1996, The British Journal of Radiology, 69, 206-214 Tl

Measurement of spin-lattice relaxation times withFLASH for dynamic MRI of the breast

'J A BROOKES, BEng, MSc, 'T W REDPATH, PhD,. FlnstP, 2F J GilBERT, FRCP, FRCR,2G NEEDHAM, BSc, FRCR, 2A D MURRAY, MRCP, FRCR

Departments of 'Bio-Medical Physics and Bio-Engineering and 2Radiology, University of Aberdeen,Foresterhill, Aberdeen AB9 2ZD, UK

AbstractUsing a variable flip angle gradient refocused imaging technique, dynamic quantitative Tl relaxation mapsacquired before and after the administration of a gadolinium contrast bolus enable the concentration-timecurve of the paramagnetic agent in breast tissue to be calculated. This imaging technique has the aim ofimproving the diagnostic accuracy of MR mammography. Measurements with phantoms of calibrated 11values have been carried out to investigate the accuracy of the method, with particular reference to errorscaused by incomplete spoiling of residual transverse magnetization and inaccurate radio frequency (RF) flip-angle settings. A clinical example is presented. The method has potential use for any patient study whichnecessitates rapid quantitation of changing in vivo Tl values as a result of contrast agent injection.

argued [10], may improve the specificity of contrastenhanced MRM.

This protocol represents a new method of measuringTI (and hence RI) in the breast. The means by whichpost-contrast changes in TI are monitored has not pre-viously been reported. In this paper, the theory behindthe protocol is outlined and experiments aimed at valid-ating the protocol as a practical clinical proceduredescribed. Sources of error such as reference RF powercalibration and incomplete spoiling of transverse coher-ence are explored. Finally, a clinical example is presented.

Note that whereas;Ti is a well understood quantity inMRI, the concept of RI is less widely used. For clarity,therefore, we refer .to TI in the text where possible.However, as we are ultimately interested in changes ofGd-DTPA concentration in tissue, and since these areproportional to changes in RI' some interchange betweenRl and TI in the texicannot be entirely avoided.

In contrast enhanced magnetic resonance mammogra-phy (MRM), the amount and rate of enhancement of alesion are often used for diagnostic evaluation, withmalignant lesions generally showing greatest and mostrapid enhancement [1-10]. However, benign lesionssuch as fibroadenoma and sclerosing adenosis areoften difficult to distinguish from malignant lesions onthe basis of signal enhancement characteristics alone,since their signal enhancement curves may also demon-strate rapid and/or high uptake of contrast agent[3,5,6-8, 10].

To improve th~ specificity of dynamic contrastenhanced MRM, a protocol derived from the variableflip-angle method [11-13] of measuring spin-latticerelaxation times (T1) has been developed. The protocolis able to produce a Tl map of the entire breast, fromtwo three-dimensional (3D) image data sets obtained atdifferent radiofrequency (RF) flip-angles, prior to injec-tion of the contrast agent gadolinium (Gd-DTPA). It isable to do this in a time much faster than would bepossible with conventional saturation recovery/inversionrecovery (SR/IR) methods of measuring Tl' Post-contrast changes in 11 are monitored by acquiringimages at one RF flip-angle only. Obtaining pre- andpost-contrast values of Tl enables the correspondingchange in relaxation rate, R1, to be calculated, by virtueof the fact that Rl is simply the inverse of Tl. Since thechange in Rl of any particular tissue is directly pro-portional to the amount of contrast agent absorbed bythat tissue [10,14], the protocol enables a Gd-DTPAconcentration-time curve to be drawn which, it has been

TheoryThe contrast agent Gd-DTPA shortens the Tl of tissue

into which it is absorbed, leading to a greater signalintensity in fast low angle shot (FLASH) images. Signalenhancement curves have been used to aid differentiationof tissues [1-10]. However, because a particularquan-tity of contrast agent causes a variable degree of signalenhancement depending on the initial Tl of the tissueinto which it is absorbed [10,14], a bias is introduced.The computer simulation in Figure 1 demonstrates howa given quantity of contrast agent absorbed by a tissueof high initial Tl will lead to a greater change in signal(ASa) than if the same quantity had been absorbed by atissue of lower initial Tl (ASb). Figures indicate valuesfor Tl at 1.0 T of the order of 1000 ms for fibroadenomaand anywhere in the range 700-1000 ms for various types

FLVOJ

whthetimrei;mogerReceived 10 August 1995 and in revised form 3 November

1995, accepted 10 November 1995.

The British Journal of Radiology, March 1996206

Tl measurement in breast MRI

S

ARi:x:.1[Gd-DTPA]

Figure 1. Simulation of signal intensitycurve for FLASH (Sjkp plotted usingEquation (1) for TR = 8.4 ms and 11 = 30°)demonstrating non-linearity of signalresponse to a given uptake of paramag-netic contrast-agent. L1[Gd-DTPA] rep-resents the change in tissue concentrationof Gd-DTPA.

laps:ime(lof

1 Tlrorsflip-l1ich

tItR I0.8 .0

ontrast

then the signal intensity ratio, P.. of the two images ateach corresponding voxellocation is given by

sin 1X1 (.1-,exp[- TRR1J coscx;)P=SI/S2= :

Sin lXi(l-exp[ -'-TRR,J coscx,)

so that, re-arrangingforRl gives

R = ~ In{~ sincx2 C~~l ~~~n IX, ~~s ~~}1 TR PSlnlXi-SInIXI

Re-arranging Equation (1) to make the product kp thesubject of the equation, we obtain

~lor2( 1 -exp_l~IRR1J cos CXlo~2)

lsuringwhich

ot pre-behindt valid-Icedure

powercoher-sented.tltity in

clarity,ossible.tlges ofese areetween

(2)

kp=(l-exp[ -TRR)J} sin CX1or2

Having estimated a'yglile for Rjfrorn two image signalintensities (Equation (2)), this value can be substitutedinto Equation (3) to obtain an estimate for the productkp. If it can then be assumed that absorption ofGd-DTPA into a tissue does not affect its proton densityor T.z, and taking care to keep the imaging system gaincharacteristics constant, post-contrast injection changesin R) can be monitored simply by acquiring images at athird RF flip-angle, CX3, and using the consequent valuefor 53, along with the estimate for kp, in Equation (1),giving (after re-arranging)

1 (kp sin CX3 -83 COS CX3)R.~__==-ln~-_- -~ (4)

(3)

,f tissue

signalSignal

ltiation

.quan-r signal:

tissue>duced.es how1 tissueL signal

~d by avalues

lenomaIS types

of malignant tissue [15, 16]. Hence the possibility existsthat a fibroadenoma may demonstrate greater signalenhancement than malignant tissue, despite absorptionof the same concentration of contrast agent.

By monitoring changes in tissue Rl' rather than signal,a physiological parameter which is independent ofimag-ing pulse sequence is observed: This removes the biasinherent in signal intensity observations and provides ameans of standardizing measurements from differentimagers. It is then possible to produce Gd-DTPA uptakecurves, the concentration of Gd-DTPA absorbed by atissue being proportional to the change in Rl of thattissue, with the aim of improving the specificity ofdynamic MR mammography. Weisskoff et al [10] havereported using inversion recovery echo planar imaging(EPI) to quantitate changing Rls for this purpose. Rlhas been monitored dynamically by a different method,using a 3D FLASH pulse sequence. Previous work[11-13] has shown how to calculate Tl (and hence Rl)values from two image data sets taken at different flip-angles. The mathematical analysis below outlines themethod by which post-Gd-DTPA changes in Tl and Rlcan be quantitated.

Rl measurementThe equation predicting signal intensity S for the

FLASH imaging sequence, assuming a homogeneousvoxel and TE« T2*, is [14]

kp( 1- exp[ -TRR1]) sin cxS = (1)

(1- exp[ -TRR1] cos cx)

where k is the system gain; p is the proton density; cx isthe RF excitation flip-angle; T R is the RF pulse repetitiontime; TE is the echo delay time; Rl is the spin-latticerelaxation rate and T2* is the spin~spin relaxation timemodified to include the effects of magnetic field inhomo-geneity and variations in tissue magnetic susceptibility.

If two images are obtained with flip-angles !Xl and !X2'

'."'- TR t kp sin IX)-S) J "

RF flip-angle optimizationDue to thermal noise in the imaging system, random

errors are introduced into S1 and S2' As a result, theimage intensities at any given voxel will be S1 :t AS1,S2 :t AS2. Consequently, the Rl of a voxel calculated bythis method will be in error. Optimization on the combi-nation of flip-angles (lXI' 1X2' IX) that gives least errorin Rl and Rl.new is necessary. From Equation (1),

Vol. 69, No. 819 207'ch 1996

J A Brookes, T W Redpath, F J Gilbert et al T1

R1=!.(TR,cxI,CX2,{J).Acx2 = 0, then

Assuming that: LlTR = LlIX( =

oR!dR! = -LIpo{3

Now, P=!2«(XI,CX2)=St/S2, so that

I{OP.~)2 rop __)20P}2 { oP 12Ap = ~ 1-;;S-; ASI\ + 1 ~ AS2~'

If we assume ASt = AS2 = AS then

AP=PAS fflV{~ }2+ {~}2

~1~1. S;

(6)

I

gIVing

oR! If 1.).2f 1./2

{ 1 } 2 { 1 } 2

=P~V1~t +1~rARIAS (5)

where

oR, , 1,-.

op

Fig(a)val

AR

A~

m,RIestin,In,EqmelIS

re,

(assuming ASt = AS2 = I1S3 = AS). By calculatingARl.new/AS over a range of a3' the minimum value ofARt.new/AS suggests the optimum value for a3'Computation of ARt.new/AS obtained the same valuesregardless of whether (al, St) or (a2' S2) were used inEquation (6), suggesting a30pt=47° for a Tt of 150msand a30pt = 20° for a Tl of 1100 ms, as shown in Figure 4.Note that these T;limits are still expected to cover thewhole range of Tl s that might be found in the breast,even after the injection of Gd-DTPA. (Figure 8(b), show-ing post-Gd-DTPA changes in Tl' retrospectively provesthis assumption to be valid.) Taking the average of thesetwo values for a30pt suggests the optimum set of RF flip-angles (al, a2,1X3)opt to be (5.5°, 30.5°, 33.5°).

Sources of errorThe protocol uses gradient refocused echoes to pro-

duce images, as a result the signal observed during theseechoes will be reduced by a factor of exp(- TE/~*). Inthis protocol TE is set to as small a value as possible inorder to reduce this potential source of error. This willalso reduce errors due to possible changes in tissue ~arising from the absorption of Gd-DTPA.

Several potential problems with regards to RF flip-angles may contribute to the errors observed in T; (andhence Rt) estimations. These include deviation in theoverall flip-angle, spatial variations in flip-angle acrossthe plane of the slice as a result of inhomogeneities inthe RF field power delivered across the field of the slice(Bt inhomogeneities) and spatial variations in flip-angleacross the thickness of the slice [12]. Flip-angles are setby linear variation of the amplitude of the RF excitationpulse. This requires an initial calibration to determinethe transmitter amplitude necessary in order to achievea reference flip-angle, which is typically chosen as 900 or1800 (the transmitter amplitude used to provide a 90°excitation pulse would then be halved to obtain a 450excitation pulse, for example). Deviation in the overallflip-angle might be caused either by non-linearity in theRF amplifier or by an error in the calibration ofthe amplitude of the RF excitation pulse required toachieve the reference flip-angle.

It is assumed in the above theory that no residualtransverse magnetization remains at the time of the nextsampling pulse. This condition is satisfied whenTR» T2*, which is clearly not the case for the TR of8.4 msused in this protocol. The coherence of transverse~

-sinjX;sina:2(cosa:2-cos!Xi)~

TR{fJsin ~i- sin IXl)(psin (X2 COS (Xl -sin (Xl cos a2)

The partial derivative aRl/opis obtained by differen-tiation of Equation (2). By ass4ming values for Tl andTR, Equation (5) can be computed for a complete rangeof RF flip-angles ill and iX2' Iti~ then merely atpatterof selecting the combination of !Xl and a2 that gives thesmallest yalue for ARl/AS..In o~der that th~ temporal r~solution of the protoc~lIS as hIgh as posslb~e; a TR of 8.4 ms was chosen, thIsbeing the minimu~possiple TR on ou: imaging sy~teriifor a ~D FLASH pulse sequence. With regard to thechoice of values for Tl over which to perform the com-puter simulation, the following data were taken intoaccount. These data being the Tl s of breast tissues at1.0 T [15]: fat, 175 ms; fibrocystic tissue, 765 ms; paren;.chyma,800 ms; malignant tissue, 900 ms; fibroadenoma,1000 ms. In light of these figures, it was decided tooptimize Rl measurement accuracy over a Tl range ofl50-ll00ms. Figure2 shows the contour maps pro"duced by calculating ARl/AS for different combinationsof !Xl and a2 at the outer 1imits of this range. At a Tl of150ms, flip-angles (al,aJopt=(8°,44°) are suggestedwhilst at aTl of 1100 ms, flip-angles (aI, iX2)opt = (3°,17°)appear to be the optimum choice. Taking the average ofthese two sets of flip-angles, the final choice of(!Xl' aJopt = (5.5°,30.5°) is arrived at. Figure 3 plotsARl/AS for each of these three sets of flip-angles overthe whole range of 150 < Tl < 1100 ms, from which itwill be seen that the final choice of flip-angles does indeedgive least error in Rl over the range of tissue Tl s thatare expected to be present in the breast.

As a result of random errors in Sl, S2 and S3 beingpropagated into Equations (3) and (4), optimization on

The British Journal of Radiology, March 1996

Va.i

?t oJ 7

tofor

(4»)(2)

an).leseS

2

T1 measurement in breast MRI

8080

6060

(X,CX24040

(6)

ling~ of

CX3.luesI in'ms.e4.the:ast,ow-Iveslese:Iip-

20 20

0 0

a 20 40 60 80 80600 20 40(1,0..

(a) (b)

Figure 2. RF flip-angle optimization Jor the pre-contrast T) d'4ta; computer generated contour plot$ of AR)/AS for:(a) T) = 150ms and (b) Tt= ll00ms. Contour.lines represent percentage increases (as indicated) of ARI/ASabove its minimumvalue.

>ro-lese

.Ine in

will

: T 2

!lip-andtherosss in;lice

19le, setlionlIne[eve0 or

900

450

:rallthe

ofI to

Figure 3. Computer generated plot ofAR./AS against T, for three possible com-binations of RF flip-angle. The third com-bination (5.5°, 30.5") was suggested bytaking the mean of the two combinationssuggested by Figures 2a and b.T,(ms)

magnetization is removed by RF spoiling [17]. If thisRF spoiling was incomplete, one would expect to see Tlestimations become increasingly inaccurate with eitherincreasing Tz or decreasing TR as a consequence ofincreased signal intensity above that predicted byEquation (1). Elimination of residual transverse mag-netization by increasing T R to satisfy the above conditionis not desirable because temporal resolution would bereduced, compromising the efficiency of the protocol as

a tool for monitoring dynamic changes in "T1 over alarge volume.

The protocol presented here excites a 3D slab anduses two phase-encoding gradients in addition to thereadout gradient, in order to produce an image. Thuserrors due to intravoxel slice profile effects can be ruledout. To investigate flip-angle errors, the commercial cali-bration of the reference (1800 flip-angle) RF transmitteramplitude was checked against an independent flip-angle

iua!lexthen.ms

erse

2091996 Vol. 69. No. 819

500.0

~ T, = 150 ms

-_T,=IIOOms4000

~ 300.0t.S

~200.0

"-~=::::::::::::::

100.0

0.020 40 60 80 100

J A Brookes. T W Redpath. F J Gilbert et at

most from the signal intensities predicted byEquation (1), giving poorer estimates for the Tl of thesample. The solutions were calibrated at 25 °C on aBruker CXP100 spectrometer (Bruker AnalytischeMesstechnik GMBH, Rheinstetten, Germany) operatingat 40.5 MHz. The solutions were im~ged at 23 °C witha 3D FLASH sequence of 32 slices (4 mm slice thickness)and a sampling matrix of 214 x 256 (350 x 350 mm2Fay), TR = 8.4 ms, TE = 3 ms. Each image data set took60 s to acquire. Nominal RF flip-angles of 6° and 300were used, these having been chosen following compu-tational simulation (described earlier) of the noise errorassociated with a whole range of possible combinationsof flip-angles.

Clinical data were obtained from a patient who wasimaged as part of a separate clinical trial to evaluatedynamic Gd-DTPA enhanced MRI of both breasts.Patients with clinical or mammographic suspicion oftumour recurrence following wide local excision andradiotherapy for breast cancer were included in the clini-cal trial. Ethical committee approval was obtained, andinformed consent obtained. Imaging was carried out withthe patient positioned prone in the imager. Prior topatient positioning a 21 G intravenous canula with longline flushed with saline was inserted into an antecubitalvein. Images were acquired before injection of contrastagent using nominal RF flip-angles of 60 and 30°. Afterinjection of a rapid bolus of Gd-DTPA (0.1 mmol kg-1patient-mass; "Magnevist", Schering AG, Berlin,Germany), images were acquired with a nominal RF flip-angle of 30°, at 1 min intervals. No check was made onthe Siemens RF flip-angle calibration, as was the caseprior to imaging the copper, chromium and manganesesulphate solutions. The pulse sequence Fay, timing andsampling parameters used were the same as reported inthe previous paragraph.

a3

Figure 4. Computer generated plot ofARI,.ew/AS against 1X3for both TI =150 ms and 11 = ll00ms.

calibration scheme. The possibility of transverse coher-ence effects was investigated by imaging sets of solutionswith different Tz/Ti ratios.

MethodsAll imaging was carried out on a Siemens Magnetom

Impact 0.95 T (40.5 MHz) system (Siemens AG,Erlangen, Germany), transmitting on the body coil andreceiving on a dedicated double breast surface coil.

A sequence based on the method of Perman et al [.18]was implemented to check the Siemens RF flip-anglecalibration. This consisted of a train of three single side-lobed sinc RFpulses (cx:--a-cx) in the presence of a constantslice selection gradient of 1.8mTm-1. Each RF pulsehad a duration of 5120~ and was apodised using aHanning window. Interpulse timings were '1 = 20 msand '2 = 60 ms. Such a sequence produces three freeinduction decay (Fill) signals, one primary spin-echo,one stimulated spin-echo and three secondary spin-echoes, the second of which occurs at time '2 afterthe final RF pulse with amplitude proportional toIcos(cx) sin(cx) sin2(1X/2)i, and exhibiting a sharp minimumwhen cx = 90°. This spin-echo was used to create a 10 mmslice profile (field of view (FOY) 400 mm, 128 x 128acquisition matrix; the selection gradient also providedfrequency encoding) through the centre of two 500 mlpolythene bottles filled with paramagnetically dopedwater and placed in each half of the breast coil. Regionof interest (ROI) analysis obtained an average signalover each half of the breast coil. This value was thenobtained across a wide range of flip-angles in order tolocate the relative position of the minimum signal.

The accuracy of the technique was investigated usingthree sets of solutions, each set containing eight sampleswith T1 in the range 150 to 1100 ms. The compoundsused to make the solutions: CuSO4, Cr2(SO4)3 andMnSO4, were intended to give high (-1.0), intermediate(-0.6) and low (-0.2) values of T2/T1, respectively. Ifany transverse coherence remained in spite of RFspoiling, the solutions with highest T2 would deviate

ResultsA clear minimum at 1040 in Figure 5 suggests that the

actual RF flip-angle being delivered is 13.5% less than

200.0.U-IS breast coil

.RHS breast coil

150.0

Signal strength

100.0

~ ..~~. ..0"I"

"~o"~ 0-"-f

50.0

0.00.0 200 40.0 ro.O 80.0 100.0 120.0 1400

Requested (nominol) RF flip-angie

Figure 5. Breast coil reference RF transmitter amplitudecalibration.

Figul(a) (c(%1.=

Vol.!The British Journal of Radiology. March 1996210

11 measurement in breast MRI°t et !II

I by)f theon atische'ating

withcness)mm2took

d 300

mpu-errorltions

that requested. Figure 6 predicts the inaccuracy in T1 asa result of a given systematic~rror in the calibration ofthe reference RF transmitter amplitude.

The solutions were imaged with nominal RF flip-anglecombinations of 6°, 300 and 7°, 35°. The latter pair ofexcitations are equivalent to actual 60 and 30° exci-tations, once the error in the calibration of the referenceRF transmitter amplitude suggested by Figure 5 hasbeen taken into account. The results are plotted inFigures 7a and b.

Figures 8b and c show T1 and R1 data calculated fromsignal intensities (Figure 8a) obtained by ROI softwareover three areas of interest within the breast of a 52-year-old patient with tumour recurrence in her left breast atthe scar site of previous surgery. This was subsequentlydiagnosed as invasive ductal carcinoma.

) wasLiuateeasts.In ofand

clini-, andwith

)r to

longlbitalltrastAfterkg-1erlin,.flip-Ie oncase

mese: and~d in

~

To (ms)

Figure 6. Computer generated plot of signal intensity ratio Ii'against T1, in order to estimate systematic error in 11 due tomis-setting of the reference RF transmitter amplitude..1 the

than

DiscussionThe calibration method used to check that the correct

RF transmitter amplitude was being delivered suggestednominal RF flip-angles of 7° and 35° were necessary inorder to deliver actual excitations of 6° and 30°. InFigure 7b, the data lie much closer to the line of identity,at least up to 900 ms, than in Figure 7. This retrospec-tively verifies the accuracy of Perman et aI's calibrationmethod over that which is automatically performed bySiemens software. The Siemens method of calibratingthe reference RFtransmitter amplitude involves applyingthree RF pulses (cx/2-cx-a/2), measuring the ratio of theamplitudes of the spin-echo occurring after the secondRF pulse, and the stimulated-echo occurring after thethird RF pulse. This ratio is proportional to I cos(cx/2) Iand tends to a sharp minimum when cx = 180°, Plottingthe functions Icos(cx/2)1 and Icos(cx) sin(cx) sin2(cx/2)1 out,only a marginal difference in change of gradient at theminima (located at cx = 180° and cx = 90°, respectively) isseen. This suggests that both methods should be equallyaccurate. However, the Siemens method requires thecollection of two signals rather than one (as is the casefor the method of Perman et al). Thus the subsequentcalculation of a ratio may render the Siemens methodmore susceptible to error.. Further work will be necessaryto evaluate the relative accuracy of the two techniques.

Figure 6 suggests that a ~ of 750 ms will be estimatedas approximately 6O5ms for a -10% error and 540 msfor a -15% error in calibration of the RF transmitteramplitude. The data in Figure 7a, certainly for the copperand manganese solutions, show that a Tl of 750 ms wouldbe estimated as approximately 550 ms. This implies anerror in RF flip-angle calibration in the range of -15%to -10%, concurring with the prediction obtained fromFigures 5 and 6. From this, it can be concluded that theerrors in the T1 estimations (for ~ s less than 900 ms)are understood and correctable.

The ~ estimated for the copper sulphate (high ~/~

.copperg chrom",m'"""'OQneSe

2!XD.O

1750.0

1500.0

12500 t

Estimated T, 11m.0 l

I750.0 r

500.0 I

200.0 t

L00OJ)

,~

O,

2&1.0

'-'-400 (a) (b)

Figure 7. Imager estimated TI values plotted against spectrometer calibrated TI values for nominal imager RF flip-angles of:(a) (aI, aJ = (6°,30°) and (b) (aI, aJ = (r, 35°). In both cases, estimated TIs are calculaed from Equation (2) using values ofal = 6°, a2 = 30°.

itude

Vol. 69. No. 8191996 211

J

A Brookes. T W Redpath.. F J Gilbert et al Tl2000 30000

°1n<I"e25000 r,

2CXXJ,O r'

-Leskjn

.Fat.--Blood

pool

150.0

vacu

pemm

lesion

Fat

Blood pool

Signal 100.0 T, (ms) 1500.0 t

:;<

;..-

~r1

1 OCKJ,O ~

5(X),O l

,~500..-

~

cceiJ

0.00:0~ ~ '

0 2.0

lime (minutes)

(a)

", 3.Q0.0 '-

0.0desaItbeHsch~lu10TI01toartuib,bI

aofus

6.0 Lesion

Fat

Blood pool5.0

4.0

Figure 8. (a) Signal intensity, (b) Tl and (c) Rl are plottedagainst time (post-injection of Gd-DTPA) for ROIs drawn overa patient's heart, around the site of a suspicious lesion, andover adjacent fatty tissue.

~

R,. (s') ~.O/

20

r'1.0 f'r"V

O.OO~ 10 2.0lime (minutes)

3.0

Co

actiJSJbeh~

astofdjtrdjreVo

ccsep<erp<ca

arto

ratio) solutions proved to be no more inaccurate thanthose for the manganese sulphate (low ~/TI ratio)solutions (see Figure 7). There is, in general, somereduction in accuracy at T1 above 900 ms. Long ~ aredifficult to measure accurately, due to the fact that athigh TI, large changes in ~ result in only small changesin signal intensity. Had the TI of the copper sulphatesolutions proved to be more difficult to estimate cor-rectly, this would have pointed strongly to the possibilitythat the Siemens FLASH sequence was not completelyspoiling residual transverse magnetisation that remainedat the end of a T R interval. Transverse coherence effectscan thus be ruled out as a possible source of error in the~ estimations.

Clinical data were acquired using nominal RF flip-angle settings (aI, a2, a3) = (6°,30°,30°). The final flip-angle is different to that suggested by the optimizationprocedure described earlier by 3.5°. The angle a3 was setto the same value as a2 in order that the conventionalmethod used by the examining clinicians, which involvessubtracting pre- and post-contrast images so that non-enhancing tissue disappears in the subtracted image dataset, was not changed. As Figure 4 shoWs, the rate of

change of ARt.new/AS with respect to IX) is relatively lowfor 25° < IX) < 35°. This discrepancy is not expected tocompromise the accuracy of the estimations of postGd-DTPA ~ (and hence Rl) values.

Figure 8b plots the Tl of several tissue types as afunction of time post-Gd-DTPA injection. ROls weredrawn on the patient images around a suspected lesionlocated originally from pre- and post-contrast subtrac-tion images, over an area of adjacent fatty tissue andover the heart. Signal intensities from these ROIs werethen used to calculate the Tl plotted in Figure 8b,using Equations (2)~(4) and values of (lXi- IXl- IX)) =(6°,30°,30°). The graph shows the ~ of fat remainingconstant at approximately 260 ms, while the lesion Tldecreases from a pre-contrast value of 1100 ms to 300 ms3 min after injection of Gd-DTPA. The value for fat fallswithin the range 240 ms ::t 28% predicted by Bottomleyet al [16] (at 40.5 MHz), whilst the initial value for thelesion is only 5% outside the range predicted (again byBottomley et al [16]) for "miscellaneous" tumours;816 ms::t 28%.

Figure 8b shows that post-Gd-DTPA Tl do not fallbelow 150 ms, the lower limit of the ~ range over which

\

1212 The British Journal of Radiology, Marcp 1996

'ert e! al

AcknowledgmentsThis work was supported by a granLfromTenovus

(Scotland). Mr Jason Brookes is a research studentfunded by the Engineering and Physical SciencesResearch Council (UK).

ion

od pool

Tl measurement in breast MRI

optimization on the RF flip-angles was carried out. It isnot expected, then, that this optimization would berendered invalid as a result of Gd-DTPA shortened ~.

Finally, in Figures 8a and c, signal intensity and Rlvalues generated from the same ROIs that produced thecurves in Figure 8b are shown, demonstrating the typicalpeak enhancement of signal for the heart within the firstminute, the lesion enhancement curve, and non-enhance-ment of the fatty tissue.

The temporal resolution of the protocol was 60 s. Thiscould have been made faster (say 15 s) by reducing toeight the number of slices interrogated (rather than 32),or by reducing the in-phase resolution. Greater temporalresolution is attractive because it would allow moredetailed characterization (i.e. a greater number of datasamples) of the first 3-5 min post-Gd-DTPA injection.It is this period that i~ most important in differentiatingbetween benign and malignant disease [2,4,8,9].However, a trade off has to be made between speed ofscan and area covered by the scan, as Kerslake et al [9]have pointed out. Their protocol has a temporal reso-lution of 12 s, but they are only able to image four slicelocations, thus covering only a small region of the breast.This is not desirable for routine MRM, since a clinicallyor mammographically observed lesion may be difficultto locate once the patient is inside the MRI scanner,and because detection of multifocal and/or secondarytumours outside the covered region would not be poss-ible. One possible way around this problem would be tobring the patient back for a second imaging session, witha higher temporal resolution limited to a specific regionof the breast, after the whole breast had been imagedusing the protocol described earlier.

--'3.0

plottedlwn overion, and

rely low:cted toof post

ConclusionsIt has been shown that it is possible to estimate ~

accurately up to 900 ms, over a large 3D volume, in atime much less than would be possible with conventionalSRjIR methods. Several possible sources of error havebeen either quantitated or ruled out, and the methodhas been shown to produce clinically realistic data. It isa method that is potentially applicable to any dynamicstudy of a 3D volume where quantitation of the uptakeof paramagnetic contrast agent might prove to be ofdiagnostic value. Future work will require a broad spec-trum of clinical cases to be examined, to evaluate thediagnostic value and specificity of the technique. Imageregistration would improve the accuracy with which ~values are estimated and would also allow more accuratecomparisons of data obtained from subsequent imagingsessions of a particular patient (e.g. with a higher tem-poral resolution over a smaller volume, once areas ofenhancement had been identified). Finally, it may bepossible to incorporate a physiological model into thecalculations that would enable other physiological par-ameters such as capillary permeability and leakage spaceto be measured [19].

es as aIs were:llesion;ubtrac-;ue and'Is were~ure8b,2' IX3) =

naining:sion 11300 msfat fallsttomleyfor the

gain bylmours;

References1. KAISER, W A and ZEITLER, E, MR imaging of the breast:

fast imaging sequences with and without Gd-DTPA (pre-liminary observations), Radiology, 170, 681-686 (1989).

2. STACK,JP,REDMOND,OM,CODD,MBETAL,Breastdisease: tissue characterisation with Gd-DTPA enhance-ment profiles, Radiology, 174, 491-494(1990).

3. HARMS, S E, FLAMIG, D P, HESLEY, K LandEVANS, W P, Magnetic resonance imaging of the breast,Magn. Reson. Q., 8,139-155 (1992).

4. DAO, T H, RAHMOUNL A, CAMPANA, FETAL,Tumour recurrence versus fibrosis in the irradiated breast:differentiation with dynamic gadolinium enhanced MRimaging, Radiology, 187. 751-755 (1993).

5. HARMS, S E, FLAMIG, D P, HESLEY, K LET AL, Fat-suppressed three-dimensional MR ~aging of the breast,Radiographics, 1,3,247-267 (1993).

6. HARMS, S E, FLAMIG, D P, HESLEY, K LET AL, MRimaging of the breast with rotatingd~livery of excitation offresonance: clinical experience with pathologic correlation,Radiology, 187,493-501 (1993).

7. HARMS, S E and FLAMIG, D P, MR imaging of thebreast, J. Magn. Reso/l. Imaging, 3, 277-283 t 1993).

8. FLICKINGER, F W, ALLISON, J D, SHERRY, R M andWRIGHT, JC, Differentiation of benign from malignantbreast masses by time-intensity evaluation of contrastenhanced MRI, Magn. Reson. Imaging, 11, 617-620 t 1993).

9. KERSLAKE, R W, FOX, J N, CARLETON, P J ET AL,Dynamic contrast-enhanced and fat suppressed magneticresonance imaging in suspected recurrent carcinoma of thebreast: preliminary experience, Br. J. Radiol., 67, 1158-1168(1994).

10. WEISKOFF;R M, HULKA; C A;' SMITH, B ET AL,Dynamic NMR imaging of the breast using echo planarimaging. In Proceedings of the Society of MagneticResonance in Medicine, Vol. 1 (New York) (Society ofMagnetic Resonance, Berkeley), p. 119 (1993).

11. HOMER, J and BEEVERS, M S, Driven-equilibriumsingle-pulse observation ofT, relaxation. A re-evaluation ofa rapid "new" method for determining NMR spin-latticerelaxation times, J. Magn. Reson., 63, 287-297 (1985).

12. FRAM, E K, HERFKENS, R J, JOHNSON, G A ET AL,Rapid calculation of T, using variable flip angle gradientrefocused imaging, Magn. Reson. Imaging, 5, 201-208(1987).

13. WANG, H Z, RIEDERER, S J and LEE, J N, Optimisingthe precision in ~ relaxation estimation using limited flip-angles, Magn. Reson. Med., 5,399-416 (1987).

14. HITTMAIR, K, GOMISCEK, G, LANGENBERGER, KET AL, Method for the quantitative assessment of contrastagent uptake in dynamic contrast-enhanced MRI, Magn.Reson. Med., 31, 567-571 (1994).

15. MURPHY, W A and GOHAGAN, J K, Chapter 35,Breasts. In Magnetic Resonance Imaging, ed. by D D Starkand W G Bradley Jnr (Mosby, St Louis), pp.861-886(1988).

not fallr which

rch 1996 213Vol. 69, No. 819

J A Brookes, T W Redpath, F J Gilbert et al

18. PERMAN, W H, BERNSTEIN, M A and SANDSTROM,1 C, A method for correctly setting the RF flip angle, Magn.Reson. Med., 9,16-24 (1989).

19. TOFTS, P S, BERKOWITZ, B and SCHNALL, M D,Quantitative analysis of Gd-DTPA enhancement in breasttumours using a permeability model, Magn. Reson. Med., 33,564-568(1995).

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16. BOTTOMLEY, P A, HARDY, C J, ARGERSINGER, R Eand ALLEN-MOORE, G A, A review of IH nuclearmagnetic resonance relaxation in pathology: are T. and T2diagnostic? Med. Phys., 14, 1~37 (1987).

17. ZUR, Y and BENDEL, P, Elimination of the steadystate transverse magnetisation in short TR imaging. InProceedings of the SocietJ' of Magnetic Resonance inMedicine, Vol. I (New York) (Society of Magnetic Resonance,

Berkeley), p. 440(1987).

'K4H

AppendixQuantitation of post-contra.~t rela.xation rate, R,.new

The full expression for R,.new in terms of 8,,82 and 83 is

'MFAUE

Slor2 sin(a3)

r{

{

f

{

rt(

R..new ~lnTR

Dupt!quatiSSlMRmentechmo~are!boll

is dfconIto 1

althstrel

This expression was differentiated with respect to 51, 52 and 53 using the PC software package "Mathcad" (MathsoftInc., 1986-1992) to obtain analytical expressions for iJRI.new/iJ51, iJRI.new/iJ52 and iJRI.new/iJ53, which were sub-sequently used to calculate ARI.new/A5.

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214 The British Journal of Radiology, March 1996 Vol.