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Algebraic method to synthesize specified modal currents in ladder resonators: Application to noncircular birdcage coils
Author(s) -
De Zanche Nicola,
Pruessmann Klaas P.
Publication year - 2015
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25503
Subject(s) - inductance , algebraic number , resonator , modal , electromagnetic coil , computer science , physics , quadrature (astronomy) , algorithm , topology (electrical circuits) , control theory (sociology) , mathematical analysis , voltage , mathematics , chemistry , quantum mechanics , combinatorics , polymer chemistry , optics , control (management) , artificial intelligence
Purpose Detectors such as birdcage coils often consist of networks of coupled resonant circuits that must produce specified magnetic field distributions. In many cases, such as quadrature asymmetric insert body coils, calculating the capacitance values required to achieve specified currents and frequencies simultaneously is a challenging task that previously had only approximate or computationally inefficient solutions. Theory and Methods A general algebraic method was developed that is applicable to linear networks having planar representations such as birdcage coils, transverse electromagnetic (TEM) coils, and numerous variants of ladder networks. Unlike previous iterative or approximate methods, the algebraic method is computationally efficient and determines current distribution and resonant frequency using a single matrix inversion. The method was demonstrated by specifying irregular current distributions on a highly elliptical birdcage coil at 3 Tesla. Results Measurements of the modal frequency spectrum and transmit field distribution of the two specified modes agrees with the theory. Accuracy is limited in practice only by how accurately the matrix of self and mutual inductances of the network is known. Conclusion The algebraic method overcomes the inability of the existing inductance equalization method to account for all elements of the inductance matrix and the inability to accommodate modal currents that are not (co)sinusoidal. Magn Reson Med 74:1470–1481, 2015. © 2014 Wiley Periodicals, Inc.