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2114IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 10, OCTOBER 2006

Communications

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.

I. INTRODUCTION

Quadrature coils can be used to increase the signal-to-noise ratio

(SNR) in magnetic resonance imaging (MRI). Typical applications of

quadraturecoilsarefoundintheimagingofahumanhead,inwhichthe

twocoilscanwraparoundthesample[1].Duetotheproximitybetween

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

coilsistopartiallyoverlapthetwocoilstocompensatefortheinductive

coupling between them [2]. 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 [3], [4]

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

coilsaremorethan170dB.Theseresultsshowthatthenewdecoupling

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:

hthui@itee.uq.edu.au).

B. K. Li and S. Crozier are with the School of Information Technology and

Electrical Engineering, University of Queensland, Brisbane QLD 4072, Aus-

tralia.

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-

tionsandmakingthecoilsresonateat adesiredfrequency??.Thefixed

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

following form:

? ? ? ???? ? ? ???? ??

(1)

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

pickedupbythequadraturecoilsandcontainboththevoltagesinduced

0018-9294/$20.00 © 2006 IEEE

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 10, OCTOBER 20062115

bytheactiveslice,denotedby??and??,andthecoupledvoltagefrom

the other coil. By using the superposition principle, we can write

?? ? ????? ??? ???

?? ? ???? ? ??? ???

? ??

(2)

(3)

? ??

where??and??aretheterminalcurrentsonthecoils,and???

are the new mutual impedances [3] 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 [3]

? and???

?

? and???

? ,thecurrentdistributions??and??onthetwocoilsexcited

???

?

???

??

(4)

and ???

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-

plingmethod.Thefirstisthepercentageerrorofthecombinedvoltages

defined by

% error of the combined voltage ??? ? ???

????

? ???%(5)

where ??? represents the norm of the complex number ? and ? and

??are, respectively, the quadrature-combined decoupled voltage and

ideal voltage given by

? ? ??? ???

??? ??

(6)

(7)

?? ???

?

with ??

pling. The second criterion is the isolation between the two coils and

is defined by

?and ??

?being the ideal terminal voltages without mutual cou-

??? ? ?????

???? ??

???

??

??

???? ? ???

and

? ?? ??

(8)

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 [5], 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

TABLE I

% 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 [6]. 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 [7]. 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 [8].

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 [5], 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

other.

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

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2116 IEEE 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.

operations,thepositionofthehumanhead(andsotheactiveslice)may

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

largerthanthatobtainedbythenewmethodandtheisolationsaremuch

smaller than those produced by the new method.

REFERENCES

[1] J. Wang, Q. X. Yang, X. Zhang, C. M. Collins, M. B. Smith, X. H. Zhu,

G. Adriany, K. Ugurbil, and W. Chen, “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., vol. 48, pp. 362–369, 2002.

[2] B. Roemer, W. A. Edelstein, C. E. Hayes, S. P. Souza, and O. M.

Mueller, “The NMR phased array,” Magn. Reson. Med., vol. 16, pp.

192–225, 1990.

[3] H. T. Hui, “Improved compensation for the mutual coupling effect in

a dipole array for direction finding,” IEEE Trans. Antennas Propagat.,

vol. 51, no. 11, pp. 2498–2503, Nov. 2003.

[4] ——, “A new definition of mutual impedance for application in dipole

receiving antenna arrays,” IEEE Antennas Wireless Propagag. Lett.,

vol. 3, pp. 364–367, 2004.

[5] X. Zhang and A. Webb, “Design of a capacitively decoupled transmit/

receive NMR phased array for high field microscopy at 14.1 T,” J.

Magn. Reson., vol. 170, pp. 149–155, 2004.

[6] R. F. Harrington, Field Computation by Moment Methods.

away, NJ: IEEE, 1993.

[7] J.KoikkalainenandJ.Lötjönen,“Reconstructionof3-Dheadgeometry

from digitised point sets: An evaluation study,” IEEE Trans. Inform.

Technol. Biomed., vol. 8, no. 2, pp. 377–386, Jun. 2004.

Piscat-

[8] I. J. Gupta and A. A. Ksienski, “Effect of mutual coupling on the per-

formance of adaptive arrays,” IEEE Trans. Antennas Propagat., vol.

AP–31, pp. 785–791, 1983.

Ultrasonic Liver Discrimination Using 2-D

Phase Congruency

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.

I. INTRODUCTION

Quantitative tissuecharacterizationtechniques(QTCT)arebasedon

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

depositedinthelivercellstocausebloodlossandleadtofibrosis.When

nodules surrounded by chains replace the damaged or dead liver cells,

the liver architecture is distorted by occurrences of coarse nodules of

cirrhosis [1].

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 [2]–[6]. 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 (?) [5].

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.

edu.cn).

*P. Shi is with the Institute of Image Processing and Pattern Recognition,

Shanghai Jiaotong University, Shanghai 200030, China (e-mail: pfshi@ sjtu.

edu.cn).

B. Hu is with the Department of Ultrasound in Medicine, Shanghai Sixth

People’s Hospital, Shanghai Jiaotong University, Shanghai 200025, China

(e-mail: binghuzz@263.net).

Digital Object Identifier 10.1109/TBME.2006.880907

0018-9294/$20.00 © 2006 IEEE