Computer-assisted design of surface coils used in magnetic resonance imaging. II. Rotational discrimination nonlinear regression analysis and the design of surface coils.

For a number of reasons, it is desirable to fabricate coils which, for a known current, shall produce predetermined values of the magnetic field intensity at a number of points within a nuclear magnetic resonance imager. The calculation of the magnetic field intensity at a set of points involves the integration of the Biot-Savart equation for all components of the segments of conductor which make up the coil. This process in itself is a rather formidable task. When this process is parameterized in terms of coil diameter, coil spacing, etc. the problem is to determine the values of these parameters to match values of magnetic field intensities which are desired. The problem thereby increases in complexity to the point where, by ordinary methods, the problem becomes intractable. A generalized solution technique has been developed on a digital computer to implement the rotational discrimination nonlinear regression techniques of Faris, Law and Letcher to find the best solution to this problem. The problem is posed by integrating the Biot-Savart equation. This produces algebraic expressions for incorporation into the optimization program which is executed on a computer in a conversational mode. This technique was employed to specify the dimensions of a rectangular surface coil for the investigation of the whole human spine.

Computer-assisted design of surface coils used in magnetic resonance imaging. III. The design and construction of two long twin axial antennae for imaging of the whole human spine.

Two modified folded dipole MRI surface coils were designed, constructed and tested. These antenna which are long twin axial lines use the effective distributive capacitance resulting from the distance between two longitudinal elements to provide tuning. The principal advantage of this type of antenna is the ability to image longer objects such as vertebrae, spinal cord, and longer portions of the extremities. This type of antenna shows less localized high intensity in the image due to a more evenly distributed current pickup from the sample. The coils were designed by calculating theoretical magnetic field distribution for the twin axial coils. These were obtained by integrating the Biot-Savart equation. This gave excellent agreement with an MR image of a di-electrically uniform phantom. As antennae of this sort are nonlinear in response, giving rise to an image intensity nonuniformity, computer software for the MR image was developed to correct the image intensity profile over the experimental volume. The software significantly improved the image quality by reducing the saturated intensity of the region near the antenna, thereby revealing detailed structure of the tissue being imaged.

Computer-assisted design of surface coils used in magnetic resonance imaging. I. The calculation of the magnetic field.

For a number of reasons, it is desirable to fabricate coils which, for a known current, shall produce predetermined values of the magnetic field intensity at a number of points within a nuclear magnetic resonance imager. The calculation of the magnetic field intensity at a set of points involves the integration of the Biot-Savart equation for all components of the segments of conductor which make up the coil. This process in itself is a rather formidable task. When this process is parameterized in terms of coil diameter, coil spacing, etc. the problem is to determine the values of these parameters to match values of magnetic field intensities which are desired. The problem thereby increases in complexity to the point where, by ordinary methods, the problem becomes intractable. This note describes an algorithm and offers a computer subroutine to calculate magnetic fields for coils of arbitrary shape and complexity for fixed currents.