Theoretical and computational multiple regression study of gastric electrical activity using dipole tracing from magnetic field measurements

The biomagnetic inverse problem has captured the interest of both mathematicians and physicists due to its important applications in the medical field. As a result of our experience in analyzing the electrical activity of the gastric smooth muscle, we present here a theoretical model of the magnetic field in the stomach and a computational implementation whereby we demonstrate its realism and usefulness. The computational algorithm developed for this purpose consists of dividing the magnetic field signal input surface into centroid-based grids that allow recursive least-squares approximations to be applied, followed by comparison tests in which the locations of the best-fitting current dipoles are determined. In the second part of the article, we develop a multiple-regression analysis of experimental gastric magnetic data collected using Superconducting QUantum Interference Device (SQUID) magnetometers and successfully processed using our algorithm. As a result of our analysis, we conclude on statistical grounds that it is sufficient to model the electrical activity of the GI tract using only two electric current dipoles in order to account for the magnetic data recorded non-invasively with SQUID magnetometers above the human abdomen.