Signal-to-Noise Optimization for Sodium MRI of theHuman Knee at 4.7 Tesla Using Steady State

Alexander Watts, Robert W. Stobbe, and Christian Beaulieu*

Sodium magnetic resonance imaging of knee cartilage is a

possible diagnostic method for osteoarthritis, but low signal-

to-noise ratio yields low spatial resolution images and long

scan times. For a given scan time, a steady-state approach

with reduced repetition time and increased averaging may

improve signal-to-noise ratio and hence attainable resolution.

However, repetition time reduction results in increased power

deposition, which must be offset with increased radiofrequency

pulse length and/or reduced flip angle to maintain an accepta-

ble specific absorption rate. Simulations varying flip angle, rep-

etition time, and radiofrequency pulse length were performed

for constant power deposition corresponding to ~6 W/kg over

the human knee at 4.7T. For 10% agar, simulation closely

matched experiment. For healthy human knee cartilage, a 37%

increase in signal-to-noise ratio was predicted for steady-state

over ‘‘fully relaxed’’ parameters while a 29% 6 4% increase was

determined experimentally (n 5 10). Partial volume of cartilage

with synovial fluid, inaccurate relaxation parameters used in

simulation, and/or quadrupolar splitting may be responsible for

this disagreement. Excellent quality sodium images of the

human knee were produced in 9 mins at 4.7T using the signal-

to-noise ratio enhancing steady-state technique. Magn Reson

Med 66:697–705, 2011. VC 2011 Wiley-Liss, Inc.

Key words: osteoarthritis; sodium; magnetic resonanceimaging; cartilage; human knee

INTRODUCTION

Osteoarthritis is associated with degenerative cartilage injoints that results in pain, swelling, and reduced motionand flexibility. Proper treatment of the affliction is de-pendent upon early diagnosis; however, the relativelysmall morphological changes that occur during early pro-gression of the disease may be difficult to detect usingstandard clinical proton magnetic resonance imaging(MRI) (1–3). A molecular indication of the initial stagesof osteoarthritis is the reduction of proteoglycan mole-cules in the collagen matrix of the cartilage (4,5). Proteo-glycans contain negatively charged glycosaminoglycanside chains which create a negative fixed charge densityin the cartilage matrix (6). Positively charged sodiumions are attracted to the glycosaminoglycan chains, and

as such sodium MRI has been proposed as a method todetect and quantify cartilage degradation (7,8). However,

compared to water (i.e., proton), sodium suffers from

low concentrations in vivo (�300 mM vs. 50 M), and a

four times lower gyromagnetic ratio, resulting in a much

lower signal-to-noise ratio (SNR) that makes the acquisi-

tion of clinically useful images within an acceptable

scan time difficult. Higher static magnetic field strengths

and optimal pulse sequences are therefore key to over-

coming this limitation.

Sodium in knee cartilage (and other tissues) exhibits

extremely rapid biexponential T2 (9,10) relaxation and

thus signal loss can occur if the echo time (TE) is not

kept short (e.g., sub-ms). T1 relaxation for sodium (10) is

also very short which facilitates rapid scanning with

shorter repetition time (TR) than typically used for pro-

ton MRI. Three dimensional gradient echo sequences

have demonstrated the feasibility of sodium MRI of the

human knee in vivo (7,8,11–13); however, these

approaches are suboptimal as they required long TE val-

ues of 2–6.4 ms. Three dimensional projection imaging

permits extremely short TE and has been implemented

for sodium knee imaging either with twisted (TE ¼ 0.4

ms) (14,15) or with straight radial projections (TE ¼ 0.16

ms) (16). A recent paper achieved high resolution axial

images of patellar cartilage using the 3D cones acquisi-

tion trajectory (17). Nonselective hard radiofrequency

(RF) pulses are also essential to achieve short TE in these

3D projection sequences. However, mere reduction of TE

to the lowest possible limit is not enough to optimize

SNR under biological conditions. For a given flip angle,

short pulse length (hence low TE) requires high transmit

power. Since specific absorption rate (SAR) is propor-

tional to B2o, tissue heating constraints can become pro-

hibitive at higher field strengths which are otherwise

beneficial for sodium imaging. As such, an integrated

optimization approach to maximize SNR is desirable.

The optimization of sodium SNR under SAR con-straints has been investigated for the human brain (18).This method is known as projection acquisition in thesteady state (PASS), and involves reducing the TR signif-icantly which is only permissible if the excitation radio-frequency power is reduced by using smaller flip anglesand/or longer pulses. Several previous sodium MRI stud-ies of the human knee in vivo have used long TR valueson the order of 80–100 ms both to minimize any signalsaturation due to T1 and to satisfy SAR constraints(12,15,16). However, in a given scan time, the reducedTR of the PASS method allows the collection of extraprojections which can be averaged to produce an SNRbenefit over the standard higher power short TE/long TRscan, also known as a tissue sodium concentration (TSC)

Department of Biomedical Engineering, University of Alberta, Edmonton,Canada.

Grant sponsors: Natural Sciences and Engineering Research Council(NSERC), Alberta Innovates—Health Solutions.

*Correspondence to: Christian Beaulieu, 1098 Research Transition Facility,University of Alberta, Edmonton, AB, Canada, T6G 2V2.E-mail: christian.beaulieu@ualberta.ca

Received 3 August 2010; revised 17 December 2010; accepted 27December 2010.

DOI 10.1002/mrm.22838Published online 24 March 2011 in Wiley Online Library (wileyonlinelibrary.com).

Magnetic Resonance in Medicine 66:697–705 (2011)

VC 2011 Wiley-Liss, Inc. 697

approach for its ability to quantify sodium content withminimal relaxation weighting. The significant SNR bene-fits are possible even though the pulse length (hence TE)must be increased (with associated greater T2 decay) toconform to SAR regulations. SNR increases of �40% forPASS over TSC in the same scan time have been shownfor human brain tissue at 4.7T (18). Knee cartilage neces-sitates further evaluation since the permitted SAR ishigher and the relaxation parameters differ than that ofhuman brain.

High resolution is necessary for imaging cartilagegiven its very thin structure; however, because of therelatively low signal offered by the sodium nuclei in car-tilage, sodium imaging hovers on the cusp of utility.Improved resolution facilitated by the potential SNRadvantage of PASS may be of considerable value. Thepurpose of this work was threefold: (i) to simulate opti-mal pulse sequence parameters for improved SNR ofPASS over TSC at a constant SAR, (ii) to verify experi-mentally the predicted SNR enhancement first in agargel phantom and second in healthy human kneecartilage, and (iii) to demonstrate the achievable imagequality of PASS for sodium MRI of the human knee invivo at 4.7 Tesla in a clinically feasible scan time. Simu-lations of optimal parameters for PASS sodium MRI ofknee cartilage are also given for the more common fieldstrengths of 3T and 7T.

METHODS

Simulations

Sodium signal was simulated (18) for a range of combi-nations of RF pulse length (to which TE is proportional),flip angle and TR, yielding constant sequence powerdeposition; relative SNR was then calculated from simu-lated signal by considering increased averaging within aconstant scan duration. The relative magnitude of trans-verse magnetization present at TE in a steady-statesequence was simulated by solving the set of differen-tial equations describing the evolution of the sodiumdensity operator under the influence of RF excitationand both T1 and T2 relaxation (19–21) for nine consecu-tive RF pulses and TR periods; the relative magnetiza-tion at TE was obtained following the last RF pulse atwhich point a steady-state had been achieved. Gradientspoiling was included in the simulation by summingfour solutions of steady-state magnetization, eachincluding a different off-resonance value at the locationof the gradient pulse in the sequence, such that trans-verse magnetization was dephased to its first null pointover a given voxel volume. Both T1 and T2 relaxationare addressed in the quantum mechanical simulation byinclusion of the (nuclear quadrupole related) interactionpower spectral density at the frequencies of 0 Hz (J0(0)),vo Hz (J1(v0)), and 2vo Hz (J2(2v0)), on which T1 and T2

relaxation depend.Optimization for maximum SNR under SAR constraint

involved simulation for a variety of TR, RF pulse length(tRF) and flip angle (y) parameter combinations such thata constant average sequence power was maintainedaccording to the following physical relationship asdescribed by Haacke (22).

SAR aB20 � h2

TR � tRFThe simulations of cartilage will differ from human braingiven the unique relaxation characteristics and thegreater SAR permitted for extremities. For pairs of TR,chosen over a range from 20 to 100 ms, and RF pulselength, chosen over a range from 0.1 to 0.45 ms, an asso-ciated flip angle was calculated to maintain a constantpower which corresponded with a SAR of �6 W/kg inthe human knee at 4.7 Tesla. The value of 6 W/kg, whileconservative according to RF maximum depositionguidelines (which allow 12 W/kg for extremities) waschosen because sodium protocols often involve longerduration scans, in addition to the fact that knee size andthus coil loading is highly variable. Inclusion in the sim-ulation of a constant 0.06 ms system delay following RFexcitation, yielded TE values in the range of 0.11–0.285ms. To extract predicted SNR benefit, the simulated rela-tive transverse magnetization obtained for each TR, sRF,and y combination was multiplied by 1=

ffiffiffiffiffiffiffi

TRp

to accountfor the standard deviation of noise reduction related toaveraging within a constant scan duration.

The quantum mechanical quadrupolar spin signalsimulations required the relaxation parameters of thesodium nuclei. While the goal of this article was notquantifying sodium relaxation, estimates were neededfor the simulations of signal evolution for sodium inboth agar and human cartilage in vivo at 4.7T, ratherthan to rely on literature values. The T1 and T2 relaxa-tion parameters for a 10% (500 mM) agar phantom weredetermined by measuring normalized signal intensityduring inversion recovery and variable TE experiments,respectively. Relaxation parameters of sodium in agar(n ¼ 5) were determined to be T1 ¼ 19.2 6 0.2 ms (mono-exponential fit), T2

*slow ¼ 14.4 6 0.9 ms, T2

*fast ¼ 2.2 6 0.1

ms at 4.7T. From this relaxation data, a spectral densitymodel of J0(0) ¼ 408 Hz, J1(v0) ¼ 46 Hz, and J2(2v0) ¼ 23Hz was chosen for simulation. The high agar concentra-tion of 10% was chosen due to its similarity to humancartilage for sodium relaxation characteristics (23).

Using the 3D-TPI acquisition, inversion recoveryexperiments measured T1 using least squares regressionanalysis of image intensity in cartilage in several loca-tions in the knee. Inversion times of TI ¼ 3, 7, 15, 25,40, and 70 ms were acquired, and TR was adjusted toensure a constant delay of 100 ms between the excitationpulse and the following inversion pulse. The projectionset had a nominal resolution of 1.5 � 1.5 � 6 mm3, TE ¼0.261 ms, and total acquisition time for all six inversionrecovery scans was 38 min. A monoexponential fit of theT1 relaxation experiment resulted in a T1 (695% regres-sion confidence interval) of 19.3 6 3.7 ms for sodium inthe knee cartilage of a healthy volunteer, aged 30. A T1

value of 18.4 6 2.8 ms was found in the same experi-ment on a second healthy volunteer, aged 31. Based onthese preliminary results, a T1 relaxation value of 19 mswas chosen for simulation. This value compares reason-ably well to those of excised bovine cartilage encoun-tered in the literature at field strengths of 2–7T, wherethe T1 ranges from 16 to 23 ms (8,10,23–25). Difficultywas encountered in the determination of T2 parameters

698 Watts et al.

in femoral-tibial cartilage using a variable TE experi-ment. Biexponential fitting could not account for thevery rapid initial signal decay (TE < 1 ms). As such, theparameters of T2

*slow ¼ 10 ms and T2

*fast ¼ 1 ms that were

measured using multiple quantum techniques were takenfrom literature (15,26). This resulted in a spectral densitymodel of J0(0) ¼ 922 Hz, J1(v0) ¼ 78 Hz, and J2(2v0) ¼ 22Hz for human cartilage in vivo.

Pulse Sequence Design

Based on the results of the simulations (to be discussedin the first part of the Results), 3D-TPI acquisitionparameters were chosen for both TSC (flip angle ¼ 90�,pulse length ¼ 0.12 ms, TE ¼ 0.12 ms, TR ¼ 90 ms, 1 aver-age) and PASS (flip angle ¼ 74�, pulse length ¼ 0.25 ms,TE ¼ 0.185 ms, TR ¼ 30 ms, three averages). Note that TEis calculated as half of pulse length plus the system acqui-sition delay (equal to 0.06 ms for both protocols).

Both protocols had a nominal voxel volume of 2.56mm3, with dimensions of 0.8 � 0.8 � 4.0 mm (definedby 1/(2*kmax)), and constant acquisition times of 9 minsfor each TSC or PASS data set. The number of projec-tions was 6000, each with a twist (p) of 0.196 and read-out length of 18.6 ms, designed for a Hamming-like sam-pling density shape (27). The pulse sequence involvesthe application of a hard nonselective RF pulse to excitethe volume of interest. After the system acquisition delay(60 ms), the readout gradients are applied for the readoutlength as k-space is sampled along the projection trajec-tory (3D center out twisted projection). Following read-out, the spins are spoiled by the application of spoilinggradients; refocusing pulses equivalent to the negative ofthe integral of the readout gradient curve are appliedsimultaneously.

Phantoms

Two phantoms were constructed for use in validation ofmethodology. An agar phantom with 10% agar by weightwas made by dissolving agar powder in boiling waterand adding NaCl so that overall sodium concentrationwas 500 mM. It was used to verify experimentally thepredicted SNR advantage of PASS over TSC from thesimulations. In addition, a saline phantom was used forthe assessment of resolution achieved by the implementedprojection set. Sequential sets of holes were drilled ina rectangular piece of acrylic (90 mm � 90 mm, 12 mmthickness) such that the hole diameters were equivalent totheir spacing for each set, ranging from 5.0 mm to 1.0 mm.The acrylic was placed inside a plastic bottle so that theacrylic face was perpendicular to the long axis of the bot-tle. The bottle was then filled with saline at 250 mM andbubbles were removed from the hole sets.

Experiments

All sodium MRI experiments were performed on a Var-ian Inova 4.7T whole body scanner (Walnut Creek, CA)with a single tuned 53 MHz 12 rung custom home-builtbirdcage knee coil (diameter 17.8 cm, leg length 10 cm).RF transmitter peak output was 2.5 kW. Maximumreadout gradients applied were 9.9 mT/m, and spoiling

gradients were 30 mT/m. Sodium images using both TSCand PASS parameter sets, keeping spatial resolution thesame, were acquired for the saline resolution phantomand 10% agar phantoms, and the right knee of 10healthy volunteers (age 26 6 4 years). All volunteerssigned informed consent forms as required by the Healthand Research Ethics Board at the University of Alberta.

Data Analysis

Projection set design (including generation of gradientand refocusing files), image reconstruction, and region-of-interest (ROI) analysis was performed using customsoftware utilities (in Matlab). ROI were drawn in threedistinct locations in each sagittal knee image: patellarcartilage, femoral/tibial cartilage junction, and purelyfemoral cartilage. Variation in knee size and cartilagedistribution between subjects made the evaluation of car-tilage sodium signal using exactly corresponding ROIsdifficult. To ensure that values derived from ROI analy-sis were representative of signal strength in the cartilage,ROI were averaged over at least three slices of cartilagetissue for each location. All signal ROI were drawn fol-lowing the visible cartilage contours in the sodiumimages; dual windows in the analysis program allowedequivalent ROI to be drawn (for a given subject) for SNRcomparison between the PASS and TSC images. SNRvalues were calculated by taking the mean value of pix-els in signal ROI and divided by the standard deviationof pixel value in the noise ROI, located in the imagebackground. As background noise in absolute valueimages follows a Rayleigh distribution instead of Gaus-sian, the SNR value was then multiplied by a correctionfactor of 0.665.

RESULTS

Simulations

The simulation results for both 10% agar gel (a–c) andhuman cartilage (d–f) are shown in Fig. 1. Figure 1a,dshow the flip angles associated with each combination ofTR and RF pulse length such that average power deposi-tion remains constant. Figure 1b,e demonstrate thepotential SNR benefit to be gained from averaging atlower TR. Finally, Fig. 1c,f demonstrate the amount oftransverse signal (displayed as a percentage of total lon-gitudinal magnetization in a relaxed state) for each TRand RF pulse length combination. The key point to noteis that at lower TR, despite having less transverse signalper RF pulse, the simulations show a predicted SNRbenefit which is derived from extra averaging of theshorter TR scans.

The simulation results were used to choose the exactparameters for our TSC and PASS scans. The TSC pa-rameter set required an extremely short pulse length tominimize signal loss at the centre of k-space, resulting ina choice of 120 ms. Also for the TSC set, a flip angle of90� was desired, as this maximizes transverse signal.Together, these factors resulted in a TR choice of 90 msfor the TSC protocol to satisfy SAR. To simplify averaging, aTR of 30 ms was chosen for the PASS parameter set – thiswould enable three averages in the same total acquisition

Sodium MRI of the Knee at 4.7T 699

time as the TSC parameter set. At this value, a choice of250 ms for pulse length resulted in a high predicted SNRgain while maintaining pulse length reasonably low. Theflip angle value of 74� was read from the intersection ofthe above TR and pulse length values in the flip anglesimulations (Fig. 1a for agar and 1d for cartilage).

Given the above parameters, comparison of the SNRbenefit for each protocol resulted in the prediction of a38% gain in SNR for the PASS protocol over TSC foragar gel phantoms (Fig. 1b). A similar SNR benefit forPASS over TSC of 37% was predicted for human carti-lage (Fig. 1e).

Phantom Validation

A comparison was made between the SNR gain pre-dicted by the simulations for the 10% agar and thatobserved in the sodium images of the agar phantom.Figure 2 shows the results of the scans, which have been

scaled so that the standard deviation of the noise isequivalent in each. The TSC image (Fig. 2a) has lowersignal intensity in the agar compared to the PASS image(Fig. 2b). Figure 2c displays the experimentally deter-mined SNR increase of 39% 6 2% (n ¼ 3), which agreeswell with the 38% increase predicted above.

Human Volunteers

The human cartilage scans (Fig. 3a,b) compare images ofthe knee using PASS with those using TSC parameters.Cartilage tissue is well delineated in both scans. How-ever, noticeably more noise (as quantified by 6 standarddeviation of relative pixel intensities in an ROI drawnoutside the tissue) is present in the TSC (mean of 613.6, n ¼ 10) than in the PASS (mean of 6 11.1, n ¼ 10)acquisition. The extra noise is visible in both the centralbone as well as outside the tissue. The simulation results(Fig. 1e) indicate that there should be a 37% increase in

FIG. 1. Simulations of sodium

signal at 4.7T in 10% agar phan-tom (a–c) and human cartilage(d–f). a,d: Flip angles for a con-

stant SAR of 6 W/kg over arange of combinations of pulse

length and TR. TSC parameters(pulse length ¼ 0.120 ms, TR ¼90 ms, flip angle ¼ 90�) are

marked with an X while PASS pa-rameters (pulse length ¼ 0.250ms, TR ¼ 30 ms, flip angle ¼74�) are marked with an O. b,e:Predicted SNR benefit of PASS

over TSC when averaging isused to equate scan time. c,f:Transverse magnetization is

expressed as a percentage oftheoretical full signal (TR suffi-

ciently long to produce zerosteady state, TE infinitesimallysmall). Despite reduced trans-

verse magnetization of PASScompared to TSC after a single

RF pulse, PASS parametersshow a significant SNR benefitdue to the three times averaging

permitted by the shorter TR.

700 Watts et al.

SNR when using PASS instead of TSC for the same scantime and SAR. The mean SNR benefit (averaged overall three regions) in the 10 volunteers was 29% 6 4%(Fig. 3c) for PASS over TSC, which is lower than thatpredicted by simulation.

To determine if there were any regional variations, theSNR for both parameter sets was also reevaluated sepa-rately for the three different cartilage areas describedabove and shown in Fig. 3a. A significant and equivalentincrease in SNR was found in all three areas (Fig. 4).The SNR gains correspond to consistent average percent-age increases of 29% in each area.

A combined SNR increase over all three ROIs (normal-ized by ROI area) was calculated per subject for eachprotocol. Individualized analysis (per volunteer) of com-bined SNR values showed some variability in the results;however, there was a significant SNR benefit of 22–36%(mean of 29% 6 4%) in all 10 volunteers (Fig. 5). Theexcellent quality of PASS images is displayed in Fig. 6for three orthogonal acquisitions each acquired in 9 min.The axial orientation (Fig. 6a) shows clear delineation ofthe patellar cartilage; the popliteal artery is also visible inthe bottom center of each image. In the coronal orientation(Fig. 6b), there is a clear separation of the tibial and femo-

ral cartilage in the posterior condyles. The sagittal imagesdemonstrate delineation of femoral and tibial cartilage, aswell as contours of the surrounding tissue and patella.

DISCUSSION

The use of smaller flip angles and longer RF pulse lengths(and longer TE) to offset SAR increases associated with ashorter ‘‘steady-state’’ TR to allow increased averaging pro-duced a sizeable SNR increase in sodium scans for bothagar gel phantoms and human cartilage in vivo. There wasexcellent experimental agreement with the simulation pre-diction for the agar phantom. While a substantial SNR ben-efit was found for human cartilage in vivo, it was �8%absolute below that predicted by the simulations.

There are several possible reasons why the SNRadvantage of steady-state imaging predicted from simula-tion was greater than that measured in human knee carti-lage. This discrepancy could be the result of an under-estimation of T1; a T1 value of �24 ms (as opposed tothe value of 19 ms used in the simulations) would pro-duce predicted SNR benefits which are in agreementwith the observed results. It is also possible that thespectral splitting of sodium in cartilage as the result of

FIG. 2. Agar gel (500 mM Na, 10% agar by weight) phantom sodium images for (a) TSC and (b) PASS acquisitions. Image intensitieshave been scaled so that both possess the same standard deviation of noise. c: The predicted SNR increase of 38% correlates well

with the experimental value of 39% 6 2% (n ¼ 3).

FIG. 3. Sodium MRI of the knee, sagittal orientation, using either (a) TSC parameters (flip angle ¼ 90�, TE/TR ¼ 0.120/90 ms, one aver-age) or (b) PASS parameters (flip angle ¼ 74�, TE/TR ¼ 0.185/30 ms, three averages). Both images were sampled with the identical 3Dtwisted projection acquisition scheme, and scan times are equivalent at 9 mins each. c: The observed SNR increase (averaged over

three regions in the sagittal view of the knee) is significant, but is lower than the value predicted by simulations. In (a), ROI locations forsodium intensity measurements are shown for (i) patellar cartilage, (ii) femoral-tibial cartilage, and (iii) purely femoral cartilage.

Sodium MRI of the Knee at 4.7T 701

long-range order (19,28,29) may influence this optimiza-tion. Macroscopically disordered spectral splitting mayalso explain the initial rapid decay in the cartilage T2

*

measurement experiment and the inability to fit a biex-ponential curve. It is likely that a combination of theseeffects may be responsible for the disagreement betweenthe predicted and observed SNR benefits. Finally, theinfluence of partial volume effects of cartilage withsurrounding tissue (including bone and synovial fluid)in conjunction with the difficulty of measuring signalintensity in a tissue that is as physically small as kneecartilage may be responsible for the intersubject variationin the SNR benefit.

Sodium magnetic resonance image quality is affectedby fast T2

* relaxation, which causes blurring. As a result,effective spatial resolution (quantified by the ability todistinguish between objects) is worse than nominal spa-tial resolution (defined by 1/(2*kmax)). Our images, whilenominally 0.8 � 0.8 mm2 in-plane, can only distinguishbetween holes in the resolution phantom which are1.4 mm apart or greater (Fig. 7). However, despite imageblurring, twisted projection imaging with PASS may pro-vide the best compromise between acceptable SNR, lowTE and adequate coverage of k-space. Our results showhigh quality images for a nominal voxel size of 2.56mm3, which compares favorably relative to 3D gradientecho sequences whose nominal voxel sizes range from5.4 to 14 mm3 and whose TE range from 2 to 2.4 ms(7,8,12). Our results at 4.7T (SNR 8-10, TE ¼ 0.185 ms,scan time 9 mins) also compare well relative to recentsodium human knee images at 7T using radial projectionreconstruction (SNR �30, TE ¼ 0.16 ms, nominal resolu-tion 3.4 mm3, scan time �14 minutes) (16) and cones(SNR �17, TE ¼ 0.6 ms, nominal resolution 2 mm3, scantime �26 minutes) (17).

The PASS technique involves increasing T1 weightingsignificantly (from 1 to 21% based on T1 ¼ 19 ms) andT2* weighting slightly (from 7 to 11% based on T2

*fast ¼ 1

ms and T2*slow ¼ 10 ms). The increase of T1 weighting in

PASS deviates from an absolute TSC approach, whichcould result in reduced quantification ability. However,some sensitivity to T1 may have an advantage. Ifdegraded cartilage shows an increase in T1 compared tohealthy cartilage, as has been shown in bovine cartilage(10,30), then a reduction in TR would result in increasedsteady-state effects. This would in turn result in reducedlocal signal and an increased ability to determine regionsof degradation. This form of contrast may prove useful;several studies have investigated different contrast mech-anisms for sodium MRI of cartilage such as inversion re-covery (24) or triple quantum filtered imaging (15). Therelatively small increase in TE (from 0.120 to 0.185 ms)which results in the small T2

* weighting increase men-tioned above should have only a minor effect on sodiumquantification capability.

The benefits of PASS are available at field strengthsboth stronger and weaker than 4.7T. SAR is much lessrestrictive at 3 Tesla, and for TSC imaging with flipangle ¼ 90� and TR ¼ 90 ms, RF pulse lengths as shortas 0.05 ms could theoretically be implemented for thesame SAR of �6 W/kg as that of this study. Simulationsuggests a PASS sequence with flip angle ¼ 77�, pulselength ¼ 0.11 ms, and TR ¼ 30 ms (the same TR as thatof this study) would yield 40% more SNR than the theo-retical TSC case (Fig. 8b). At higher fields such as 7Tesla, SAR is much more constraining, and for a TSCsequence with flip angle ¼ 90� and TR ¼ 90 ms, RFpulse lengths must be increased to 0.27 ms for the sameSAR. At 7 Tesla simulation suggests a PASS sequencewith flip angle ¼ 63�, RF pulse length ¼ 0.40 ms, andTR ¼ 30 ms would yield 31% more SNR than the TSCcase (Fig. 8e). The SNR benefits stated above assume thesame relaxation parameters for cartilage as used abovefor simulation at 4.7T and the absence of quadrupolarsplitting. Note that while a 30 ms TR was used forexperiment in this study, facilitating comparison at 3�the averaging of the TSC approach for the same scan du-ration, the PASS sequence could be implemented witheven shorter TR values for increased SNR benefit at eachfield strength. Note also that while the relative benefit ofsteady-state sodium imaging of the knee with respect to

FIG. 5. Percentage SNR benefit over all three cartilage regions

ranged from 22 to 36% for PASS over TSC in 10 healthy volun-teers. Mean (6SD) value is 29% 6 4%.

FIG. 4. SNR values (6SD) in the cartilage for both TSC and PASSparameters. The PASS protocol shows an SNR improvement of

29% in all three areas. A two-tailed paired t-test found that theincrease in SNR of PASS over TSC was statistically significantwhen divided by region (P ¼ 0.002). Note that the 6 bars are in-

dicative of intersubject variability and not measurement error.

702 Watts et al.

TSC imaging is diminished with increasing fieldstrength, this does not imply reduced value for imagingat 7T in general, which will benefit from Bo relatedincreases of magnetization.

CONCLUSIONS

Excellent quality sodium images of the cartilage in thehuman knee within a reasonable scan time of 9 mins at4.7T were demonstrated using the Na-PASS technique in

which longer RF pulses and smaller flip angles, togetherwith shorter TR are used to allow increased averagingwithin SAR constraints. While there was a substantialSNR benefit of nearly 30% with the use of PASS insteadof TSC at 4.7T, the experimental measurements inhuman cartilage in vivo fell short of the predictionsmade by simulations. This may have been due to inter-ference from quadrupolar splitting, inaccurate T1 relaxa-tion parameters used in simulation, or partial volumeeffects from the inclusion of synovial fluid in the

FIG. 6. Sodium images of the

knee of a healthy volunteer at4.7T using the Na-PASS pulsesequence (6000 projections, p ¼0.196, readout length 18.6 ms).a: Axial, (b) coronal, and (c) sag-ittal planes were acquired sepa-

rately in 9 mins. Apparentdistance between slices (calcu-

lated by taking the field of view,dividing by inverse filter size, andmultiplying by the number of

reconstructed slices between thedisplayed slices) is 8 mm for (a)

and (c), and 5 mm for (b). Thenominal voxel size is 0.8 � 0.8 �4.0 mm3. SNR in the cartilage is

�12. Left and right sides aremarked by L and R letters for the

axial and coronal orientations.

Sodium MRI of the Knee at 4.7T 703

FIG. 8. Simulations of sodium sig-

nal in human cartilage at 3T and 7Tassuming the same relaxation pa-rameters used for the 4.7T simula-

tions. a,d: Flip angles for a constantSAR of �6 W/kg over a range of

combinations of pulse length andTR. TSC-like parameters for eachfield strength are marked with an X

while PASS-like parameters aremarked with an O. b,e: PredictedSNR benefit of PASS over TSC at3T (40%) and 7T (31%). c,f: Trans-verse magnetization after a single

RF pulse is expressed as a percent-age of theoretical full signal (TR suf-

ficiently long to produce zerosteady state, TE infinitesimallysmall). Recall that three times more

averages can be acquired with theshorter TR of PASS over TSC forparameters shown with O and X.

[Color figure can be viewed in theonline issue, which is available at

wileyonlinelibrary.com.]

FIG. 7. a: The resolution phantom containing saline at 250 mM demonstrates the effective resolution of the projection set using intensityprofiles at (b) 1.2 mm spacing, (c) 1.4 mm spacing, and (d) 1.6 mm spacing along the horizontal plane (top edge of the phantom). e,f,g:Similar resolution is demonstrated in the vertical plane (right edge) for the same spacing sets.

704 Watts et al.

cartilage ROI. The SNR benefit that was demonstratedcan enable improved resolution and/or reduced scantime. Future work will concentrate on the evaluation ofthe PASS versus TSC approaches with respect to detect-ing reduced sodium content in the knee cartilage ofpatients with confirmed osteoarthritis.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the agar phantomrelaxation data from A. Tsang.

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Sodium MRI of the Knee at 4.7T 705