Compartmental Modeling And Tracer Kinetics

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.

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.

This new advanced text/reference book presents compartmental models or flow models from an applications perspective. Flow models are used when there is a flow of information or materials, such as fluid of money or energy between the components of a system. They are widely used in biomedicine but have also useful applications in studying ecosystems, input-output analysis, competition, models, and epidemology. In order to provide a complete and balanced presentation, the book is organized in four parts. Part 1 is devoted to the theory of digraphs; Part 2 addresses Markov chains; Part 3 discusses differential equations; and Part 4 presents the theory of compartmental models, addressing the relations between dynamics of the solution and structure of the model. Key applications discussed include ecosystem models, fluid transfer, competition models, tracer kinetic experiments, and network flows. Essential topics and methods are presented in an accessible style with many examples: directed graphs, differential equations, Markov chains, and compartmental model construction. The material provides a thorough and comprehensive presentation of compartmental models, model construction and applications. All advanced students, practitioners and professionals in bioscience and applied mathematical modeling will find the book a useful and excellent reference.

Radioisotope-based molecular imaging probes provide unprecedented insight into biochemistry and function involved in both normal and disease states of living systems, with unbiased in vivo measurement of regional radiotracer activities offering very high specificity and sensitivity. No other molecular imaging technology including functional magnetic resonance imaging (fMRI) can provide such high sensitivity and specificity at a tracer level. The applications of this technology can be very broad ranging from drug development, pharmacokinetics, clinical investigations, and finally to routine diagnostics in radiology. The design and the development of radiopharmaceuticals for molecular imaging studies using PET/MicroPET or SPECT/MicroSPECT are a unique challenge. This book is intended for a broad audience and written with the main purpose of educating the reader on various aspects including potential clinical utility, limitations of drug development, and regulatory compliance and approvals.

This book constitutes the refereed proceedings of the 20th International Conference on Information Processing in Medical Imaging, IPMI 2007, held in Kerkrade, The Netherlands, in July 2007. It covers segmentation, cardiovascular imaging, detection and labeling, diffusion tensor imaging, registration, image reconstruction, functional brain imaging, as well as shape models and registration.