SE538834C2 - Method of extracting information about a sample by nuclear magnetic resonance measurements - Google Patents

Method of extracting information about a sample by nuclear magnetic resonance measurements Download PDF

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Publication number
SE538834C2
SE538834C2 SE1551719A SE1551719A SE538834C2 SE 538834 C2 SE538834 C2 SE 538834C2 SE 1551719 A SE1551719 A SE 1551719A SE 1551719 A SE1551719 A SE 1551719A SE 538834 C2 SE538834 C2 SE 538834C2
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sample
diffusion
measurements
magnetic resonance
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SE1551719A
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SE1551719A1 (sv
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Topgaard Daniel
Lasic Samo
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Cr Dev Ab
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Priority to SE1551719A priority Critical patent/SE538834C2/sv
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Publication of SE1551719A1 publication Critical patent/SE1551719A1/sv
Priority to CN201680077398.6A priority patent/CN108471982B/zh
Priority to AU2016382683A priority patent/AU2016382683B2/en
Priority to PCT/SE2016/051311 priority patent/WO2017116300A1/en
Priority to KR1020187021414A priority patent/KR20180098357A/ko
Priority to CA3008241A priority patent/CA3008241A1/en
Priority to US16/065,086 priority patent/US11112476B2/en
Priority to JP2018532460A priority patent/JP7227438B2/ja
Priority to BR112018012800A priority patent/BR112018012800A8/pt
Priority to EP16882195.7A priority patent/EP3397154B1/en

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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A61B5/055—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves  involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/48—NMR imaging systems
    • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
    • G01R33/543—Control of the operation of the MR system, e.g. setting of acquisition parameters prior to or during MR data acquisition, dynamic shimming, use of one or more scout images for scan plane prescription
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
    • G01N24/08—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using nuclear magnetic resonance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/448—Relaxometry, i.e. quantification of relaxation times or spin density
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/48—NMR imaging systems
    • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
    • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
    • G01R33/563—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution of moving material, e.g. flow contrast angiography
    • G01R33/56341—Diffusion imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
    • G01V3/14—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with electron or nuclear magnetic resonance
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B2576/00—Medical imaging apparatus involving image processing or analysis
    • A61B2576/02—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part
    • A61B2576/026—Medical imaging apparatus involving image processing or analysis specially adapted for a particular organ or body part for the brain
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/40—Detecting, measuring or recording for evaluating the nervous system
    • A61B5/4058—Detecting, measuring or recording for evaluating the nervous system for evaluating the central nervous system
    • A61B5/4064—Evaluating the brain
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
    • G01N24/08—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using nuclear magnetic resonance
    • G01N24/081—Making measurements of geologic samples, e.g. measurements of moisture, pH, porosity, permeability, tortuosity or viscosity

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Description

538 834 An objective :sf the present ínxfentíxff: soncspt is 1:e prox-fíše a naetíxøfä af axïractiïag 'š.nfí11'xï1atien abmnï Which :fnabâe-.fls an šrnpfoxfcxí rcsøšxfixïg povzezf in tcnzqs :af pmbing prøçscràšes af :išaïïusing canfzapawnczzts m” âhe sanæpis. Fufihcr m* aítemaaàivc aahjacïiwfcfs m be unáersïaød íhaïn the føšífsxßfing, :äacamšiïug ta an azgfcct af the prsäeni' ínvemiva cnmccpâ, there is pravšfcïflfd a. maïhocí oïfswzáracting informatínx: about a sanynïe, the :nßiïzøá aomprísímg: perfbrming a pâuraïity of :magneïâc rfssønanc-:f nxaasurenrems m1 the: sampk, each measurenacnt incíuáí11g subjccnhg the sarnpíe in an cncfiašíiïg scqucnca, at šeæst a çari øftha: :sazwace bßing adapted in encnäe a :naxgnfitíc resnnfuïce signaí attenuaâícuaa fil e ha :aucïaar reiaxatíos: and cíifííxsiisn, veharazin at icast one pafanwter s? a grwadíent pzišsc seqxaczaca: of :m erwmiiïxg sequencfi is vaxícd beàwssx: at: âsast a subseâ of said 'píuraiâty fifr1sasureftïxenaïafi, .fmcš .at lass: :me measïarfiinfifni af subset íncšudes s, gradient pxaísa æøqueïaae having àífffuzsiaaxveriaavaïing tsnsør rfrpfcscnïatiøz: *wiâh iïvizffi: âhaæz: om: nørl-zazfø fizígszrvašus, and xvšzeraín šeast a sušfiset n? said pluraâíty* of :neasursmcxsis íncšmífi: encoááng for different ícvcís ofmagzvetšs rfissozlazæaza sšgïçnziš aiïenuaïioaï du: tf: :aucšear reiaxaticsn; and ßxtracïísïg inibrmatzïoi: :fra-Siri the saimpíø frczn signais rfzsuštiaag ämm said píuraïity of nxagncftim rer-Sonance measurernens, (Én: infisrrnaíion inæšuåizxg nuašear reiaxaxtioxl and diffusion charfmtafršstics ïør tha san1pïs3 'Tha inw-'antäfve sonccpt is basaå -zm :Éae ínsšgšït that pris? art prnáøcois efiaabiírlg cåïaxacïfzfrízaïíoiz of šïcferogenesëuä aanšsauarcßpin: .nfnatizríaís .rnezy ös augïrnentad by :ncasurernczïâs encøcíing fm* áífïïerezït íevßis fins. difíèrent ciegfsas) :sf naagrxsztic x'-ifsc»nancæ:: lgxlaí aítanuaïíøn aim: ïø nxxssíšfi' r reíazflation, 'ifhcrebyy cšifííïßiun sbarz-:ctcrífitics may be ccrfeïaïcd With chafaszàfsrísiâcs mi" ïhe zaucíffiar raešaxaticsn m" the nxacïeaa' spin system :vi tšaf: sæxsrnpíæ. 'Eíïc :n-.etEf-.fad hears-e gtsraïswídss a measïzs oi" fas-maräng aaucšeax' 'fsšaxaêiaxrx characerzfsííars of fiivffxasíawx: øozngfiønflnfs än the sanapíæ. “ïšxís may be aclaíexfcáw :aren in the giffefience øfunïy subtie cišíïèreriaes in ïšaa 'imtmpic of anisßïragníc; fíšffusímx mi” ïhe fiomponems. 'š“hus_, :he to chaífavctcríze of distínguísíi properties efiiifïäsizxg cnmpcmanàs rnay hä imprewscíš, A gzøsnïfiçanffinï may *safe-r m a cønqaonenï of àhe sampšf: wfíti: æ disíínct áiffnsšaän characterísiie, such. as s. ciistiïzct ísoifaspflc am 'Éfør anisotïffipis ášfñaszívšïy.
A dífiíwíomenøndíxzg àensør ræpraserztatšawf: of a gradienï pluisfi: sasqzzcnae :may alm bf: reffsrre-:í in 3:; a. -iíšfiïzsâfin--eaacodifïg Itensøx* a'~ag__aresentatíoza ä of a nwagzfietic graašísnt puâsf: acquencc G sf* a naAagnaftšaz :neasmfltmczæït a :anser raprssentzaiíon b, ' »of a gradient puiss S; of a rnagmzâic reßfßrzancc 4 šï :f f \ _ _ Q ancasxxrc ncnt i), E: bcixxg, gisfcïz 'Gi-x f? = šbïššf Våg: , wšufffc efif; a: tamcæíepcizašent C'\ dephasing vector (xvhish is propørtifsszaï to ßníåifzfßzzäf j; is the tärna: of' som íšarmaiieän. ßxccamišngšyf, the gradient gvušse sequenße of the ai ana miæasz1raameïxt oífsaíií subseí inav ba. gmerated sim-ä *that diäzsiflzï cnatodšng 'censur rfipresciaâatißn h of said gradíanï pušse seqazcnce ts more iïfaaaa. Qrir: nonficrø exgezævaíuc-z, 538 834 The at ieast a subset e? ihe 'píurezšiïy' of measmeanexzts ufhcrsšz: at ieeast om: pamatneter of greuiient puisaf seqzzenea: varíed, and šïxcixzdárg ieast one measurenzexxà inešuding s: gradient puíäe sequenc-e having dšffusímx--encocšing tes-nam representatiml ævifh more fbs-m one :xmm-zercf eigenvaiave, naay hc rcšextred ta as a. ïrst. sub-set vi' ihe pínraíity ivfïnnafasslrenizenïs.
The least a sub-set af the pâuraåštj; of maasuresncfaats íncïurïing aansøáíng for dífferen: levels af :nagnetíe ra-:sozæarzace sivnaš stiafsauaieíasmx (hu: tu :malen rešaxaliun n-say “ne 'effcrffeaí to as second subset øí”tE1e pïeazrašity sf naezaaxsfafzneniä. íïrsà subseï and the :ae-små saxbsef. rnzsgf eßnïgašetiäây oveflagfiping (ine. xvhareia: the first and th: secencš subseà :may reššsr ica :ha subset), partšaišgf oxfcrïzzppifzg sr zzonfoveri.appi.n.g, fäfscørriiaagly, each one of piuraíšty id? nuagneíšc rïfsonaance naeasurenwenifls :ay bi: yaeifforsncd using a respefftšwfe cozfnšxiaaatiaaa of a difñssinn f-:ncodíng a mzciear ïeïaxaïiør: ermmšírlg. Tbas: paramsàers ef" the encßcšeixïg sang' ense cnnïmíiíng the eriaødíxagg sf the magncstíc rcsarance signed atáenraaiíøn :has te nufzšcar rašaxation and áíffusiun rnay be to aa a set an* aøquisíií-:m pafarneiers. zfxà' a subseà :of sæšai píuraírïty ofmagneiíc rssunaariae rneasureiïaenïs may he períbrzned Lzßíng different sets of ac-fguísiïioxx paranïeters. fäceøniixzg 'm one enxbøaišxzaent saië at íeasï me paramfeter m" a gfaaåienet pulae scfg-.iezxce is varšeeí “qaeiweezx measufexrxeiïeis if of ihe. íïrst subsetf: te 'provide dífíštrenï aiifïíxsion enaodíxïg in âhe» semgsše. Said at ififasi one parazneier of a graáient pulse seqasenee may 13:-: xfarieaï between measuremmaàs tm encsde tha' dííïereixt levels of signal attenuatiuaa. A: ieast one an' f. conabínairåcßn så a snodušatios: of a grmššfifnt paflse scqufmce, :i gradient amgzâštude, anåiør an awršexxtatían of th: diffzisiozl øncmíiflg may be xfaafíed beïween. rneasafenëentsh .àcaordíng m one enïfàodšnïxent af. ic-:así a saab-set mi" the pÉun-:Éity of :neasuxenxents (ag. tïze seaflønd subszvï.) include :faaeodixag fin" diïèreni iesfeís ef attenuatioxw due to :mass-farsa reíaxaatrïøf: andfm' lcmgítuášïxaš rešaxaiïínn. ffxccøz'ding m one eznït-audiznrzaxt extras-ting ínførmatíon ínaíudes estšrnatízïg a represenàatiøn of a probabilinfy êístfihisâiun iriciicating e, pznbaiïxišíåy to ñzzd. a particular cnnfaïainaiígan of anueieax* rešzsxaàífsï: cïiaracàerasïics am âíffusšei: Characteristics in the Sarxïšfiïß.
'The çazzfïšßabíliiy distršâvazitíævn may tšfms ínüšcaxte em esïšanaxïe ßag, as a nxmwber “ßeïxflaeam G and i) of the praïisaaššíty' m: íikešàšxooá thai a partíßuiar cnmïsízxatiøïa af nxwšeazr feiaaexaiicfn fzharsfsïterisïícs ancš diffusflmfl characterisàics exists in :fine sanígpše.
Tšïf: pwfßšøzlkvišítj; ciistriïïæiïírßxx ïnzsy índšszate a respestivfi: prøbaïsiíšflty' far each ene of a pizzraïítyf nä* aiííïeraiæâ eurxlliïnatíisnä :isf nuclear reíaxaišßn cbezsraeierísïíes and dífíízsíøz: charaee exfšstics, A combination. sf xnicieai* ralaxaatíexx Characteristics and fíífïässioa: øšxaraaceteršstícs may ímzíxadc a combinasšßn of: a íongzftudinaâ zmiífør a ïransversc rcšzaxatiian rate, and one m' more afí; :m ismtrogíc :iiešñnaiaærg en aníscstrøgtsšc cšiffiisiawæz amd :m oriczziatínza of? a cíšfiïxsríon teiamr. 'Éïåïe prczbabiiíïy' distríïfnzïíøn naay estimated 'hascd m: an equzxtšülï relatíng cake signals resuítíng flm-om said pšufaišty of mezzsuremcntä tu ksmeš sind the prnbabiïity disiríbæztšßn, xvhereín the eonnpfineazts m" åhe Reine! are 'uased un an aequísitšmï palrameter anal a diiïusieaï :fr a rššaxæitšøsa cšzaaracteristešc. The pzfcsbaïtníäity dísïributien :may he esïírnàieå ”ajg -e eti-.rrníxxšng a sniuâieär: in the equaïifaim "fbe ueatíøn :may reïaie the .s-ivgrials resušting *fann saaiarå Zgfišuaraíítjv' si' nweaszxrcfixncixis ta prmiufs: ef" :ha kex-nal and *Jae pmbabišiflf :iisiríhutšorn 538 834 ha music-fn* feíaxoxiíssn oharaoiofšsätics onö- ïhs fiííÉïïzsíon charaoteršsïâcs may åëo ostíïnaàed Lzsing the probabišity ršístfíbxatfíon.
Tho nucicaf roïaxatšoa: charaoterístícs oftho exaraotodo íní-"orzna_iš_o:1 nzay include oatšnwate of a transvorsa: reiaxotífiwx: foto andf-*or a lorzgiâudinaaí rolaxazion 'Tho exïraoïed ínâhfinaâiiwz: :nay incâode, for each oorr-poncnt of tíio san1p1fl,, a. :ospooíšflxo osïïnnaito of a transvcrse rošaxatiasn rate; ancífox' a: š_o:1gi'fx.1 dinafl roíaxåatiof: rate.
Tha :šiíffusiozx oharaoâerísàiyos of oxtracrtoii šníoxmaíifm :may inoíuäe an ostínmtfi of :m šsoàropic diñüsåxfštjz. 'šSšfio diffusion chafaotefistics of the oxàraoàad infofatoazïšcwn :may inßšuäe, for oomponoaair fr? :Tio sanefrqfišwo, a respective: onímaàe of ísoàršßpíc cíiffíJsiX-ÉK3I, Tha diífusion cífzaracterristícs of the oxtractcd infann-aktion inc-im o :in ostisfrxato of an axxísaxtropíaf ašíffizoiviiyf. Tho aíífïïxsšcïn, charaßteršsàíos faffïho extraoïad ínffarmatšaun inoiuflo, for saab Ccnfnpofiont fßftl-*æo saoafnpïo, 2: resgvootiïfe of an aaaísotlfopíc» diffusivifiy: Tha (iifàsíoiï ohoaraotofiístícs of *fhc exïractfiaí inforrnaïíon nzay irxciuáo :m ostiimaio of en ofrioizioaeïioï: of a, díiï'us.ior1 :Rosor B reprosoniíazg díífiosion for a cfznnoonoxït in too sample, The dífííxsíon oharactorístšos of (En: oxtracteá .šoforrrzatiçsn ntzay íncíazåo, :for eacša oornpononï of' th: saznpifz, a rospectívo ostimate of an oïísntzætion ofa :ššíïusíorz tonas? å? roprcscnotiizg difzfïlsion íbr said conxponozzà, diffusion »ctorístißs :of the fzxiraacico. ánfomfatšizïx :may inoiucío osiimaæof of tha ešflunoxzis of a: cšifšíssiaæn: tonsor i) ropresoratiïag difífosioz: for a oonæpoïacffiaxâ' in åho sompíe. The difíïasšoozï charaotofístífzs of the oxmactoü šæašlarnzaticßn may šoošuafif; fax' aaah oomgsononfi; in åho sanfqfišo, afstíznïates an” the fziemeaïts of a. :íšffïïisiori tsnsïor B repfessnotiïag áíí*íï1sioni"f,=r said component, Accordšfig io one ombooïixaxonï m: least s. pan oftho onooašing saquonoc of each nïoaasufcroneoï is adapiod to foràher ensx-ofífi a »phasc variation oštho 1 1agnci,íc fesosaaaxco sign-ai ciao to a flow' in the samgaäfe. “ïhe motïfmd may íïxrthor ooznpršso :zxtracting infornfzatiavn aboui àšm sampšo inoâutšskxg flowxf charaoiorisïioos.
Tho nucíoar reåaxatáoxx oharacàerisišcs, »the áifñlsion charaoteïïflsïicß anofor thf: ffmsw= charaotorisáios of thf: extractfzd ínïïzraïnairïon .rnay- ba: med io geoerato Contrast in aa: kiííí ámago of tšxo saafopšo.
Ešríefdfsscrioiion sufïåâxc :irawixxos 'The above, as smell m; acidíišozzfaš ffiašects, íltaturas and axcšvaaaïages of th: prßserzt ínvzfnafíwfe concept, vvšíš os: ífiaàiox' Lanclefstood ährough tina fißâšaæxvíng íííustraiivc and nonfšifnšiiog åetaššoá description of gn-ofmfoai ambodixnen-:s of tïrao prosa-aa: šnxfoiatis-fe concept, sa-'ítïz rcšsrenco to :Em appcruíeai draxvízzgs. íïig. 3 schomati>zaiiy ilšustraïos an of on NïwíR :noasuroanont soqzacaïcc.
Fíg. 2 iâiaas-“zroàes exemašvíos of aoqušsštiivxx garotocols which :nay “oo usoå m oxtract information aoouà a sample.
F 3 iííuszïralts-s an oxanzpše of a rancíon: acquisâïåofx gzrfntfßcflvl which nzay “bo :asocï to cxiraoi íntffjmuaïšox; abouà a. sample and associatocš oxgzofiïnoaitaš rosults.
Pig. 4 is flow cšæarï of a meihaæaš of aximattiiag :ïzzíorzïxatíooo qabout a sampšo.
*Dsïaiicd dosorš oïíor: aäfïffïfsíïeïïoä onïïëøííoíšïïïêïäïß To faoiïštataa zindersianäšorxg o? the prosorzt ínvenove concept, a aåzsoofision of some tïraoomâioai conccnts xviií now' “oo provided veiïh roforonoe io the: draxviawgs. 538 834 Tiwcfry Râïåaxaííøïï. and dšffuxšisxx “NlvïR fixparímenís usi: 11); pcïriïíxrrncd vwåtš: gmísf: sflsagufizxcfis cLt-niprisšïug a "bšfoek xafšfgš: raiaxsziifan vad dšíïfhsšnn erumdíng prßceåixæg a black »with detectiøn as išíustrated :xfíïh :ha gamer-Lai puise sequence: in Féguzre ia ami a. spccific šntqxíclnentaicšfin in Fâgim: lb, Accør-ziinghf, Fšgzzre 'la shaævs em “cncoding block” »všfašch maxfšuíaïcs iha Nås/ÅR. sigïlai according ”fa the vaiucs af the rsíaxatšozz raies and the difY-.ifziøn tensør, a “detectícyn bíucšz” where šhe 'NMR signal šs reaå om (ag. as a åspsc-tnxnw m' an inzage), Figure íb šiâustratßs :m pušse seq-.ience Wim ššíš* anö i. raxííofrzæcgiafinatçf puâsafs (narrøw .and 'wsafš *aeïïšcal äixzss), :naáušatccâ gfasiícnts En three uršhøgnnaí directions (solid, cíasåhsd, am! døtted íiiïesš, and àeïefited siggnai (izïšxíck søiid šine). 'Fhfiz signal is nïodušatecí by 'sfsngiüsaššsxaví rfisßovsry, traansxfersê rfiïaxatiawxx, :and Lšiflšïílsšor; by 'tha factavfs, ra-spaaziíxfely, §jï--~cx;:>{--~r;;,šê;}:§, cxpíêfïgšëáä, :anslå æ>zgæ(-»h:fl) as ufiflí “ae äcscríbed in detail in th: ffiiåanafing: Sâartiflg šrurr an inííiaš. stats vøiti: cfsrnplfïx transwerse 'zïaagïxfiàizeaïicsïl :vik-y ecguaí ts ïfifro, *the fim? 9%” EF puixe fííps the ifingittidwínafa rnagvstizaïion in? inte: the àraxxsvaërsc: píaam. During the tiïmvaizæivay' Wiik. :ïxufatiøn n, iii-f: šcßxlgitazaíifiaí magsæïizaàien recßvcrs tawvards 'aim ihøænuai aquišáíariuzn vakna #24;- wšth the “šcmgíïaazïísxaí Vrsiavxatšsn mia RE. “ïhe ssctfmd 9G* puïszfi ñršps ræcøverczfí maígnaiizaaïígsfx inte àšzc transvfirsc pšam: wvherfi: it decesyfi iøwxfards :fam *with âhc àransvarac fciaxatšon rate få; for a. :ämm pcriød befmfe it is áfitectfid, [šgxfixag f; sríoiš., a. tánmwšatgfififndcïmt magnsiia: íïæšxi grafiizznt. G-(í) {G,-(á) (I,,,(§) Gßàfi? is ap-píâed. 0:" a šíørxaavgeïifizteam aniscatrøpíc mcaíiunl, mc evolution: +31" àšm Itwaš rnßgnetízsxtíøaa = 27,1 " 'ansaty is gâwšsrx hy* the B1fic11--'I'ø1'r:2j,f equatiøn: ti... "11 “<7 fi- (å: f? .- M A _ i m > = i» fyzšägfs- f w v '1:-\»}fn,>,{f,;} u; å? and; ärm (H21 f f ~,, ._ , -fl ' .- _ fi; ^ =~~R,§.fn¿§_:*,ff¥----nzoyf V - IE-ÉfmzÅzZJf) ááš) Ü. :ha cíetectšnn pæršmš san ha avbáaixxeeš integrating Eqs. (Tf: and Q), jršsšzišng f \ f “ f *~ 3 R _ . ~ exgíf f, R; expif rgš? b : Bjfaxpfia» w/Jg, (313 in the derivaïtiøaa m" ššq, (3), št has bean assumcfí ting in additínn :a diffusšuín, àhf: :noíficuics fifma vvith vaíøcíty v thai; rcrnasíns aerzstaaxwâ. :hrcughout the appiicatšiïz: n? nfmàian-ençgzfššfiæ gxfzmšeniä ísgmšsf* fm: ñawë, 'Fšwl ezaaxfszzš*^~<_; íísr- âïr-»szszsâaiionaí naomm is ëxpíít int-z: wšgsgzx* ~-»ï:=xza:~§,s»:zx_zxg smzzzss* a and itâæs xxx1iëšzzøsxiïzfif~azrz-çazâxag::anser äs. f' "i ha . 'I-. __ _ _, 4- __, 1- - flgï sxpressšozl ä; :E ršsfszïzvzafix a ;§f:..s:ía.r ísanüxxxsf, æfleíxzaï... xxfïnï-:zfi »ïxpucxtly b ; B = , <4) -1 xßxhare íg" {_x:,__xf,fr}. 'Tha tmsur b is: gi 'ven b y the integraiš b = jq{f,k1” ífšflfff <3? (i wherszf :gíïffi tha: šfiiraewíepezïâaxït ciephasing Yes-Kn' 538 834 a' = ' fr, ._ . q§f§= rjßàfifšfiff' afiï» ES and n; :ha of :sim førzinatšøn, :Äz-v. wvhifre (å. The vecißr :i eqnaås first anammat va? ïhe graašicnt acøøraširag m ß 1 všëxeäšgïfin (vy Û Tha fish-semi signai S ifs propø-rtâonaí ts tïše vniuxfie šntsgrai S u: å raw Mr. (å) r F01* macrosccwgaâc h.stc:rogenco¿x sanxpíf: xfqíšumfa, the sâgfixaí be vxriivifiz: as an fzrïsfsnføh: auferage of a ionxgitudinai fešaxatiøn fås-tm' (931), transvcrsc rcšaxatiavn factor (íïïgfjs and a transšatæforuaš, mfistion fallet-ar (Tš, 'g \ 'X \ s= 3§«;vw§;:;ï;, :91 wšïen: Så;- ís the signaí wøzfiaí ba: ffratainaní .šf the experiment is :nacka ínsensitšwfi io thf: rešazxastiivxz mid translatiüfiaí :neâíüxl cfffifezïs :aïexzïiozlsíï above. The signal can "im :fxpšicitljf *Åfrin-en as %, J: , äga) i ~ expii- f; fi; Éexgaš-ffczwišg E: : fifwzxpfila: - v/lä, (i T) \ where: smutsa an snserrïbls awrage :war rnícføscfipšc a-.nxfârnnzfnexats *with .fiisïinct xfašueq: 93.21, Eg, E, and v. Tha Åšaxštíaå íaafiensityf 3.3 is tim signed tim ufoušd "se fibtaincd han r; fwo, ;f;=é3, ašš fiierncrats b :mä :a zem. in terms ef' the nxuítídinïensiaænaš pmæbaišæâitjy' disâributiozï, P, *the sig-mi cam hc: sxpreåscd E13! få Sh:*ïizfšiz*3312flàxsflbzzJizzflëgasfavaz*Reg w \. ß m :a to ab :o :za m' ae: f.\* \\* N- «imyrfffffffffKc~>fl§--mW <1» 0 B i? Ü i) f) Û-W-W-W 4. ..annaßnfißzzfinzšwgaavflvlavädfiëafig »víïich is an izatcgrai. :r-flnsførm »väx-are tim kemafiï 531V - -}, giva-n. åßy Kífx:ïzfèzaßšïzsåzsfbzazfbzß»šäsffïnfïwaß»~~ U-Rwßzfgr; -Dm3:a»ÜzzfB23»Ûzsfl/'ißëwvaštï Ü V) [I expífw f! få ff rg RQ å? : Üïšfixp ia - vl I “abc »ašfix'an~áixnensiønal (3 ÉBI: prošvabiliij: dšstršbuâšzvx: :Dfkïghšfhßg g, :Üg-g, Ãïšgg, 1333, Ü;=_3,'V;, V3 ,V3} ÉÛ ïhfâ N01? Üïšiï ïëy Vñïïßiïlg :ha :fšernenïs efthe *vfsícciàiyflefizcvodíxïg veøtor :x and *the üiffæasíaæzwzxacodålig; ïensuxf ä; åh: 3 šnfïøgtfendeznt wfeífscšty cømpnnenà and tšw índepsncícrnt difïfusíøzi tsnsor compmwsxts :ein ba: rneasurßd. Eags. (HT: afad (ä V) reñecff fbe faan :hair the entangieai :šnfctfrxnafšøxa azšwßui the ášffiwfsiøn tensør size, sïzïaapa, ørianiatšøn, tim: flfßxaf vešocity' and the ícxngítudíxxaš and tranxxfcrsc rcifixfaåiun .rateS anay, in aßcørdance xvith :ha prcsem 538 834 ímffzaativf; mcthøci, b: fiiscntanëísai hy carntrøåïing the acquisiiíøï: parametars and acquirízxg the rnuitidinxensioixaí signaê, S, aåxnfc. Nam that the effcaats of spatáaíšy er tenf:;tsø1'as3f incohercaïï flcn-xf, šntra “sfsxffï inceherent mawaíun (Ivíšufl, are accauntecâ fm? in the diffusinfi tansør cnmpzïsnanäs aäcwe åsae (11) ariasí {ïå1*f;f_§_ 'lïšáe puise sequerrae (Fígum ä) is rnßdifïeai ir; :suck Way that time experimentsr 'has confircïš æfåtšxc amquisfítifor: paraznefcafs in ïhf: š<çrnc1('lfif), En *sho pršzzcigfætš sysïmn fsfthe bien-sar, the eígsanvaïues älg-Å; šw-y; and are íucaíecš en ïíw dšagonaí wvâzšíf: all off-vdíagøxaaf: eielnczm; ars zero: n f) n. 'f-,,,,,,,,,,,,,,,,,,,,,., ø-i' Far simpšicšty, the *fštvâšüxvizag azmiysis appíifis to the :pccífic Szasz-x xvhea: bath b ami i? m: axísyzïïnfaetrís. ïàfllsn the âwenasr .is axisymrnfstric, ther: img bï-ñ axad it :faxa be ufrštier: :as a ß 0% ß G (m å 0 :s a, \ ü svíacrs 5,15 bgg and år; am the axiai and radiaí cigcxwaluas, respefstíxfsšyt.
Wåziïc csnventíønal åâffasiøn fnsthosifi are bassä m1 b-tffxxsaërs xvitïï oníy (me nam-zerø æígsïwaízfis, rss-ent meihacis far sàfluáying :nicraxscopiur áiíïasieax anšsaïropy mšy' nn variaiicfn of :ha nllmbei' ofnenfzsro síge-:xw-*ašazes to Acmíe àhc: signa-ai 4sviïh ifiiíärmatíoix abouï the nzagaxâtaisíes, sšxfipes, and Qrisntaïšnïzs av? díffusi-:ën àensnrs.ïS'2Ü*2S*24'21'22“w Vëhasn àhe 'iensrar i? is axísyznïnetfíc, åt be paraxneierizafzi xs-'íth :ha irame b, aniscstraxpy hä, and axríentaiíon ifiiíåš,fiïfl}.24'ï"he *v-'aixxes ufb anci bå are giæfcr; by the axial amcí raáiaí eígcnw-'alufif-s, ö” anê ål, x-fía. .åïflfifëliïfi (34) and (15) Bífffusioxï Nïwfiíš. am? .Ivišiš nfzetímds ïtmed en tšc âiqiskz-xlií“a.nnøx' pušse seaguczuce are Eínaiïad ts the *falun 15A i, meaning thai: bšš is the Gnšy n<>11~::2:'ø cigenvadufi. Isoävroïïic §Éi.ffu.sion. snccsdingzšäls is equivalent fi; m G, inq§i3fšng ašš eígenvaíufis ara 'nonf zeru and c-r-qzlaí: bë by in anaíagy xvítix Eqs. ííffš) and (i S), axialây symmmiric dšïtïssšøn teusÅor-s can be paxarniætzëríëißá vvitš: tšae šsofïfigßíc average Gm, aanisøtxwwpj; DN :and orienâatiaän (ågè), s-vhšcíx are faåatmí m fm: arm; i csígenvašæies, D* and Dm tâzroughzä ”Ü * 53., .Au '\ ssc- få E? 7.13 :små 538 834 Xåfítía this pax'arnetex'šzatiøïn, the tensm' scaïar yarßaíuct in Eq. s: 1G) man ha cßnrasnienàiy expressed as bzmmb' [i -1-zfiån,,_ßggufi=ffißvf;h_fiš, fas; im what-a få is tlëe angle inf: wveßn íhe: nlaíx: syrnrrasztry axczs m” the b and H tensßrs.
Thfoagïï siamšard iriganoanfzïry, it om: be shuewn âhat É9 f-”x ^-...f cssß == aäøsíäir-esši + cesííiš -dg}si11{š)sinšš..
The fizctors “àëšíaænvizïg i: ir: Eq. ífíšš) can be intsrpratfifd an sfïefztâww: dífïsißn cøefñßâent S, Wíxšcš: can be exysíšcíiíjy' 'swfíïten as i? i! + 'EEFÅBAPÉ (ice-s Goos ä? + cosüb flfpšsín Emin :få (gg) Fmïn EQ. (20) it is ska: that ïhe 'cliffusšxfšty :measured 'svíth cavzaveïatioixaš Sâfqšsšszaí- nacthflåß, æviâh Evß is a namtríviaš szombinazior: ofïha propcrišcs of tšw b am? B ïensors.
Assuïning illa: fixera is no c-øíxerfirnt íïøw, v 9, små bath å; and ä) saw: äzxisglsïsxnfitríc, them EQ. (ïlü) aan be fevfritien ax =<- w Q 1 sg.fïa.,,,fz,ge»,a>«à,æ,ffi}mxfif j (i_13;,¿...}§q,~si11@fififi¿§,wíwazëgcëßfil, m u ü c “gig f: f) i v miiziizh is an intægraai. transfum: wfšzerfi âhf: kernaï EQ ~ - ~ Lä, given by :wa ß? :wifi , «~ exp? r i E; sxpi» *r BR: (22) ex fsßísn -ëf 'àísâ Äšéiïg ícfss (êcøs f? + cosííflï) ~ ggšsín Gain ëÉÉ, maïßs tífifif sizs-dínïcnsißrzaå gffíššïß pmbaïvšiiíyf distribution .Pífš;_.ššg,ßtm,ßà,â,gâë} in the 5D signal Slår;,-rg,šæ,fäåfi,í~š,fišš}. Eags, (RE) and :'22 rcfleet the :futazigiaaci inførnxaiiifin aêßcsxat the :íiíïïxsiøn tcnsm' simpa? azršsntaiifan :må the Ioixgítudínaš and. transversc relaxatšøn ratas. in accoráaruas sw-"itšz the present iraventixfc mcïšxazaš, :his inforn-xatícafi car; be: (Éísexxtafisgšad 113' cmxïrošiíng acquisition. pafameïars :mfl acqušriaag :ha mušt~ldixraensiozïzzš signal, S, absw, Non: :hifi the effëcâs af spatíaííy of tenïpøfzary šsacøhcrezxt ñmv ars inešudeci in :ha dšfïïxsšaxn tensør. 'The puâsfi sequenøfi (Figure 1; is naodšlñcd auch way thai the exparíïrxenter has contmï mf the acqušsâiímf: parramaetcrs išxs ksrïmi ('23) ”Hm ašisïïíhutšiwn is xtzaænnszíízsaí: 1:: ->_\ :r i * 'år *P P a , \ ..-~f- _-- (n. j g fyiïš,323,¿.I§SÛWÃ{,_,šš,f,av,2:i:;>s1f: rßdšffißàafi,sí,aïrfïaífš.k === ä; (25) G i! 941319 U íníšsmïatían ahuuâ ïšzs áistríbutínxf: can ba cflziained by' asqxliríng as a šísnctšca: s? (n ,r;,;,b,å=à,,iš,<ïfi) and inxfcïïing ('23). Fm* :Ez-e purpøss: mf :iaiia anaiysis, íšq, (2 i) can ha izxto :matrix form 538 834 'svherc s is *factor 12-5” acquirecš far N :Liifïsrfinï comšeinfatsflons mi” (rhrbšyäbàâíšßßïijg g äs flxcstoz' e? :fmxpïitudcs of ßs-f dissmfiaä cøfrapavsæeïats {_.!=3;§R;,D;_<,,,19¿,Û,:f:), and K is a: .fi«š"*.
Vsišmez: :Ba #13-, Eíq, (i ä) reducfid te üišwbí). :sn 9 which is šndeçezxfíenï af the :íišfissifin tfinsøa* anisøüfaypy Ifiå am csršenïaaiišon Lßšggëjzf *n this casæ, Eg, (2 il: can. be: simp1ííïæelt<1 Siïï/ïïâ-”bßsfi z w \ 'špåüizwgäfiñï däâ f i) ü '13 with the kemai .ííšf- - - } nnw given. by fc: , à, bà šš, få z RE JÉM ~ exp (4 f, Ei - QR: kxpí- blšw I? (2171: xvíïer-:ïf P{R~_.,}?-¿,š),-fl,} :Ås the BI) prøbabiiiïy' aiisïríkwuïšcrxx avi' finåšxzg a dšíïfusiøn tensür co1n§3øne§1ï\with_tš:<2 va3.11c:s,f?;, Bg, :md B59. Åcquísšfiøf: prøïvczæšs* En v-šëw (sf âhe asbuve, :en exampše maasa1.=.'e1nf::1ï. sßrícs :nay ínciude ïneasurenzcïzís with švå efíafi-:r them uxxíïyg as weší sanïpšíïag uf at ícaßt ans of' àíaïm: pafiødfi f; amš v; at more :han an: xfašuc, tifacrcïwy gšvšzzg infnrmaâšgan abcmt the isutrogßšcalßf aves' diffuzsüfity, the ašíffimšun aniæßirswpy, and Jm mzcšear' feïaxaïšøz: of ïfñæ aiiffusflïßg wrnpaanexrâísšš and tia-air cmfrsšaâ-.ínxïsí ïixani; Tåes Lä? such prntocoís dispíaïxßé in Figure Gszsxerašly, fhc gauïse sëfgzxenfi-:fies am Varia: :axch way tšxaï the aßzqušsiïšcæn paraïnßtars in tån: kfirneš (givfia: šfiy equafxioxx (23)) nlay 'be cmatrolšefí, in täae šígasres, .ssaznpicaí daia pašxïïs an: gxšøítså in :ål pßssibšflf 2D prqšccïifæns sf 6D accguisštiosx :passa ufití1iå';a :íšmafisasiøns íøngiàuzšiïsaí. reßuvery ikna n, transxferse dcphasšng tårna :nzignituzie sf m: b~tensur ä, anísoirfspgf si* tha à-»äciïsor 5,1., and srientaííøn si' tha åß tënsur (íšfisïää. Figure Ea, ssïíznavtíon vf SD cavrrešaticzïa oí'ta'ansxfeffse cšaxaàifin faïe RQ, 'isf1tro;ffíc díffusíviiff' Ilšsw clifšusšun terisør axxíso-tfüpgyf 33A, axl-å: dšïfxzsíøn itezfssør øršefztatíøn (ššfigå). Figsm: 2 , enabšcs csitšnflzaíiøzfi s? a. 5D afarrešaíš .n fy? íffinginsfzššaxaí raïaxaàifm rate få, ísotrnpâc åiffuflaiwfítj: Ešm, diffasfzízçr-x: icnsaor anisutropgr 33, and ciíffissíøní tsnacn' orienfaïizßn (zëlqfà. Figure Läs enahies estínaazinn. 09:: öß cørrreieafzisn m? ÉQngit1Ldšnai, reíaxaïinn fair: R 1, tfsnssferse miaxatinxi raw H2, iszøbroyašs diffusšvšt ' ålw, aíiáffifisisïn: tensør axxisotraxšffy' D and áifšïtzsífyn temsnr arâcntation (Ebjê). Figure 'id is símííæsr m firas Fšfigaaïe 2.0, írut šmgršements pseuàcwraneiaaxfi samgwíüxg øf fiac fšf) zaßquisiïíaæz: Tha ßxearfiplšfis shøvvaf, in 2:a aïafi 'b crzabïes sfiïánäatiaxn, a? corr-:fšfitšnxzs bezíwean àšzc díffusršoza tomma' lsaramcters {D,~$._>,1Él>¿,š3,~;å) and íïfm reåaxaàiafin E; m' Kg, rstsnfictšæfešyg mlíiiis the. sanxpïíaag schsnaes in Fígzzre 2G and d. enables :astirnraišfsn »sf :ha aorrešaxfšnns beâwveaz: (íšisßišàšéågšfš amâ bath ofiš; and The éí) aaaqrüsítšaïsn Spams írg,rg,šv,åß,š,išë,iïïfè be saxïzïßíafsïw ævith the pxzíse :fzsagzlsršcs in Figur: ib, ífßtšxsr øptáfans insända :ha pa: saqzieïxc-:fi introaâucøci by Tøpgazzrcšë; anä further mflfiiiíïsci hy Eriksson ašf” m asålßw åån' cøaïtàxuaus saïnpïing af fas :Så dšnaeånäioxx.
B3f adding an irziïíaí Qfi” gfsaaïse and subsfiqïicnt racßvsry daíay 1; to this “âšic Erikssfin 538 834 ai, seqmfaztae, fuií öïš emqušsitiæn spam-e beafomcs acccssíbkf. Aitíaøugh these dàiïïfrent 'praætoccais :may prflwída a-fívaniagas in áííffirazæi scamazicus, it shæwuïd be nuïed ïhai, åh: the šnventive íåea zænderšyšfig :ha general inxfefitíve concßšfiâ, any puísc sequencïe :znabiång prafhing m" the :acquisitißn paranwter nwy ba: zasscí, Prcfarabíy, pssšsf: sequeïxcss :znabling varíatíavn m? the asquisitinn. paramcàers 1' varáahles fif_~zf;,zfg,šf,š;,k,®,flší>) bsfixsfcan the :neasuz-enaenzs ef' :he sxparínmxt :may bf: :asså ïí' the aamisoirapy' b), is rastfícisd bl; 1, åt íbšïQw-”s íímn (Zfífj) 'cäat an ambígisiäiss rezëušt is øbtaínfsd when Då is ncwzsrcs and valuss fif å? and. fi: are unknovøn. Ei* Dim is :fre :main pararneifir :sf intarasá, âšzeïa *sfzneífšcíaí m carry' uni the :rnaasufeïn .nås »with få G where the saoonfš tenta mf' ššq. (Züj: hecmnes :mä the afffiacts af »zíifixsíasza tc-:nsor amšsawtropy' avmå orisntaxâiisn šïraaïøf: xviíí be aíßsfisït fiunfz me: signal S. fäscaäraíing to ( i i) and (3 i fa, comprisíng a inom gcïzcraâ ínïpšeïnfieríxtaàiivix the present inventívfe nïefíwd, ánfcwnnatšfin about aíí ïhf: cicnxents ef än: diffusion :ars-sur få, iíncíudíng tsnsnrs *wšthcmt synametzgf amï ïlfusiaf orícntaííøxx in the íaboratfiry íïaanc af rafemxcs, ihf: šnfåvranaiiün aha-mi fluxaf x-feiacítgf, ih: šøngitudínal aim ïransvfcrse míaxaiiøn can ba. disenïangšed and szozïeiated, Elvfarßzpåeï eapsfnrïfrzerf: En the: fifišßxvíng, an cxzinïpša: u? a ¿31~e:of-of-p1-ina:ipic cxgzeriunz-:nt xviší šsc :iescršïned as wvfsíš tha rfisxiíís themßíf: Ifšarsvziaffß preparfzåffan A revarsß hexagønxaš. iyfstropíc šifgušd cryšatal was prsspareci hy :nixíng sodíun: E53- bisíßeth3«}hexxäx;:)-É fbå šflXn1ï§11tane~2-§L1Efe :um (133 ufrïäí» } with 33,4» tzim®tï1fyfåpe11ta4ne (_ wVtÉP/Lw) anfí avatar (f-“áåš vwëffè) in a, 3G viaí. Afïsr exifizxsíxfe mazmaí mixíng :mä fieïitrifugatioïz tu :wake iius: :nixiurß hümegeïxefizië, 9.5 m1 vvæas itraínsfexrfed in a 5 flxnzïflšïvíšâ tubes. Üfhc reværsc hfifxagcnaï phase: is tïrwrmßaiyïaanzizzašlg' sâaíaíe at 25 'ïílfí and inte e: reverse rnicešíar phase at ešaxfated tenïperaifurc. "Fhe Sanzpíe was stuàíed a: 29 “C wxfšxers tha revfs-rsze haxagßnal and reverse míceíšar jphascs afiocxist, :Råiflš affairs: crcgz.f.fsz'äsføfie NïvíR ex¿1§vr1?n1f:n.ts xx-'zare paffmïïaificå un. a. ššfukcr fåïíI-.íüíš spectromsisa- :xpcratíng at: 535.13 MB: EH resßnzmcfl šïaqusmïsgff. Tha spcüåromster squipgfifxi. With sm HJ? T uitïäshifišdfid nmgmæt fitïfifci. “wfith a ïvíšíïëš caicrøímagirwig pmba capabíß of cieíšveïíng magnctic fiaæid gradients vfiti: ampšštazaie 3 Tim in ïšrrse orthuganal dirfzstâoxzs. 'ïhc iiquiá crystaišins sample xwas sfixdied wviïš: a nïqçšifiecå æfmsion. n? the tršpšfæåatiznïišaïeê ßcho puäse: sa-.quence intreducefi by 'Fepgararaššfl here aiiowíng íiær signal e-ncudíng xn-itšz :iii :sf 'the variabïcs ír;,rf¿,š,š.>å,išš,®fi as càssøribed in the theory sectían abfix-wz, The apprnaeh en” randønq sennpíísag, as ilšxasirateá 'in Fšgurs Ed, vfas zzasaí to sfsâeci 1624 pøinïs of fail? acquisition space. act. .ai xfašucs of the asquisitšaæn *Jaršahšes are fixfzwm in Figgures ša-b, Folšnwwíng 'she puísf: sßquence black *with reíaxaticßïa anaš fiåfñisißn cncawzíing, signaš »was sšfitectefi as a» free: ízaducïion deøay (Fïïšä, e, hfågäaafzzsohßtifzn spszctnm: upøn Fouršc-:r transførnzatíøïl. The 'water :rænnance- 'aina »vas šntegraifid and smvrcd før further anaâysšs.
Data arzaåßFsí-.ç :and sfíxuašizfizrsk>rz Tšxa 6D distríkyuâion estimated ïsx* nusnfizršcai im-'erse šntegrai ïransífffirrn ïafïšcg. (21) « - - 'i í » så. using a nan negatws šeast squarss QNNLS) :neïhod . 538 834 Ta wásuaíixc ih: ccnlgaaixents sf” the six--ziiznsnsâonai 55513; gfirobahšššty' distrihuüflwn H32;,ššg,íši$f,,üåä,íå,ffiië, än: :zompßnsaaïs aware conx-fnivficl xßfiïh tha kcnfiifå and anappei m å: gaicš. 'ïhfs sämsta-ai cmzn.pnnf:n.ïs of ,ï}¿¿fi}__,_ wars ufifid m caifièäilaais nriaxïiatiaëx: aiätriëïztšaës: fixncïšøïl (íšïšï), Hffåg-*BL :which wviis áíæpåajfcfi spïrasficai :inesh vffíth racïšurs scæfleæi by êbe dirsctíoëizïíšy' damn len: vaíue m? š-ïf šlgíf).
A síïrnïíar g-røcfzdure nmy bs whsn inciudársg »feiecity cncoding and. :zsßwàšng før all the dífifízsíon fensm' ešernenzs accøniíng m Eçgs, (Ai å) amd (i. 'i få.
Ercarrgnïenïbr ßbf-zfz'fzf'ng raswfïs* fr: Pig. 36.1) Tim 633 distríbzxtiøaa F{_R1,1~3;¿,i'>,¿w.í}¿,9.ç5} fifsïízinfatfixi. with. a hfifiïstirflppíng procedura as følkmfs: å) fåfranga the signal S amfi zæßquisition varizflf-Ies (jr;,'zf;,š2,¿;gå,횥,&í1f) as Pak 1024 :t-nšaanfln xfefimrs. ~^ ~ 2) Läs raracíorn sarnpäing x-*ziàšx repíaccsnent ie :za-sats a “buntstragw fesaançše”°“ of the vector s frorn 31:: fåalš set nfae-quírefš nian: points. 3) Crsats .eïf == Síêü “a=srnpat~nfinïs” by' saašectírzg random poáxzífi tha ëD Uf:fïfišlLšogfišàyiogíißši),š<:g{,ï3_¿),::osiffi},f,í2} space xwithin the ïinzíïs - 1 fl ïßgíhfis) få i, 4.3.3 f? íøggšffiz) ïš 3.7., ~iï f? šøgqfifšëí) få 43.3. »ii Eßgíßi) ~» 8.3, få 129519) å, ami G fgëfš 11% (Ixmverå åugšïiïfi, iegi: 3213, ÃOgiIÄDEEZä, ïfigíiëiiâ, and cøzšéïå) to RE, 562, IRL, and å, :) Canverï and 2.11 :o lägg ancš 23A wfíth Eqs, iié) (_ iïf), 6) Expand. the “vcfctsrs wifi: M eicnwnts {;?;,R2,Ü.;S,,,D,Ä,fi,ç5) zzzïd clerncnts (tg _. ï;_.¿>,¿f¿,奚,*ïï} inào .fïíxN 1naïriceS, få (faic-ušate the fvflwhf mi-vtríx 'with the .kameš K by' inse-ning the (1É;,ÅYE¿,.Ä¥,YSÜ,.BÉ\, 94512» {-rj_.rg_,à,.ö__à,®,<ílß} nëatríccs iztato EQ _ sfâiï). å; Sa! *e (iïåj) før the .Ii-f = 5% ccxianfnn veartnr p rising ÉwNLS ïncthnå. Läs a nøn-Eimitínfg exampíø th: íssgnønnafg rmitiïaf: Of Iwfïaàiab ššâülššz :may ba: usedšá). 53) Sciect :åns cmnpanmxts wviïh non-.zexwß xfaíues in me; vßattnr p and díscafd the nïšacrs. iüfïvíutate” the caßnxpanezïts fran: stegfi 9) by rmaitipi.yín.g th: vahics (af (ifšhâg, ßwïfiàf) xvith randam mmhcf bøiwzfen. 0.9 and 1.1 and by adding random narmbers hctawasn -2° ami 4-2* to fflzfa angíes (åågäq _ i i) Repsai step 31:. 1172.) Rx-:place conxpnnezzts Emm step 1 š} wítå: the. nan--zera cflanzpøsxcnàs frmfx: step få and the nmtaiad søfïzgaiïanazxäs ia. _. ïß “i 13; steps äšyš få.) ïüg tírfxas :ziniså “ *- ššflzz: :šísïeïšned »factar p. bl; Rsgveat stup: 2'}«I' 3:) 'íüg tírnss 'm crfirzzxàc- a Qi* 3 G3 wficfiers p. íiišf: the coxfiçan anta *with narbzeiï: :azxægfišwíízxašaë the RGB sfecïoïfls gp. lfïsåíïalc-ušate aïí possíbïe- šï) :uni 23* prqšecïíuns øf_šl{_ššfl,.šš*g,íl;,y,,ílï,åjæ hy íšaussian søzrvøšutiflsn Qi” the iíiscreiaf ar-ørnpaaxæents frisim step Ei) ontß iDGfi-r ÉGÜ rscfl-:axxgxxíaf in the Éíogßäï), íogíšššzfk, iøgííäm), and šog{¿JH/1l§¿_} V7; šiïisplay* :Inc 233 and ED distïšbxsïiozas as canfscsua' påßts and tracfis. 18:: Sešsct crmfnpnr-.enizs with š?¿š.-"D¿ > 2G. 11 538 834 Caícušaïfi the micmïaïion fiisàributiøn ñaïficticië. Pgfâågzö) hy Gaussian conxføizxiiífzï: ef' the åšscrete cornpfsrmnàs íiïïsnf: step 19) anta a: spšæeïícaí :rzssh "eøšth 303' nodcs, ïššspiay' the ašâstríhmxïiawn >P{9,çf>) a sphefifiztvziï nxesh wizh ihc: radšufi íbr ëaeša :nash paint samlad by the carrfsspfßnfiling value caífP( šåçš).
Ræ,v:¿«:š1ï.s' F ša-b Shan-v me aaquisštifaxx prntocoš sign-ai S' and; vahzcs nå" frå, rg, år. 15A, få, and üß as funcïiøa: ef amquísšàicvn nuníhar. Prošectizwzas of the: fasâi :ïaàsol :išsiríšïaxtiaaaa P(3šš;,í<í2,_šI->;$,,,¿I?¿,ß?,qfi} síisgsíajvfcai in Eíwrc The shows 253 pfasjccfittiozïs fbr each pair si' pazraxsïaeïars Eg, Kg, àïšggn, :and .Ûw-*kïà (cmntuur pëavis) wvslï as 1D gr-:øjflffitiøxzs (hfacfifsš. The sign-ai Sw sszaïc1aíatßfà fšfnan âhc àistríbutíøn and resícšzzzxï (SW 51-5) píøttfió in Figure: 'Tha values u? (Såfif) ínaiícats a. signaifltgwraøiss raíšo for aiata points acâ-qušrfsd with f; mo, :g G, and i; f). Since the studied sarnpše cørrqtsršsfzs: rexfsrsaf micfiššar and rarflaæzzäc 'axexagonziwš phaacs, we expect àxvø :va -ar aomgmyafzzzïs svith :šistšzzzs-i: xfæxšues nå" ihe :iiffusisvrz emxfsøirøpy: oïvf: isfitrsæpíc; ccnnpoxzcrlt fran: ths revarse rnicešíes and sne xwiih vaïues evšfßcï approachíng i. Sianíaxg 'safåtåä EQ pfçgjšectšfïsns šïâif), Pífig), 1>(¿?;$.¿}, anrš šføfiïšfi-fßl), »va inom: that :ha twfi cnnagoneaïïs aan only' 'mf rssošs-'cd in the R;- IlI*5¿.»"l3¿-dšn1cn_$ions, vzhile thsy are indšstíxxgaxishaíuís in àths RE» and äs-v-hcššrnensions. ”Fhfz gueak vøídtíxs incíxxíe cimtrâbïæàions finn: ä: zmcermínïyf, gšvfiníg risfi m ciífšèraænt pøsiiíons ef* cfirnpaniænts lär each af :Exc- bfintsfárap Tïfzc: resolutiozx in Rydimffinsion nxakss it possibšfi: to date-ct suhtíe áiíïerænces in Dgw än :the 2D projffction Åüåïšíyßïššäa) auf! io verify ïízaï bmš: c-snïgvoaxcnts havfi ídemícal få, in the: 2D projeuïíun Pfiššhßïë).
'Tim 5:a Fšgurf* Se. shnws th: 2D ørianàatifßn fiisïríïrnstiøn flznßïían (fílïßiï) Pflfléïfiçfi) fn: the: cnmpønenï with I i a spherícal .faaasšx with radiuf-z scaåeai by* the: ciímctšonaíåy' dcpcndent xfaíue af Pí ååçlàß 'Tim Fdnctiøx: infáícznæs thai fin: srystaíšites øf the; revørsa 'zæexagoïsaš are alšgneaš in än: dia-emma ïhe Eabnratoryf rc-:Fcrc-:nw íífirne, *sæfniciä cøizxcšdes vvíih àhe :main nnægixsïifi iïeíd. illezsrfxråtzišfßfi :Lgfezvzšëfldirrzeffzis Fig. 4 iíšustratss a genefaš fícxrv chart of a naeàåafßci fßf cxàffaactirng íníhz-xïaaiíaa: afnfiut a saiïxçic. 'The sample xzxzay' for exampiæ a hšošøgícaí sanïpše inciusiing avatar, such braízz tisszxa var ïvíßgtfisëy saimpšes n? (susgsesnsionaf) of 3:13: organs cclš, Tviore gensraiíy, the saunpïe inciudafl. a nacka: spin. systern »whose propærtias may nïeasurad. íßf; :nafieíic resønaïzss tarcsfnxzicglißs.
'Fila methmí rnay' bf: períixfxïfififd using a. siaflcæsíltíxcfisznt NfviR speaifoïneïeíx' s! Pvïšíï devic-s. is xafeíbšanvoxfaaa En :ha an, .fanrh aiewises may :include ene m' :nere gamc-essors 5:11' ofintroíiing ïhe upcraïšøn, av? me: aievice, iratef aššia Izhc genwaïíon of the :nagzïefíc grasššsnt puåsfi: css, tim acquisitim of as xmzíi as samgaïizxg :små digiáizing the mßaaairød sšgxlaís fm' šbrmíaïg :Éwía rcprcëentiïzg acquirfisí signals, Tha gersßratíofi: of the reíaxfiaïiøn enasoölšng sequmces ari-:i the diffmšnn encocšâxag magzxetíc graclâmï puíse seapmnizazs ny? bf: šangflamezxïcü :as-ing softvøazre instauctíßfis ævhícïz :may än: stnræd :m a corrspxafier rfsafiabša nas-dia (amg. on a ncmtrsiaxsítavzfy amngrutax- rczldahšc sturagc mediuzïaj: :må be excafzitzëaå by one sr :nam pmcessørs mi" the devšafi. Tha sofnn-'ars šnsïraxciíaxxzs :rzay exasfnpie be stored in a. pre:granficfzxzïfoš sacïioaa ofa :nsnxory of âšfw devâer-c, är» xvhích the one- or rnøfs prøssssørs oftha ciax-fšce Eaas íïnaiificted dam :figareåazsnting the: rneasxarcznexxts may 'ne stored in data. 12 538 834 mßnzow m” the aíævice, m øf a cnnwpuit-af m' the like. xvhích may aomïeaztfzd tha dsvíae.
Tha infnnnfatšfßï: cxtracïifsfa and caašoušsstšarns forrníïag parï oi' :nšztïzsná :may be psríïcn-n-:cá hy a pracsssíng åcz-'ísfi The operations nmy ha ínapïaarnxentcii in a sei mf” sefifåt\ffaz'e ínsmicïicsxxs which :my be :itorexi or czinb:;aaíieaå nn a zmn-iransitory caurzïputai' rfzadabíc mccíia and ba: cxceutcd hy the pzxuecasíng, Em' ínsizmca 'Läs safïwxfajfflr inastrïacàrianns :nay 'as stef-så år: a ;>x*og:'an1f'co:1âr*š Seat-iaf: of a. nïenafsry' sf the NMíš specïaxäxnæter f' NER! :šexfise ami sxecïsteai by mv: ar 1110:13: proet-ffissanf axxxiis of tšac spscffsømeïer f' de fins. Ncwfiflfez* it equašly passibíf: to many :mt the caašoïsšatioxxs m: za dexfíue »sfhšsšz is sagaaraíe íåroxn the NåAR sgmctrfxzxxetsi' af ïwfííiš dmficeš for axaanpíe am a. cnnzputer. “šfšïs :íæxfšce and me coanïnnsz* nïay' fm cxzxmgïie he azfangßfí ti: mzmnunšcats: via a coïnnwuniczatinn nsâwwrk such m: a: LANffKÄ/'Liffxšš 0:' Vis. sanne othfifi' Sexia! ar paiæaíïsí cænnnurxicaàisïn šnieršace. i: shamšaí funkar ítfe :ams ihai, instead of using äøftwfare. ifist:'11<::ïšxt«ms, tha aupafraiixxx: sf the nmzfthçuá naay ha ímpismsnïerí a pmcfsssírag dfsvšaf-e in ih: forna. avi* :ícfíicaàed aiiwtruíiffyf si' the devšcf: f' aompuiex' srmh as in min: m' :vara inififgraíad. cšfcuíts, år; one aa' man: appïicaiÅfin-specífis isaàagræztcê ciaxsuits (låíšïíïs) m: fšcidqßrøgranïnïvabis gaia amagvs (FPGAÅQ), m maine a ífexæ-f fixeæïnpíes.
Viith reference to 4, :ha nïethød cømïgršscs perfona-:izag a. pâurašity of magnctíc rcsmaancs mcaäurcnuemïs m: "Läs san-:pšc ístep 4ü2~l tiarøugša 492-11), Each :measure-zman irlcfiudes subjcctízzg iâxe sarnpíe (ie. :he nxacícas' system af tåw saznpíc) m :m cnæodixfmg sequcncfi of sncfiåíng block, At Esast a para mi* the fincødâng ssqaaczacc-z of each :neasarfsmeziï iæ adaptad ta cmzade a magneïic fcsonazxcæ: signal attenuazíon due *m *sofia :mcicaï rcíaxaàíøn anfi dífifäasífin within the sarnpša, The pharalíiy ef :nczxsuzxïnacïais nuy ba. perfnmxeflš i: ssqzicnce nafhz-:rcin the nïcasurenlcfiïs are ps-:rfbrnxefzcš in tisrra, :ms følkrxvízzg aix(:iï'1f:1'.
The sncøàing' seqzasncs fifeacfš: :nfiasazreæïxenï íncšuzícs am RF' signfaš sequencaa eflcodfirsg .<1 pafftícuíaz* reh-:xaàiøaï sensitiviày' in ihf: sarnpïie. The encavcííng sequaence så" :ras-h nïsasxxrernent further šnciuaíes a ågradierat puise seqxaeiace pqøxfiüizxg ciifñxsšoxa enwfiing in the* sarnpíe, Pig, í :šisaï-æzsseai eariifir íšíusâraiøs unc pawsesšvbïe exaazïzpie anfan ense-Släng *oi-ssk including an RF signaš sequsnce :må a gßsdric-:at puíse equencfs. í-ïcsxæ-fexfer, ßther tjøpes nfferxcøding ïxšøcks are equašiy ífvøssibíiæ.
Generašiy, boíh spin echø cncøaiàaags and stšrmsšataai echo sncødíngs ïnay ha useií. ån. eitšaszf case :ha RF siggnaš ssagucrxcc may cïxcøfía for atzafxxuatífin due w :mšy iongštudifuäí, :July transxfersf: ireíar-:aïiøn m* bath Éøngíàudinai :na-å àranvëvfifirss faíaxaâi-øn, Ünc exaanpíe secgïxmzcf: may ímsšmšfi a åsšngie 90° pzzfise aanai za singic 38%* ïfiuïse. The 'simíng axfths gmšicní se guaznce in rfsiaifm w :ine 180” puísfi may isf: varisci. Fm' instans: the ggwaàícrxt guzísfi: samla-noe :may be gsfirformfsd pråm is; m* fiubseqf-.lent ic- the ïâåü° puEs-z-z. Sfzxferaí sazch seqazcnccs :may bf: rspeaïcá beiiara acquisíïiønfáafzeanïíasrz.
"Examífiïes of stirmxlafsd æcha: sßaguerzces :Ray incíucâc a ñrsi 9G” pušse; a seaomi 90” írfïišsa and a third 99* "file gradifint gamlas s-eagueaase naay be psaføzwneå :ha th: second. FBÜ° pxaísas, andfm' sgzhsfisquffnt m the thirö* 9G” puisa: (ia. “afsefbre »the dctccàies: bšøck). 'ïšzfisc exatnqaics sequerxces ears lï-refl-wfcafer nfeerešy' gazxßviáeaš ilíustratixfe exaanpíss mixer seqacnaes are aisø possíbšs, Encoáiaag far :ššfåïšzrfsrat ífiæfais ufsâgznai attenuatíørl dm: to 'ïranswersâs reïaxatšàcæxu amífor imzgiàudinal Wreíavxfitífsn :may "be achieved by varying a. relativa timirag of the pušses cïfišie RF s-'ignaå saqucncs. Fm šrnïtanc., En ihc -szxarnpie sequance såßovm än i different attenuatifar: due to traxmfcrse reíaxaticwzz nïagf isf: achiavad Ewy* vaxyiiïg f: betvmcn ai Eeasï a subset af tïäe snßasursfiïents, 'Üiffersni atíaruatšfixï due tf: 13 538 834 íoïaígitxlfiiïnïaší rešaxaffion :may Abfi: achifsxfsfi äy xfargfing 'n bcixvcen Bzast a ssfisfzt m? the maasxxrexriarats.
Each zïæezsßçureniexxt oífiha plurality nfsxaszasureïnaaxts :may 'incšuüc an encøding hissa-k providing a ræspcctwe c-snaïßánaíieæxz of a reiaxairáfisn sensitivity' ezicuaíing and áiffusimæ cncaxíing. “Fhs paremwtcrs of the cnæodíxag ïuíosïz. canïztroiiizaíg àšm rešaxatícm sensitivity and fšiífïzs-ian cnc-Gciíng, :sf :aaah naeasxærcznezat may be refafimïd, m as a, se: af acquísítímz paranasters. 'äïfitšx reference to E., each cornïsixzzztšaan m' se: :may :ïæïsïmëägïsxïsiëršš nä: pašfïšszzzíefzz' 'gsæçšsfià fx: tšše ilšustratafë. acquísitiøïa space. ifkccsßrcâíïagšy' ñrst åšxr åwš 1311' at? 'i ;_..\¶¿"ɧ.::f§1ší§¿,f of :nfzessxlrcnuzïxts may incíuàe :zncødiaïg yvïsviišššxfsg a. lâï-fsi: (är 'ššäš ïfznffizxí n? sígnaš aïtcnuatšnn :Líxw m nucíass' .rešzæxatiøaa små :i âïïïsï fån? isšš áššïíïsšøxz. vaës'š.=fi:<ëaíš_sïigg. A seconâ (of (fi-ëšjïh) :neasurfinzszni mf' the gtfïuraíiïyf si' :measurements naay ínáf-šsšaíaè mïfisixšjšzfigg. *§z*<>~<-=šs:å“šzx;gï; vaà-:ëxmzš šm* .älšfiä kfxfei of attenuaíion :ïazä :in mulšmar :fßšzsxzäšiazßm amš a xaäsøzxzí im {Åš~š' \ fšííïhßsiaëa: e§1§f0dir:g_ The seßimd êfaa' {>§~i~;í_ _ a? ' flaåš". ašïïàïfltzfiëšfšäššïw rišiifi m iziàšç rïíaxafišun :may bf: difšeren: man: sr eamzsš ä: ïhi; cfsf .šflfiš šavafš, 11%* s: * a.à§:f:::â:¿ïšø:x due tu :aufisiæar reïaxatiaän. The: sacmxå šaäiï sj'š~š*zïiïï-f'““'_š aiíëffiísšíxßf: :ïzsïaikïåššëg may* -..§¥:“'e*t§2=ï fram :är fsaäuaâ ia the års: (nr im) cšáíïusíßïx fizxcfafiing* Measurements naagf be acqyišrcd in an :srcífzz-íy' by parførsnírag a .små of series of nïaasurcmsfits whsfsšn, fm cash series of nwasxsresnexaaïs, :me paranfsxæïcz' varšerí bemvccax :neasurcmænts and :ha :väser paramstsrs are Exffšd ñxßïí fšisaíavsøaš in àh-e aïæwøe exaznpíe experiment scctim: it aïsø pøssíbâe to pcrfarzn rnaasurcanenïs xvhiïe randnzníyf gaaraxnctafr cor_nš:=i.naài.nn.s *within the acquásitígwn sgaaca: ot°i:1ts1'<:st.
At ífiz-:sï 9:16: si' ïha piuraaíity ef mfifessurernents includes an :fncßäing hšock ccmxprising grachsïït pxsšss sequfinße bax-ing a. difiízsiforveïzaaædiaxg :armar ïs;f:rssåa:1t.atio:1 b vviïh man: :han om: nønfzæro ašígenvalue. Tim graáienä. pulse saqucïace 11%' each sne ef saíê at ica-s: :me of :ån-z pâurašíty' of rncsureznfifnts include snn-dušate-:i 'magnctic ñfifíä gradíafnïs in ørthogonai aíírsctíaæzæs. Läs may b: :xndenstoavai finm the âheury sccííon., thšs anabšes isastrawgvíc xrïliffusíez: anæorïing in the pie (íïn-wíying a âwtafns-rn' wštíx 'three non-såra mld equal s-zígfznvaiuicäl) cs:- anšwtrügfiic åiffzxsíca: encoášw in the in 'avs ar mura dinïcnsíons (ine. ašn: perpc-*nsíšcuâaæfl geørníafiricaš axfifs).
The mßasLu-emsnts, mïiïcr than ti v, iaf-ist naeavsmcïncxzt šnciuding a gradient sfiquence having a diffüasínwzwanuflsaiíng tensna' reprflsantaïíon b vøâtša »mmuiz :Eran :mc non~z1ïr år: ísoítmpic dššffíssšør, an_ísfin'opšc ë-ifñsšon anáfbr gradient puaíse sequesaces praxfíding ønædinxcnsâcnaí díffïxsšawzæ fsncøcššxxg (ins. “stíck” dâfíízsïíon enr-ssfiing sequcanßes). fkísfantagæavusšyf, :nfsre than ß-n-f m” tha-f pïurzflifj, fßf rneasureïncïafis :may irzciufif: graëíenh puísc sifqusnçtes vwhích has/fe» a: respective encodísag ïenmr repfesantaâioaa ä; xviti: :han ma: nnnßzfsriæ aiganxfaíuc. 'E“}1:: of" isauârfßïßio -tliíïasioïz fixæcodizïg awniißëzwr difïïvssnà dfsgraes amd/ca' mícntations s? aïxiästriøgæía diffusion cziæøfšíng away be mš:~':aaš«n,caí än tha sarnpše fm' sašçš :aims :han :ana nzæasxirfixnfizxïtws. fkscuvrdíxxg to :äs sfnethod, ai íeasï ana paramctïfs' of tha gradienï pušsc secgumcaæ šs vaxifid “natwcffzn a: šsasi a sušfiset ef me. pšuraišiy of rneasurmnezaïs in prnvšxíe differmt cíiíšízsíøn ancßciiaag in the sanzgzšsâ, Far instans-e, an orícniatšun sf Vibe gradient pušsf: sequcnce :may be varíeâ ëetwsfcaz: 'measurements to ancßdf: diffusícn in difiïarænt dšfeßtíons sf tha smfnple. With referera: in the abawe tšnam-yf amd cxampša experiment scctšnns, thf: at Iaast ene pazfaxtnfifcr ef the gradient pxxísaf sequence :may irzcíudie the paèramsâsrs išš andfegsr (i) *which :may he varg-g; benwßeï: a suïßëet of píumííiy af zneasurernsnïs. »v .l :w b. 'aa 14 538 834 The at í-aasi me: pzxrazmïfter si" the gradient puåsc scqucxïcs my “de warifzfl heiwccn mcasurarnfinïs tu :matade for diffizrsnï 'aevfišs of sígnaš. atïenzxaïíeëi: dns m aišffhsšon. For ínstaracs: a maxirnuirl ampšitude øí tha gsadíaxxt anašíuz' f. rncxíuïaíåøn of :the gfadšænit puisc søqzxmcfz :may be xfaxied baâxvsen measureanmalrs. ïífiïh rcfsrcnee io tha afbflxfe tïmcwry' and exampâe expfirimsnt sections, the at âsast cm: paramaàfsr uífihe gfacíiemt 'äsc secgzzerzcc: rnay include th: pairamefiífirs if» amífnr šfå.
Eaciï rneaisxarfirzaent 482-1 , ..., 462-11111213' inciude a àetacíion "Jwíøszši (mf. Efig. i) ufhcrcín echo atbzzïuaïion, signaís fcsíísïxxvàng ïbe. crxstodíng scquenco :may ha rficßrácai, 'ifihe gnai rcszihïívng fifim tha fifsïnmíííy ufanafaæxarenwzfnís may' ha: recoráed dam. The dam may ha stfnxed åäö? f: fiber data, processing. ”šfhe data nxay for ifimsirazïcc be stores? än a. data mcxnisry' oftha device, m' oflaf. ccunputex' m' âhe Eíke “afi/'fiícåtz may ha con11s<:ïe§š to dexícß, Wítí: reference m :ha ahm-'c àšzeaëry and sxanzpåe ax periment secàísëns, íthß data meg: Iacuïcåad "in se signaš vector al. in ætsp 464 fafthe izaeïhmí, infbmazætíøn :ämm the sanïpšs :fxtracited fr-nni the signsziæ resaaaštxfng flun: i-hf: pšurašiiy mf' :nagneâšc rasønaxace rnezimarerraeixts 4824, ..., fï-íšiïfix. 'Thff infomxatifisn extrac-tecí im step 494 incšuåšzß xmcíear reíaxatíea: and. aiišïusiüïx characifirístiats fm the sampífi. A probaäiíity* dístríbuâiíawn may hä: fistíïnatøaï wšæízshí indicaies a prßbahiíity' ia íšzïd :i parâicmfiax' cßïnbåzïatiozl of nuszíaar rcšaxatioaí: characïeršstics and fišffaisioa: cšzaractfifršsiics in the sarnïlwis.
“She prnbabiiity dšstributiøn rnay br: estínmteai based m: :in uatißn rešatíxzg echo signaís rsamšàirag fimfn said pïuraíiây of rncfisursnients “m a, kemfifš ami the prob-abífašiy' fiiisïríblitíøsï, måasrcšn ïbcf Gostnpønfints sf the: kærneí are baszfsd m. an aßqušsiaínn paranfxetfiæs" armé a fiâiïiízsšøn m' a rašaxatízxn chawautcfistio. The fiqazaïšøn and ma: Rescue! may fur ínszâanue “ha given by Equafíczzs li amš 11* pfzfsafzatecí in :ha thexaryf sfzstšazx m' by ecinzatícns 21 and 22. Tha processing dafafiite .may pcrfnrn: a nxmzfiraí aiguriïšznz fur sstirrmšïag thf: gzrøbzsíæíâiiy disàriïsyation, far ínfštanca: by pcrførmšng a. nuïnmrícal. šnverse ímsgraš árazïsåågrsz: offi-.qïlation H of 21, 'íïm probabíšíty dístributim: prøvšdfiæ rlzxfqvrnzaiian: ahfmt tha :axaaåaar rfz-.ïaxzæïiiøxï characteñstícs and síifïuaion cšæaractefistics of the dífñzsing comp-zßnßntís) n? ih: sampie. Fm' ínstaæce, pariiexaiar cønïbânatâazfln of mielear reâaxatícßïa cšinraßàæristícs and :íífäzsiøäa cšfsractæristícs may deterrnimad to be prcsmí in åke sampíe if the pruïëabïíííty distfšhutím: ímíšcæsßtss swsbstzaniizaí probahíiíty for this particular ßarnbinaåíoax (eg. a, prfibašvšššïy exzf-ecfäšng a prcáfetemínæd threshoid prøïxabiššáyfs.
Data represemiixzg cxtrazcifsá šïïíbwnatiaï-n (saach as the probaïinfiíïgf fiíísíršbutíivxä araífšía? a: cmïzbiiæaatiøníwiïafífiinaïiüns iaf ïicífsaï reiaxaïíøn ßharaicïerisàícs and diffusífiax cšzaramïsristšcs åeïerminecå to ba: in ihf: saampše) nxay be øufput by the procmsíng dcvíc-c amš storeai in the: Gaia wanna-ry, ïäfití: retïzrence m the absve theøqf cxaznpša sxpfifrânz-*snf sacïínzïs ïhe. nucififar rcíaæxaïifin. cšïmaaàferistšcs may íixciufí-a :m csâíznatc nia transvcrss reíaxation raâe R; azuifør a, iongàtudizïai rfcšaxatšon, :rate E; for cash cafrnponent in tha sarnpíæ.
The difïusioxz: characâeršstics of åhf: extractcë, ifírïørrxæatiura nxayf insända m: cstimatc af :m isoârßgfiiz: :íifiaisiwfity fm :faah canwpofiæexxf in the sampâe, Tha sstânflats nå' thf: isoïmpša: diffusšwfiiy :raay íšßr irzfitarace b: cgvlaaniiiíïcd by :ha paranvstez* Dm ess câefiïafid the àhcfiry section.
The cííffusíün characxz-:Iíswiics u? :ha extrastsaí inibrxnatiør: :may incšzzde am cstirnatc ofam axxisütropšc âííïzxsšvâáy far coxnígøzaent sampic. The cstšinate ef the anisfltropic díffusiviày may fm* šxxstaaïce be by Bå åeišfifid in fsagxeatiawz: in tíïe tšxeory sectiøn.
The fšiffizsiesa charaßteñstics af the extfactcd infaannaciaun :may inc-ände an, cstimaw of an ørientatšfin ef a dítfñasiøn tansor E) rcpreseuvzšng difñfusšaxx: för each 538 834 caaíszpßxxcxxt in the siampía, 'fixa oršanåïaišen may fur iawtaruze be quantíñcfi hy åçf: aieífnzäd in iïfic ïheaary* ssctríms.
The difíízsiun charaßteristtías m" the cxiraatcai ânšsrrnaišßflf: :níay irïaiaafíe extinmtes of the æâeznents of coxnpenents of diífiasioz: tanßøa' Q rcpræzsantâng díffiçxsíøn før each snnæponent in ïhe sanlpše. The eïemenis sf the dâffusifln :anser i? rnay inc-lucia 13-; 1, En, Dy, D23, 133; as deñmsd in tha tïnerary seaàiavn. .åcccrsaiíng to *th-c rnethnd a: Eeast a pan af tha* encøclïizxg sfiquc-:nce af each nxsasurfianssnt :amy funkar hä: adapâffid ti: srecødc før a gtsšaasa vaxfíaïion af the :nfagnetic 'rcaonazfice signziâ due ti; a .fïfmf år the sarnpše. Tšxf: flfßuf serasitiviqwf rzææay íæc enszedvcd ïfiy cßmïroiššng wfelocitä-wanccfdšng »factor a. êeñzxeeí in fiquatšøn i? in âfnc thcury' .äecttíaäxn For instance, ihf: vešocšïy-encadixxg var-tar a. mßay' be vafisaš Evfiiwecifx :neasuïfime-Ixts ßfaï a :subset of the “pluraššiy mi' nzeassxxreïnaïzts 45324, ÅÜÉ-n. nxethoaíå :may asconfiíaagâyf further conægvríse extraåctšng šnfcrmatiøa: abfiuï, ïhf: íkgm-sf ahsnfacäsršsiics, in :ha šrrøezxïiæfe aøfscapt has maink 'man descríbßd 'with refsrcncc tc» a. išmítsaï nuaïzbafx' of exavmpšifs. Hfiævex-'sfrig as is rfiadííy :ipfpfracšaïcd by a pcrsøn sšailšed in ïíw arà, avthez* fixampïfss: âhan tån? finfäs diæckussci añsßve ara eqzxzišiy' pxfissiífßie mfithix: tim sccpe of the šnvfiixiiæfe oafizzcegaï, as cífzñxxeii by thfi appendad cïaíïns. Fm" insiasaßif, the method fflšsczzssed in caxuïcctiean vf-'íïh Fíg. 4 may än períofmecí as an NMR :n.:..â§'1nfï \afhssreán the :neasur-aaš sigïnaís refïmzt the distributâmx :sf :haracærâsišxss of the samapša The :neasureïnenis may aslterïaaïvfsfe be psïíbrlïïc-:í as part si" an Pvfiiší nxethawd. 'in that case spatíaš :faacocšiaag naay ba: appšíeci ti: 'am sampk: in s. :naxzsxfzr 'which per se is knowvn in tha Sšgzwšs S nmy áhfireby be acqfziïed 'íhf #321 få; pixeifvwcxfvsí sf tha sanqaåe and ínšímnatíøn šnciudšng the nzuzíear rsšaxaàšnn amš díffíssâøn Qkaractcrístics äíscxzssc-xi above naay ha extracted on a pixeïfäfoxai hssviä. The extracted infønnaiíox: fnay accordinginsf ba :asså w gcnarais æosxtrast än MRí ixnazga. 16 538 834 avs discšfiašure, ene or :nom nuinbcrs än superssífgfit ïsfcr to a csrraspaënciíngšy' :aumb-.zræd :ræíëzrexæass ciocasmsmï in tim foííoxafing Iis: a: raferezacas: iïfwí. S. Prins. :Všïfšå cgfäraszøxï-ffizrrfiï-unzzš :rzøzíøæ (Cambridge U :ivfirsityf Pauxas, Canabrrkâgc, Éfšiïšë).
ZP. "i". âlïaiiaghasz, Tfxzrzsäaåzlfßnaš dyrmnzifxß* nza__gfzartíc.f rss-ønafæcre (Üxford ïšnivcrsíï§f fšress. Ûxford. IZÜÅ šK.. P. Vxfïaíttai, and A.. ïvíacšf-lajy, I. Resan. S13, 334 flíåäššïfi. qE. Û. Sïfiëjskaí, J. (Skam. Phys, 43, 359? (1953. :få mine mfg. ßxw. ißsï. 1192 (sväva).
”F š. Bäasser, E. Äfïaïtiaílfi, and I). Bihan, Bißp'n§,fs. 3. êá, 259 íïlfš94). #1. D. Tüurníea", S. Ivíøri, amí Å. ífzenfaans, ïwfíäigrz. Rfisfiuri. Nífid. áš, B32 (ÉÛÉ 1:3.
Mari, R C. hä". *Jam Zijï, ÄVšR. Bšosfnetï. 3.5, f-šéåš (2062), R.. üärsiner, amå A. G. Safensen. Raniiat. Ümzol. 21. 14% (lm E; i .ing ä: ;z:'..,fï§?vššš ššš.i§r;n§x§.. 3:3, š. (Éüüåï). 4_ ;,-..- *ff-R :ä à-fièiïfrß. .Fšïgffi .B än.. .¿:@>95f:. “šïfl íïäaïzæg., små ¥}._-{š.- {I:ï::'};=.;š} .«§:f:x. ïïšszzr.. Sno. EEE. “E35 ifš 9991:. *ñ-ä *ii :::-a.§§<:._;3.§>.-1.:.. wc: ii; išma, s; ïffiyë. 12.9, m3: gzfifm). šššxeïzxesíx ai., NMR Bífmfxcd. 133, ïfiš? (BÛÉ G). m3. Finsïaz*b1z.s-:E1.,.A:1§u. Ešsp. 'NNšR Spcctrøsc. 72, 225 (àêš. šfa.
Tßlagaard, hfííarnipflxrcalss Nícsøporøns ïk-fïafåfsr. Eššâš, 48 {2í}í S). 335. Erškssoxz. S. ï).'š1@pgafirai,_š. 2%, 15 (2313).
Tnpgfiard., hiiczxzzpfiroxis hfšssagwgarßus ïvíaïar. WE, 5G (ïäüííß), 203. Lasiš ef? ai., Front. Fhysias 2, li (ÉÜIÅIL QÉJ. Sjöíumš e: ai., J. ívíagfi. Eason, Z-íšï, 15? (2015). ïšléïff. Szczepasækiæwflicz e: ai., Nfiumifnage HM, Z-'iš (293 S). fÜN. Síietfzïcsl: ef! ai.. Rasen, švšeßí. in press).
Eríkfssavn ef ai., J. Charm. Fhys. ÉÅÉ. ífšflišiïš íjšíiiíšfië. al, P. de .fähxxeífía ßíízaríizzs, and B. Tnpgaaærcï, ššubxnitïeä.
D. "i“<>1:mi::f1*e.ffai., Nexnfašnïaga: 23.. 11376 íšßfi-fi).
C. "šïärfeg PEWS. Raw. .ïíš-š, 563 (_1956). '“'Åx(I.~F. Räfßstíx: e; ai., ívšed. ïrnage íïøifnput. Comput. .åssšsn ïntsrwf. N35, 2Û9{2Ü14}. "ß-s. Mon, .ana F. s. svz. van 9:31. rvnlgn, Rfisßn. mm; n, çlws). ß. .ma n. a.. šfiíwß, NMR simnfia. 15. 45.5 gzonz). šiåiæssaï-n. e: azí., .Éïzægjjfâzcriznis anafpfßfifgfrrzzris' än zetzgeeïfsaäzø* fißfzfiëšon (åshfn Vxfíšey 30113 Lcd, 1998). 1” :fm namn: føfkf., nanci., MA, 5).
BBB. šifrzm, Išia§n1etríka 53, SSE? (íššffšïš.
MC. L. Lavøsfæn and R. J. Hansen.. ššlsšafifag* ifrasz sgu;:zref.s~ prøbfefffzs (Frentšca-ëizaïi, fiiïngïcwcød (Éïifiš, *NL _i9?4} 17

Claims (11)

538 834 Claims
1. l. A method of extracting information about a sample comprising: performing a plurality of magnetic resonance measurements on the sample, each measurement including subjecting the sample to an encoding sequence, at least a part of the sequence being adapted to encode a magnetic resonance signal attenuation due to nuclear relaxation and diffiasion, wherein at least one parameter of a gradient pulse sequence is varied between at least a subset of said plurality of measurements, and at least one measurement of said subset includes a gradient pulse sequence having a diffusion-encoding tensor representation with more than one non-zero eigenvalue, and wherein at least a subset of said plurality of measurements include encoding for different levels of magnetic resonance signal attenuation due to nuclear relaxation; and extracting information about the sample from signals resulting from said plurality of magnetic resonance measurements, the information including nuclear relaxation and diffusion characteristics for the sample.
2. A method according to claim l, wherein said at least one parameter of a gradient pulse sequence is varied between measurements to provide different diffusion encoding in the sample.
3. A method according to any of claims 1-2, wherein said at least one parameter of a gradient pulse sequence is varied between measurements to encode for different levels of signal attenuation.
4. A method according to any of claims l-3, wherein at least one or a combination of: a modulation of a gradient pulse sequence, a maximum gradient amplitude, and an orientation of the diffusion encoding is varied between measurements.
5. A method according to any of claims l-4, wherein at least a subset of the measurements include encoding for different levels of signal attenuation due to transverse relaxation and/or longitudinal relaxation.
6. A method according to any of claims l-5, wherein extracting the information includes estimating a representation of a probability distribution indicating a probability to find a particular combination of nuclear relaxation characteristics and diffusion characteristics in the sample.
7. A method according to any of claims l-6, wherein the nuclear relaxation characteristics of the extracted information includes an estimate of a transverse relaxation rate and/or a longitudinal relaxation rate for the sample.
8. A method according to any of claims l-7, wherein the diffusion characteristics of the extracted information include an estimate of an isotropic diffusivity.
9. A method according to any of claims l-8, wherein the diffiasion characteristics of the extracted information include an estimate of an anisotropic diffiasivity. 18 538 834
10. A method according to any of claims 1-9, Wherein the diffusion Characteristics of the extracted information include an estimate of an orientation of a diffiasion tensor D representing diffiasion for a component in the sample.
11. A method according to any of claims 1-10, Wherein the diffusion characteristics of the extracted information include estimates of the elements of a diffusion tensor D representing diffiasion for a component in the sample. 19
SE1551719A 2015-12-29 2015-12-29 Method of extracting information about a sample by nuclear magnetic resonance measurements SE538834C2 (sv)

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EP16882195.7A EP3397154B1 (en) 2015-12-29 2016-12-22 Method of extracting information about a sample by nuclear magnetic resonance measurements
BR112018012800A BR112018012800A8 (pt) 2015-12-29 2016-12-22 Método para a extração de informações sobre uma amostra
PCT/SE2016/051311 WO2017116300A1 (en) 2015-12-29 2016-12-22 Method of extracting information about a sample by nuclear magnetic resonance measurements
AU2016382683A AU2016382683B2 (en) 2015-12-29 2016-12-22 Method of extracting information about a sample by nuclear magnetic resonance measurements
CN201680077398.6A CN108471982B (zh) 2015-12-29 2016-12-22 通过核磁共振测量提取关于样本的信息的方法
KR1020187021414A KR20180098357A (ko) 2015-12-29 2016-12-22 핵자기 공명 측정들에 의한 샘플에 대한 정보 추출 방법
CA3008241A CA3008241A1 (en) 2015-12-29 2016-12-22 Method of extracting information about a sample by nuclear magnetic resonance measurements
US16/065,086 US11112476B2 (en) 2015-12-29 2016-12-22 Method of extracting information about a sample by nuclear magnetic resonance measurements
JP2018532460A JP7227438B2 (ja) 2015-12-29 2016-12-22 核磁気共鳴測定により試料に関する情報を抽出する方法

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CN108471982A (zh) 2018-08-31
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