A Technique for Rapid Single-Echo Spin-Echo T 2 Mapping Marshall S. Sussman, 1 Logi Vidarsson, 2 John M. Pauly, 3 and Hai-Ling Margaret Cheng 2,4,5 * A rapid technique for mapping of T 2 relaxation times is pre- sented. The method is based on the conventional single-echo spin echo approach but uses a much shorter pulse repetition time to accelerate data acquisition. The premise of the new method is the use of a constant difference between the echo time and pulse repetition time, which removes the conven- tional and restrictive requirement of pulse repetition time T 1 . Theoretical and simulation investigations were performed to evaluate the criteria for accurate T 2 measurements. Meas- ured T 2 s were shown to be within 1% error as long as the key criterion of pulse repetition time/T 2 3 is met. Strictly, a sec- ond condition of echo time/T 1 1 is also required. However, violations of this condition were found to have minimal impact in most clinical scenarios. Validation was conducted in phan- toms and in vivo T 2 mapping of healthy cartilage and brain. The proposed method offers all the advantages of single- echo spin echo imaging (e.g., immunity to stimulated echo effects, robustness to static field inhomogeneity, flexibility in the number and choice of echo times) in a considerably reduced amount of time and is readily implemented on any clinical scanner. Magn Reson Med 64:536–545, 2010. V C 2010 Wiley-Liss, Inc. Key words: T 2 mapping; rapid imaging; transverse relaxation; single echo spin echo; volumetric imaging; human imaging Since the early days of MRI (1,2) and continuing on to the present, T 2 mapping has held out the promise of providing novel, quantitative information in a variety of pathologic conditions. Some examples include the evaluation of cartilage integrity (3,4), tumor characteri- zation (5,6), prostate imaging (7), dynamic contrast studies of cerebral perfusion (8), measurement of iron burden (9), and tracking of iron-labeled particles (10). Past studies have also demonstrated that epilepsy and various neurodegenerative disorders, including multi- ple sclerosis, stroke, and Alzheimer’s and Parkinson’s disease are discriminated with improved sensitivity and specificity when T 2 measurements are taken (11– 13). Despite its potential benefits in a wide range of appli- cations, routine use of T 2 mapping in the clinical set- ting is rare. One major reason for this lack of clinical translation is likely due to limitations associated with the pulse sequences for T 2 mapping. The simplest and most widely available method for in vivo T 2 mapping is single-echo spin echo. With this technique, multiple image acquisitions are performed at different echo times (TE) to sample the T 2 decay curve. However, as we will show in this study, the main disadvantage of this approach is that it requires long pulse repetition times (TR) (typically, several times T 1 ) to ensure T 2 accuracy. This results in excessively long scan times. Further- more, because optimal signal-to-noise ratio (SNR) effi- ciency is typically achieved at repetition times signifi- cantly less than this (14), conventional single-echo spin echo tends to have low SNR efficiency. A significantly more rapid alternative for in vivo T 2 mapping is multie- cho spin echo. This pulse sequence uses a train of slice-selective 180 pulses to obtain data at different TEs during a single TR. Because the data acquisition time is used efficiently, T 2 mapping data sets can be acquired in less than 10 min (15). However, the multie- cho spin echo approach has several limitations. First, imperfections in the train of 180 pulses, together with the application of slice-encoding gradients, can lead to complex stimulated echo patterns (16–19) that, in turn, can bias quantitative T 2 data measurements (16–18). A second problem is that the train of 180 pulses can de- posit significant heat into the patient, which may be particularly limiting at higher field strengths. Third, multiecho techniques are constrained in the number and choice of TEs that can be acquired. In turn, this constrains the ability to optimize the SNR efficiency of the acquisition (20). Finally, the multiecho spin-echo pulse sequence is not available on all clinical scanners. Other rapid methods have also been proposed for accu- rate T 2 measurement (21–23). In this study, we present a rapid T 2 mapping tech- nique based on the single-echo spin echo pulse sequence. The key distinction of this technique from the conventional (i.e., long TR) method is that a much shorter TR may be used. Data are acquired much more rapidly while retaining all of the advantages of conven- tional single-echo spin-echo imaging. A preliminary demonstration of this technique has been presented else- where (14,24). In this paper, a detailed analysis and vali- dation of the technique are performed. First, the theoreti- cal basis of the technique is developed. Simulations are then performed to investigate the conditions required for T 2 measurement accuracy. Finally, validation is done through phantom studies, and in vivo results are pre- sented in cartilage and brain. 1 Medical Imaging, University Health Network, Toronto, Ontario, Canada. 2 Diagnostic Imaging, The Hospital for Sick Children, Toronto, Ontario, Canada. 3 Electrical Engineering, Stanford University, Stanford, California, USA. 4 Research Institute, The Hospital for Sick Children, Toronto, Ontario, Canada. 5 Medical Biophysics, University of Toronto, Toronto, Ontario, Canada. *Correspondence to: Hai-Ling Margaret Cheng, Ph.D., Department of Diagnostic Imaging, The Hospital for Sick Children, 555 University Avenue, Toronto, Ontario M5G 1X8, Canada. E-mail: [email protected]Received 2 October 2009; revised 27 January 2010; accepted 16 February 2010. DOI 10.1002/mrm.22454 Published online in Wiley InterScience (www.interscience.wiley.com). Magnetic Resonance in Medicine 64:536–545 (2010) V C 2010 Wiley-Liss, Inc. 536
Transcript
A Technique for Rapid Single-Echo Spin-Echo T2
Mapping
Marshall S. Sussman,1 Logi Vidarsson,2 John M. Pauly,3
and Hai-Ling Margaret Cheng2,4,5*
A rapid technique for mapping of T2 relaxation times is pre-sented. The method is based on the conventional single-echospin echo approach but uses a much shorter pulse repetitiontime to accelerate data acquisition. The premise of the newmethod is the use of a constant difference between the echotime and pulse repetition time, which removes the conven-tional and restrictive requirement of pulse repetition time �T1. Theoretical and simulation investigations were performedto evaluate the criteria for accurate T2 measurements. Meas-ured T2s were shown to be within 1% error as long as the keycriterion of pulse repetition time/T2 �3 is met. Strictly, a sec-ond condition of echo time/T1 � 1 is also required. However,violations of this condition were found to have minimal impactin most clinical scenarios. Validation was conducted in phan-toms and in vivo T2 mapping of healthy cartilage and brain.The proposed method offers all the advantages of single-echo spin echo imaging (e.g., immunity to stimulated echoeffects, robustness to static field inhomogeneity, flexibility inthe number and choice of echo times) in a considerablyreduced amount of time and is readily implemented on anyclinical scanner. Magn Reson Med 64:536–545, 2010. VC 2010Wiley-Liss, Inc.
Since the early days of MRI (1,2) and continuing on tothe present, T2 mapping has held out the promise ofproviding novel, quantitative information in a varietyof pathologic conditions. Some examples include theevaluation of cartilage integrity (3,4), tumor characteri-zation (5,6), prostate imaging (7), dynamic contraststudies of cerebral perfusion (8), measurement of ironburden (9), and tracking of iron-labeled particles (10).Past studies have also demonstrated that epilepsy andvarious neurodegenerative disorders, including multi-ple sclerosis, stroke, and Alzheimer’s and Parkinson’sdisease are discriminated with improved sensitivityand specificity when T2 measurements are taken (11–13).
Despite its potential benefits in a wide range of appli-cations, routine use of T2 mapping in the clinical set-ting is rare. One major reason for this lack of clinicaltranslation is likely due to limitations associated withthe pulse sequences for T2 mapping. The simplest andmost widely available method for in vivo T2 mappingis single-echo spin echo. With this technique, multipleimage acquisitions are performed at different echo times(TE) to sample the T2 decay curve. However, as we willshow in this study, the main disadvantage of thisapproach is that it requires long pulse repetition times(TR) (typically, several times T1) to ensure T2 accuracy.This results in excessively long scan times. Further-more, because optimal signal-to-noise ratio (SNR) effi-ciency is typically achieved at repetition times signifi-cantly less than this (14), conventional single-echo spinecho tends to have low SNR efficiency. A significantlymore rapid alternative for in vivo T2 mapping is multie-cho spin echo. This pulse sequence uses a train ofslice-selective 180� pulses to obtain data at differentTEs during a single TR. Because the data acquisitiontime is used efficiently, T2 mapping data sets can beacquired in less than 10 min (15). However, the multie-cho spin echo approach has several limitations. First,imperfections in the train of 180� pulses, together withthe application of slice-encoding gradients, can lead tocomplex stimulated echo patterns (16–19) that, in turn,can bias quantitative T2 data measurements (16–18). Asecond problem is that the train of 180� pulses can de-posit significant heat into the patient, which may beparticularly limiting at higher field strengths. Third,multiecho techniques are constrained in the numberand choice of TEs that can be acquired. In turn, thisconstrains the ability to optimize the SNR efficiency ofthe acquisition (20). Finally, the multiecho spin-echopulse sequence is not available on all clinical scanners.Other rapid methods have also been proposed for accu-rate T2 measurement (21–23).
In this study, we present a rapid T2 mapping tech-nique based on the single-echo spin echo pulsesequence. The key distinction of this technique from theconventional (i.e., long TR) method is that a muchshorter TR may be used. Data are acquired much morerapidly while retaining all of the advantages of conven-tional single-echo spin-echo imaging. A preliminarydemonstration of this technique has been presented else-where (14,24). In this paper, a detailed analysis and vali-dation of the technique are performed. First, the theoreti-cal basis of the technique is developed. Simulations arethen performed to investigate the conditions required forT2 measurement accuracy. Finally, validation is donethrough phantom studies, and in vivo results are pre-sented in cartilage and brain.
1Medical Imaging, University Health Network, Toronto, Ontario, Canada.2Diagnostic Imaging, The Hospital for Sick Children, Toronto, Ontario,Canada.3Electrical Engineering, Stanford University, Stanford, California, USA.4Research Institute, The Hospital for Sick Children, Toronto, Ontario, Canada.5Medical Biophysics, University of Toronto, Toronto, Ontario, Canada.
*Correspondence to: Hai-Ling Margaret Cheng, Ph.D., Department ofDiagnostic Imaging, The Hospital for Sick Children, 555 University Avenue,Toronto, Ontario M5G 1X8, Canada. E-mail: [email protected]
Received 2 October 2009; revised 27 January 2010; accepted 16 February2010.
DOI 10.1002/mrm.22454Published online in Wiley InterScience (www.interscience.wiley.com).
Magnetic Resonance in Medicine 64:536–545 (2010)
VC 2010 Wiley-Liss, Inc. 536
THEORY
In virtually all traditional T2 mapping techniques, it isassumed that signal acquired at different TEs follows apure monoexponential decay:
SðTEiÞ ¼ e�TEiT2 i ¼ 1; :::;n ½1�
Following data acquisition, a variety of techniquesmay then be employed to fit a monoexponential curve tothe data for the purpose of extracting the T2 parameter(25). However, as we will show, when acquiring datawith the single-echo spin echo pulse sequence, theassumption of pure monoexponential decay holds onlyunder certain conditions.
The conventional single-echo spin echo pulse sequence isdisplayed in Fig. 1a. A 90� radiofrequency (RF) pulse tipsthe magnetization down into the transverse plane. A 180�
refocusing RF pulse is applied at time TE/2. Spin echo for-mation occurs at time TE, and data are acquired. To deter-mine the signal characteristics at TE, the Bloch equationsmust be used to calculate the signal in the steady state. Asderived in Appendix A, the steady-state signal of single-echo spin echo is given by Eq. 2. This derivation assumesTR � T2, such that transverse magnetization decays tozero before the end of each TR. This assumption will bemaintained throughout the paper.
Mssxy � 1� 2e�
ðTR�TE=2ÞT1 þ e�
TRT1
h ie�
TET2
Assumption: TR � T2½2�
In Eq. 2, the steady-state magnetization has an undesir-able dependence on TE: the magnetization behavior isnot purely monoexponential over different TEs. As aconsequence, bias will be introduced into T2 estimatescalculated upon the monoexponential assumption.
The reason for the TE dependence of the signal can beunderstood by examining Fig. 1b,c. Following the initial90� RF pulse, the transverse magnetization decays due toT2, and the longitudinal magnetization begins to recoverdue to T1. Following the 180� refocusing pulse, the mag-netization is inverted and then again undergoes T1 recov-ery. At a time around TE (justified later on), the magnet-ization passes through zero. In the remaining time, TR �TE, the longitudinal magnetization then recovers fromzero. Since TR is constant, the amount of T1 recoveryand, therefore, the magnitude of the subsequent signaldepend on TE.
To eliminate the TE dependence, a further requirementthat TR � T1 is necessary. In this case, the magnetiza-tion will recover completely to its equilibrium value ineach TR. The signal will then be the same for all TEs,and Eq. 2 will reduce to:
Mssxy � e�
TET2 Assumption : TR � T2
TR � T1½3�
Equation 3 represents a pure monoexponential T2
decay as a function of TE. In this regimen, unbiased esti-
mates of T2 may be obtained. However, since typical invivo T1 values are in the range of 1 sec (2), the TR � T1
requirement will necessitate a TR value of several sec-onds. Depending on the number of different TEs forwhich the acquisition is repeated, scan times can be pro-hibitively long. The single-echo spin echo technique istherefore impractical for most clinical applications.
Rapid Single-Echo Spin-Echo T2 Mapping Method
In an attempt to speed up data acquisition, a modifica-tion to the conventional single-echo spin echo techniqueis proposed. Instead of the TR � T1 condition, werequire only that TE � T1. With this less stringent con-dition, it is shown in Appendix B that Eq. 2 is reducedto:
Mssxy � 1� e�
ðTR�TEÞT1
h ie�
TET2 Assumption : TR � T2
TE � T1
½4�
Using the conventional acquisition approach of a con-stant TR, Eq. 4 still has a TE dependence and thuswould not represent pure monoexponential decay. How-ever, if instead of using a single TR for all TEs, we nowvary TR with each TE such that TR � TE is constant, Eq.
FIG. 1. The single-echo spin echo pulse sequence. a: Pulse
sequence timing diagram. Roman numerals indicate correspond-ing time points in all panels of the figure. Plots of (b) magnetiza-tion and (c) Mz at different points in the pulse sequence. Initially,
the magnetization is aligned along the z-axis with magnitude equalto the equilibrium magnetization (M0). The 90� RF pulse tips the
magnetization into the transverse plane. The transverse magnet-ization then decays due to T2, and the longitudinal magnetizationbegins to recover due to T1. Following the 180� refocusing pulse,
the magnetization again undergoes T1 recovery. At a time aroundTE, the longitudinal magnetization goes through zero. Subse-quently, Mz recovers from zero for a time TR � TE. If TR is con-
stant, the amount of T1 recovery, and therefore the magnitude ofthe subsequent signal, varies with TE. If instead TR is varied with
TE such that TR � TE is constant, then the amount of T1 recovery,and thus the subsequent signal, is constant for all TEs.
Rapid T2 Mapping 537
[4] is then given by:
Mssxy � ke�
TET2 Assumption : TR � T2
TE � T1
TR� TE¼ constant for all TE0s
½5�
where k ¼ 1� e�ðTR�TEÞ
T1 is constant for all TEs. With thisslight modification, a pure mono-exponential decay maybe achieved.
To interpret this result graphically, consider the course ofthe longitudinal magnetization in Figs. 1b,c. Immediatelyfollowing the 90� pulse, the longitudinal magnetizationbegins to recover from zero. Following the 180� pulse, thelongitudinal magnetization is inverted and again begins torecover. If the T1 recovery curve can be considered to be lin-ear up to this point, then the amount of T1 recovery prior tothe 180� at time TE/2 will be exactly equal to the amount ofT1 recovery between the 180� and time TE. Under these cir-cumstances, the longitudinal magnetization will be zero atTE. If TR is then adjusted such that TR � TE is constant forall TEs, then the amount of longitudinal recovery from TE toTR, and thereforeMz, will be the same for all TEs. The linearbehavior of the T1 recovery (up to the time of TE) is guaran-teed by the condition that TE� T1 (see Fig. 2).
The TE � T1 assumption may be violated in tworegimes: TE � T1 and TE �T1. First, consider the TE � T1
regimen. Since TR � TE by definition, a violation in thisregimen also implies that TR � T1, in which case magnet-ization will recover to the equilibrium value for all TEs.The signal will therefore behave according to Eq. 3 (i.e.,no TE dependence). As a consequence, we need only beconcerned with violations in the TE � T1 regimen.
MATERIALS AND METHODS
A series of simulations and experiments was performedto characterize and validate the rapid single-echo spinecho T2 mapping method. First, simulations were per-formed to characterize the conditions under which the
technique is valid. Next, phantom experiments were per-formed to confirm theoretical predictions. Finally, invivo experiments were performed to demonstrate practi-cal applications of the technique.
Simulations
Simulations were conducted to characterize the behaviorof both conventional (a.k.a. constant TR) and rapid(a.k.a. constant TR � TE) single-echo spin echo techni-ques. Data generation was performed using the exact sol-utions to the Bloch equation outlined in the Theory sec-tion and appendixes. Data fitting for T2 measurementwas accomplished by performing a linear fit to the log ofthe simulated data at different TEs, using MatLab(release 7.6; The MathWorks, Natick, MA).
The first characterization examined the behavior ofboth rapid and conventional methods as a function ofTR; the prime determinant of acquisition speed. Datawere simulated using a T2 value of 50 ms, and 10 loga-rithmically spaced TEs between 5 and 75 ms were usedto sample T2 decay. For the constant TR technique, sim-ulations were performed for a range of TRs between 80ms and 750 ms. For the constant TR � TE method, thesame base TR values, increased by TE on each echo,were used. To isolate effects related to assumptions onTR (i.e., TR � T2 or TR � T1) from possible confound-ing effects related to violations of assumptions on TE(i.e., TE � T1), a long T1 value of 500 ms was used toensure that TE � T1 for all TEs.
The second characterization examined the impact ofviolating the TE � T1 assumption. The same parametersas in the first simulation were used. However, shorter T1
values were evaluated: T1 ¼ 50 ms, 100 ms, and 500 ms.With the maximum simulated TE (¼ TEmax) being 75 ms,these T1 values resulted in TEmax/T1 ratios of 1.5, 0.75,and 0.15. These ratios focus on the regimen TE � T1, inwhich errors due to violating the TE � T1 conditionmay be appreciable (see rationale provided in the Theorysection).
The last simulation examined the behavior of the newtechnique as a function of echo spacing. The TEs usedfor this simulation spanned the same range as the previ-ous simulations (i.e., from 5 ms to 75 ms). However, thenumber of echoes was varied between two and 50, corre-sponding to a range of echo spacing between 1.4 ms and70 ms. To facilitate the examination of different TEs,echo spacing was linear, rather than logarithmic, as inthe other simulations.
Phantom Experiments
Phantom experiments were conducted to validate experi-mentally the behavior of the constant TR � TE single-echo spin-echo technique. Phantoms were prepared tomimic a range of physiologically relevant T1 and T2 val-ues, using either manganese chloride (MnCl2) or gadolin-ium-diethylenetriamine penta-acetic acid (DTPA) (Gd;Magnevist; Berlex Canada, Lachine, Quebec, Canada) asthe doping agent. These agents were used for the pur-pose of manipulating the T1/T2 ratio (9.5 for MnCl2 (26),1.2 for Gd (27)) to span the range likely to be
FIG. 2. Plot of exponential recovery. During the first part of the re-covery (i.e., TE/T1 �1), the curve can be approximated by a line.It is in this linear regimen that the approximation of Eq. 4 is valid.
538 Sussman et al.
encountered in clinical imaging (1,2). To prepare thephantoms, deionized water was doped with either agentand serial dilutions were performed to generate a rangeof T2 values (�20, 40, 80, 160, and 320 ms). Each prepa-ration was placed in a circular vial, and all phantomswere placed in a larger beaker of water to minimize back-ground susceptibility differences.
MR imaging was performed on a 1.5-T MR scanner(Signa Excite HD; GE Healthcare, Waukesha, WI) usingthe standard GE quadrature head coil. Three separatesingle-echo spin-echo acquisitions were performed forthe purpose of validating theoretical predictions of mag-netization behavior and determining if accurate T2 val-ues may be obtained with a short-TR pulse sequence.The first acquisition was a long-TR scan. This was usedto derive gold standard reference T2 values. The othertwo acquisitions were short-TR scans, one using a con-stant TR and the other the constant TR � TE method.Relevant pulse sequence parameters included matrix ¼128 � 128, field of view ¼ 30 cm, slice thickness ¼2mm. For each of the three pulse sequences, eight sepa-rate logarithmically spaced echoes (TE ¼ 10, 15, 22, 33,49, 73, 108, and 160 ms) were acquired individually. Forthe long-TR scan, a TR of 3000 ms was used (total scantime ¼ 51.2 min). For the constant TR, short-TR scan, aTR of 320 ms was used (total scan time ¼ 5.5 min). Forthe constant TR � TE, short-TR scan, a nominal TR of320 ms was also used. However, the actual TR wasincreased by TE for each echo acquisition, such that TR� TE was constant for all echoes (i.e., TR ¼ 330, 335,342, 353, 369, 393, 428, and 480 ms). The total scan timefor the constant TR � TE scan was 6.5 min. Followingdata acquisition, pixelwise T2 data fitting was performed,and the mean T2 and standard deviation were then cal-culated in each vial over an region of interest (ROI) ofapproximately 50–60mm2 in size.
Two separate assessments were performed to evaluatethe phantom data. The first looked at the degree of line-arity between the constant TR � TE method and the con-ventional long TR approach. This was accomplished byassessing the correlation between these two quantities.The second assessment took a closer look at the relation-ship between the magnetization behavior and theoreticalpredictions based on the Bloch equations. To evaluatethe agreement between experimentally measured T2 val-ues and theoretical predictions, the latter must be basedon the true T2 in each phantom. Prima facie, one maysimply consider using directly the T2 values measuredwith the long-TR scan as the reference T2s. However,upon closer inspection, it is clear that, even here, T2 ac-curacy may be biased by possible T1 effects. Moreover, itwas additionally determined that the steady-state mag-netization is affected by amplitude of RF field (B1) inho-mogeneities. These factors can potentially cause signifi-cant deviation from theoretical predictions. Therefore,simulations (based on the exact analytic solutions ofMulkern and Williams (28)) were used to assist in thederivation of gold standard reference T2 values. T1 val-ues were calculated using the reference T2 values andpublished T1/T2 ratios for Gd and MnCl2 (26,27). Theexpected magnetization behavior of the TR ¼ 3000 mssequence was first simulated for input T2 values from 5
ms to 500 ms in 400 logarithmically spaced steps, overof a range of B1 values (from 90% to 110% of the nomi-nal (i.e., 100%) value). T2 fits were then performed onall simulated data. (Again, note that due to T1 and B1
effects, the T2 values calculated from the output of thesimulation were not necessarily equal to the true T2
input values). For each B1 value, the simulated T2 valuesthat most closely corresponded to the experimentallymeasured T2 values were then identified. The input T2
values used to generate these simulated T2 values werethen considered to be the gold standard reference T2
values.With the set of reference T2 values determined, an
assessment of the short TR magnetization behavior wasthen performed. For each B1 value, the correspondingreference T2 values were used to simulate magnetizationbehavior for the short-TR sequences. As with the long-TR scans, due to T1 and B1 effects, the T2 values calcu-lated from the output of the simulation were not neces-sarily equal to the true T2 input values. These simula-tion-derived T2 values were then compared to thosemeasured experimentally with a x2 calculation:
x2ðB1Þ ¼X5i¼1
ðTtheory2i
ðB1Þ � Texp2i
Þ2=s2T
exp2i
½6�
where the sum was taken over all five T2 vials, Ttheory2i
(B1) are the theoretically predicted T2 values in each vialcorresponding to a particular B1 value, and T
exp2i
,s2T
exp2i
are the mean and standard deviation, respectively,of the experimentally derived T2 values over an ROI ineach vial. The B1 value that produced the lowest v2
value was considered to provide the best fit for the data.A fit was considered to have no significant discrepancyif the calculated v2 value corresponded to a P valueabove a 5% threshold.
In Vivo Experiments
Two separate in vivo experiments were performed todemonstrate the practical utility of the constant TR � TEsingle-echo spin echo technique. In the first experiment,T2 maps of knee cartilage were acquired. Eight logarith-mically spaced echoes were used (TE ¼ 10, 14, 19, 27,37, 52, 72, and 100 ms). A nominal TR of 320 ms waschosen, with the actual TR used incremented by TE tomaintain a constant TR � TE (i.e., TR ¼ 330, 334, 339,347, 357, 372, 392, and 420 ms). Other relevant scan pa-rameters included matrix ¼ 256 � 256, field of view ¼15 cm, and slice thickness ¼ 3mm. Total scan time was12 min. For the second in vivo experiment, T2 maps ofthe brain were acquired with the constant TR � TEmethod. To evaluate the effectiveness of the technique,T2 maps were also acquired using constant TR pulsesequences (both short and long TR). The TEs, TRs, andmatrix size were identical to those used in the phantomexperiments. The field of view was 40 cm, and the slicethickness was 5mm. To provide a second independentassessment, a multiecho T2 mapping acquisition wasalso performed with 12 echoes and TE ¼ 6 ms. All otherpulse sequence parameters were the same as the single-echo acquisitions.
Rapid T2 Mapping 539
RESULTS
Simulations
Figure 3 illustrates the TR behavior of both rapid andconventional single-echo spin echo techniques. Clearly,the conventional constant TR method (dashed line)incurs significant errors from violating the TR � T1
assumption. In fact, when TR/T1 �0.2, the error in esti-mated T2 is almost 60%! In contrast, the proposed rapidconstant TR � TE method (solid line) is accurate over abroad range of TRs since the stringent requirement of TR� T1 need not be observed. Small errors arise only at
very short TRs when the remaining condition, TR � T2,is unmet. However, the error in T2 remains verysmall: about 5% for TR/T2 �1.5 and less than 1% forTR/T2 �3.
Figure 4 illustrates the dependence on TE/T1 for theconstant TR � TE method. Provided that the TR � T2
assumption is maintained, violation of the TE � T1
assumption appears to have limited impact. For exam-ple, in the region where TR/T2 �3, all of the differentTE/T1 data have discrepancies in T2 values on the orderof 1% or less. To provide further insight into this result,Fig. 5 plots the discrepancy between signals derived
FIG. 3. Simulation of the fractional error in T2 as a function of TRfor the conventional constant TR (dashed line) and proposed con-stant TR � TE (solid line) single-echo spin-echo techniques. An
input T2 value of 50 ms and a T1 value of 500 ms were used. Onthe horizontal axis, the TR/T2 and TR/T1 values are also displayed.
The new technique allows the use of much shorter TRs withoutincurring significant error.
FIG. 4. Simulation of the fractional error in T2 as a function of TRfor the constant TR � TE single-echo spin echo technique for dif-ferent TEmax/T1 values. This simulation used a T2 value of 50 ms
and T1 values of 50, 100, and 500 ms to generate different TEmax/T1 ratios. On the horizontal axis, the TR/T2 values are also dis-
played. In the region where the TR � T2 assumption is main-tained, violations of the TE � T1 assumption appear to have alimited impact. For example, in the indicated region where TR/T2�3, all of the different TE/T1 data have discrepancies in T2 valueson the order of 1% or less.
FIG. 5. Simulation of the percentage discrepancy normalized to
M0 between signals derived with and without the TE/T1 assump-tion (i.e., Eqs. B4 and A5) for (a) TR ¼ T2, (b) TR ¼ 3T2, and (c)TR ¼ 6T2 as a function of TE/T1 for the constant TR � TE method.The simulations used T2 ¼ 50 ms and T1 values of 50 ms (solidline) and 500 ms (dashed line). Note the difference in scale
between the plots. Also note that the simulation evaluated TE upto the nominal TR.
540 Sussman et al.
with and without the TE/T1 assumption (i.e., Eqs. B4and A5) for the constant TR � TE method. For the simu-lations with TR/T2 �3 (Fig. 5b,c), the discrepancy is lessthan 1% over the full range of TE/T1 values. Since thislies well below the SNR limits of most clinical MRIscans, there will not be any impact on T2 calculations.For the simulation in Fig. 5a that violates the TR/T2 �3requirement, significant discrepancy is observed fromsome TE/T1 values.
Figure 6 plots the percent discrepancy in T2 as a func-tion of echo spacing. Clearly, the echo spacing has avery minor impact (0.1%) on the results.
Note that while the above simulations were performedwith specific T1 and T2 values, the same results areobtained for any species with the same ratios of T1/T2.In practice, the results are qualitatively similar for otherT1/T2 ratios (data not shown). Finally, note that thesimulated results are virtually unchanged when differentnumbers of echoes are used (data not shown).
Phantom Experiments
Figure 7 illustrates the results of phantom experimentsfor Gd- and MnCl2-doped water (indicated by the symbol‘‘*’’). Clearly, the T2 values provided by the short-TR,constant TR � TE technique are linear with respect tothe long-TR reference data over a much larger range ofT2 values than the short-TR, constant TR counterpart. Infact, the correlation between the constant TR � TE andTR ¼ 3000 ms data is greater than 0.99 for both Gd andMnCl2 data sets. Some slight deviation from linearity canbe observed at the largest T2 value of 320 ms. The reasonfor this deviation is violation of the TR � T2 condition(TR � T2 for T2 ¼ 320 ms).
To further characterize the behavior of the magnetiza-tion, the black and blue solid lines in Fig. 7 illustrate theresults of fitting the Bloch equations to the experimentaldata. As discussed in the Materials and Methods section,the B1 error was used as a free parameter of the fit. Thex2 values for the Gd and MnCl2 fits are 12.3 and 14.3,respectively, and correspond to P values of 0.14 and0.08. Thus, there is no significant discrepancy between
experimental data and theoretical predictions at the 5%level. The fitted B1 errors for the Gd and MnCl2 data are7% and 1%, respectively, which are well within therange of expected B1 errors (29).
In Vivo Experiments
Figure 8 illustrates the results of constant TR � TE sin-gle-echo spin echo T2 mapping of cartilage. Note thecharacteristic gradient in T2 values from the deep to su-perficial surface of cartilage (30) caused by magic angleeffects on the ordered collagen network (31). The rangeof T2 values is in agreement with previously publishedvalues for healthy cartilage (30).
Figure 9 shows the results of the brain experiment.Qualitatively, the TR ¼ 320 ms T2 maps exhibit greaterdiscrepancy with the reference TR ¼ 3000 ms and multi-echo data than do the TR � TE ¼ 320 ms T2 maps. Theabsolute discrepancies are quantified in Table 1. Theconstant TR � TE method clearly provides an improve-ment in T2 mapping accuracy over the constant TRmethod when using short TRs. Note, however, that the
FIG. 6. Simulation of the percentage discrepancy in T2 as a func-tion of echo spacing. The simulations used T2 ¼ 50 ms and T1values of 500 ms (solid line) and 50 ms (dashed line). The echoesspanned the range from 5 ms to 75 ms.
FIG. 7. Gd and MnCl2 phantom results. The plots illustrate experi-
mentally derived T2 values for the short-TR single-echo spin echotechniques versus the long-TR reference. Black and blue data
points (*) correspond to the constant TR � TE and constant TRtechniques, respectively. The black and blue lines are theoreticalcurves fitted to the data via the Bloch equations. The free param-
eter of the fit was the B1 error. The x2 error and P value of the fitare indicated in the legend. The listed R2 value corresponds to the
constant TR � TE data only. [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com.]
Rapid T2 Mapping 541
constant TR � TE discrepancies shown in Table 1 areslightly larger than those in the phantom experiments.There are two possible reasons for this. First is motion-related error in the T2 calculations. A slight shift in sliceposition between the different pulse sequences wasnoted, likely due to the lengthy duration of the examina-tion (1.5 h). This motion is evident in an altered visual-ization of the ventricles between different pulse sequen-ces (Fig. 9). A second possible source of discrepancy isthe cerebral spinal fluid (CSF). Due to the very long T2
value of CSF (T2 �2 sec (23)), the TR � T2 conditionwill not be satisfied for even the TR ¼ 3000 ms scan. Asa result, CSF partial-volume effects may have an impacton the calculated T2 values. In fact, this phenomenonmay affect the accuracy of the multiecho pulse sequenceT2 data as well (32). The multiecho data may also beadversely affected by stimulated echoes. To provide fur-
ther insight into the relative T2 accuracy of the differentpulse sequences, Table 2 compares the calculated relaxa-tion times with published literature values acquired witha variety of pulse sequences, including high-quality exvivo spectrometer data (33). The constant TR � TE dataare consistent with literature values, whereas the con-ventional long-TR and multiecho methods tend to over-estimate. The T2 overestimation is more pronounced ingray matter, which may be due to partial-volume effectsnear the CSF. In these regions, the constant TR � TEapproach may provide an advantage, since the signalfrom long-T1 species is reduced.
DISCUSSION
The simulations and experimental findings of this studydemonstrate that the constant TR � TE, single-echo spinecho technique is an accurate and rapid method for T2
mapping. The rapid acquisition stems from the ability touse short TRs, a regimen in which large errors were pre-dicted and observed using the conventional constant TRapproach. The constant TR � TE method therefore pro-vides all the advantages of gold standard T2 measure-ments based on single-echo spin echo, including flexibil-ity in choosing the number of echoes and their spacing,but does so in a relatively short time period.
Conventional constant TR techniques require twoassumptions: TR � T2 and TR � T1. In the case of theconstant TR � TE technique, the TR � T1 requirement isreplaced with the restriction TE � T1. The results of thisstudy demonstrated that even this restriction is not verystringent. It was found that violating this condition pro-duced very modest effects on the resulting T2 values(1% error). As a consequence, the only significantrestriction of this technique is TR � T2. This restrictionis necessary for eliminating the transverse component ofthe magnetization on each TR. In the future, eliminatingtransverse magnetization could instead be accomplishedwith RF and/or gradient spoiling. In such a case, theconstant TR � TE technique could potentially be appliedwith virtually no restrictions, and very short TRs couldbe used.
It should be noted that the simulations performed inthe present study followed the T2 decay curve only up to1.5 times the T2 value. For clinical scanning, this is areasonable assumption as the signal will have decayed toonly about 20% of its initial value. For many tissues, the
FIG. 8. T2 map of cartilage as a color overlay on an anatomicknee image. Note the characteristic gradient in T2 values from the
deep to superficial surface of cartilage.
FIG. 9. In vivo T2 maps of the brain acquired with the referencelong-TR methods (single-echo TR ¼ 3000 ms and multiecho) and
the short-TR methods (constant TR ¼ 320 ms and constant TR �TE ¼ 320 ms). The TR ¼ 320 ms T2 data are significantly differentfrom the reference datasets. In contrast, the TR � TE ¼ 320 ms
T2 data are similar to the reference data, except where CSF ispresent.
Table 1
Discrepancy of Brain T2 Relaxation Times Between Short-TRMethods (Constant-TR and Proposed Constant TR-TESingle-Echo) and Reference Long-TR Scans (Single-Echo and
Multiecho)*
Reference long-TRa
spin echo pulse
sequences
Short-TR single-echo spin echo
TR ¼ 320 ms
TR � TE ¼320 ms
Single-echo 34 6 11% 16 6 16%
Multiecho 27 6 15% 7 6 21%
*Values are reported as median 6 standard deviation (units of
milliseconds) over the entire brain.aTR ¼ 3000 ms was used.
542 Sussman et al.
signal will lie close to the T2 mapping noise threshold(SNR 5) (3) at this point. However, in some ex vivoapplications, with significantly better SNR, it may bepossible to follow the decay curve for a longer period oftime before reaching the noise threshold. In this case,simulations have indicated that larger T2 discrepanciesmay be expected.
The results of this study indicate that the number ofechoes and echo spacing have only a very small effecton T2 mapping. In theory, this suggests that only a smallnumber of echoes should be used to allow for the short-est scan time. In practice, one should be cautious whenusing a very small number of echoes as the fits can behighly sensitive to systematic errors (e.g., motion, flow).For example, one ‘‘bad’’ data point could have a signifi-cant impact on the T2 fit if there are only a limited num-ber of echoes.
The phantom results indicated a very high degree of lin-earity between the gold standard long TR and the constantTR � TE techniques over a broad range of T2 values. Slightdeviations from linearity were only observed at the largestT2 value, for which the TR >3T2 condition was violated.On the other hand, significant deviations from linearitywere observed using the short TR, constant TR method.These results imply that provided the TR >3T2 conditionis met, the constant TR � TE technique provides accurateT2 mapping.
Over the course of the investigations into the constantTR � TE technique, we examined a number of factorsthat could potentially affect the steady state of the mag-netization. Among these, we found that B1 errors werethe most significant. To completely reconcile experimen-tal data with theoretical predictions over the full rangeof T2 values examined, it was necessary to include con-sideration of B1 errors. However, if the analysis is re-stricted to the TR >3T2 regimen, B1 errors do not have asignificant impact and need not be considered. This canbe observed in Fig. 7 by the excellent linearity betweenthe TR ¼ 3000 ms and constant TR � TE data at all T2
values except T2 ¼ 320 ms, which violates the TR >3T2
condition.In vivo, it was found that the constant TR � TE
approach generated T2 values that were similar to bothconventional long-TR and multiecho pulse sequences,although some discrepancies were observed. The T2 val-ues calculated from the constant TR � TE method werecloser to published literature values, however. Potentialsources of error such as CSF partial volume effects andstimulated echoes that would be expected to preferen-
tially increase the calculated T2 values for long-TR andmultiecho approaches were, in fact, observed. These factssuggest that the constant TR � TE technique may be moreaccurate in vivo than the long-TR and multiecho methods.On the other hand, it is also possible that simple slice mis-registration played a significant role in the observed dis-crepancy. Further study is required for a more completecharacterization of the causes of discrepancy in vivobetween the different methods.
Compared with conventional constant TR approaches,the ability to use short TRs with the constant TR � TEmethod provides a significant increase in both overallspeed as well and SNR efficiency (14). With long TRs,the magnetization achieves (nearly) full recovery eachrepetition interval. In contrast, with a sufficiently shortTR, magnetization will lie in the linear T1 recovery regi-men (see Fig. 2). In this case, signal is proportional toTR, which is much more SNR efficient.
Another approach to T2 mapping is to acquire multipleechoes in each TR (i.e., a Carr-Purcell-Meiboom-Gillapproach). The major advantage of this approach over sin-gle echo methods is efficiency, since a larger proportion ofthe scan time is spent acquiring data. On the other hand, amajor drawback of multiecho sequences is that they canbe quite sensitive to errors caused by inhomogeneous RFfields (B1) and static fields. The main problem is that theseinhomogeneities can lead to errors in flip angles, which,in turn, give rise to phase artifacts (e.g., streaking, mirrorghost images (34)) and stimulated echoes (16,17). Thestimulated echoes can substantially distort echo ampli-tudes (35) and result in erroneous T2 measurement. Phaseartifacts and stimulated echo effects manifest on the sec-ond and third echo, respectively (18), and are thereforenot an issue in single-echo imaging techniques such as theconstant TR � TE method presented in this study. Strat-egies have been proposed to address these limitations ofmultiecho imaging, such as phase rewinding (19), phasecycling (36), and spoiler gradients (37) to eliminate spuri-ous echoes, or adiabatic pulses (38) and composite pulses(37) to compensate for B1 and static field inhomogeneity.However, these strategies may not eliminate all spuriouscomponents and often require specialized pulse sequencedesign and provide only single-slice imaging. For thesereasons, single-echo acquisitions have remained the goldstandard.
Comparison against several other rapid T2 mappingapproaches should also be considered. A variant of multie-cho imaging using fast spin echo is commonly used forrapid T2 mapping. Instead of producing a different
Table 2Brain Tissue T2 Relaxation Times Measured Using Spin Echo Techniques: Reference Long-TR Single-Echo and Multiecho Versus Pro-
posed Constant TR � TE Single-Echo*
Tissue
Reference long-TR spin echoaShort-TR single-echoTR � TE ¼ 320 ms LiteratureSingle-echo Multiecho
*Values are reported as mean 6 standard deviation (units of milliseconds) over five different regions in each tissue type.aTR ¼ 3000 ms was used.
Rapid T2 Mapping 543
T2-weighted image on each echo, fast spin echo uses theechoes to fill different phase-encode lines, thereby reduc-ing acquisition time. However, T2 values tend to be overes-timated (15) due to abnormally high signals in later echoescaused by stimulated echo pathways (19). Furthermore,depending on the phase ordering, fast spin echoapproaches may suffer from the same T1 contaminationissues as single-echo spin echo. It may in the future be pos-sible to apply a constant TR � TE approach to fast spinecho to reduce these latter types of errors. Non-spin-echosequences have also been proposed to gain acquisitionspeed. Examples include gradient-echo-based techniquessuch as snapshot fast low angle shot (39) and T2FARM (40)that can acquire T2 maps in under 30 sec for low-spatial-re-solution applications. However, these specialized sequen-ces are not readily available, and being gradient-echosequences, they are much more sensitive to off-resonanceand susceptibility artifacts. A more recently proposed gra-dient-echo approach is based on a steady-state free-preces-sion sequence (41). This method is rapid and offers highspatial resolution and comparable accuracy to conven-tional T2 methods. However, similar to other T2 methods,it is sensitive to B1 error, and it suffers from appearance ofvoids or artificially low T2 due to SSFP off-resonancebanding artifacts. It also requires a measurement of T1 inits calculation of T2, bringing the total acquisition time totens of minutes.
There is one other short-TR single-echo spin echo T2
mapping technique, proposed by Tofts and Johnson (42),that bears some similarity to the present approach. In theirmethod, dependence on TE is eliminated by introducing asaturation pulse to destroy the longitudinal magnetizationafter the echo at TE. Following the saturation pulse, themagnetization is allowed to recover for a designatedperiod of time. Like the present technique, this forcesthe same T1 recovery period for all TEs. The main disad-vantage of this approach is that the saturation pulsereduces the available magnetization and thus causes areduction in SNR. A further reduction in SNR efficiencyalso results from the additional time required to performthe saturation. A final minor disadvantage is that thisapproach requires a specialized (i.e., nonstandard) pulsesequence.
The proposed constant TR � TE, single-echo spin-echomethod provides a method for rapid T2 mapping. In thefuture, it is possible to envision additional strategies thatmay be employed to further improve acquisition speed.One strategy could be to adopt more efficient k-spacesampling trajectories, such as spiral (43) or radial (44)patterns for each spin echo. Another approach could beto acquire more than one line of k-space per echo, as inan echo planar imaging (45) or fast-spin echo. All ofthese strategies may provide additional flexibility inoptimizing the overall scan efficiency.
In conclusion, the proposed constant TR � TE, single-echo spin echo approach allows accurate T2 measurementwith a considerably reduced scan time compared to con-ventional T2 mapping. It is immune to limitations associ-ated with other rapid alternatives, such as stimulated ech-oes in multiecho sequences, static field effects in gradient-echo based methods, and image distortions from non-Car-tesian k-space sampling. Moreover, it offers flexibility in
the choice of echo number and spacing and is readilyimplemented on all clinical scanners.
REFERENCES
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normal tissue hydrogen NMR relaxation times and relaxation mecha-
nisms from 1–100 MHz: dependence on tissue type, NMR frequency,
temperature, species, excision, and age. Med Phys 1984;11:425–448.
2. Bottomley PA, Hardy CJ, Argersinger RE, Allen-Moore G. A review of1H nuclear magnetic resonance relaxation in pathology: are T1 and
T2 diagnostic? Med Phys 1987;14:1–37.
3. White LM, Sussman MS, Hurtig M, Probyn L, Tomlinson G, Kandel
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This appendix provides the derivation of the steady-statemagnetization for single-echo spin echo (Fig. 1). It is
assumed that the initial equilibrium magnetization has avalue of unity and lies along the z-axis. Subsequently,the 90� RF pulse tips the magnetization into the trans-verse plane. Immediately following the 180� pulse, theBloch equations can be used to show that the transverseand longitudinal magnetizations are given by:
M1xyðt ¼ TE=2þÞ � e�
TE=2T2 ½A1�
M1z ðt ¼ TE=2þÞ � e�
TE=2T1 � 1 ½A2�
Assuming that TR � T2, it can be shown that thetransverse and longitudinal magnetizations at TR aregiven by (46):
M1xyðt ¼ TRÞ � 0 ½A3�
M1z ðt ¼ TRÞ � 1� 2e�
ðTR�TE=2ÞT1 þ e�
TRT1
h i½A4�
During the next cycle, the magnetization achieves asteady state. The steady-state signal is therefore given bythe magnitude of the transverse magnetization at the TEon this cycle:
Mssxyðt ¼ TEÞ � 1� 2e�
ðTR�TE=2ÞT1 þ e�
TRT1
h ie�
TET2 ½A5�
Again, note that Eq. A5 is valid under the assumptionof TR � T2.
APPENDIX B
This appendix provides the derivation of the rapid sin-gle-echo spin-echo T2 mapping method. The startingpoint of this derivation will be Eq. A5. The objective isto derive conditions under which the bracketed term inEq. A5 is the same for all TEs. If this can be achieved,there will be pure monoexponential decay over all TEs.
Equation A5 can be rewritten as:
Mssxyðt ¼ TEÞ � e
�TET1 e
TET1 � 2e�
ðTR�TEÞT1 e
TE=2T1 þ e�
ðTR�TEÞT1
h ie�
TET2 ½B1�
A first-order Taylor expansion (e�TET1 � 1� TE=T1) is then
used to simplify some of the exponential terms in Eq. B1:
Mssxyðt ¼ TEÞ � ð1� TE=T1Þ
ð1þ TE=T1Þ � 2e�ðTR�TEÞ
T1 ð1þTE=2T1
Þ þ e�ðTR�TEÞ
T1
" #e�
TET2 ½B2�
Expanding Eq. B2 and eliminating like terms yields:
Mssxyðt ¼ TEÞ � 1� e�
ðTR�TEÞT1 þ ðTE=T1Þ2e�ðTR�TEÞ
T1
h ie�
TET2: ½B3�
Since we are considering only first-order terms in TE/T1,the (TE/T1)
2 term can be dropped, and Eq. B3 reduces to:
Mssxy � 1� e�
ðTR�TEÞT1
h ie�
TET2: ½B4�
Note that the first-order Taylor expansion will be validunder the condition:
