Techniques in treating the bioelectromagnetic source imaging problems and their application

We present the theory and application of non-invasive or minimally invasive imaging of bioelectromagnetic sources. We are not concerned with imaging secondary effects of the sources (that might be used to infer their location), such as changes in tissue oxygenation, blood flow, or glucose utilization (as with BOLD or dynamic gadolinium functional MRI strategies, or PET). Thus, we are directly concerned with providing images of source currents or source potentials. These sources reside in "excitable tissues", such as brain, heart, gut, and skeletal muscle. While we will not be conducting a comprehensive literature survey, this chapter is intended to provide an overview of the general approaches and trends in bioelectromagnetic imaging that presently characterize the field. Within reason, we attempt this by considering the relevant physiology, physics, engineering, and mathematics that in concert allow a coherent understanding of the present state of affairs. Accordingly, this chapter’s sections are arranged as follows: • General Principles - Modeling of excitable tissue - Physics of bioelectromagnetism - Engineering issues: Signal acquisition - Mathematical methods • Source Categories - Brain: Source physiology, dipole localization, imaging formulations, linear versus nonlinear problems- Heart: Source physiology, endocardial, epicardial, and transmembrane potential imaging - Smooth and Skeletal muscle: Source physiology, inverse problems related to electromyography and electrogastrography.