Image theory and applications in bioelectromagnetics

Investigation of bioelectricity phenomena has gained recently a steadily increasing interest in medical and engineering applications. This chapter deals with the computational aspects of bioelectromagnetic interactions and their related bioelectric processes, aiming to provide a better physical understanding of the effect of functional electrical stimulation (FES) on biological tissue and to Set-Up models that can provide quantitative insights into this bioelectromagnetic phenomenon. These goals are achieved here by an explicit image series construction of the macroscopic electromagnetic field within the multilayer tissue. The novel image series expansion scheme, outlined here for quasistatic Green’s function in multilayer media, utilizes a unique and explicit recursive representation for Green’s function. Our recursive construction convergences under rather general constraints on the media parameters. The usefulness and effectiveness of the proposed analysis is demonstrated through an hybrid scheme, combining image series and moment method procedures, that are capable of handling effectively layered medium problems excited by an electrode array. The inclusion of a collective image term, expressed in a closed form asymptotic evaluation of the series remainder integral, significantly accelerated the image series convergence and the overall algorithm speed and accuracy. This proposed computational procedure can be used as a simple tool for producing analytical data for testing numerical subroutines applied to simulate direct (FES) and inverse (bioelectromagnetic imaging) problems in biomedical applications.