2114IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 10, OCTOBER 2006
A New Decoupling Method for Quadrature Coils in
Magnetic Resonance Imaging
H. T. Hui*, B. K. Li, and S. Crozier
Abstract—A powerful decoupling method is introduced to obtain decou-
pled signal voltages from quadrature coils in magnetic resonance imaging
(MRI). The new method uses the knowledge of the position of the signal
source in MRI, the active slice, to define a new mutual impedance which
accurately quantifiesthe couplingvoltagesandenables themtoberemoved
almost completely. Results show that by using the new decoupling method,
the percentage errors in the decoupled voltages are of the order of 10
and isolations between two coils are more than 170 dB.
Index Terms—Decoupling method, magnetic resonance imaging (MRI),
mutual impedance, quadrature coils.
Quadrature coils can be used to increase the signal-to-noise ratio
(SNR) in magnetic resonance imaging (MRI). Typical applications of
the two quadrature coils, however, strong mutual coupling can lead to
the failure of obtaining independent signals from the two coils. There-
fore, decoupling methods become a necessary consideration in quadra-
ture coil design. The most popular decoupling method for quadrature
coupling between them . However, overlapping of the two coils will
force the coils to lose orthogonality. In this paper, we introduce a new
decoupling method to remove the mutual coupling effect in quadra-
ture coils. This method has its origin in antenna array analyses , 
but uses the knowledge of the position of the signal source in MRI,
the active slice, to define a new mutual impedance which quantifies the
coupling voltages between two quadrature coils and enablesthem tobe
removed from the terminal voltages almost completely. Results show
that by using the new decoupling method, the percentage error in the
decoupled voltage is of the order of 10??% and isolations between two
method is more powerful than previous decoupling methods.
II. NEW METHOD
A. Basic Theory
Consider two quadrature coils shown in Fig. 1(a) for the imaging of
the human head. The two coils are placed on a cylindrical surface with
a diameter of 30 cm (radius ? ? ?? cm) and separated 90?apart, as
shown in Fig. 1(b). A typical active slice in a human head imaging
is modeled as an elliptical slice with a minor axis ??????, a major
Manuscript received February 8, 2005; revised March 17, 2006. Asterisk in-
dicates corresponding author.
*H. T. Hui is with the School of Information Technology and Electrical En-
gineering, University of Queensland, Brisbane QLD 4072, Australia (e-mail:
B. K. Li and S. Crozier are with the School of Information Technology and
Electrical Engineering, University of Queensland, Brisbane QLD 4072, Aus-
Digital Object Identifier 10.1109/TBME.2006.881783
Fig. 1. Quadrature coils for human head MRI. (b) Human head model and rel-
ative position of quadrature coils.
axis ??????, and a thickness ?. The coils are identical and in a rect-
angular shape with length ? and width ? and are made with a thin
conducting strip of width ?. Four fixed capacitors and one tuning ca-
pacitor are placed around the coils for smoothing the current distribu-
capacitors are labeled by ??? ??? ??, and ?? and the tuning capac-
itor is labeled by ??. The two coils are matched to an external system
impedance of 50 ? through a matching circuit. The distribution of the
induced magnetization? ? on the active slice is assumed to have the
? ? ? ???? ? ? ???? ??
where ?? and ?? are, respectively, the magnitudes of the magneti-
zation along the ? and ? directions. ?? and ?? are assumed to be
constant throughout the slice.
Now let the received signal voltages across the terminal loads ??of
the quadrature coils be ?? and ??. These voltages are the actual ones
0018-9294/$20.00 © 2006 IEEE
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 10, OCTOBER 20062115
the other coil. By using the superposition principle, we can write
?? ? ????? ??? ???
?? ? ???? ? ??? ???
are the new mutual impedances  between the two coils. To calculate
by the active slice are first determined. Then, the voltage ?? induced
across the terminal load of coil 1 due the current distribution ?? alone
(with the active slice removed such that ?? ? ?) is calculated. By the
definition of the new mutual impedance 
decoupled voltages ?? and ?? can be found from (2) and (3) for any
actual terminal voltages ?? and ??. Strictly speaking, the decoupled
voltages ?? and ?? are not 100% coupling free. This is because ter-
minal quantities (terminal voltages and mutual impedances) are being
used to describe a distributed system (the electric and magnetic fields).
? can be calculated similarly. Once ???
? and ???
? are known, the
B. Performance Criteria
Two criteria are used to measure the performance of the new decou-
% error of the combined voltage ??? ? ???
where ??? represents the norm of the complex number ? and ? and
??are, respectively, the quadrature-combined decoupled voltage and
ideal voltage given by
? ? ??? ???
pling. The second criterion is the isolation between the two coils and
is defined by
?being the ideal terminal voltages without mutual cou-
??? ? ?????
???? ? ???
? ?? ??
It measures the relative amount of signal that leaks (couples) from one
coil to the other. The first criterion in (5) has not been used before but
is the most direct and simple one for measuring the performance of a
decoupling method. A similar isolation criterion as the one in (8) was
used before in , although its meaning may not be exactly the same.
III. RESULTS AND DISCUSSION
The new decoupling method is demonstrated using computer simu-
lations. The current distributions on the quadrature coils, the new mu-
tual impedances, the terminal voltages, the electromagnetic field gen-
erated by the active slice, and the electromagnetic coupling between
the two coils are all calculated numerically by using the method of
% ERRORS AND ISOLATIONS OF QUADRATURE COILS USING NEW DECOUPLING
METHOD AND OPEN-CIRCUIT VOLTAGE METHOD
Fig. 2. Percentage of error of combined voltage and isolations produced by
new method when slice’s center position deviates from origin along ? axis.
moments . The quadrature coils in Fig. 1 have the following di-
mensions: ? ? ?? cm, ? ? ?? cm, and ? ? ? cm. Assuming
a static magnetic field ?? ? ??? T, the capacitor values to make a
single isolated coil nearly resonant at ?? ? ?? MHz are found to
be ?? ? ?? ? ?? ? ?? ? ?? pF and ?? ? ???? pF. The
self-impedance is calculated to be ????? ? ?????? ?. The dimensions
of the active slice are ? ? ??? cm, ? ? ???? cm, and ? ? ???? cm,
which are based on a human head model taken from . The center
of the active slice is placed at the origin ?? ? ??? ? ??? ? ??. The
induced magnetization is taken to be ?? ? ?? ? ? A/m.
The computed results of percentage error of the combined voltage
and the isolations are shown in Table I. The new mutual impedances
between the two quadrature coils are ???
? ????? ? ????? ?. It can be seen that the percentage of error
is of the order of 10??%, and the isolations are more than 170 dB. A
comparison has been made with the open-circuit voltage method .
The conventional mutual impedances used in that method are found to
be ??? ? ??? ? ???? ? ????? ?. It can be seen that the percentage
of error produced by this method is about 30%. The isolations are only
about 16 dB. Its decoupling power is much weaker than that of the new
decoupling method. In a recent study , it was reported that a capac-
itive decoupling network can achieve an isolation between two phased
array coils of 20–40 dB. This is much smaller than the isolations that
can be achievedby the new decouplingmethod. However, this compar-
ison is based on the assumption that isolation in both cases is taken to
be a measure of the relative amount of signal coupling from one coil to
As shown previously, the calculation of the new mutual impedance
relies on the accurate knowledge of the position of the active slice,
which is assumed to be placed with its center at the origin. In real MRI
? ????? ? ????? ? and
2116IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 10, OCTOBER 2006
Fig. 3. Percentage of error of combined voltage and isolation produced by
open-circuit voltage method when slice’s center position deviates from origin
along ? axis.
not be exactly placed at this position and may also be under a constant
change during the imaging process. The effect from the deviation of
the active slice position from the origin has to be determined. Fig. 2
shows the change of the percentage of error of the combined voltage
with the deviation of the slice position along the ? axis. The change of
the isolations is also shown. It can be seen that even when the active
slice deviates over a substantial distance, the percentage of error is still
smaller than 0.3%; whereas, the isolation is still greater than 70 dB.
Note that if the change of the active slice position is too large, one can
always reposition the quadrature coils so that the error resulting from
the deviationofslice positionis stillkeptwithin small values,asshown
in Fig. 2. Fig. 3 shows the percentage of error and isolations produced
by the open-circuit voltage method with the slice moving along the ?
axis. It can be seen that the percentage of error and isolations remain
quite stable. This is because the open-circuit voltage method does not
take the slice position into account. The percentage of error is much
smaller than those produced by the new method.
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Ultrasonic Liver Discrimination Using 2-D
Guitao Cao, Pengfei Shi*, and Bing Hu
Abstract—In this paper, we present an experiment to extract liver
features using two-dimensional phase congruency, which is invariant to
changes in intensity or contrast, to try to avoid the influence of machine
settings. The effectiveness of our method was tested on three classes of liver
images and shows the potential for physicians to quantify liver pathology
in clinical diagnosis.
Index Terms—Biomedical ultrasonics, image classification,liver,medical
image processing, phase measurement.
extracting parameters from the returned ultrasound echoes for the pur-
pose of identifying the type of tissue present in the ultrasound scan
plane. For the case of liver parenchyma, where a different disease re-
veals a different liver architecture that is microscopically built up by
protein chains, there is an explicit correspondence between the values
of the parameter and the visual appearance of the ultrasound image.
If toxins, inflammation, metabolic derangements, or other causes have
damaged the liver, more than normal amounts of collagen fiber can be
nodules surrounded by chains replace the damaged or dead liver cells,
the liver architecture is distorted by occurrences of coarse nodules of
Typically, fibrosis and cirrhosis have to be diagnosed by biopsy,
which may cause some problems such as hemorrhaging, infection, or
injury totheorgan. Treatmentwith theuseof diagnosticultrasound has
been a useful and noninvasive clinical method for over two decades.
Several researchers diagnosed diffused liver diseases from ultrasound
images assisted by computerized tissue classification –. But due
toitsqualitative,subjective,and experienced-basednature, theexisting
methodsall require the same machinesettings for the scannerto ensure
the fidelity of the tissue because the attenuation of ultrasonic waves
depends on the machine settings, such as contrast and gain (?) .
If these requirements cannot be fulfilled, the feature extraction and
classification may be greatly influenced. So, a novel feature extraction
method, which is called phase congruency, invariant to those external
Manuscript received April 14, 2005; revised November 12, 2005. Asterisk
indicates corresponding author.
G. Cao is with the Institute of Image Processing and Pattern Recognition,
Shanghai Jiaotong University, Shanghai 200030, China (e-mail: maggie@sjtu.
*P. Shi is with the Institute of Image Processing and Pattern Recognition,
Shanghai Jiaotong University, Shanghai 200030, China (e-mail: pfshi@ sjtu.
B. Hu is with the Department of Ultrasound in Medicine, Shanghai Sixth
People’s Hospital, Shanghai Jiaotong University, Shanghai 200025, China
Digital Object Identifier 10.1109/TBME.2006.880907
0018-9294/$20.00 © 2006 IEEE