Constructing a Birdcage Coil, Facilitating Freedom from the MRI Cage'

1
Constructing a Birdcage Coil, Facilitating
Freedom from the MRI Cage.
Edward Hawkins, Hiroyuki Fujita, Xiaoyu Yang,
Robert W. Brown Dept. Physics, CWRU 10900 Euclid
Ave., Cleveland, OH 44106
Solutions are of the form
In FIG. 5, changing the value of the matching
capacitor changes the reflection coefficient of
the transition from the coaxial cable to the
coil. In the Smith Chart, this appears as a
change in the radius of the circle representing
the standing wave ratio (SWR). The coil is
matched by adjusting the matching capacitor so
that the circle crosses 50 O along the x-axis of
the Smith chart, where the reactance is 0 O.
Adjusting the tuning capacitor does not change
the reflection coefficient significantly, since
the load is several orders of magnitude larger
than the relative change. The coil is tuned by
adjusting the tuning capacitor until the resonant
frequency desired, the Larmour frequency,
coincides with the point on the circle at which
the impedance is all resistance and has a
magnitude of 50 O.
where f is orthogonal to the z direction in FIG.
1. Using the Biot-Savart Law, one can show that
for an infinitely long birdcage coil, the
sinusoidal current distribution formed creates a
magnetic field of the form
with the directions of x and y given in FIG. 1.
RESULTS
y z Bo
x
FIG. 1 Schematic Diagram of a Low-Pass Birdcage
Coil. The capacitors are oriented as shown,
along the legs of the birdcage coil. The legs
and end-rings of the coil are taken as inductors,
with inductance given by
where the inductance (L) is in µH, and the
length (l) and width (w) of copper tape are given
in meters. The theoretical inductance is only an
approximation in practice because of the many
corners of the physical coil, which drastically
change the true inductance.
FIG. 8 MRI images a kiwi and a phantom at 7.0
T, obtained using the experimental birdcage coil.
Clockwise from upper left axial kiwi image
using RARE (multiple spin echoes), sagittal kiwi
image using RARE, axial kiwi image using a
diffusion-weighted protocol to show a bruise in
the kiwi, and an axial image of a phantom
obtained using RARE.
FIG. 6 Axial homogeneity as transmitted power
(dB) vs. axial distance (cm) for the 63.80 MHz
Coil. The horizontal line at -10 dB is the cutoff
for homogeneous B1 behavior, corresponding to 90
of the power input into the coil using a network
analyzer returning through a pickup used to
measure the magnetic field. This sets the FOV of
the coil. For the 63.80 MHz coil, FOV 6 cm,
for the 300.5 MHz resonator, FOV 5 cm.
FIG. 4 Tuning and Matching Each Quadrature
Mode of the Birdcage Coil. Because the birdcage
has a large reactance (2kO), matching capacitors
are added in series. Using tuning capacitors
added in parallel minimizes their impact on the
homogeneity of the coil. This setup also
necessitates building coils with resonant
frequencies higher than the desired resonant
frequency, since tuning can only decrease the
frequency.
CONCLUSIONS
1) Custom RF coils manufactured at a fraction
of the cost of commercial coils have comparable
SNR because of the ability to construct a coil
with a FOV very near the size of the sample. 2)
At high ( 300 MHz), the effects of higher order
terms in the Tropp theory become more pronounced.
Further study of these effects constitutes one of
the most active new fields in MRI.
FIG. 2 One Node of the Birdcage Coil for
Analysis Using Kirchoffs Laws. Analysis of the
N loops of the birdcage coil leads to N equations
and an impedance matrix of the form of FIG. 3.

ACKNOWLEDGMENTS
Jeremy Heilman and Mark Griswold help with
electronics and the network analyzer Tim Eagan
help with understanding the theory of the
birdcage resonator Chris Flask and the Small
Animal Imaging Center funding and lab space
FIG. 7 Logarithmic variation of B1 transmitted
(dB) vs. Axial Distance (cm). Linear fits of the
data show that the field drops off from near
total transmission at the center of the coil in a
linear fashion on a decibel (dB) scale. This
knowledge can be used in postprocessing to
increase the SNR of images taken using the coils.
FIG. 3 Impedance Matrix for a Birdcage Coil with
N 8 Legs. This matrix corresponds to the
general case displayed in FIG. 2. For the coils
fabricated, C1 0. Using the impedance matrix
and Ohms law, the resonant frequencies of the
birdcage coil can be theoretically calculated.
FIG. 5 Screenshot from the Network Analyzer
depicting a tuned and matched coil. The blue
trace is the Smith Chart, and the yellow trace is
the variation of reflected power (dB) with
frequency. The range depicted is 62 MHz 64
MHz.