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Optimized efficient liver T1ρ mapping using limited spin lock times

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IOP PUBLISHING

PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 57 (2012) 1631–1640

doi:10.1088/0031-9155/57/6/1631

Optimized efficient liver T1ρmapping using limited

spin lock times

Jing Yuan1, Feng Zhao1, James F Griffith1, Queenie Chan2

and Yi-Xiang J Wang1

1Department of Imaging and Interventional Radiology, The Chinese University of Hong Kong,

Shatin, New Territories, Hong Kong, People’s Republic of China

2Philips Healthcare, Philips Electronics Hong Kong Limited, Hong Kong, People’s Republic of

China

E-mail: jyuan@cuhk.edu.hk

Received 27 June 2011, in final form 26 January 2012

Published 7 March 2012

Online at stacks.iop.org/PMB/57/1631

Abstract

T1ρrelaxation has recently been found to be sensitive to liver fibrosis and

has potential to be used for early detection of liver fibrosis and grading.

Liver T1ρimaging and accurate mapping are challenging because of the long

scan time, respiration motion and high specific absorption rate. Reduction and

optimization of spin lock times (TSLs) are an efficient way to reduce scan

time and radiofrequency energy deposition of T1ρimaging, but maintain the

near-optimal precision of T1ρmapping. This work analyzes the precision in

T1ρestimation with limited, in particular two, spin lock times, and explores

the feasibility of using two specific operator-selected TSLs for efficient and

accurate liver T1ρmapping. Two optimized TSLs were derived by theoretical

analysis and numerical simulations first, and tested experimentally by in vivo

rat liver T1ρimaging at 3 T. The simulation showed that the TSLs of 1 and

50 ms gave optimal T1ρestimation in a range of 10–100 ms. In the experiment,

no significant statistical difference was found between the T1ρmaps generated

using the optimized two-TSL combination and the maps generated using the

six TSLs of [1, 10, 20, 30, 40, 50] ms according to one-way ANOVA analysis

(p = 0.1364 for liver and p = 0.8708 for muscle).

(Some figures may appear in colour only in the online journal)

Introduction

MRI offers a variety of mechanisms to produce different contrasts in anatomical and

functional images. In addition to T1, T2and T2

in the rotating frame) is another relaxation parameter that represents the time constant of

transversemagnetizationdecayduringtheapplicationofanon-resonantcontinuouswave(CW)

∗, T1ρrelaxation (the spin–lattice relaxation

0031-9155/12/061631+10$33.00© 2012 Institute of Physics and Engineering in MedicinePrinted in the UK & the USA1631

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1632 J Yuan et al

radiofrequency (RF) pulse, i.e.spinlock (SL) pulse, aligned withthe net magnetization vector.

With T1ρrelaxation, there is potential to investigate interactions between motionally restricted

water molecules and surrounding macromolecules due to the high sensitivity of T1ρto low

frequency motional and static processes. T1ρrelaxation has been proposed for various clinical

applications. For example, T1ρrelaxation can be used as a sensitive biomarker to detect early

stages of intervertebral disk degeneration (Blumenkrantz et al 2006, 2010, Johannessen et al

2006, Nguyen et al 2008) and cartilage degeneration in osteoarthritis (Duvvuri et al 1997,

Mlynarik et al 1999, Regatte et al 2003, Li et al 2009). T1ρrelaxation variation has also been

investigated as a predictor of Alzheimer’s disease progression (Borthakur et al 2006, 2008,

Haris et al 2009). Recently, Wang et al found that T1ρrelaxation is sensitive to liver fibrosis

and has potential tobeused forliver fibrosisdiagnosis and assessment(Wangetal2011,Sirlin

2011). Different from T1ρimaging of intervertebral disk, cartilage and brain that are almost

stationary, in vivo liver T1ρimaging is subject to respiration motion that may compromise

the accuracy and precision of T1ρmapping. Therefore, a short scan time for in vivo liver

T1ρimaging is essential.

Accurate and precise T1ρmapping is challenging under the scan time constraint because

multiple SL times (TSLs) are required for T1ρ-weighted magnetization preparation and a

long delay time is usually necessary in the SL pulse sequence for longitudinal magnetization

restoration. SL pulses are also sensitive to magnetic field heterogeneities. SL pulses with

different TSLs may introduce different spatially distributed banding-like artifacts in images

thatmaycompromisetheaccuracyofT1ρmapping.Inpractice,theuseofhighSLfrequenciesis

helpfulinalleviatingtheseartifacts,however,remarkablyincreasesthetotalspecificabsorption

rate (SAR) and RF energy deposition in patients.

The reduction of TSL numbers is an apparent strategy to enhance T1ρimaging efficiency.

However, the reduced TSLs have to be optimized to minimize the mapping uncertainty.

T1ρ relaxation is conventionally described as an exponential decay with respect to TSL,

similar to T1and T2. Many studies have been conducted on the choice of optimal selection of

observation time (e.g. inversion recovery time for T1measurement) to produce the smallest

estimation error for T1and T2mapping (Becker et al 1980, Weiss et al 1980, Sezginer et al

1991, Bain 1990, Taitelbaum et al 1994, Jones et al 1996, Zhang et al 1998, Fleysher et al

2008). Although T1ρmapping with limited TSLs could be inspired from these studies, there

are still some limitations and restrictions in the previous studies. The optimal observation

times proposed for T1or T2mapping are usually illustrated either in complicated mathematical

equations (Weiss et al 1980, Weiss and Ferretti 1985a, 1985b, Becker et al 1980, Zhang

et al 1998) or in implicit criteria (Bain 1990). The scan time efficiency of the proposed

optimal observation time is not usually maximized. More importantly, most studies are

completely based on theoretical derivation or numerical simulation without experiment

verifications. In addition, the distinctive characteristics of T1ρimaging, such as high SAR

and sensitivity to field heterogeneity, make accurate T1ρmapping under the critical time

constraint even more challenging than T1and T2mapping. To the best of our knowledge,

no optimized efficient acquisition strategies have been proposed for T1ρ imaging and

mapping.

In this study, we first simplified the theoretical analysis based on a two-parameter

exponential T1ρrelaxation model so that only two optimized TSLs were required to minimize

the estimation variance and maximize the time efficiency. These two optimized TSLs were

determined by mathematical analysis and then tested by Monte Carlo numerical simulation.

Finally,theT1ρmappingprecisionwiththeoptimizedtwoTSLswasconfirmedexperimentally

by in vivo rat liver T1ρimaging.

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Efficient T1ρmapping with limited TSLs 1633

Figure 1. The schematic of a rotary echo SL pulse imbedded bFFE SL pulse sequence.

Methods

Theoretical analysis

T1ρrelaxation can be normally described as a three-parameter exponential decay function with

SL time TSL, as shown in equation (1):

Si= A · e−TSLi/T1ρ+ B,

where A, B and T1ρrelaxation are the three parameters to fit. Siis the acquired image intensity

attheSLtimeofTSLi.Giventhattheflipangleofthepreparationpulse(90◦

restoration pulse (90◦

after the restoration pulse shows purely exponential-decayed components (Charagundla et al

2003), so the image intensity can be simplified as a two-parameter exponential function of

S0and T1ρ:

Si= S0· e−TSLi/T1ρ,

where S0isthebaseline image intensityacquired atTSLof zero.The standard deviation?σiT1ρ

?∂T1ρ

Thenoiselevelδiisusuallydeterminedbythereceiverhardware,imagingprotocolandsample

properties, and independent of SL duration, so can be rewritten as a general term of δ. By

substituting equation (2) into equation (3), it is derived that

?∂T1ρ

The term S0/δ is defined as the equilibrium signal-to-noise ratio (SNR). When a series of N

SL times (i = 1, 2,..., N) is used, the aggregate standard deviation (σT1ρ) is dependent on

many factors, such as the individual standard deviation (σiT1ρ), the exponential decay model,

as well as the least-squares fitting (Zhang et al 1998, Weiss and Ferretti 1985a, 1985b, Weiss

et al 1980, Becker et al 1980).

Here, the standard deviation analysis can be significantly simplified since only two TSLs

are specified for optimal T1ρestimation. The first specific SL time TSL1(i = 1) is selected as

zero or a very small duration relative to the true T1ρvalue (T1ρt). As such, S1is approximated

as S0(S1≈ S0). Meanwhile, S1is normally much larger than the noise, i.e. S1? δ. The second

SLtimeTSL2(i=2)shouldbeselectedsufficientlyfarawayfromTSL1toavoidapronounced

deviation for large true T1ρvalues (T1ρt? TSL1and T1ρt? TSL2). Meanwhile, TSL2is also

required to satisfy S2? δ to avoid an overwhelming noise level. It is derived that

σ2

S2

0

∂s2

S2

1

∂s2

(1)

xinfigure1)andthe

−xin figure 1) are well calibrated to 90◦, the longitudinal magnetization

(2)

?

or variance?σ2

iT1ρ

?due to the presence of noise (δi) for TSLican be written as

σ2

i

∂Si

iT1ρ= δ2

?2

.

(3)

σ2

iT1ρ= δ2

∂Si

?2

=δ2

S2

0

?∂T1ρ

∂si

?2

=

1

SNR2·

TSL4

i· (logsi)4

i

s2

where

si=Si

S0.

(4)

2T1ρ=δ2

?∂T1ρ

?2

≈δ2

?∂T1ρ

?2

=

1

SNR2·

TSL4

2

s2

2· (logs2)4=e2·TSL2/T1ρ

SNR2

·

T4

1ρ

TSL2

2

.

(5)

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1634J Yuan et al

By neglecting the covariance factor between S1and S2, σ2T1ρis approximately equal to the

aggregate σT1ρ. As seen from equation (5), T1ρestimation variance is inversely proportional to

the square of SNR. It can also be proved from equation (5) that the minimum of σ2

at a TSL2that is equal to the true T1ρvalue to be fit.

2T1ρis found

Numerical simulation

DeviationsofT1ρestimationweretestedbyMonteCarlosimulationonMATLAB(MathWorks,

Natick, MA, USA) for different true T1ρvalues by using different combinations of TSLs. In

Monte Carlo simulations, signals were generated according to equation (2) with the given true

T1ρvalues and the selected TSLs. Rician noise was added to each signal at the mean level of

δ = 0.01S0(SNR = 100). These noise-imposed signals were then least-squares fitted using

equation (2) to obtain the estimated T1ρvalues. Here the T1ρdeviation was reported as the

absolute difference between the true T1ρvalue and the best fitted T1ρvalue in the presence

of Rician noise. Each simulation was repeated 60000 times, sufficiently large to obtain the

reliable and smooth estimated T1ρdistribution. Note that no assumption of S1≈ S0was made

in Monte Carlo simulations.

T1ρimaging

Five male Sprague-Dawley rats with weight of 200–250 g were scanned under appropriate

animal ethical approval. T1ρimaging was performed on a 3 T clinical scanner (Philips Medical

Systems, Best, The Netherlands) using a T1ρprepared multi-slice 2D balanced fast field echo

(bFFE) (or balanced steady-state free precession, SSFP) sequence (Witschey et al 2008) with

a four-channel human wrist array coil. A schematic for the SL bFFE sequence is shown in

figure 1. A spectrally selective RF pulse was used for fat suppression followed by the

T1ρ preparation module in which a B1-insensitive rotary echo SL pulse was embedded

(Charagundla et al 2003). In the bFFE module, a half-alpha pulse and four startup pulses

were used first to approach the steady state but with T1ρ-weighted preparation maintained

(Witschey et al 2008). Normal phase alternating bFFE readout was used for acquisition

with a centric acquisition order to maintain the T1ρ-weighting of images during the transient

status. Eighty k-space lines were acquired for each shot acquisition. A delay time (TD) of

5000 ms after each shot acquisition was set to restore equilibrium magnetization prior to the

next T1ρpreparation. Primary imaging parameters included TR/TE = 5.0/2.5 ms, FA = 30◦,

FOV = 80 mm, pixel size = 0.3 mm, slice thickness = 2 mm, slice number = 6, NSA (number

of signal average) = 4 and receiver bandwidth BW = 128 kHz. A SL time series of 1, 10,

20, 30, 40 and 50 ms was applied and the SL frequency was 500 Hz. A sensitivity encoding

(SENSE) factor of 1.5 was used for scan and constant level appearance (CLEAR) was applied

for coil sensitivity correction during reconstruction. The total scan time was around 20 min

for each rat scan.

All images were processed using a home-made MATLAB program to generate T1ρmaps

according to equation (2). T1ρmaps generated from all SL times were compared to those

generated from the selected SL times in the full series.

Results

Theoretical analysis and numerical simulation

Figure 2(a) shows a plot of the estimated T1ρstandard deviation distribution for the true

T1ρ range from 15 to 140 ms using different TSL2durations according to equation (5).

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Efficient T1ρmapping with limited TSLs1635

(a)

(b)

Figure 2. (a) The theoretical standard deviations of T1ρestimation for the true T1ρrange from

15 to 140 ms using different TSL2durations; (b) a zoomed plot of (a) showing the T1ρstandard

deviation within a narrower true T1ρfrom 20 to 80 ms.

(a)(b)

Figure 3. Monte Carlo simulation results: (a) comparison of the T1ρestimation deviations when

using different TSL combinations. (b) The T1ρestimation deviations using different combinations

of two TSLs.

Figure 2(b) shows a zoomed plot of figure 1(a) within a narrower range. The deviation is

generally smaller than 4.5 ms by using a TSL2within the range of 20–80 ms for the true

T1ρvalues within the same range. The optimal TSL2was found to be 50 ms through a 1 ms

step-wise search within the true T1ρrange of 10 to 100 ms.

ThehistogramsofbestfittedT1ρvaluesintheMonteCarlosimulationwereapproximately

normally distributed in the presence of Rician noise. Figure 3 shows simulation results. In

figure 3(a), the TSL combination of [1, 10, 20, 30, 40, 50] ms gave the smallest deviation

sum (the area under the curve) in the true T1ρrange of 10 to 100 ms. The TSLs of [1, 20,

40, 60, 80, 100] ms gave smaller deviations for true T1ρvalues larger than 60 ms but much

larger deviations for small true T1ρvalues. For two TSLs of [1, 50] ms, every individual

T1ρdeviation was smaller than 4 ms. The deviation was just slightly larger (<1 ms) than the

corresponding deviation with the TSLs of [1, 10, 20, 30, 40, 50] ms. It is interesting to find

that T1ρdeviation for [1, 50] ms was even smaller than that for [1, 20, 50] ms. Figure 3(b)

shows the T1ρdeviations using different combinations of two TSLs. [1, 50] ms provided a

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1636 J Yuan et al

Figure 4. T1ρ-weighted rat liver images acquired at different TSLs. The mean image intensity ratio

of signal (S) to noise (N) ROI is used for SNR estimation.

good compromise in T1ρestimation for wide true T1ρranges, and had the smallest deviation

sum in total, consistent with the theoretical analysis. Agreeing with equation (3), simulation

also showed that T1ρdeviation is inversely proportional to the SNR for true T1ρvalues larger

than 20 ms by using different two-TSL combinations.

Experiments

Figure 4 shows T1ρ-weighted in vivo rat liver images acquired at different TSLs. The SNR was

estimated as the mean intensity ratio of the signal region-of-interest (ROI) (S in figure 4) to

the noise ROI (N in figure 4). The signal ROI was selected as a square region in the rat liver

that had relatively homogenous intensities. The noise ROI was selected to be a position-fixed

background square region that was relatively close to the rat liver but without motion induced

artifact to account for the effect of coil sensitivity correction on noise calibration by CLEAR.

In general, the liver SNRs were sufficiently high (SNR > 40) for T1ρmapping.

T1ρmaps generated from the different combinations of TSLs are shown in the first row of

figure5.TheT1ρmapgeneratedfromthefullseriesofsixTSLswasusedasabaselinereference

for comparison. The second row shows the corresponding coefficient of determination (R2)

maps.TheoverallR2>0.9indicatesthatexcellentfittingwasachieved.NotethatR2wasalways

1 for fitting with only two TSLs of 1 and 50 ms. The third row shows the absolute T1ρmap

differences from the baseline reference. The T1ρmaps generated from TSL combination of

[1, 20, 50] and [1, 50] ms show very small discrepancies compared to the reference T1ρmap.

However, no apparent improvement of T1ρestimation is achieved with a TSL combination

of [1, 20, 50] ms compared to [1, 50] ms. In comparison, the T1ρmaps generated from TSL

combinations of [1, 10, 20] and [10, 20, 30, 40] ms were considerably different from the

baseline reference.

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Efficient T1ρmapping with limited TSLs 1637

Figure 5. Rat liver T1ρmapping comparison. The top row shows the T1ρmaps generated from the

different TSL combinations, of which the very left one is a baseline reference for comparison. The

middlerowshowsmapsofthecoefficientofdetermination(R2)forthecorrespondingT1ρmapping.

The bottom row shows the T1ρmap differences compared to the baseline reference.

(a)(b)

Figure 6. Box plots of pixel T1ρvalues in the liver ROI1 (a) and muscle ROI2 (b) as shown in

figure 5. In the liver ROI1, the difference between the medians of the first three boxes is smaller

than 1 ms. The p value of a one-way ANOVA analysis is 0.1364 (>0.05), indicating no significant

difference. In the muscle ROI2, an even smaller difference in the T1ρmaps is found (ANOVA p =

0.8708). Pixels are drawn as outliers (+) in the box plot if they are larger than q3 + 1.5x(q3 – q1)

or smaller than q1 – 1.5x(q3 – q1), where q1 and q3 are the 25th and 75th percentiles, respectively.

To quantitatively analyze the T1ρmap difference for different TSL combinations, two

representative ROIs were drawn (as shown in figure 5) on liver (ROI1) and muscle (ROI2).

T1ρvalues in these two ROIs were compared by the box plots shown in figure 6. In the liver

ROI (figure 6(a)), the difference between the medians of the first three boxes is smaller than

1 ms. Their notches also overlapped with each other, indicating that their true medians did

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1638 J Yuan et al

not differ with 95% confidence. The T1ρdistributions within 25th (the lower edge of the

box) and 75th percentiles (the upper edge of the box) are all smaller than 2 ms. However,

the median and the T1ρdistribution of the fourth and fifth boxes were significantly different

from the reference (the first box on the left). A one-way ANOVA was applied to analyze the

statistical difference between the first three boxes. The p value was 0.1364 (>0.05), showing

no statistically significant difference of T1ρestimation. In the muscle ROI (figure 6(b)), an

even smaller T1ρestimation difference (p = 0.8708) was found. This may attribute to the

smaller respiration motion effect, the absence of major blood vessels and the smaller tissue

heterogeneity in muscles.

For the other four rats, the T1ρmaps obtained by using all TSLs were not significantly

different (averaged p = 0.1684 in livers and p = 0.8508 in muscles) from those obtained by

using the TSLs of 1 and 50 ms.

Discussion

In principle, more TSLs are considered to be more likely to achieve precise T1ρestimation.

However, when TSLs are all much shorter than the true T1ρvalue, large estimation deviation

can be introduced. On the other hand, TSLs that are too long may result in images with low

SNRs. For T1ρestimation with two TSLs, having an approximate value of S0by using a very

short TSL should be important. In both simulation and experiments, it was interesting to find

that the use of the combination of [1, 20, 50] ms did not improve the precision in T1ρmapping

as compared to TSL combination of [1, 50] ms. However, this finding may be only valid for

the situation of high SNRs larger than 100.

The simplified derivation presented in equation (5), although consistent with the full

theoretical frame described in literatures (Weiss et al 1980, Zhang et al 1998), has limited

validity for only two particularly selected TSLs. For a specific application, a pre-knowledge

of true T1ρvalues of interest is quite useful. In this study, the TSL combination of 1 and 50 ms,

although considered optimal for the true T1ρrange of 10 to 100 ms, is particularly suitable for

liver T1ρmapping because the normal and the fibrosed rat livers have T1ρvalues within 40–

65 ms (Wang et al 2011), and normal human livers have T1ρvalues within 40–50 ms (Singh

et al 2011). This TSL combination should also be robust for T1ρmapping in other soft tissues

such as brain and cartilage as their T1ρvalues are usually smaller than 100 ms.

T1ρ deviation using the optimized two TSLs is inversely proportional to the SNR

(equation (5)) in theory. Although this conclusion was derived by assuming S1 ≈ S0, it

was verified by the Monte Carlo simulation, where no such assumption was made, that this

conclusion could still be valid even for a low SNR. This indicates that the noise imposed

on TSL2dominates the T1ρdeviation. It is worth noting that this inverse proportionality

is independent of the noise type. As the SNR is also proportional to the square root of

the NSA, a relevant interesting question would be whether it is useful to measure signal

intensities at two TSLs with higher SNR or at more TSLs with lower SNR during the same

measurement time. According to equation (5), T1ρdeviation should be inversely proportional

tothesquarerootofNSA.Referringtofigure3(a),T1ρdeviationusingTSLsof[1,50]mswith

doubled NSA only at TSL2of 50 ms may be comparable with that using TSLs of [1, 10, 20,

30, 40 50] ms.

To ensure the precision of T1ρmapping with limited TSLs, a high SNR for T1ρ-weighted

images is of critical importance. For this reason, RF coils with high sensitivity and pulse

sequences with high SNR efficiency are preferable. As the SNR is also dependent on many

other factors such as pixel size, NSA, TE and TR, all these factors should be optimized

according to the specific application.

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Efficient T1ρmapping with limited TSLs 1639

The susceptibility of T1ρimaging to B0and B1field inhomogeneity related artifacts

may compromise the robustness and reliability of using a limited number of TSLs for

T1ρmapping. Unlike the case for multiple-TSL acquisition, the presence of artifacts by using

two TSLs would result in considerable T1ρdeviation that cannot be compensated through

least-squares fitting due to the lack of extra data points. Therefore, the minimization of field

inhomogeneity related artifacts is critically important. Good volume shimming should be

helpful to reduce B0inhomogeneity, particularly for SSFP sequence. A rotary echo pulse

(Charagundla et al 2003) was used in this study to minimize the banding artifacts caused

by B1field inhomogeneity. To further reduce the B0inhomoegentiy induced artifacts, a SL

pulse that is insensitive to both B0and B1field inhomogeneity could be applied (Witschey

et al 2007). In a pilot study of human liver T1ρimaging that we are conducting, it is shown

that good breath hold of subjects is also of importance to reduce field inhomogeneity related

artifacts.

By the use of the optimized two TSLs, the scan time was reduced approximately by a

factorof3withoutcompromisingtheT1ρmappingprecision,comparedtoanacquisitionusing

a full series of six TSLs. For T1ρmapping for moving organs such as liver, the reduction of

TSLsmayreduceinter-scanbulkmotiondisplacementbutnotintra-scanmotionartifacts;good

breath hold of subjects should be of essence to reduce respiration artifact for the translation to

human scan. In terms of RF energy deposition, SL RF SAR level is proportional to the square

of the flip angle of SL pulses within the unit pulse duration (Witschey et al 2007, Collins

et al 1998), equivalent to SL frequency. Therefore, the average SAR was not reduced by the

reduction of TSLs. However, the total RF energy deposition by the SL pulses is approximately

reduced by a factor of 3. This method is also compatible with other means such as keyhole

(Wheaton et al 2003), parallel imaging (Pakin et al 2006), and off-resonance SL imaging

(Santyr et al 1994) for further reduction of SAR. Currently, we are testing the human liver

T1ρimaging using the rotary echo SL pulse with the SL frequency of 500 Hz; SAR deposition

is generally under the allowable food and drug administration limits of 0.4 W kg−1averaged

over the whole body, as indicated on the MRI console, confirming its safety for translation to

human T1ρimaging.

In conclusion, optimized T1ρmapping with high precision using two optimized specific

TSLs was proposed for liver T1ρmapping. This technique is able to significantly reduce scan

time and total RF energy deposition for T1ρimaging, in particular at high field strength.

Acknowledgements

This work is supported by Hong Kong ITF grant ITS/021/10 and Research Grants Council

grant CUHK475911 and SEG_CUHK02.

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