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Author: David H. Anderson
Publisher: Springer Science & Business Media
ISBN: 3642518613
Category : Science
Languages : en
Pages : 312
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Book Description
This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a proof is indicated by ~. Sub section titles are utilized to make it easier for the reader to skim over detailed material on a first reading and make the entire manuscript somewhat more accessible, especially to nonmathematicians in the biosciences. The preparation of this monograph has been a long task that would not have been completed without the influence of a number of individuals. I am especially indebted to H. T. Banks, J. W. Drane, J. Eisenfe1d, J. A. Jacquez, D. J.
Author: David H. Anderson
Publisher: Springer Science & Business Media
ISBN: 3642518613
Category : Science
Languages : en
Pages : 312
Get Book Here
Book Description
This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a proof is indicated by ~. Sub section titles are utilized to make it easier for the reader to skim over detailed material on a first reading and make the entire manuscript somewhat more accessible, especially to nonmathematicians in the biosciences. The preparation of this monograph has been a long task that would not have been completed without the influence of a number of individuals. I am especially indebted to H. T. Banks, J. W. Drane, J. Eisenfe1d, J. A. Jacquez, D. J.
Author: DH. Anderson
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Claudio Cobelli
Publisher: Springer Science & Business Media
ISBN: 0306468336
Category : Technology & Engineering
Languages : en
Pages : 455
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Book Description
1. Introduction. 2. Fundamentals of Tracer Kinetics. 3. The Noncompartmental Model of Multipool Systems. 4. The Compartmental Model. 5. Identifiability of the Tracer Model. 6. Using the Tracer Model to Estimate Kinetic Parameters. 7. Compartmental Versus Noncompartmental Kinetic Parameters. 8. Parameter Estimation: Some Fundamentals of Regression Analysis. 9. Parameter Estimation in Noncompartmental Models. 10. Parameter Estimation in Compartmental Models. 11. Precursor-Product Models. Appendices. Index.
Author: John Alfred Jacquez
Publisher:
ISBN:
Category : Biological models
Languages : en
Pages : 586
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Book Description
Deals with basic linear and nonlinear systems and graph theory, distribution of tracer-labeled materials, connectivity, and identifiability
Author: R.M. Lambrecht
Publisher: Springer Science & Business Media
ISBN: 3642500366
Category : Mathematics
Languages : en
Pages : 518
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Book Description
Author: Keith Godfrey
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 320
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Our goal is to quantify regional physiological processes such as blood flow and metabolism by means of tracer kinetic modeling and positron emission tomography (PET). Compartmental models are one way of characterizing the behavior of tracers in physiological systems. This paper describes a general method of estimating compartmental model rate constants from measurements of the concentration of tracers in blood and tissue, taken at multiple time intervals. A computer program which applies the method is described, and examples are shown for simulated and actual data acquired from the Donner 280-Crystal Positron Tomograph.
Author: Karl-Ernst Biebler
Publisher: World Scientific
ISBN: 9814522236
Category : Mathematics
Languages : en
Pages : 349
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Book Description
This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given. In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.
Author: Magdy M. Khalil
Publisher: Springer
ISBN: 3319400703
Category : Medical
Languages : en
Pages : 621
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Book Description
This book offers a wide-ranging and up-to-date overview of the basic science underlying PET and its preclinical and clinical applications in modern medicine. In addition, it provides the reader with a sound understanding of the scientific principles and use of PET in routine practice and biomedical imaging research. The opening sections address the fundamental physics, radiation safety, CT scanning dosimetry, and dosimetry of PET radiotracers, chemistry and regulation of PET radiopharmaceuticals, with information on labeling strategies, tracer quality control, and regulation of radiopharmaceutical production in Europe and the United States. PET physics and instrumentation are then discussed, covering the basic principles of PET and PET scanning systems, hybrid PET/CT and PET/MR imaging, system calibration, acceptance testing, and quality control. Subsequent sections focus on image reconstruction, processing, and quantitation in PET and hybrid PET and on imaging artifacts and correction techniques, with particular attention to partial volume correction and motion artifacts. The book closes by examining clinical applications of PET and hybrid PET and their physiological and/or molecular basis in conjunction with technical foundations in the disciplines of oncology, cardiology and neurology, PET in pediatric malignancy and its role in radiotherapy treatment planning. Basic Science of PET Imaging will meet the needs of nuclear medicine practitioners, other radiology specialists, and trainees in these fields.
Author: Magdy M. Khalil
Publisher: Springer Nature
ISBN: 3030652459
Category : Medical
Languages : en
Pages : 571
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Book Description
This book provides comprehensive and detailed information on the scientific bases of nuclear medicine, addressing a wide variety of topics and explaining the concepts that underlie many of the investigations and procedures performed in the field. The book is divided into six sections that cover the physics and chemistry of nuclear medicine besides associated quality assurance/quality control procedures; dosimetry and radiation biology; SPECT and PET imaging instrumentation plus CT imaging technology in hybrid modalities; data analysis including image processing, reconstruction, radiomics, image degrading correction techniques, along with image quantitation and kinetic modeling. Within these sections, particular attention is paid to recent developments and the advances in knowledge that have taken place since release of the first edition in 2011. Several entirely new chapters have been included and the remaining chapters, thoroughly updated. Innovations in the ever-expanding field of nuclear medicine are predominantly due to integration of the basic sciences with complex technological advances. This excellently illustrated book on the subject will be of interest to not only nuclear medicine physicists and physicians but also clinical scientists, radiologists, radiopharmacists, medical students and technologists.
