Modelling Optimization and Control of Biomedical Systems

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Publisher : John Wiley & Sons
ISBN 13 : 1118965590
Total Pages : 326 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Modelling Optimization and Control of Biomedical Systems by : Efstratios N. Pistikopoulos

Download or read book Modelling Optimization and Control of Biomedical Systems written by Efstratios N. Pistikopoulos and published by John Wiley & Sons. This book was released on 2018-01-09 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows the newest developments in the field of multi-parametric model predictive control and optimization and their application for drug delivery systems This book is based on the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project, which was created to derive intelligent computer model-based systems for optimization of biomedical drug delivery systems in the cases of diabetes, anaesthesia, and blood cancer. These systems can ensure reliable and fast calculation of the optimal drug dosage without the need for an online computer—while taking into account the specifics and constraints of the patient model, flexibility to adapt to changing patient characteristics and incorporation of the physician’s performance criteria, and maintaining the safety of the patients. Modelling Optimization and Control of Biomedical Systems covers: mathematical modelling of drug delivery systems; model analysis, parameter estimation, and approximation; optimization and control; sensitivity analysis & model reduction; multi-parametric programming and model predictive control; estimation techniques; physiologically-based patient model; control design for volatile anaesthesia; multiparametric model based approach to intravenous anaesthesia; hybrid model predictive control strategies; Type I Diabetes Mellitus; in vitro and in silico block of the integrated platform for the study of leukaemia; chemotherapy treatment as a process systems application; and more. Introduces readers to the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project Presents in detail the theoretical background, computational tools, and methods that are used in all the different biomedical systems Teaches the theory for multi-parametric mixed-integer programming and explicit optimal control of volatile anaesthesia Provides an overview of the framework for modelling, optimization, and control of biomedical systems This book will appeal to students, researchers, and scientists working on the modelling, control, and optimization of biomedical systems and to those involved in cancer treatment, anaesthsia, and drug delivery systems.

Mathematical Modelling in Biomedicine

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Publisher : Springer Science & Business Media
ISBN 13 : 9400954921
Total Pages : 273 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Mathematical Modelling in Biomedicine by : Y. Cherruault

Download or read book Mathematical Modelling in Biomedicine written by Y. Cherruault and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Modelling and Control in Biomedical Systems 2006

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Publisher : Elsevier
ISBN 13 : 0080479499
Total Pages : 576 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Modelling and Control in Biomedical Systems 2006 by : David Dagan Feng

Download or read book Modelling and Control in Biomedical Systems 2006 written by David Dagan Feng and published by Elsevier. This book was released on 2006-09-19 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling and Control in Biomedical Systems (including Biological Systems) was held in Reims, France, 20-22 August 2006. This Symposium was organised by the University of Reims Champagne Ardenne and the Société de l’Electricité, de l’Electronique et des TIC (SEE). The Symposium attracted practitioners in engineering, information technology, mathematics, medicine and biology, and other related disciplines, with authors from 24 countries. Besides the abstracts of the four plenary lectures, this volume contains the 92 papers that were presented by their authors at the Symposium. The papers included two invited keynote presentations given by internationally prominent and well-recognised research leaders: Claudio Cobelli, whose talk is titled "Dynamic modelling in diabetes: from whole body to genes"; and Irving J. Bigio, whose talk is titled "Elastic scattering spectroscopy for non-invasive detection of cancer". Two prestigious industrial speakers were also invited to give keynote presentations: Terry O'Brien from LIDCO, whose talk is titled "LIDCO: From the laboratory to protocolized goal directed therapy"; and Lorenzo Quinzio of Philips, whose talk is titled "Clinical decision support in monitoring and information systems". A valuable source of information on the state-of- the-art in Modelling and Control in Biomedical Systems Including abstracts of four plenary lectures, and 92 papers presented by their authors

Modelling and Control in Biomedical Systems

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Publisher : Pergamon
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Modelling and Control in Biomedical Systems by : Claudio Cobelli

Download or read book Modelling and Control in Biomedical Systems written by Claudio Cobelli and published by Pergamon. This book was released on 1989 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hardbound. This volume provides a complete and up-to-date review of the recent developments and trends relating to modelling and control in biomedical systems in research, diagnosis and therapy. Focus is placed on methodological issues relevant to modelling and control as well as to the various physiological systems of the organism visited from a control viewpoint. Contains 98 papers.

Modeling and Control in the Biomedical Sciences

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Author :
Publisher : Springer
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Modeling and Control in the Biomedical Sciences by : Harvey Thomas Banks

Download or read book Modeling and Control in the Biomedical Sciences written by Harvey Thomas Banks and published by Springer. This book was released on 1975 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom experience and on my research efforts with several colleagues during the intervening period. The narrow viewpoint of the present notes (use of optimization and control theory in biomedical problems) reflects more the scope of the CMC lectures given in August, 1973 than the scope of my own interests. Indeed, my real interests have included the modeling process itself as well as the contributions made by investiga- tors who employ the techniques and ideas of control theory, systems analysis, dif- ferential equations, and stochastic processes. Some of these contributions have quite naturally involved application of optimal control theory. But in my opinion many of the interesting efforts being made in modeling in the biomedical sciences encompass much more than the use of control theory.

Modeling and Control in the Biomedical Sciences

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642662072
Total Pages : 123 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Modeling and Control in the Biomedical Sciences by : H.T. Banks

Download or read book Modeling and Control in the Biomedical Sciences written by H.T. Banks and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom experience and on my research efforts with several colleagues during the intervening period. The narrow viewpoint of the present notes (use of optimization and control theory in biomedical problems) reflects more the scope of the CMC lectures given in August, 1973 than the scope of my own interests. Indeed, my real interests have included the modeling process itself as well as the contributions made by investiga tors who employ the techniques and ideas of control theory, systems analysis, dif ferential equations, and stochastic processes. Some of these contributions have quite naturally involved application of optimal control theory. But in my opinion many of the interesting efforts being made in modeling in the biomedical sciences encompass much more than the use of control theory.

Control Applications for Biomedical Engineering Systems

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Publisher : Academic Press
ISBN 13 : 0128174625
Total Pages : 476 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Control Applications for Biomedical Engineering Systems by : Ahmad Taher Azar

Download or read book Control Applications for Biomedical Engineering Systems written by Ahmad Taher Azar and published by Academic Press. This book was released on 2020-01-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Applications for Biomedical Engineering Systems presents different control engineering and modeling applications in the biomedical field. It is intended for senior undergraduate or graduate students in both control engineering and biomedical engineering programs. For control engineering students, it presents the application of various techniques already learned in theoretical lectures in the biomedical arena. For biomedical engineering students, it presents solutions to various problems in the field using methods commonly used by control engineers. Points out theoretical and practical issues to biomedical control systems Brings together solutions developed under different settings with specific attention to the validation of these tools in biomedical settings using real-life datasets and experiments Presents significant case studies on devices and applications

Optimization and Control of Dynamic Systems

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Publisher : Springer
ISBN 13 : 3319626469
Total Pages : 679 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Optimization and Control of Dynamic Systems by : Henryk Górecki

Download or read book Optimization and Control of Dynamic Systems written by Henryk Górecki and published by Springer. This book was released on 2017-07-26 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.

System Modelling and Optimization

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Publisher : Springer
ISBN 13 : 0387348972
Total Pages : 635 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis System Modelling and Optimization by : J. Dolezal

Download or read book System Modelling and Optimization written by J. Dolezal and published by Springer. This book was released on 2013-06-05 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings volume contains carefully selected papers presented during the 17th IFIP Conference on System Modelling and Optimization. Optimization theory and practice, optimal control, system modelling, stochastic optimization, and technical and non-technical applications of the existing theory are among areas mostly addressed in the included papers. Main directions are treated in addition to several survey papers based on invited presentations of leading specialists in the respective fields. Publication provides state-of-the-art in the area of system theory and optimization and points out several new areas (e.g fuzzy set, neural nets), where classical optimization topics intersects with computer science methodology.

Introduction to Modeling in Physiology and Medicine

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Publisher : Elsevier
ISBN 13 : 0080559980
Total Pages : 337 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Introduction to Modeling in Physiology and Medicine by : Claudio Cobelli

Download or read book Introduction to Modeling in Physiology and Medicine written by Claudio Cobelli and published by Elsevier. This book was released on 2008-02-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified modeling textbook for students of biomedical engineering provides a complete course text on the foundations, theory and practice of modeling and simulation in physiology and medicine. It is dedicated to the needs of biomedical engineering and clinical students, supported by applied BME applications and examples. Developed for biomedical engineering and related courses: speaks to BME students at a level and in a language appropriate to their needs, with an interdisciplinary clinical/engineering approach, quantitative basis, and many applied examples to enhance learning Delivers a quantitative approach to modeling and also covers simulation: the perfect foundation text for studies across BME and medicine Extensive case studies and engineering applications from BME, plus end-of-chapter exercises

Biomimicry for Optimization, Control, and Automation

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Publisher : Springer Science & Business Media
ISBN 13 : 1846280699
Total Pages : 934 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Biomimicry for Optimization, Control, and Automation by : Kevin M. Passino

Download or read book Biomimicry for Optimization, Control, and Automation written by Kevin M. Passino and published by Springer Science & Business Media. This book was released on 2005-09-08 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomimicry uses our scienti?c understanding of biological systems to exploit ideas from nature in order to construct some technology. In this book, we focus onhowtousebiomimicryof the functionaloperationofthe “hardwareandso- ware” of biological systems for the development of optimization algorithms and feedbackcontrolsystemsthatextendourcapabilitiestoimplementsophisticated levels of automation. The primary focus is not on the modeling, emulation, or analysis of some biological system. The focus is on using “bio-inspiration” to inject new ideas, techniques, and perspective into the engineering of complex automation systems. There are many biological processes that, at some level of abstraction, can berepresentedasoptimizationprocesses,manyofwhichhaveasa basicpurpose automatic control, decision making, or automation. For instance, at the level of everyday experience, we can view the actions of a human operator of some process (e. g. , the driver of a car) as being a series of the best choices he or she makes in trying to achieve some goal (staying on the road); emulation of this decision-making process amounts to modeling a type of biological optimization and decision-making process, and implementation of the resulting algorithm results in “human mimicry” for automation. There are clearer examples of - ological optimization processes that are used for control and automation when you consider nonhuman biological or behavioral processes, or the (internal) - ology of the human and not the resulting external behavioral characteristics (like driving a car). For instance, there are homeostasis processes where, for instance, temperature is regulated in the human body.

An Introduction to Modeling of Transport Processes

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Publisher :
ISBN 13 : 9781107188525
Total Pages : 503 pages
Book Rating : 4.1/5 (885 download)

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Book Synopsis An Introduction to Modeling of Transport Processes by : Ashim K. Datta

Download or read book An Introduction to Modeling of Transport Processes written by Ashim K. Datta and published by . This book was released on 2010 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Organized around problem solving, this book gently introduces the reader to computational simulation of biomedical transport processes, bridging fundamental theory with real-world applications. Using this book the reader will gain a complete foundation to the subject, starting with problem simplification, implementation in software, through to interpretation of results, validation, and optimization"--Provided by publisher.

Modelling and Control in Biomedical Systems 1997 (including Biological Systems)

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Publisher : Pergamon
ISBN 13 :
Total Pages : 386 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Modelling and Control in Biomedical Systems 1997 (including Biological Systems) by : D. A. Linkens

Download or read book Modelling and Control in Biomedical Systems 1997 (including Biological Systems) written by D. A. Linkens and published by Pergamon. This book was released on 1997 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paperback. This volume contains the 90 papers presented at the 3rd IFAC Symposium on Modelling and Control in Biomedical Systems held in Warwick, UK from 23-26 March 1997. Significant work in the field of biomedical systems analysis and design is taking place throughout the world and the opportunities for technological interchanges offered by symposia like this one are extremely valuable for the progress and stability of effort and vision in this important human-centred field.The symposium was multi- and inter-disciplinary in nature with the choice of topics solicited covering the major systems' components and functions of complex physiology. The remit was also extended, on this occasion, beyond mammalian physiology to that of biological systems. Therefore, a special session was devoted to the modelling and control of botanical systems with the aim of providing an exchange of ideas with biomathematicians.

Biomedical Applications of Control Engineering

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Publisher : Springer
ISBN 13 : 3642372791
Total Pages : 281 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Biomedical Applications of Control Engineering by : Selim S. Hacısalihzade

Download or read book Biomedical Applications of Control Engineering written by Selim S. Hacısalihzade and published by Springer. This book was released on 2013-03-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomedical Applications of Control Engineering is a lucidly written textbook for graduate control engineering and biomedical engineering students as well as for medical practitioners who want to get acquainted with quantitative methods. It is based on decades of experience both in control engineering and clinical practice. The book begins by reviewing basic concepts of system theory and the modeling process. It then goes on to discuss control engineering application areas like: Different models for the human operator,dosage and timing optimization in oral drug administration, measuring symptoms of and optimal dopaminergic therapy in Parkinson’s disease, measurement and control of blood glucose levels both naturally and by means of external controllers in diabetes, and control of depth of anaesthesia using inhalational anaesthetic agents like sevoflurane using both fuzzy and state feedback controllers. All chapters include three types of exercises constructed to: Review the concepts discussed in the chapter, allow the reader to apply the newly acquired techniques and subject related facts on simple problems, and indicate directions for open ended theses projects. Appendices on Optimal Control and Fuzzy Control meant as refreshers on those control engineering techniques used throughout the book are also included.

Modeling and Simulation in Biomedical Engineering: Applications in Cardiorespiratory Physiology

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Publisher : McGraw Hill Professional
ISBN 13 : 0071714464
Total Pages : 216 pages
Book Rating : 4.0/5 (717 download)

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Book Synopsis Modeling and Simulation in Biomedical Engineering: Applications in Cardiorespiratory Physiology by : Willem L. van Meurs

Download or read book Modeling and Simulation in Biomedical Engineering: Applications in Cardiorespiratory Physiology written by Willem L. van Meurs and published by McGraw Hill Professional. This book was released on 2011-08-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: THEORY AND PRACTICE OF MODELING AND SIMULATING HUMAN PHYSIOLOGY Written by a coinventor of the Human Patient Simulator (HPS) and past president of the Society in Europe for Simulation Applied to Medicine (SESAM), Modeling and Simulation in Biomedical Engineering: Applications in Cardiorespiratory Physiology is a compact and consistent introduction to this expanding field. The book divides the modeling and simulation process into five manageable steps--requirements, conceptual models, mathematical models, software implementation, and simulation results and validation. A framework and a basic set of deterministic, continuous-time models for the cardiorespiratory system are provided. This timely resource also addresses advanced topics, including sensitivity analysis and setting model requirements as part of an encompassing simulation and simulator design. Practical examples provide you with the skills to evaluate and adapt existing physiologic models or create new ones for specific applications. Coverage includes: Signals and systems Model requirements Conceptual models Mathematical models Software implementation Simulation results and model validation Cardiorespiratory system model Circulation Respiration Physiologic control Sensitivity analysis of a cardiovascular model Design of model-driven acute care training simulators “Uniquely qualified to author such a text, van Meurs is one of the original developers of CAE Healthcare’s Human Patient Simulator (HPS). ...His understanding of mathematics, human physiology, pharmacology, control systems, and systems engineering, combined with a conversational writing style, results in a readable text. ...The ample illustrations and tables also break up the text and make reading the book easier on the eyes. ...concise yet in conversational style, with real-life examples. This book is highly recommended for coursework in physiologic modeling and for all who are interested in simulator design and development. The book pulls all these topics together under one cover and is an important contribution to biomedical literature.” --IEEE Pulse, January 2014 “This book is written by a professional engineer who is unique in that he seems to have a natural understanding of 3 key areas as follows: the hardware involved with simulators, human physiology, and mathematical modeling. Willem van Meurs is one of the inventors of the model-driven human patient simulator (HPS), and so, he is very qualified to write this book. The book is written in a clear way, using the first person throughout, in a conversational manner, with a style that involves posing questions and answering them in subsequent text. ...The book starts with a very useful introduction and background chapter, setting out the scene for the rest of the book. ...I have used his book in enhancing my own talks and understanding human patient simulation and can strongly recommend it.” --Simulation in Healthcare December, 2012 Reviewed by Mark A. Tooley, Ph.D., Department of Medical Physics and Bioengineering, Royal United Hospital, Combe Park, Bath, UK.

Modeling and Control of Drug Delivery Systems

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Author :
Publisher : Academic Press
ISBN 13 : 0128211954
Total Pages : 410 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Modeling and Control of Drug Delivery Systems by : Ahmad Taher Azar

Download or read book Modeling and Control of Drug Delivery Systems written by Ahmad Taher Azar and published by Academic Press. This book was released on 2021-02-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Control of Drug Delivery Systems provides comprehensive coverage of various drug delivery and targeting systems and their state-of-the-art related works, ranging from theory to real-world deployment and future perspectives. Various drug delivery and targeting systems have been developed to minimize drug degradation and adverse effect and increase drug bioavailability. Site-specific drug delivery may be either an active and/or passive process. Improving delivery techniques that minimize toxicity and increase efficacy offer significant potential benefits to patients and open up new markets for pharmaceutical companies. This book will attract many researchers working in DDS field as it provides an essential source of information for pharmaceutical scientists and pharmacologists working in academia as well as in the industry. In addition, it has useful information for pharmaceutical physicians and scientists in many disciplines involved in developing DDS, such as chemical engineering, biomedical engineering, protein engineering, gene therapy. Presents some of the latest innovations of approaches to DDS from dynamic controlled drug delivery, modeling, system analysis, optimization, control and monitoring Provides a unique, recent and comprehensive reference on DDS with the focus on cutting-edge technologies and the latest research trends in the area Covers the most recent works, in particular, the challenging areas related to modeling and control techniques applied to DDS

Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control

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Publisher : Academic Press
ISBN 13 : 0323902030
Total Pages : 530 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control by : Ahmed G. Radwan

Download or read book Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control written by Ahmed G. Radwan and published by Academic Press. This book was released on 2021-10-22 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. Presents a simple and comprehensive understanding of the field of fractional-order systems Offers practical knowledge on the design of fractional-order systems for different applications Exposes users to possible new applications for fractional-order systems