Bioelectric phenomena have been a part of medicine throughout its history. The first written document on bioelectric events is an ancient Egyptian hieroglyph of 4000 B.C. describing the electric sheatfish. Bioelectromagnetism is, of course, based strongly on the general theory of electromagnetism. In fact, until the middle of the nineteenth century the history of electromagnetism was also the history of bioelectromagnetism. From the viewpoint of modern science, bioelectric phenomena have had scientific value for the past 200 years. Many of the fundamental contributions to the theory of bioelectromagnetism were made in the nineteenth century. Only in the past 100 years has bioelectromagnetism had real diagnostic or therapeutic value. As we know, this is actually the case for most of medicine as well.

During the past few decades, the advances in the theory and technology of modern electronics have led to improvements in medical diagnostic and therapeutic methods and, as a result, bioelectric and biomagnetic phenomena have become increasingly important. Today it is impossible to imagine a hospital without electrocardiography and electroencephalography. The development of microelectronics has made such equipment portable and has increased their diagnostic power. Implantable cardiac pacemakers have allowed millions of people to return to normal life. The development of superconducting technology has made it possible to detect the weak biomagnetic fields induced by bioelectric currents. The latest advances in the measurement of electric currents flowing through a single ion channel of the cell membrane with the patch clamp have opened up completely new applications for bioelectromagnetism. With the patch clamp, bioelectromagnetism can also be applied to molecular biology, for instance, in developing new pharmaceuticals. These examples illustrate that bioelectromagnetism is a vital part of our everyday life.

This book first provides a short introduction to the anatomy and physiology of excitable tissues, and then introduces the theory and associated equations of bioelectric and biomagnetic phenomena; this theory underlies all practical methods. The book then describes current measurement methods and research results and provides an account of their historical development.

The chapters dealing with the anatomy and physiology of various organs are necessarily elementary as comprehensive texts are available in these disciplines. Nevertheless, we wanted to include introductory descriptions of the anatomy and physiology of neural and cardiac tissues in particular so that the readers would have a review of the structures and functions upon which electrophysiological models are based. We have also introduced readers to the relevant vocabulary and to important general references.

The theory of bioelectromagnetism deals mainly with electrophysiological models of bioelectric generators, excitability of tissues, and the behavior of bioelectric and biomagnetic fields in and around the volume conductors formed by the body. Because of the nature of the bioelectric sources and the volume conductors, the theory and the analytic methods of bioelectromagnetism are very different from those of general electromagnetism. The theoretical methods are presented as a logical structure. As part of this theory the lead field theoretical approach has been emphasized. Besides the obvious benefits of this approach, it is also true that lead field theory has not been discussed widely in other didactic publications. The lead field theory ties together the sensitivity distribution of the measurement of bioelectric sources, the distribution of stimulation energy, and the sensitivity distribution of impedance measurements, in both electric and magnetic applications. Moreover, lead field theory clearly explains the similarities and differences between the electric and the corresponding magnetic methods, which are tightly related by Maxwell's equations. Thus, all the subfields of bioelectromagnetism are closely related.

We have aimed to present bioelectromagnetism as a theoretical discipline and, in later chapters to provide much practical material so that the book can also serve as a reference. These chapters also provide an opportunity to introduce some relevant history. In particular, we wanted to present the theory and applications of bioelectricity in parallel with those of biomagnetism to show that in principle they form an inseparable pair. This gave us an opportunity to introduce some relevant history so that readers may recognize how modern research is grounded in older theory and how the fundamentals of many contemporary methods were actually developed years ago. Our scope in the later chapters is necessarily limited, and thus readers will find only an overview of the topics (applications). Despite their brevity, these applications should help clarify and strengthen the reader's understanding of basic principles. While better measurement methods than those existing today will undoubtedly be developed in the future, they will necessarily be based on the same theory and mathematical equations given in this book; hence, we believe that its underlying "truth" will remain relevant.

This book is intended for readers with a background in physics, mathematics, and/or engineering (at roughly the second- or third-year university level). Readers will find that some chapters require a solid background in physics and mathematics in order to be fully understood but that most can be understood with only an elementary grounding in these subjects.

The initiative for writing this book came from Dr. Jaakko Malmivuo. It is for the most part based on lectures he has given at the Ragnar Granit Institute (formerly Institute of Biomedical Engineering) of Tampere University of Technology and at Helsinki University of Technology in Finland. He has also lectured on bioelectromagnetism as a visiting professor at the Technical University of Berlin, at Dalhousie University in Halifax, and at Sophia University in Tokyo, and has conducted various international tutorial courses. All the illustrations were drawn by Dr. Malmivuo with a microcomputer using the graphics program CorelDRAW!. The calculations of the curves and the fields were made with MathCad and the data were accurately transferred to the illustrations.

The manuscript was read and carefully critiqued by Dr. Milan Horá ek at Dalhousie University and Dr. David Geselowitz of Pennsylvania State University. Their valuable comments are acknowledged with gratitude. Sir Alan Hodgkin and Sir Andrew Huxley read Chapter 4. We are grateful for their detailed comments and the support they gave our illustration of the Hodgkin-Huxley membrane model. We are grateful also to the staff of Oxford University Press, especially Jeffrey House, Dolores Oetting, Edith Barry, Roaalind Corman, and Alasdair Ritchie. Dr. Ritchie carefully read several chapters and made detailed suggestions for improvement. We also thank the anonymous reviewer provided by Oxford University Press for many valuable comments. Ms. Tarja Erälaukko and Ms. Soile Lönnqvist at Ragnar Granit Institute provided editorial assistance in the preparation of the manuscript and the illustrations. We also appreciate the work of the many students and colleagues who critiqued earlier versions of the manuscript. The encouragement and support of our wives, Kirsti and Vivian, are also gratefully acknowledged.

Financial support from the Academy of Finland and Ministry of Education in Finland is greatly appreciated.

We hope that this book will raise our readers' interest in bioelectromagnetism and provide the background that will allow them to delve into research and practical applications in the field. We also hope that the book will facilitate the development of medical diagnosis and therapy.

Tampere, Finland	J.M.
Durham, North Carolina	R.P.
September 1993