Radiofrequency Field Calculations
In order to excite nuclei to a state in which they produce a detectable signal, a radiofrequency (RF) magnetic field, B1+, must be applied. The available signal will depend in part on the magnitude and phase of this applied B1+ field throughout space and time. To receive signal it is necessary to have one or more receive coils (or antennas). By the principle of reciprocity, the received signal is proportional to the RF field B1- produced when driving the receive coil(s). The frequency of these fields is directly proportional to the strength of the static field, B0. It is advantageous to use a strong B0 field in MRI, but as the frequency of the B1 fields increases, two things happen electromagnetic wavelength effects make it more difficult to maintain homogeneous RF fields, and stronger currents are induced in conductive tissues, potentially leading to heating of the patient.
We have developed several methods for calculating the RF fields during MRI. Many of the models of the human body we have developed for this purpose are available for use with xFDTD software through Remcom, inc. We have developed methods for calculating signal-to-noise ratio, signal intensity distributions on reconstructed images, and many other important entities for MRI as functions of the RF fields and coils. Our calculation methods regularly show excellent agreement with experiment, and our calculations have been valuable in many applications, including coil design and explanations of surprising MRI phenomena.
Figure 1: Distributions of the magnitudes of the RF field (||B1||) and eddy current density (||J||), absolute values of the counter-clockwise (B1+) and clockwise (B1-) rotating components of B1, calculated signal intensity on a gradient-echo image (SIcalc), and experimental signal intensity on a gradient echo image (SIexp) for a low excitation power.
Figure 3: Image intensity using low-acceleration archetypal SENSE or SMASH reconstruction (Ss) distributions for head in 16-element array at 300, 400, 500, and 600 MHz (7 to 14 T)before and after optimization of image homogeneity on plane shown by variation of magnitude and phase of currents in transmit coils. Scale gives fraction of mean intensity value on plane shown. Values less than 50% of the mean value appear as 50% (black). Even at 600 MHz, all Ss values on the plane are within 10.6% of the mean after optimization.
- Collins CM, Liu W, Swift BJ, Smith MB: Combination of optimized transmit arrays and some receive array remethods can yield homogeneous images at very high frequencies. Magn Reson Med. 2005 Dec;54(6):1327-32.
- Van de Moortele P-F, Akgun C, Adriany G, Moeller S, Ritter J, Collins CM, Smith MB, Vaughan JT, Ugurbil K. B(1) destructive interferences and spatial phase patterns at 7T with a head transceiver array coil. Magn Reson Med. 2005 Dec;54:1503-1518.
- Sun L, Collins CM, Schiano JL, Smith MB, Smith NB. Adaptive real-time closed-loop temperature control for ultrasound hyperthermia using magnetic resonance thermometry. Concepts Magn Reson Part B 27B. 2005 May;51-63.
- Liu W, Collins CM, Smith MB. Calculations of B1 distribution, specific energy absorption rate, and intrinsic signal-to-noise ratio for a body-size birdcage coil loaded with different human subjects at 64 and 128 MHz. Applied Magn Reson. 2005 Jan; 29:5-18.
- Lazovic J, Stojkovic DS, Collins CM, Yang QX, Vaughan JT, Smith MB. Hexagonal zero mode TEM coil: a single-channel coil design for imaging multiple small animals. Magn Reson Med. 2005 May;53(5):1150-7.
- Collins CM, Liu W, Schreiber W, Yang QX, Smith MB. Central brightening due to constructive interference with, without, and despite dielectric resonance. J Magn Reson Imaging. 2005 Feb;21(2):192-6.
- Yang QX, Wang J, Collins CM, Smith MB, Zhang X, Ugurbil K, Chen W. Phantom design method for high-field MRI human systems. Magn Reson Med. 2004 Nov;52(5):1016-20.
- Collins CM, Liu W, Wang J, Gruetter R, Vaughan JT, Ugurbil K, Smith MB. Temperature and SAR calculations for a human head within volume and surface coils at 64 and 300 MHz. J Magn Reson Imaging. 2004 May;19(5):650-6.
- Liu W, Collins CM, Delp PJ, Smith MB. Effects of end-ring/shield configuration on homogeneity and signal-to-noise ratio in a birdcage-type coil loaded with a human head. Magn Reson Med. 2004 Jan;51(1):217-21.
- Collins CM, Smith MB. Spatial resolution of numerical models of man and calculated specific absorption rate using the FDTD method: a study at 64 MHz in a magnetic resonance imaging coil. J Magn Reson Imaging. 2003 Sep;18(3):383-8.
- Alecci M, Collins CM, Wilson J, Liu W, Smith MB, Jezzard P. Theoretical and experimental evaluation of detached endcaps for 3T birdcage coils. Magn Reson Med. 2003 Feb;49:363-370.
- Wang J, Yang QX, Zhang X, Collins CM, Smith MB, Zhu XH, Adriany G, Ugurbil K, Chen W. Polarization of the RF field in a human head at high field: a study with a quadrature surface coil at 7.0 T. Magn Reson Med. 2002 Aug;48(2):362-9.
- Yang QX, Wang J, Zhang X, Collins CM, Smith MB, Liu H, Zhu XH, Vaughan JT, Ugurbil K, Chen W. Analysis of wave behavior in lossy dielectric samples at high field. Magn Reson Med. 2002 May;47(5):982-9.
- Collins CM, Yang QX, Wang JH, Zhang X, Liu H, Michaeli S, Zhu XH, Adriany G, Vaughan JT, Anderson P, Merkle H, Ugurbil K, Smith MB, Chen W. Different excitation and reception distributions with a single-loop transmit-receive surface coil near a head-sized spherical phantom at 300 MHz. Magn Reson Med. 2002 May;47(5):1026-8.
- Vaughan JT, Garwood M, Collins CM, Liu W, DelaBarre L, Kim SG, Adriany G, Andersen P, Merkle H, Goebel R, Smith MB, and Ugurbil K. 7T vs. 4T: RF power, homogeneity, and signal-to-noise comparison in head images. Magn Reson Med. 2001 Jul;46:24-30.
- Alecci M, Collins CM, Smith MB, and Jezzard P. Radio frequency magnetic field mapping of a 3 Tesla birdcage coil: experimental and theoretical dependence on sample properties. Magn Reson Med. 2001 Aug;46:379-385.
- Collins CM, Smith MB. Calculations of B(1) distribution, SNR, and SAR for a surface coil adjacent to an anatomically-accurate human body model. Magn Reson Med. 2001 Apr;45(4):692-9.
- Collins CM, Smith MB. Signal-to-noise ratio and absorbed power as functions of main magnetic field strength, and definition of "90 degrees " RF pulse for the head in the birdcage coil. Magn Reson Med. 2001 Apr;45(4):684-91.
- Collins CM, Li S, Smith MB. SAR and B1 field distributions in a heterogeneous human head model within a birdcage coil. Specific energy absorption rate. Magn Reson Med. 1998 Dec;40(6):847-56.
- Strilka RJ, Li S, Martin JT, Collins CM, Smith MB. A numerical study of radiofrequency deposition in a spherical phantom using surface coils. Magn Reson Imaging. 1998 Sep;16(7):787-98.
- Dardzinski BJ, Li S, Collins CM, Williams GD, Smith MB. A birdcage coil tuned by RF shielding for application at 9.4 T. J Magn Reson. 1998 Mar;131(1):32-8.
- Collins CM, Li S, Yang QX, Smith MB: A method for accurate calculation of B1 fields in three dimensions: effects of shield geometry on field strength and homogeneity in the birdcage coil. J Magn Reson. 1997 Apr;125:233-241.
- Li S, Collins CM, Dardzinski BJ, Chin CL, Smith MB. A method to create an optimum current distribution and homogeneous B1 field for elliptical birdcage coils. Magn Reson Med. 1997 Apr;37(4):600-8.