accurate diagnosis and appropriate care. Beyond Myalgic Encephalomyelitis/Chronic Fatigue Syndrome will be a valuable resource to promote the prompt diagnosis of patients with this complex, multisystem, and often devastating disorder; enhance public understanding; and provide a firm foundation for future improvements in diagnosis and treatment.
Author: Ricardo Almeida
Publisher: World Scientific Publishing Company
ISBN: 1783266422
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.
Author:
Publisher: World Scientific
ISBN: 9811223092
Category : Medical
Languages : en
Pages : 125
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Book Description
A novel public health concept, the Fangcang Shelter Hospital was first proposed by Professor Wang Chen, an academician of Chinese Academy of Engineering, in Wuhan, China, in February 2020. While responding to the coronavirus disease 2019 (COVID-19) outbreak, medical staff faced the pressing situation of limited medical supplies, which led Professor Wang Chen to the suggestion of converting large-scale public venues such as exhibition centers and indoor stadiums into shelter hospitals to receive large number of patients, as this involved minimum time and monetary costs. The five essential functions of Fangcang Shelter Hospitals (isolation, triage, provision of basic medical care, frequent monitoring and rapid referral, and essential living and social engagement) enable shelter hospitals to receive patients with mild to moderate symptoms of COVID-19, and have the greatest impact on isolating the source of infection and expanding the area's health-care capacity.Two of the first three Fangcang Shelter Hospitals set up in Wuhan were redeveloped by Zall Group Property from existing buildings, while Zall Foundation was responsible for the provision of essential medical supplies and logistical support to facilitate the running of these shelter hospitals. In total, the two shelter hospitals have been instrumental in diagnosing, treating and curing 3663 patients. Under the medical expertise and guidance of Professor Wang Chen, as well as inputs from Zall Foundation's crews who contributed to the design, renovation and operation of these shelter hospitals, this manual encompasses knowledge and experience distilled from the running of these Fangcang Shelter Hospitals. Covering five important aspects, namely the proposal, design, renovation, operation, and logistical support for shelter hospitals, this booklet aims to be a useful reference for other epidemic prevention and control efforts in regions around the world. The manual has been translated into more than 20 languages.
Author: Institute of Medicine
Publisher: National Academies Press
ISBN: 0309182158
Category : Medical
Languages : en
Pages : 376
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Book Description
The emergence of severe acute respiratory syndrome (SARS) in late 2002 and 2003 challenged the global public health community to confront a novel epidemic that spread rapidly from its origins in southern China until it had reached more than 25 other countries within a matter of months. In addition to the number of patients infected with the SARS virus, the disease had profound economic and political repercussions in many of the affected regions. Recent reports of isolated new SARS cases and a fear that the disease could reemerge and spread have put public health officials on high alert for any indications of possible new outbreaks. This report examines the response to SARS by public health systems in individual countries, the biology of the SARS coronavirus and related coronaviruses in animals, the economic and political fallout of the SARS epidemic, quarantine law and other public health measures that apply to combating infectious diseases, and the role of international organizations and scientific cooperation in halting the spread of SARS. The report provides an illuminating survey of findings from the epidemic, along with an assessment of what might be needed in order to contain any future outbreaks of SARS or other emerging infections.
