This book presents a comprehensive treatment of electromagnetic analysis and design of three key devices used in a magnetic resonance imaging (MRI) system, namely, the magnet, the gradient coils, and the radiofrequency (RF) coils. It also includes the analysis and characterization of the interactions of electromagnetic fields and a biological subject.

Because of the importance of MRI, a large number of scientists and engineers have been working in this fast-growing field. As a result, many books on MRI have been published. However, most of these books deal with the principles of MRI and imaging techniques. Few of them provide a detailed treatment on the analysis and design of the hardware of an MRI system from the engineering perspective. The lack of a reference book on this topic has been an inconvenience for a growing number of MRI engineers for many years. This work is intended to remove this inconvenience. Although the materials covered here can be found in electromagnetics textbooks and MRI literature, it is a rather time-consuming task to search and organize them in an easy-to-understand format. Therefore, what contained in this book is the result of my digestion of other people's work combined with my understanding of electromagnetics and some of my own work.

In 1994, our department started to offer a new course entitled ``Magnetic Resonance Principle and Instrumentation'' to the graduate students in bio- and electrical engineering at the University of Illinois at Urbana-Champaign. The course covers topics such as RF and gradient coil design, nuclear magnetic resonance (NMR) coherence excitation and detection, NMR signal analysis and processing, design of biological studies, and MRI safety hazards. I was asked to cover the analysis and design of magnets, gradient coils, and RF coils. Since there was no textbook available on these topics, I prepared a set of course notes to be distributed in class. These course notes now form the basis of this book.

This book contains five chapters. The first chapter is a simple introduction to MRI, which is intended for students who do not have any knowledge about MRI. The second chapter is on the basic concepts of electromagnetics and the emphasis is on the topics that are closely related to MRI. These include Helmholtz and Maxwell coils, inductance calculation, and the magnetic fields produced by some special cylindrical and spherical surface currents that form the foundation for birdcage and magnet designs. Chapter 3 deals with the basic principles for the analysis and design of gradient coils for MRI applications. It includes the design of gradient coils using discrete wires and the target field method for the design of gradient coils, including shielded coils, using distributed currents. The analysis of RF coils is covered in Chapter 4. The methods of analysis described include a simple one based on the equivalent lumped-circuit model and a rigorous one based on the integral equation formulation. The chapter also includes a brief survey of some special-purpose RF coils. The final chapter describes analytical and numerical methods for analysis of the electromagnetic field in biological objects, a problem that is important for high-frequency MRI.

To help the readers understand some basic electromagnetic phenomena and RF coil characteristics, I wrote a software program called MRIEM that can be downloaded from my home page. It can be used to analyze a variety of RF coils and to calculate the RF fields in the human head. To supplement and reinforce the concepts and ideas presented and to facilitate the use of this book in the classroom, I have also designed a number of exercise problems which are included.

This book is written for engineers, physicists, and graduate students working in the field of MRI. It can also be read by electrical engineers who wish to understand the hardware of an MRI system. The readers are assumed to have the basic knowledge (undergraduate level) of vector algebra, circuits, and electromagnetics.