Methods for quantitative relaxation parameter mapping: measuring T 1 and T 2

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1 thods for quantitativ rlaxation paramtr mapping: masuring T and T 2 ISR April 8 th 29 Hawaii Paul S Tofts Chair in Imaging Physics, Brighton and Sussx dical School, BN 9PX, UK : w: qmri.org w2: vrsion y. Introduction. Th principls of masuring th two rlaxation tims of most intrst, T and T 2, ar givn, followd by practical approachs. Quality assuranc using phantoms and normal brain whit mattr is dscribd. Approachs to implmnting tchniqus on commrcial clinical scannrs ar givn. An up-to-dat vrsion of this documnt and th accompanying PowrPoint slid show ar availabl at in addition to othr matrial on quantification. Th radr is assumd to undrstand th basic concpts of spin and gradint chos, invrsion rcovry, rlaxation, Bloch quations and slic slction. Although T 2 * masurmnt has not bn discussd, th mthods ar similar to T 2 ; howvr it has to b rcognisd that th masurd valu is dpndnt on how wll th magnt is shimmd. 2. Principls of T masurmnt Th longitudinal rlaxation tim T is dfind by th Bloch quation for longitudinal rlaxation (in th absnc of an applid RF fild): d o = [] dt T This is an xponntial approach of th longitudinal magntisation from som starting valu to th quilibrium valu. Aftr a puls of flip angl (FA) θ, th solution is: + t + + ( ( ) ) ; ( ) = ( )cosθ [2] = ( - ) and ( + ) ar th valus of just bfor and aftr application of th puls. For rpatd application of th puls at intrvals TR, w hav: ( TR) ( ) [3] = and th stady stat solution to this for ( - ) is: cosθ ( ) = [4] Th signal is proportional to th transvrs magntisation : = ( )sinθ = sinθ [5] cosθ

2 Thr ar 4 main approachs to masuring T : a) Partial Saturation rcovry. Rpatd 9 o pulss ar applid, usually with a spin cho. Eqn 5 thn bcoms th familiar form: ( t) = ( ) [6] By using 2 valus of TR, th ratio of signals givs T. Optimum valus of TR ar chosn to giv on squnc T w (T -wightd) and on PDw (PD- wightd), i.. approximatly TR =T and TR 2 =3T. Using a rang of at last 3 TR valus givs good prformanc ovr a wid rang of T valus; qn 6 is last squars fittd to th rsulting masurd signals. For this approach to giv an accurat rsult, th 9 o puls must fficintly dstroy th longitudinal magntisation; this is particularly critical if a short TR is usd, sinc th rgrowth of is small and any rsidual magntisation lft aftr th puls is thn significant compard to this. B rrors will rsult in a flip angl othr than 9 o bing applid, at last in som parts of th sampl. This approach is rlativly slow and infficint (compard to th spoilt gradint cho mthod, whr a mor optimal FA can b usd s blow). b) Spoilt gradint cho By moving from a spin cho to a spoilt gradint cho, TR can b rducd whilst still giving a rasonabl SNR, rsulting in a much fastr imaging squncs. Th signal is givn by qn 5. For a narrow rang of T valus a pair of masurmnts at 2 valus of FA suffic; ths would optimally b T w (high FA) and PDw (low FA, oftn with som signal avraging). For a larg rang of T valus a st of at last 3 FA valus should b usd, and qn 5 fittd to th masurd imag intnsitis. Inaccuracis aris, particularly at short TR s, from thr factors: i) incomplt spoiling of th puls (so that stady stat transvrs magntisation builds up), ii) longitudinal rlaxation during th puls (th puls duration is not ngligibl compard to TR) and iii) FA rrors, particularly at 3T. Th mthod can achiv good covrag vry quickly, using a 3D acquisition, with typical TR valus down to 5ms. c) Invrsion rcovry. Both th spin cho and th gradint cho mthods abov ar vulnrabl to B (i.. FA) rrors. Th IR mthod, although slowr, is intrinsically mor accurat bcaus it dos not rly on th application of a puls with an accuratly known FA. Th gnralisation of th IR squnc is on with 2 rpatd pulss of FA=θ and θ 2, sparatd by an invrsion tim TI (whr θ and θ 2 ar nominally 9 o and 8 o ): [θ TI - θ 2 (TR-TI) ] n (2 - ), th valu of just bfor th 2 nd puls, dtrmins th signal: ( cosθ ) cosθ TI ( 2 ) = cosθ cosθ2 [7] Stting θ and θ 2 to thir nominal valus of 9 o and 8 o givs th familiar qn: TI 2 ) = ( 2 ) [8] ( 2

3 Howvr th mor intrsting outcom is that for arbitrary flip angls (i.. qn 7), by adjusting th invrsion tim TI, whilst kping θ, θ 2 and TR fixd, th signal taks th form: (2 : TI) TI = A + B [9] whr A and B ar constants (which dpnd on θ, θ 2 and TR s qn 8). Thus a st of signals at a rang of TI s can giv an accurat T valu, rgardlss of B rrors, and without th nd for full rlaxation (i.. no nd for TR»T). Th downsid to this IR approach is that squncs ar rlativly slow (sinc th invrsion tim must b includd). d) Spcialist mthods Thr ar a numbr of spcialist mthods, which diffr quit substantially from th convntional mthods dscribd abov. Ths includ Look-Lockr, DESPOT, DESPOT2, and TAPIR. Thy ar oftn vry fast, and somtims can function in th prsnc of B rrors (although at th xpns of wors SNR). Thy may b vulnrabl to off-rsonanc ffcts, and usually rquir intimat accss to th R imagr to implmnt th squncs. 3. Principls of T 2 masurmnt Th dfinition of T 2 coms from th Bloch quation for th dcay of transvrs magntisation (again in th absnc of an applid RF fild): d = [] dt T 2 A FID includs dcay from both rvrsibl and irrvrsibl ffcts. By forming a spin cho, som sourcs of dcay ar rvrsd (rfocusd); ths com from tim-invariant sourcs, principally local static fild inhomognitis causd by sampl suscptibility or magnt B inhomognity. Any obsrvd dcay in th cho coms from irrvrsibl (i.. tim-dpndnt) ffcts, largly arising from motion of th magntic dipols. Th amplitud of th spin cho, aftr application of 9 o and 8 o pulss, is: ( TR, TE) TE 2 = ( [] ) Of cours this is rducd if th pulss with nominal valu 9 o or 8 o ar incorrctly st (providd TR>T ). Providd that th pulss ar lft unchangd, and that only TE is altrd, thn w can still obtain th corrct valu for T 2 from imags collctd at svral valus of TE. ( TE) TE 2 = A [2] Th rcovry tim for aftr th 8 o puls is variabl (T rc = TR TE/2), and for good accuracy TR should b kpt long nough that TR-TE max >5T (othrwis th longr TE acquisitions hav rducd signal, giving an artificially low valu of T 2 ). Practical squncs ar oftn dsignd to produc two chos (a dual cho squnc) by using two slctiv rfocusing 8 o pulss; th amplitud of th 2 nd cho may b rducd not only by T 2 losss but also by incomplt rfocusing by th 2 nd 8 puls. Thus to obtain an accurat T 2 valu multipl chos should in principl b avoidd. Slic slctiv 8 o pulss ar particularly badly bhavd, and in multipl cho squncs can giv th phnomnon of slic thinning, whr subsqunt rfocusing oprations los transvrs magntisation. Thus progrssiv cho 3

4 dcay may b sn in a multi-cho squnc, vn if T 2 is vry long, as for xampl in watr or CSF. A hard (nonslctiv) puls will rfocus bttr, but usually cannot b usd in a multislic acquisition squnc. Thus th gold standard for T 2 acquisition is likly to b a singl slic singl cho squnc, rpatd at svral cho tims, with long TR. Extra slics (wll sparatd) can b addd to improv covrag and spd. Th accuracy should b monitord; this will dgrad as slic cross-talk incrass with slic numbr and closnss. Thr is no such paramtr as T 2 2 T 2 drivs from Bloch s thortical modl of nuclar magntisation (qn ), and in ral biological tissu th transvrs magntisation almost always dcays with svral T 2 valus 3,4. Watr compartmnts in diffrnt biological nvironmnts ar sufficintly isolatd from ach othr (i.. thr is slow nough xchang, at last in brain), that ach on dcays almost indpndntly. In brain whit mattr, th signal from four compartmnts can b obsrvd indpndntly, using a singl slic multi-cho squnc, typically with 6 chos, timd from 2-ms. Clarly rfocusing is crucial, and hard 8 o pulss ar usd. With this insight, it is vidnt that stimating T 2 from a dual-cho multi-slic squnc is quit fasibl; howvr th stimatd (mono-xponntial) T 2 valu will dpnd crucially on th TE valus chosn, as wll as th quality of th rfocusing puls. 4. B ffcts ost of th mthod dscribd for T and T 2 ar vulnrabl to B (i... FA) rrors, particularly whn run in th fastr mods. Th four principls mchanisms ar: i) inaccurat and variabl stting of FA in th scannr prscan procdur ii) slic slction ffcts in 2D squncs produc a distribution of FA valus across th slic profil; modrn 3D squncs largly ovrcom this ffct (although th pulss ar still slightly slctiv) iii) dilctric rsonanc, particularly at 3T and highr, causs th RF fild to b highr nar th cntr of th objct than nar its priphry iv) th RF transmission coil gnrally producs a nonuniform fild, although body coil xcitation (using th body coil not th had coil) largly allviats this problm. To obtain accptabl accuracy, good modrn mthods all tak account of B rrors in som way, ithr by stting out to dtrmin th local FA in th objct, or by dsigning a mthod that is not snsitiv to th particular valu of FA at ach location in th objct. Thr is now a rang of mthods for mapping local flip angl; som ar accptably fast, accurat and asy to implmnt Quality Assuranc using phantoms (tst objcts) and normal controls Quality Assuranc is an ssntial part of dvloping and validating mthods for mapping rlation tims 6. asurmnts in phantoms nabl th accuracy (i.. closnss to th truth) of masurmnts to b assssd, providd th tru valus ar known. Tru valus can b masurd using a gold standard squnc (i.. IR or singl spin cho), which is xpctd to bhav wll, or by using publishd valus for th phantom, basd on th concntration of compounds in th solutions (although this approach will hav accuracy limitd to mayb 5%). Phantom rlaxation tims usually incras by 2-3% pr o C, and thrfor tmpratur control and monitoring ar ssntial. Phantoms can b mad in-hous quit simply, or bought commrcially. asurmnts in normal tissu, usually brain whit mattr, ar mor ralistic than in phantoms and nabl in-vivo rliability and rpatability (tst-rtst, or random rror) to b assssd. Th rang of normal valus is rlativly narrow (CV about 5% 7 ). Rproducibility dtrmins how snsitiv a masurmnt is to changs causd by disas, ultimatly dtrmining th powr of a clinical study (whthr cross-sctional or srial), and should always b in our awarnss as w work to produc good masurmnt tchniqus. A quick stimat of th accuracy of T and T 2 masurmnts can oftn b obtaind by looking at th CSF valus; T should b about last 4.5s, and T 2 2.5s. Poor rfocusing in a T 2 squnc will rduc stimats in CSF, oftn quit dramatically. If whit and gry mattr ar th principl tissus of intrst, with much shortr rlaxation tims that CSF, thn stimats in ths tissus might still b accptabl. Sourcs of variation 4

5 includ imag nois (which usually is probably NOT th limiting factor in dtrmining rproducibility, particularly in larg ROI s), scannr instability, subjct movmnt and obsrvrdpndnt analysis procdurs 8. ulti-cntr masurmnts prsnt challngs which naturally forc us to considr th masurmnt mthodology in dtail 7. or information on QA philosophy, phantom dsign and normal valus of rlaxation tims ar givn lswhr,9. 6. asurmnt using a clinical R imagr Implmnting tchniqus for rlaxation tim masurmnt on commrcial R imagrs is still not straightforward. Rlaxation tims ar not rcognisd by manufacturrs (vndors) as having usful applications (as distinct from diffusion tnsor imaging or spctroscopy, whr thr is now much turnky softwar supplid). Som basic squncs ar availabl, along with analysis softwar. Howvr th mthods ar not particularly fast or accurat, compard to what is possibl with in-hous squncs and analysis. To writ and run in-hous squncs will rquir a rsarch agrmnt with th manufacturr, and som local R physics xprtis. T : Th mthods of choic ar th spoilt gradint cho (SPGR) and fast invrsion rcovry (FIR). SPGR is radily availabl, and 3D squncs giv good covrag in a rasonabl tim with littl slic slction ffcts (typical whol brain covrag at.5x.5x.5 mm rsolution is achivd in minuts). Thy ar howvr vulnrabl to B rrors, unlss a B masurmnt can b built into th acquisition, and this limits thir usfulnss in quantification. At.5T, using body-coil xcitation will control th B ffcts, and th rsulting B nonuniformity will at last b fixd for ach subjct, providd th positioning is controlld. FIR is slowr, yt bcaus of its invulnrability to B rrors (qn 9) it is th gold standard. IRprpard fast gradint cho or IR-prpard EPI is usually availabl. Providd th radout componnt is kpt constant, its imprfctions can usually b ignord (th P-RAGE concpt). By using a small numbr of phas ncods pr shot, or a short cho train lngth, good accuracy can b obtaind, at th xpns of long acquisition tim. As mor phas ncods or chos ar takn pr shot, accuracy dcrass slightly, which is offst by acquisition tims bcoming practical. Typically an accuracy of about 3% can b obtaind in minuts. T 2 : ost scannrs will hav a dual-cho multi-slic 2D squnc, which uss for radout ithr convntional spin cho or RARE (fast spin cho or turbo spin cho, whr svral chos and phas ncods ar collctd for ach shot). Ths provid good covrag in a rasonabl tim, and ar probably accptabl for most tissus (although th CSF valus will most likly b too low). 7. Imag analysis Simpl analysis can usually b carrid out on th imagr or an indpndnt workstation. or flxibl analysis usually rquirs stting up of an in-hous systm, typically basd on frly availabl softwar for display and simpl manipulation, oftn supplmntd by a commrcial high lvl programming nvironmnt such as ATLAB or IDL. Tst-rtst ffcts in th analysis can b studid, to find th contribution to th total masurmnt varianc. ROI analysis is a straightforward way to masur a spcifid location in tissu; histogram analysis nabls subtl ffcts in larg volums such as th brain or a tumour to b quantifid ; Voxl-basd morphomtry (VB) nabls many locations to b tstd without bias Rfrncs Th books by Haack t al and Tofts 2 contains much rlvant sourc matrial, as dos an arly papr 3. Th qri.org sit ( has matrial on quantification in R. A rcnt papr 7 on multicntr masurmnts is availabl on lin at 5

6 Rfrnc List. Gowland PA, Stvnson VL. T : th Longitudinal Rlaxation Tim (chaptr 5). In: Paul Tofts, ditor. Quantitativ RI of th brain: masuring changs causd by disas. Chichstr: John Wily, 23: Whittall KP, ackay AL, Li DK. Ar mono-xponntial fits to a fw chos sufficint to dtrmin T2 rlaxation for in vivo human brain? agn Rson d 999;4: Whittall KP, ackay AL, Grab DA, Nugnt RA, Li DK, Paty DW. In vivo masurmnt of T2 distributions and watr contnts in normal human brain. agn Rson d 997;37: Laul C, Kolind SH, Bjarnason TA, Li DK, ackay AL. In vivo multicho T2 rlaxation masurmnts using variabl TR to dcras scan tim. agn Rson Imaging 27;25: Dowll NG, Tofts PS. Fast, accurat, and prcis mapping of th RF fild in vivo using th 8 dgrs signal null. agn Rson d 27;58: Tofts PS. QA: Quality assuranc, accuracy, prcision and phantoms (chaptr 3). In: Paul Tofts, ditor. Quantitativ RI of th brain: masuring changs causd by disas. Chichstr: John Wily, 23: Tofts PS, Collins DJ. ulticntr imaging masurmnts for oncology and in th brain. (in prss) Tofts PS. Th masurmnt procss: R data collction and imag analysis (chaptr 2). In: Paul Tofts, ditor. Quantitativ RI of th brain: masuring changs causd by disas. Chichstr: John Wily, 23: Boulby PA, Rugg-Gunn F. T 2: th Transvrs Rlaxation Tim (chaptr 6). In: Paul Tofts, ditor. Quantitativ RI of th brain: masuring changs causd by disas. Chichstr: John Wily, 23: Tofts PS, Davis GR, Dhmshki J. Histograms: masuring subtl diffus disas (chaptr 8). In: Paul Tofts, ditor. Quantitativ RI of th brain: masuring changs causd by disas. Chichstr: John Wily, 23: Haack E, Brown RW, Thompson R, Vnkatsan R, Chng N. agntic Rsonanc Imaging: physical principls and squnc dsign (2nd dition). Nw York: John Wily, Tofts PS. Quantitativ RI of th brain: masuring changs causd by disas. John Wily, Tofts PS, du Boulay EP. Towards quantitativ masurmnts of rlaxation tims and othr paramtrs in th brain. Nuroradiology 99;32:

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