Guidelines for energy-efficient coils: coils designed for magnetic stimulation of the heart

Magnetic stimulation of the heart requires high magnetic field energy and results in considerable Joulean dissipation. Energetically efficient and mechanically robust coils were designed for magnetic stimulation of the canine heart. Circular coils with rectangular cross section oriented either parallel or perpendicular to the skin were employed. A reasonable compromise between coil size and energy efficiency is achieved when the outer radius is twice the target depth. Nearly optimal efficiency is obtained by coils with annular width and height of 60% and 20% of the radius, respectively. A coplanar pair of coils parallel to the skin surface requires less energy and provides a more localized stimulus than a single coil. Placing a single coil perpendicular to the skin provides stimulus localization comparable to that of a coplanar pair; however, a single coil requires approximately 4 times the energy. The large coil currents required for cardiac stimulation exert Lorentz forces on the conductors that may exceed their tensile strength, emphasizing the need for an adequate support structure. Coils fabricated along the preceding guidelines were used to stimulate dog hearts repeatedly, requiring magnetic fields with energy greater than 12,000 J, without coil failure. Although the principles for coil design described herein were applied to a cardiac stimulator, they can also be applied to coils for other tissues, resulting in less coil heating, better stimulus localization and less power consumption.