Optimal realization of arbitrary forces in a magnetic stereotaxis system

Very small implanted permanent magnets guided by large electromagnetic coils have been proposed previously as a method for delivering hyperthermia to or guiding catheters through brain tissue. This procedure is termed "magnetic stereotaxis". Early efforts employed a single coil on a movable boom, a design that proved logistically difficult to use on human patients. The present work deals instead with a design where several stationary coils are employed to develop a force on the implanted magnet. The coil current-to-force relationship is developed for this type of machine, and several optimal solutions for realizing an arbitrary static force are presented for various constraints on the orientation of the implanted permanent magnet. Costs of the different solutions are compared in several examples using a mathematical model based on the Magnetic Stereotaxis System (MSS) developed by Stereotaxis, Inc., the University of Virginia, and Wang NMR.