Biomagnetic Sources and Their Models

Over the past twenty-five years, the study of biomagnetic phenomena has evolved into an interdisciplinary research effort involving individuals whose primary training has most often been in either biology, engineering, medicine, physics, or psychology. The goal of this tutorial is to present to a similarly eclectic audience the essential physics and electrophysiology required to describe the biological sources of magnetic fields, the spatial variation of these fields, and how the sources and their fields can be modeled mathematically. Introductory physics courses tend to concentrate on simple systems such as isolated electric charges in vacuum, currents flowing in circular coils, and circuits with discrete batteries, wires, and resistors. Introductory biology courses seldom address bioelectric phenomena in detail. As a result, many of us enter biomagnetism with an intuition that is ill-prepared to describe how biological cells produce currents that flow throughout an inhomogeneous body that has a complicated geometry. It is even harder to understand the spatial variation and information content of the magnetic fields associated with these currents. In complex systems such as the human heart or brain, the simple equations presented in an introductory physics course must be written in a more general form, usually involving vector or tensor calculus. Rigorous and quantitative treatment of this material can be found in several chapters in the volume edited by Williamson et al. (1983), in the text by Hobbie (1988), and in the review by Wikswo et al. (1979). Kuffler et al. (1984) and Macfarlane and Lawrie (1989) provide comprehensive treatments of neurophysiology and cardiac electrophysiology, respectively. In this tutorial, I will concentrate on presenting a more qualitative, pictorial approach to the subject than do any of these references. I hope that I will describe the concepts in a manner that will allow someone whose background does not span all of physics, mathematics, and biology to develop an appreciation for the interdisciplinary subtleties of the subject without the distraction of numerous equations or extensive physiological descriptions. Because of space limitations, I will not discuss how magnetic materials, either of biological origin or from contamination, can produce magnetic fields.