Magnetic backprojection imaging

Abstract

The assessment of the vascular lumen is of intense interest to clinicians because of the importance of early detection and quantification of atherosclerosis. We have developed a new technique (to our knowledge) for the assessment of anomalies in electrically conductive tubular smctures like blood vessels. We inject current (minimally invasive and potentially noninvasive) into the vessel, detect the resulting magnetic flux and then backproject to show any deviations from the linear flow of blood. which can indicate the narrowing of the vascular lumen by atheromatous plaque. Preliminary results on a phantom show that attainable resolution is within 1.02 mm. Introduction The measurement of the magnetic field from the human body (biomagnetism) has been used to detect the natural current flow especially around the brain and spinal cord. The magnetic energy is not significantly distorted or attenuated by human tissues, according to both electromagnetic field theory and experiment [11. The detection of natural biomagnetism requires ultrasensitive SQUID (Superconducting Quantum Interference Devices) magnetic sensors. However the SQUID needs cryogenic conditions, which leads to a high cost of manufacturing and maintenance. The system we developed also measures the magnetic field outside of the body, as in biomagnetism, but utilizes a Hall effect sensor which is small, cost effective and easy to maintain at m m temperature. The system we are developing uses injected c m n t which is high enough to generate a magnetic field detectable by a Hall sensor, but safe enough (less than 100 mA of IO kI-k ac current) for diagnostic screening use (21. The BiotSavart law and the preliminary results of our biomagnetism studies suggest that the direction and location of current generating a magnetic field can be determined from the magnetic flux pauem. Our hypothesis is that because of plasma electrolytes, the resistivity of blood (1.75 ohm m) is much lower than that of the wall layers, i.e., tunica intima, media and adventitia (200 ohm m), of the blood vessel [31. Therefore, injected current would flow along the blood stream. The blood vessel wall works as an insuIator like in electric cable. Therefore, the backprojection lines of magnetic flux would meet at one single point which is on the center line of current carrying conductor (blood). Any abnormality in the blood vessel corresponds to a deviation from the major center line of the blood stream, which is detectable by backprojection of magnetic flux. Our model studies were directed at confming this hypothesis in vitro. Method When the current injected into the blood, i, generates a magnetic field (Ampere’s law) like that shown in Fig.1, the magneric flux density, B. is given by the vectorial form of the Biot-Savart law: where B, I, and a, are vectors and X denotes vector cross product. Therefore, the direction of B is determined by the angIe formed between dl (direction of the blood vessel) and ar (unit vector) along the direction €rom the center of blood vessel to the measuring point with a distance of r. Current flows normal to the plane of the magnetic field and the direction of magnetic field (flux density), B, is tangential to the circle of radius, r, and perpendicular to a,. Therefore, the backprojection chords L B P ~ and L B P ~ (shown in Fig.1) meet at one single point, which is the center of the current carrier (position 0 in Fig.1). The Hall effect Sensor is sensitive to the flux density. B, and generates the output voltage, VH, in which the k, d. I. and q are respectively, the gain of Hall sensor, depth, lenglh of Hall element and the electron charge. Depending on the geometry between the bias current, I, and the flux density, B, VH represents only the horizontal (Va) or vertical ( V H ~ ) component of B, i.e., B,, By. From the fact that the backprojection Line should be normal to the magnetic flux, the corresponding center location (xc, yc) of the current carrying blood stream is determined as.