Signal-to-Noise Ratio and Absorbed Power as Functions
of Main Magnetic Field Strength, and Definition of “90°”
RF Pulse for the Head in the Birdcage Coil
Christopher M. Collins
1,3
and Michael B. Smith
1,2
*
Calculations of the RF magnetic (B
1
) field as a function of
frequency between 64 and 345 MHz were performed for a head
model in an idealized birdcage coil. Absorbed power (P
abs
) and
SNR were calculated at each frequency with three different
methods of defining excitation pulse amplitude: maintaining 90°
flip angle at the coil center (center /2), maximizing FID
amplitude (Max. A
FID
), and maximizing total signal amplitude in
a reconstructed image (Max. A
image
). For center /2 and
Max. A
image
, SNR increases linearly with increasing field
strength until 260 MHz, where it begins to increase at a greater
rate. For these two methods, P
abs
increases continually, but at
a lower rate at higher field strengths. Above 215 MHz in MRI of
the human head, the use of FID amplitude to set B
1
excitation
pulses may result in apparent decreases in SNR and power
requirements with increasing static field strength. Magn Re-
son Med 45:684 – 691, 2001. © 2001 Wiley-Liss, Inc.
Key words: calculations; SNR; power; MRI; high field
Predictions of trends in signal-to-noise ratio (SNR) and
specific energy absorption rate (SAR) with increasing
static magnetic field (B
0
) strength based on MR theory, the
principle of reciprocity, and analytical RF magnetic field
(B
1
) calculations have been shown to be reasonably accu-
rate at frequencies up to 64 MHz in head- and body-sized
samples (1,2). MRI experiments are currently performed at
static magnetic field (B
0
) strengths as high as 8.0 Tesla,
where the frequency of the RF magnetic field (B
1
) for
imaging with
1
H is about 340 MHz. At these frequencies,
significant interaction between the applied B
1
field and
human tissues is expected. The effects of this interaction
on SNR and the total absorbed power are complicated, and
are dependent on the experiment being performed, RF coil
type and performance, and even on the specific subject
geometry and position in the coil (2,3).
In this study we performed calculations of SAR in the
head, the total absorbed power (P
abs
) in the head and
shoulders, and SNR on an axial plane of the head at several
B
1
frequencies between 64 and 345 MHz for an anatomi-
cally-accurate model in an idealized birdcage coil. The
head position and orientation, and the coil behavior are
kept constant so that B
1
frequency and definition of the
excitation pulse are the only variables. Electrical proper-
ties of all tissues are set appropriately at each frequency.
The excitation pulse amplitude is defined with three dif-
ferent methods at each frequency.
Since our interest was primarily in the effects of the
high-frequency RF fields on the imaging experiment, we
chose to ignore several factors that complicated both the
calculation and interpretation of the results. We chose to
consider signal from protons in water only, and to ignore
T
1
and T
2
relaxation effects in this work. This simplifies
the presentation of results, making them independent of
TE and TR, but it also removes some realism from the
simulation. We also neglected many other experimental
effects, such as those of B
0
inhomogeneity, inevitable vari-
ation in sample and coil geometry, signal filtering, and
signal amplifier integrity and performance (4). Thus, the
findings concerning signal in the images, FID amplitude,
and SNR presented here should be considered predictions
of the types of phenomena that may be seen at high fre-
quency due to behavior of the RF fields. Manifestation of
these phenomena in experiment should not be expected to
occur exactly as in these calculations.
METHODS
The finite difference time domain (FDTD) numerical
method for electromagnetics was used to calculate all elec-
trical and magnetic fields throughout a head model in an
idealized birdcage coil. This method of calculation has
previously been described in the literature (5,6). Here we
present our methods for modeling the MR experiment with
the FDTD method, and then relate the calculated results to
the MR experiment.
Head Model
A model of the human head for use with the FDTD method
was created by first segmenting 120 digital photographic
images of axial slices through a male cadaver from the
National Library of Medicine’s Visible Human Project into
20 materials (18 tissues, one free space, and one metal
dental filling), and then transforming these segmented im-
ages into a 3D grid of Yee cell cubes. One computer pro-
gram was written to perform the transformation, and an-
other was written to ensure the continuity of skin on the
outer surface of the model. Segmentation was performed
manually with reference to textbooks on anatomy and with
assistance from two practicing radiologists. At each fre-
quency, appropriate values from the literature for tissue
mass density (7–10), water content by percent mass (11),
and electrical permittivity and conductivity (12) were as-
signed to each tissue. Tissue mass density information was
1
Department of Radiology, Pennsylvania State University College of Medi-
cine, Hershey, Pennsylvania.
2
Department of Cellular and Molecular Physiology, Pennsylvania State Uni-
versity College of Medicine, Hershey, Pennsylvania.
3
Department of Bioengineering, University of Pennsylvania, Philadelphia,
Pennsylvania.
*Correspondence to: Michael B. Smith, Center for NMR Research, NMR/MRI
Building, Department of Radiology H066, Pennsylvania State University Col-
lege of Medicine, 500 University Drive, Hershey, PA 17033.
E-mail: mbsmith@psu.edu
Received 22 March 2000; revised 2 November 2000; accepted 6 November
2000.
Magnetic Resonance in Medicine 45:684 – 691 (2001)
© 2001 Wiley-Liss, Inc. 684