ABSTRACT
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.
ABSTRACT
Lithium (Li) is the lightest metal and occurs primarily in stable minerals and salts. Concentrations of Li in surface water are typically <0.04 mg l(-1) but can be elevated in contaminated streams. Because of the general lack of information concerning the toxicity of Li to common toxicity test organisms, we evaluated the toxicity of Li to Pimephales promelas (fathead minnow), Ceriodaphnia dubia, and a freshwater snail (Elimia clavaeformis). In the laboratory, the concentration of Li that inhibited P. promelas growth or C. dubia reproduction by 25% (IC25) was dependant upon the dilution water. In laboratory control water containing little sodium (approximately 2.8 mg l(-1)), the IC25s were 0.38 and 0.32 mg Li l(-1) and in ambient stream water containing approximately 17 mg Na l(-1), the IC25s were 1.99 and 3.33, respectively. A Li concentration of 0.15 mg l(-1) inhibited the feeding of E. clavaeformis in laboratory tests. Toxicity tests conducted to evaluate the effect of sodium on the toxicity of Li were conducted with fathead minnows and C. dubia. The presence of sodium greatly affected the toxicity of Li. Fathead minnows and Ceriodaphnia, for example, tolerated concentrations of Li as great as 6 mg l(-1) when sufficient Na was present. The interaction of Li and Na on the reproduction of Ceriodaphnia was investigated in depth and can be described using an exponential model. The model predicts that C. dubia reproduction would not be affected when animals are exposed to combinations of lithium and sodium with a log ratio of mmol Na to mmol Li equal to at least 1.63. The results of this study indicate that for most natural waters, the presence of sodium is sufficient to prevent Li toxicity. However, in areas of historical disposal or heavy processing or use, an evaluation of Li from a water quality perspective would be warranted.
