Yuta Kobayashi and Yasuhiko Terada * underestimation was prominent for tissues with large values of T 2. and diffusion coefficients.

Transcription

1 Mgn Reson Med Sci 2018; XX; XXX XXX doi: /mrms.tn Pulished Online: My 24, 2018 TECHNICAL NOTE Diffusion-weighting Cused y Spoiler Grdients in the Fst Imging with Stedy-stte Precession Sequence My Led to Inccurte Mesurements in MR Fingerprinting Yut Koyshi nd Ysuhiko Terd * Mgnetic resonnce fingerprinting (MRF) is promising frmework tht llows the quntifiction of multiple mgnetic resonnce prmeters with single scn. MRF using fst imging with stedy-stte precession (MRF- FISP) hs roustness to off-resonnce rtifcts nd hs mny pplictions in inhomogeneous fields. However, the spoiler grdient used in MRF-FISP is sensitive to diffusion motion, nd my led to quntifiction errors when the spoiler moment increses. In this study, we exmined the effect of the diffusion weighting in MRF-FISP cused y spoiler grdients. The relxtion times were gretly underestimted when lrge spoiler moments were used. The ws prominent for tissues with lrge vlues of nd diffusion coefficients. The is ws lmost independent of the pprent diffusion coefficient (ADC) nd vlues when the ADC mp ws mesured nd incorported into the mtching process. These results revel tht the resulted from the diffusion weighting cused y the spoiler grdients. Keywords: diffusion weighting, mgnetic resonnce fingerprinting, mgnetic resonnce fingerprinting using fst imging with stedy-stte precession, spoiler grdient, Introduction Conventionl clinicl MRI scnners cn detect disese pthologies, ut in most cses, they re qulittive in nture. In contrst, quntittive MRI mesurements could more directly reflect disese chnges nd e more helpful for disese detection nd follow-up. These quntittive MRI ssessments include T 1 nd relxtion times, 1 proton density, diffusion 2,3 nd perfusion 4 prmeters, mgnetic trnsfer effects, 5 nd other tissue prmeters. Despite mny efforts, quntittive MRI mesurements still fce technicl chllenges, e.g., reproduciility nd lengthy scn times to otin multiple prmeters. Recently, new frmework for quntifying multiple tissue prmeters in single scn, clled mgnetic resonnce fingerprinting (MRF), hs een proposed. 6 MRF hs the potentil to overcome the limittions of conventionl quntittive methods, enling routine quntittive MRF in clinicl nd preclinicl environments. Mgnetic resonnce fingerprinting uses the responses of tissues or mterils to repeted excittion nd cquisition Institute of Applied Physics, University of Tsuku, Tennodi, Tsuku, Irki , Jpn * Corresponding uthor, Phone: , Fx: , E-mil: terd@k.tsuku.c.jp 2018 Jpnese Society for Mgnetic Resonnce in Medicine This work is licensed under Cretive Commons Attriution-NonCommercil- NoDerivtives Interntionl License. Received Decemer 8, 2017 Accepted April 4, 2018 schemes. MRF cquires trnsient-stte signl with pseudorndom cquisition prmeters. The cquired signl is mtched with predetermined dictionry of possile signl evolutions clculted with pproprite tissue nd system prmeters, nd the est-mtched entry is used to ssign multiple tissue properties simultneously. The cquisition schemes tht re mostly used in the MRF frmework re the lnced stedy-stte-sed MRF (MRF-SSFP) 6 nd MRF using fst imging with stedystte precession (MRF-FISP). 7 MRF-SSFP hs the dvntge of high signl intensity, ut quntifiction of relxtion prmeters is ffected y nding rtifcts rising from the B 0 inhomogeneity. In contrst, MRF-FISP uses the unlnced grdient moment, which cn llevite the nding rtifcts, nd extends the ppliction of MRF to inhomogeneous fields tht re potentilly chllenging for MRF-SSFP. However, MRF-FISP cn e ffected y nding rtifcts where there is lrge off-resonnce vrition in n imging volume, such s in high field strengths, 8 under insufficient shimming, nd for wide FOV scnners. Moreover, it is not strightforwrd to suppress the nding rtifcts in regions where shrp susceptiility trnsitions exist, such s nsl cvities nd uditory cnls. In such cses, the use of much stronger spoiler grdients is simple wy to llevite nding rtifcts. However, grdientspoiled imging is prticulrly sensitive to diffusive motion, especilly when the spoiler grdient precedes imging

2 Y. Koyshi et l. Therefore, the incresed grdient moment in MRF-FISP lso cuses incresed sensitivity to diffusion nd motion long the grdient direction. However, the diffusion-weighting effect hs een neglected in the MRF-FISP frmework nd is not generlly uilt into the MRF-FISP dictionries tht re used for pttern mtching. The neglect of diffusion my led to flse estimtes of relxtion times. In this study, we exmined the effect of diffusion weighting in MRF-FISP with spoiler moments, nd we showed tht the diffusion effect results in, nd tht the is for tissues with lrge nd diffusion coefficients is nonnegligile even for moderte grdient moments. Methods Smples For the phntom study, we used nine test tues filled with wter with CuSO 4 (0.13, 0.4, nd 2 g/l) to lter T 1 nd nd with glycerol (0, 12.5, nd 25%) to lter the diffusion coefficient. For the reference, the T 1,, nd pprent diffusion coefficient (ADC) mps were cquired using stndrd methods. The T 1 mp ws cquired with inversion-recovery spin-echo sequences (inversion time = 20, 50, 100, 200, 400, 800, 1500, nd 3000 ms; TE/TR = 10/8000 ms) nd the mp ws cquired with multiple spin echo (MSE) sequence (interecho spcing = 10 ms, TR = 8000 ms). The ADC mp ws estimted using the stndrd Stejskl-Tnner method ( = 0, 35.1, 141, nd 316 s/mm 2 ). MRI systems The phntoms were mesured on verticl ore 4.74T system (Oxford Instruments, UK; ore dimeter = 88.3 mm) with shielded grdients, home-uilt rdio-frequency coil, nd digitl MRI console 12 (DTRX6, MRTechnology, Jpn). The field homogeneity ws out 1 ppm over 20 mm in dimeter of sphericl volume (DSV). For the in vivo study, MRF-FISP mesurements were performed on helthy C57BL/6JJcl mouse rin using smll-ore 1.5T system (ore dimeter = 280 mm; JASTEC, Koe, Jpn) with shielded grdients. The field homogeneity ws 50 ppm over 160 mm DSV. MRF pulse sequences The MRF-FISP cquisition ws initited with n ditic inversion pulse, which ws followed y N successive FISP cquisition periods with vrying flip ngle (FA) nd TR. N = 300 nd TE ws held constnt (5 ms). FA ws vried pseudo-rndomly nd sinusoidlly (5 90 ) nd TR ws vried using Perlin noise pttern (20 30 ms) (Fig. 1). To void the potentil imging rtifcts rising from hrdwre imperfections, Crtesin smpling 13 ws used for the MRF cquisition. The cquired MRF signl evolution profile ws mtched to n MRF dictionry. To correct the B 1 inhomogeneity, the B 1 dimension ws dded to the MRF dictionries, nd B 1 mp mesured with doule-ngle method ws incorported into the dictionry-mtching process. Vectorsed inner product comprisons were used s mtching lgorithm. To exmine the effect of diffusion weighting in MRF-FISP, the moment of the spoiler grdient ws vried from 2π to 32π per slice thickness. Here, we set the slice thickness to e 2.5 mm, nd the moment rnged from 9.5 to 150 mt/m ms. Conventionlly, the MRF-FISP dictionry is generted without considering the diffusion effect. To consider this effect, we generted two types of MRF-FISP dictionries; one without the diffusion effect (dictionry D ) nd one with the diffusion effect (dictionry D+). The MRF dictionries D with rnge of T 1 ( ms), ( ms), B 1 ( ) were creted using n extended phse grph (EPG) lgorithm. 14 The MRF-FISP dictionry D+ with the dditionl dimension of the diffusion coefficient D ( mm 2 /s) ws lso generted using EPG with isotropic diffusion opertors, D k t T kt L (, )= exp æ 1 2 ö ç - nd è D ø æ 1 æ 2 1ö ö DT ( k, t)= expç - ç k + k + t, where D L nd D T re è TD è 3 ø ø the diffusion opertors for the longitudinl nd trnsverse configurtion sttes, respectively, k is the Fourier spce coordinte, nd T = 1 D D ( ggt ) 2 where gg t is the zeroth moment of the spoiler grdient. For the phntom study, the slice thickness ws 2.5 mm, nd the FOV ws mm 2. The whole TR ws 12 s, nd the mesurement time ws 26 min for MRF-FISP [numer of excittions (NEX) = 1]. For the in vivo study, the slice thickness ws 2.5 mm, nd the FOV ws mm 2. The whole TR ws 12 s, nd the mesurement time ws 26 min. The mtrix size ws for ll the mesurements. Fig. 1 Ptterns of () flip ngle (FA) nd () TR used for the mgnetic resonnce fingerprinting using fst imging with stedystte precession (MRF-FISP) sequence. 2 Mgnetic Resonnce in Medicl Sciences

3 Diffusion Weighting in MRF-FISP Results Mgnetic resonnce fingerprinting using fst imging with stedy-stte precession Figure 2 shows T 1 nd estimtes from MRF-FISP using dictionry D (excluding diffusion). At smll spoiler moments, oth the T 1 nd mps suffered from nding rtifcts (indicted y rrows in the figure) nd showed lrge vritions in the estimted vlues in the region where the nding ppered. As the moment of the spoiler grdient incresed, the nding rtifcts ecme less cler, nd the T 1 nd vlues ecme lmost constnt in ech phntom. The T 1 estimtes were lmost independent of the moment, nd showed high correltion with the T 1 stndrds (Fig. 2c). However, the estimtes significntly decresed s the moment incresed (Fig. 2d), nd devited from the stndrds. The is, which ws defined s the difference etween the estimtes nd the stndrds, ecme severe (incresed negtively) s the moment incresed (Fig. 2e). For lrge moments, the is incresed negtively s the ADC incresed. For smll moments, the is hd lrge vritions ecuse of the nding rtifct. Figure 3 nd 3 show n exmple of MRF-FISP signl entries from dictionry D+ (including diffusion). The signls were lmost independent of D for the moderte moment (38 mt/m ms). However, they decresed significntly with D for the lrge moment (150 mt/m ms). Similr ehvior is oserved in the signl entries of dictionry D (Fig. 3c); the c d e f Fig. 2 Mgnetic resonnce fingerprinting using fst imging with stedy-stte precession (MRF-FISP) results oti ned without considering the diffusion effect. () T 1 nd estimtes from MRF-FISP for different spoiler grdient moments. () T 1,, nd pprent diffusion coefficient (ADC) mps from stndrd methods. Comprison of (c) T 1 nd (d) etween MRF- FISP nd stndrd methods. (e) Experimentl nd (f) theoreticl is vs ADC. 3

4 Y. Koyshi et l. c d Fig. 3 ( nd ) Exmple of entries in dictionry D+ including diffusion for T 1 = 1.2 s, = 0.8 s, nd vrying D. The moment ws () 8π/2.5 mm (38 mt/m ms) nd () 32π/2.5 mm (150 mt/m ms). (c) Exmple of entries in dictionry D excluding diffusion for T 1 = 1.2 s nd vrying D. (d) Exmple of. The signl evolution including the diffusion effect (red line) ws mtched with dictionry D nd the est-mtched entry is shown s lue line. signl intensity incresed s incresed. As shown in Fig. 3d, the signl evolutions for lrge D vlues in D+ (Fig. 3) were similr to those for smll vlues in D (Fig. 3c). This chrcteristic would led to when dictionry D ws used for mtching. To estimte the theoreticl is cused y the diffusion effect, the signl evolution in dictionry D+ ws mtched with tht in dictionry D nd the resulting is etween the true vlue nd the est-mtched vlue ws clculted. Figure 2f shows the theoreticl is for the nine phntoms. It ws negligily smll for the smll moment, while it ecme severe for lrge moments nd lrge ADC vlues. These fetures greed with those oserved in the experimentl results (Fig. 2e). To vlidte experimentlly tht the origintes from the diffusion effect, the ADC mp ws lso mesured nd incorported into the mtching processes with dictionry D+. Figure 4 shows the resulting T 1 nd estimtes. Both estimtes greed with their stndrd vlues for different grdient moments (Fig. 4c nd 4d), nd the is ws lmost independent of the ADC vlue (Fig. 4e). These results support the clim tht the mesured origintes from the diffusion weighting cused y the spoiler grdient. Figure 5 shows the theoreticl is for different grdient moments clculted without including diffusion. At fixed moment, the ecme lrger s the theoreticl nd D vlues ecme lrger. The is ws lmost independent of the true T 1. Figures 5c nd d show the is estimted for T 1,, nd D vlues of typicl tissues (Tle 1). For tissues with reltively short nd smll D vlues (e.g., white mtter nd gry mtter), the is ws not severe even with the lrge moments, ut those with long nd lrge D vlues showed severe is even with the smll moment. For exmple, the is for cererospinl fluid (CSF) (T 1 = 5000 ms, = 2100 ms, nd D = mm 2 /s) reched to 26% even for the moment of 19 mt/m ms (4p /2.5 mm). In vivo study Figure 6 shows the MRF-FISP nd MSE results for the in vivo mouse rin. estimtes from MRF-FISP excluding diffusion showed reduced vlue for the lrger moment, especilly in CSF nd in the region outside the rin. Discussion We experimentlly nd theoreticlly vlidted the diffusionweighting effect cused y spoiler grdients in MRF-FISP, which hs een neglected in the MRF-FISP frmework. In the phntom experiment, the estimtes from MRF-FISP excluding diffusion depended on the grdient moment, nd decresed s the moment incresed. The is negtively incresed s nd ADC incresed, greeing with the theoreticl results. The phntom results of MRF-FISP with the dditionl ADC mp did not show the (Fig. 4). These results revel tht the resulted from the diffusion weighting cused y the spoiler grdients. The diffusion weighting in MRF-FISP cn e understood y considering signl pthwys in the Fourier trnsformtion spce. 9,10 For FISP sequence in which TR nd FA re fixed, echoes re formed through free induction decy (FID) nd different refocusing pthwys, which include those 4 Mgnetic Resonnce in Medicl Sciences

5 Diffusion Weighting in MRF-FISP c d Fig. 4 Mgnetic reso nnce fingerprinting using fst imging with stedy-stte precession (MRF-FISP) results otined while considering the diffusion effect. () T1 nd T2 estimtes from MRF-FISP for different spoiler grdient moments. () T1 nd T2 mps from stndrd methods. Compr ison of (c) T1 nd (d) T2 etween MRFFISP nd stndrd methods. (e) T2 is vs pprent diffusion coefficient (ADC). e c d e Fig. 5 Theoreticl T2 is clculted without including diffusion. T2 is mps for () T1 = 1 s nd () T2 = 2 s. (c e) T2 is for typicl tissues s function of spoiler moment. 5

6 Y. Koyshi et l. Tle 1. T 1,, nd D vlues used for simultion. The numers in squre rckets show reference numers Tissue T 1 (ms) (ms) D ( 10-3 mm 2 /s) Gry mtter 2000* 1 (16 19) 90* 1 (16 19) 0.83 (24) White mtter 700* 1 (16 19) 70* 1 (16 19) 0.64 (24) CSF 5000* 1 (16 19) 2100* 1 (16 19) 3.2 (24) Liver 809* 2 (20) 34* 2 (20) 1.24 (25) Kidney medull 1545* 2 (20) 81* 2 (20) 2.21 (26) Kidney cortex 1142* 2 (20) 76* 2 (20) 2.26 (26) Skeletl muscle 1017* 2 (21,22) 50* 2 (21,22) 2.2 (27) Crtilge * 2 (23) 39.1* 2 (23) (28) Synovil fluid * 2 (23) 652.9* 2 (23) 1.84 (29) *1Mesured t 1.5T, *2Mesured t 3T: CSF, cererl spinl fluid. Fig. 6 Results for in vivo mouse rin. () T 1,, nd proton density (PD) from mgnetic resonnce fingerprinting using fst imging with stedy-stte precession (MRF-FISP) without including diffusion. () from the stndrd method. from configurtion sttes with higher-order k. These higherorder sttes re ffected y diffusion in stronger wy nd contriute strongly to signl ttenution within ech TR. Similrly, for n MRF-FISP in which pseudo-stedy sttes were chieved y slightly vrying TR nd FA, higher-order sttes contriute to signl ttenution, leding to the of when diffusion is not considered. It should e noted tht the clcultion results indicte tht the is is lrge for tissues with lrge nd D vlues. For exmple, lrge is of CSF ws oserved even for moderte moments (Gt = 19 mt/m ms). This moment vlue ws lso used in the originl MRF-FISP study, 7 nd ws of similr order of mgnitude to those found in previous studies. 29,30 The sme tendency ws oserved for different cquisition prmeters N, TR, nd FA (Fig. 7). Although there re high degrees of freedom in designing n MRF-FISP nd the is my depend on the cquisition scheme to vrying degrees, cre should e tken when tissues with lrge nd D vlues re estimted using MRF- FISP. is especilly pronounced when much stronger spoiler grdient is required to llevite strong nding rtifcts cused y lrge field inhomogeneities. For exmple, when the moment exceeds 75 mt/m ms, most tissues re ffected y diffusion, resulting in significnt. In the conventionl FISP, the diffusion sensitivity cn e chrcterized y the diffusion time, which is defined s 1 T D = D g G TR ( ) The regime TR < TD < T2 with the flip ngle lrger thn the Ernst ngle is the diffusion-sensitive regime in which the FID signl is highly sensitive to diffusion. Although FA nd TR re vried, MRF-FISP would hve the similr tendency, nd thus T D would give rough estimte of the diffusion sensitivity for different tissues. In MRF-FISP, TR < T D in most cses, nd tissues with T > 2 TD would e strongly ffected y diffusion. For TR = ms nd D = mm/s, T D = 1.22 s for the moderte moment of 38 mt/m ms, nd most tissues would e unffected y diffusion. As the moment increses, T D 6 Mgnetic Resonnce in Medicl Sciences

7 Diffusion Weighting in MRF-FISP c d e Fig. 7 Theoreticl is clculted without including diffusion using the sme sequence prmeters s used in Jing et l. 7 (N = 1200). is mps for () T 1 = 1 s nd () = 2 s. (c e) is for typicl tissues s function of spoiler moment. decreses nd the diffusion-sensitive regime ecomes wider, nd more tissues would e sensitive to diffusion. For the lrge moment of 150 mt/m ms, T D reduces to 78.4 ms. It cn e expected tht the diffusion weighting is lso inherently present in MRF cquisitions using lnced grdients to vrying degrees, ecuse it is prcticlly difficult to chieve fully lnced grdients ecuse of eddy-current effects, concomitnt fields, nd other hrdwre imperfections resulting in grdient devitions. The is could e llevited y using dictionry D+ nd incorporting the dditionlly mesured ADC mp into the mtching process; we vlidted this pproch with the phntom mesurements. It should e noted tht even using dictionry D+, if the ADC mp ws not incorported, diffusion nd could not e ccurtely distinguished nd estimted (dt re not shown here). This is ecuse the sequence used ws sensitive to oth diffusion nd, nd yielded similr signl evolutions for different nd D vlues. Similr prolems re often seen in the MRF frmework. For exmple, it hs een shown tht different pulse shpes used for slice selection produce different vlues ecuse the MRF sequences hve similr sensitivities to B 1 nd. Although MRF sequences hve ner-infinite possiilities of identifying mgnetic resonnce prmeters of interest, pulse sequence components should e designed nd implemented to imprt differentil sensitivity to the prmeters of interest, nd MRF sequence design nd implementtion will continue to e significnt open re of reserch to meet this requirement. Regrdless of whether the diffusion effect ws included or not, the MRF-FISP results showed vrition originting from nding rtifcts when the spoiler grdient ws wek. One simple wy of lleviting vrition is to increse the 7

8 Y. Koyshi et l. strength of spoiler grdients, s ws shown in Fig. 4. Another wy is to use shorter TRs. In this study, we used reltively long TRs compred with the originl studies, ecuse of hrdwre limittions. Modern hrdwre could use shorter TRs nd offer improved tolernce to field inhomogeneity. However, this pproch would pose limittion when the inhomogeneity is significntly lrge, such s in high field strengths nd in n imging volume where shrp susceptiility trnsitions exist. In such cses, the use of stronger spoiler grdient is the prcticl solution to overcome the nding issues. Another wy of voiding is in the MRF frmework my e to use MRF sed on doule-echo stedy stte (MRF-DESS 32 ): to increse the diffusion sensitivity, the strength of the spoiler grdient is vried nd oth FID nd echo signls re cquired. MRF-DESS is sensitive to oth nd diffusion vritions, nd ADC vlues cn lso e estimted. MRF-DESS could e more efficient thn MRF-FISP ecuse it does not require the lengthy ADC mesurements. Moreover, MRF-DESS uses stronger spoiler grdient nd hence is less susceptile to nding rtifcts. However, MRF-DESS hs severl potentil disdvntges compred with MRF-FISP. First, MRF-DESS requires high hrdwre performnce to chieve fst switching of strong grdients with high fidelity within short TR intervls. Second, MRF- DESS tends to e less tolernt of systemtic errors, ecuse the echo signls re lrgely ttenuted y the stronger spoiler grdients nd the signl-to-noise rtios re reduced. Third, MRF-DESS hs more complicted sensitivities to, D, nd B 1, nd hs the incresed similrity etween different signl evolutions. Therefore, specil cre should e tken to design the MRF-DESS sequence to differentite the nd D vlues. The protocol optimiztion 33 for DESS my serve to design the MRF-DESS sequence. Our in vivo study hs limittion tht we did not perform the ADC mesurement ecuse we needed to reduce the mesurement time to keep the mouse live. In the in vivo experiment, estimtes from MRF-FISP excluding diffusion were smller in CSF nd in the region outside the rin for the lrger moment. This is proly ecuse the diffusion coefficient ws lrge in these regions, which could e confirmed y mesuring the ADC mp using fst imging method. Conclusion Diffusion weighting cused y spoiler grdients in MRF- FISP ws vlidted experimentlly nd theoreticlly. Without considering diffusion, from MRF-FISP ws gretly underestimted for lrge grdient moments. The ws more prominent for tissues with lrge nd D vlues. The is ws lmost independent of the ADC vlue when we incorported the diffusion effect of the spoiler grdients into the dictionry nd incorported the ADC mps. These results revel tht the resulted from the diffusion weighting cused y the spoiler grdients. Acknowledgments We would like to thnk Ktsumi Kose nd Tomoyuki Hishi for their help with developing the hrdwre nd prepring the smple. This work ws supported y JSPS KAKENHI Grnt Numer JP15K Conflicts of Interest The uthors or the uthors institutions hve no conflicts of interest. References 1. Cheng HL, Stikov N, Ghugre NR, Wright GA. Prcticl medicl pplictions of quntittive MR relxometry. J Mgn Reson Imging 2012; 36: Koh DM, Collins DJ. Diffusion-weighted MRI in the ody: pplictions nd chllenges in oncology. AJR Am J Roentgenol. 2007; 188: Suhwong TK, Jcos MA, Fyd LM. Insights into quntittive diffusion-weighted MRI for musculoskeletl tumor imging. AJR Am J Roentgenol 2014; 203: Jckson A, O Connor J, Thompson G, Mills S. Mgnetic resonnce perfusion imging in neuro-oncology. Cncer Imging 2008; 8: Henkelmn RM, Stnisz GJ, Grhm SJ. Mgnetiztion trnsfer in MRI: review. NMR Biomed. 2001; 14: M D, Gulni V, Seierlich N, et l. Mgnetic resonnce fingerprinting. Nture 2013; 495: Jing Y, M D, Seierlich N, Gulni V, Griswold MA. MR fingerprinting using fst imging with stedy stte precession (FISP) with spirl redout. Mgn Reson Med 2015; 74: Terd Y. Initil implementtion of mgnetic resonnce fingerprinting on preclinicl 14.1 T scnner. In Proceedings of the 25th Annul Meeting of the ISMRM, Honolulu, Hwii, USA, 2017; Wu E, Buxton R. Effect of diffusion on the stedy-stte mgnetiztion with pulsed field grdients. J Mgn Reson 1990; 90: Buxton R. The diffusion sensitivity of fst stedy-stte free precession imging. Mgn Reson Med 1993; 29: Hrgreves BA, Rpid grdient-echo imging. J Mgn Reson Imging 2012; 36: Hshimoto S, Kose K, Hishi T. Comprison of nlog nd digitl trnsceiver systems for MR imging. Mgn Reson Med Sci 2014; 13: Go Y, Chen Y, M D, et l. Preclinicl MR fingerprinting (MRF) t 7 T: effective quntittive imging for rodent disese models. NMR Biomed 2015; 28: Weigel M. Extended phse grphs: dephsing, RF pulses, nd echoes - pure nd simple. J Mgn Reson Imging 2015; 41: Deoni SC, Peters TM, Rutt BK. High-resolution T 1 nd mpping of the rin in cliniclly cceptle time with DESPOT1 nd DESPOT2. Mgn Reson Med 2005; 53: Mgnetic Resonnce in Medicl Sciences

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