Computational Methods and Software for Bioelectric Field Problems

Computer modeling and simulation continue to become more important in the field of bioengineering. The reasons for this growing importance are manyfold. First, mathematical modeling has been shown to be a substantial tool for the investigation of complex biophysical phenomena. Second, since the level of complexity one can model parallels the existing hardware configurations, advances in computer architecture have made it feasible to apply the computational paradigm to complex biophysical systems. Hence, while biological complexity continues to outstrip the capabilities of even the largest computational systems, the computational methodology has taken hold in bioengineering and has been used successfully to suggest physiologically and clinically important scenarios and results. This chapter provides an overview of numerical techniques that can be applied to a class of bioelectric field problems. Bioelectric field problems are found in a wide variety of biomedical applications, which range from single cells [59], to organs [62], up to models that incorporate partial to full human structures [44,45,50]. We describe some general modeling techniques that will be applicable, in part, to all the aforementioned applications. We focus our study on a class of bioelectric volume conductor problems that arise in electrocardiography (ECG) and electroencephalography (EEG). 43