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MRI Birdcage RF Coil Resonance with Uncertainty and Relative Error Convergence Rates



Jeffrey T. Fong, Nathanael A. Heckert, James J. Filliben, Pedro V. Marcal, Robert Rainsberger, Karl F. Stupic, Stephen E. Russek


In a magnetic resonance imaging (MRI) system, it is necessary to excite the nuclei of a patient into coherent precession for imaging. This requires a coupling between the nuclei and a source of radio frequency (RF) power using a transmitter. To receive a meaningful signal, we also need a coupling between the nuclei and an external circuitry known as the receiver. Both the transmitter and the receiver are called RF coils or resonators, and are key components in any MRI system. In this paper, we use COMSOL 5.2a to model a NIST prototype birdcage RF coil using two low-pass coil mesh design types: Mesh-1, a series of 15 all-tetra-10-element designs with degrees of freedom (d.o.f.) ranging from 169,906 (very coarse) to 3,640,696 (very fine), and Mesh-2, a series of 15 mixed-hex-27-and-tetra-10-element designs with d.o.f. ranging from 188,812 (very coarse) to 2,615,980 (very fine). For each of the 30 meshes, we compute its first resonance frequency, fres , and its time average reflection coefficient given by S11 in dB unit. After obtaining 15 pairs of the two parameters, ( fres , S11 ), for Mesh-1 and Mesh-2, we use a 4-parameter logistic function nonlinear least squares fit algorithm to obtain an estimate of the two parameters at infinite degrees of freedom (d.o.f.) as well as their uncertainty (Unc) at one-billion-d.o.f. and relative error convergence rates (RECR). It is interesting to see that the COMSOL analysis results of the two mesh types differ significantly from each other as shown below: freq S11 Unc (S11) RECR (S11) (MHz) (dB) (%) Mesh-1 (all-tetra) 19.271 - 3.843 3.27 - 1.43 Mesh-2 (mixed) 19.365 - 4.237 10.76 - 0.54 Based on the classical theory of error estimates for finite element method and the general theory of statistical analysis, we conclude that Mesh-1 (all-tetra-10) solution is the more accurate of the two and should be chosen to compare with experimental data.
Proceedings Title
International COMSOL Users' Conference, Boston, MA, U.S.A.
Conference Dates
October 4-6, 2017
Conference Location
Boston, MA


Accuracy assessment metric (AAM), Birdcage RF coil design, computational modeling, COMSOL, DATAPLOT, electromagnetics, element type, FEM, finite element method, hexahedron element, logistic function, magnetic resonance imaging, mesh density, MRI, nonlinear least squares method, relative error convergence rate, resonance frequency, statistical analysis, super- parametric method, tetrahedron element, time-average reflection coefficient, uncertainty quantification.


Fong, J. , Heckert, N. , Filliben, J. , Marcal, P. , Rainsberger, R. , Stupic, K. and Russek, S. (2017), MRI Birdcage RF Coil Resonance with Uncertainty and Relative Error Convergence Rates, International COMSOL Users' Conference, Boston, MA, U.S.A., Boston, MA, [online], (Accessed June 7, 2023)
Created October 4, 2017, Updated May 18, 2020