Measuring magnetically induced eddy current densities in biological structures at low frequencies : circuit design and applications
Electrical eddy currents can be induced inside biological tissue by time-varying magnetic fields according to Faraday's law of induction. These eddy currents are responsible for biological effects such as visual sensations in eyes called magnetophosphenes and they accelerate the healing process of fractured bones in magnetotherapy operation. Induced eddy currents also cause neuromuscular stimulation of cardiac muscle, shown as a disturbance in the electrocardiogram and respiratory disturbance shown as a brief period of apnoea (stopped breathing) and muscle contraction in the forearm and finger. Brain cortex also can be stimulated by pulsed magnetic fields. A transient decrease in blood flow in the human skin is seen as a result of exposing the skin to pulsed magnetic fields. To study the effects of time-varying magnetic field, a method is needed to assess and measure induced current densities. Many attempts have been made to find such a method, both theoretically and practically. A theoretical model with homogenous and isotropic concentric loops of tissue was suggested but biological tissues are neither homogenous nor isotropic. A Hall effect method using a slab of semiconductor was suggested for measurement of current densities inside tissues, but this method ignored disturbances in the current pathways inside the tissue as a result of differences in impedances between the semiconductor and the tissue. A cube substitution method using platinized conductive faces implanted in the tissue does not consider problems of alignment of the probes with the direction of isopotential lines or electrode-electrolyte impedance. Also, such electrodes measure only dc current. In a method using a three dimensional electrode to provide three-dimensional information, the author did not give evidence that these electrodes have a zero field distortion, and also did not give information about measurements made using his electrodes. None of the above methods provide a solid approach to the problems of measuring induced current densities. This thesis attempts to present a method of measuring induced current density. The method is capable of measuring both the magnitude and direction of induced current densities. It uses five point electrodes, four of them applied inside the tissue while the fifth one is just in electrical contact with the tissue. The method consists of a probe configuration system, an open-loop operational amplifier and a balanced semi-floating current driver. Leakage current, which goes to the ground and causes error, can be adjusted to be very low (about 0.01% of the total output current). A pair of Helmoltz coils was employed to provide a system for producing time-varying magnetic field. The core of the coil pair was shielded and grounded by a cut metal shield, to avoid any interference from time-varying electric field. The shield was also used as a metal incubator to keep biological samples at body temperature. The heat to the shield was supplied by a unit consisting of four power transistors, and a circuit of sensing, and controlling components. The method used in this study was tested by making measurements of eddy current densities induced in physiological saline solution as a model of a biological conducting fluid. The measurements were represented by arrows, each representing a single measurement, with the length of the arrow representing the magnitude of current density and the direction representing the direction of the induced current. Because electrically induced eddy currents are dependent on electric charge density available inside tissue, and therefore dependent on tissue electrical conductivity, this thesis presents a direct and simple method for measuring complex tissue electrical conductivity. The method uses the same five-electrode system and shares the same point electrode configurations and balanced semi-floating current driver as used for eddy current measurements. The method measures both real and imaginary components of tissue complex conductivity. Both systems are gathered into one box and their functions are separated by four toggle switches. Measurements of electrical induced current densities and complex electrical conductivities for body fluids and tissues have been carried out on saline solutions with different ionic concentrations, expired human whole blood, expired human plasma, human cerebrospinal fluid (CSF) and human urine. Solid tissue such as bovine cardiac muscle and liver were also examined. Current-to-field ratios were obtained for experiments in both fluid and tissues.