This book has its origin in my experience as a teacher of pharmacokinetics in many universities in four different continents. It was not my intention to write a popular book; what distinguishes this one from many others on the same subject is its large use of algebra and calculus. For this I make no apologies; in fact a serious study of pharmacokinetics without the help of mathematics is, in my opinion, impossible. The exact definition of many pharmacokinetic quantities, even the most common, and the correct use of many equations, even the most simple, requires the constant use of mathematical language. On the other hand I have made a considerable effort to use only elementary algebra and elementary calculus, as commonly taught in most introductory university courses. For the few exceptions, when less common mathematical concepts were needed, I have supplied the necessary explanations in four appendices. The first three chapters are a general introduction to the scientific method. Chapters 4 to 12 show different specific methods to deal with pharmacokinetic pr- lems. There is considerable overlap among those chapters; this is intentional and its p- pose is to convince the reader that every problem can be solved in more than one way, including ways that were not mentioned in this book and that intelligent readers can find for their own pleasure. Chapters 13 to 17 show how different parameters of importance in pharmacokinetics can be exactly defined and measured.

This book has its origin in my experience as a teacher of pharmacokinetics in many universities in four different continents. It was not my intention to write a popular book; what distinguishes this one from many others on the same subject is its large use of algebra and calculus. For this I make no apologies; in fact a serious study of pharmacokinetics without the help of mathematics is, in my opinion, impossible. The exact definition of many pharmacokinetic quantities, even the most common, and the correct use of many equations, even the most simple, requires the constant use of mathematical language. On the other hand I have made a considerable effort to use only elementary algebra and elementary calculus, as commonly taught in most introductory university courses. For the few exceptions, when less common mathematical concepts were needed, I have supplied the necessary explanations in four appendices. The first three chapters are a general introduction to the scientific method. Chapters 4 to 12 show different specific methods to deal with pharmacokinetic pr- lems. There is considerable overlap among those chapters; this is intentional and its p- pose is to convince the reader that every problem can be solved in more than one way, including ways that were not mentioned in this book and that intelligent readers can find for their own pleasure. Chapters 13 to 17 show how different parameters of importance in pharmacokinetics can be exactly defined and measured.

The NATO Advanced Study Institute on "Cerebral Blood Flow: Mathematical Models, Instrumentation, and Imaging Techniques" was held in L'Aquila, Italy, June 2-13, 1986. Contributions to this program were received from the University of L'Aquila, Consiglio Nazionale delle Ricerche, Siemens Elettra S.p.A., and Bracco S.p.A. Recent studies of the cerebral blood circulation have lagged behind analysis of other parameters such as glucose utilization, transmitter distribution, and precursors. This Advanced Study Institute tried to fill this gap by analyzing in detail different physical techniques such as Autoradiography (including Double-Tracer Auto radiography and highly specific tracers as Iodoantipyrine, Micro spheres), Single Photon Emission Computed Tomography, Nuclear Magnetic Resonance. Each method was analyzed in regards to its precision, resolution, response time. A considerable part of this Institute was devoted to the mathematics of CBF measurement, in its two aspects, i.e. the modeling of the underlying kinetic system and the statistical analysis of the data. The modeling methods proposed included the development of a differential algebra whereby the differential and integral equations involved could be solved by simple algebraic methods, including graph theoretical ones; the statistical methods proposed included the illustration of different parametrizations of possible use in the interpretation of experimental results.

The last decade or so has witnessed tremendous progress in methodology in the field of drug development in general and pharmacokinetics in particular. Clinical pharmacokinetics is using new tools for probing into the "black box" once being ac cessible only partly through experimental techniques and, mostly through mathemati cal and computer means. Development of computerized scanning, positron emission tomography (PET), stereoselectivity and other techniques are now enabling investi gators to have better pictures of the systems they are studying. Mathematical models through computer simulation and statistical estimation, mostly due to easy access be cause of inexpensive yet powerful personal computers, are enabling us to investigate ultrastructures and their functional connectivity in more detail. As a consequence, new hypotheses are being formed and tested in various related fields. In clinical pharmacokinetics, mostly due to mathematical modeling, more accurate interspecies scaling of pharmacokinetic parameters and dosimetry can be done now-a-days. The concept of "a human is a bigger rat" does not necessarily fly as a consequence. Pharmacokinetic concepts are becoming powerful tools in meaningful carcinogenic and toxic risk extrapolation of different chemicals in humans. New dose delivery designs are being formulated using pharmacokinetic techniques for different pharmaceutical compounds. Investigations continue in the academia, research institutions, pharmaceutical, biotechnological, and agricultural industries in developmental and physiological aspects of different chemicals for the benefit of mankind. The idea of a school on "New Trends in Pharmacokinetics", from which the present pUblication was made possible, took shape over almost a year.