Calculating the movement of MRI coils, and minimizing their noise

Abstract

The design of gradient coils within Magnetic Resonance Imaging equipment is considered. These coils produce linear magnetic fields in each of the three orthogonal directions in physical space. In addition, they are turned on and off repeatedly to enhance the clarity of the image, but this produces a great deal of noise within the coil, as its shape distorts under the influence of Lorentz forces. We present a method for calculating the movement of the coil in the background magnetic field, and estimating the consequent noise levels. This involves solving for the current density in the coil coupled with equations for its elastic deformation, along with acoustic equations for the pressure in the surrounding air. Winding patterns are designed to minimize the noise produced by the Magnetic Resonance Imaging coil. References L. M. Delves and J. L. Mohamed. Computational Methods for Integral Equations. Cambridge University Press, Cambridge, 1985. L. K. Forbes and S. Crozier. A novel target-field method for finite-length magnetic resonance shim coils: Part 1: Zonal shims. J. Phys. D: Appl. Phys., 34:3447--3455, 2001. doi:10.1088/0022-3727/34/24/305 L. K. Forbes and S. Crozier. A novel target-field method for finite-length magnetic resonance shim coils: Part 2: Tesseral shims. J. Phys. D: Appl. Phys., 35:839--849, 2002. doi:10.1088/0022-3727/35/9/303 L. K. Forbes and S. Crozier. A novel target-field method for magnetic resonance shim coils: Part 3: Shielded zonal and tesseral coils. J. Phys. D: Appl. Phys., 36:68--80, 2003. doi:10.1088/0022-3727/36/2/302 E. M. Haacke, R. W. Brown, M. R. Thompson and R. Venkatesan. Magnetic Resonance Imaging: Physical principles and sequence design. Wiley, New York, 1999. J. Jin. Electromagnetic Analysis and Design in Magnetic Resonance Imaging. Biomedical Engineering Series, CRC Press, Boca Raton, 1999. P. Mansfield, B. Haywood and R. Coxon. Active acoustic control in gradient coils for MRI. Magn. Reson. Med., 46:807--818, 2001. C. K. Mechefske, G. Yao, W. Li, C. Gazdzinski and B. K. Rutt. Modal analysis and acoustic noise characterization of a 4T MRI gradient coil insert. Concepts Magn. Reson. B, 22:37--49, 2004. doi:10.1002/cmr.b.20013 W. Shao and C. K. Mechefske. Acoustic analysis of a gradient coil winding in an MRI scanner. Concepts Magn. Reson. B, 24:15--27, 2005. doi:10.1002/cmr.b.20023 W. Shao and C. K. Mechefske. Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance. J. Acoust. Soc. Am., 117:1728--1736, 2005. A. P. Boresi and K. P. Chong. Elasticity in engineering mechanics. Elsevier, New York 1987. R. Turner. A target field approach to optimal coil design. J. Phys D: Appl. Phys., 19:147--151, 1986. M. T. Vlaadingerbroeck and J. A. den Boer. Magnetic Resonance Imaging: Theory and practice, 3rd edition. Springer Verlag, Berlin, 2003. M. A. Brideson, L. K. Forbes and S. Crozier. Determining complicated winding patterns for shim coils using stream functions and the target-field method. Concepts Magn. Reson., 14:9--18, 2002. doi:10.1002/cmr.10000 B. L. W. Chapman and P. Mansfield. A quiet gradient-coil set employing optimized, force-shielded, distributed coil designs. J. Magn. Reson. B, 107:152--157, 1995. S. Crozier and D. M. Doddrell. Gradient-coil design by simulated annealing. J. Magn. Reson. A, 103:354--357, 1993.