Overview Excitatin & Signal Cllectin Prcess The Principles f Quantitative MRI Geffrey D. Clarke Dept. f Radilgy University f Texas Health Science Center at San Antni Gradients fr Spatial Lcalizatin Measuring Tissue Vlumes Measuring NMR Prperties f Tissues Tissue Physilgy Measurements Tissue Bichemistry Measurements RF Nnunifrmities RF Nnunifrmities are the Single Biggest Cause f Errrs in qmri RF Nnunifrmities Increase as the B -Field Increases Dielectric Resnance Effects Becme Prnunced at High B B TX Field Directly related t current in TX cil Depends n Q f cil & cil lading Depends n TX Cil Gemtry TX pwer aut-adjusted (pre-scan) Values shuld be knw t % % =.86 db TX nnlinearities RF pulse drp 3 4 NMR Signal () t B M δv cs( ω t) δ v = ω x,y x, y s The B RF Magnetic Field z N S x y B 5 ξ = ( m B ) where m is the (nuclear) t magnetic diple mment and B = ( B iˆ B x + Principle f Reciprcity y ˆ) j 6 G.D. Clarke, UTHSCSA
RF Pulse Bandwidth (BW) BW is inversely prprtinal t RF pulse duratin: TX FT frequency FT Apprximatin A sinc functin ( sin x x ) envelpe n the r.f. pulse prduces a nearly square excitatin prfile f the phantm.. TX FT Slice select gradient is scaled based n BW & G ss : slice thickness π = γ BW G ss frequency 7 t p FT BW frequency 8 X Resnant Frequency Offset ΔΩ/γ B eff After 9, IS NOT n y axis M M B = B +ΔΩ/γ B eff = B x y +ΔΩ z /γ ΔΩ/γ X Y B eff X Y B X Y M x M y = real M x = imaginary M z des nt cntribute t signal M z M y Y 9 Sinc Pulse Prfile M y.5 -.5 M x.5 M z -.5 - - -5 -.5.5 5-5 -.5.5 5 Frequency (khz) Frequency (khz) ms, 5-lbe, chemical shift refcused 9 8 Sinc Pulse M y.5.5 -.5 M x -.5 M z - - -5 -.5.5 5-5 -.5.5 5 Frequency (khz) Frequency (khz) ms, 5-lbe, chemical shift refcused TX RX G sl Slice Selectin rf rf Spin Ech If cnstant gradient field is n during the rf pulse: Larmr frequency f spins varies with psitin The flip angle depends n the lcal Larmr frequency and the frequency cntent f the RF field pulse the RF pulse can be crafted t cntain frequencies in nly a specified range G.D. Clarke, UTHSCSA
Slice Prfile Variatins Flip Angle varies with lcatin Due t B, B nnunifrmities Nn-linearity f Excitatin (Blch Eqns) FT apprximatin invalid fr big flip angles Blch simulatr sftware http://www-mrsrl.stanfrd.edu/~brian/mritls.html T-weighting f excitatin prfile Blch Equatins A set f simultaneus differential equatins that describe the behavir f the magnetizatin under any cnditins. dmz Mz M =γ[ Mx By My Bx ] dt T dmx M =γ[ My( t) Bz MzBy ] dt x T dmy M =γ[ Mz( t) Bx MxBz ] dt y T alng the z-axis alng the x-axis alng the y-axis Brain Hargreaves 3 4 Pr RF Pulse Calibratin Miscalibratin f FSE 8 rf pulses (left image) is crrected (right image) B Field Mapping - Purpse a. Needed fr accurate measurement f many NMR parameters, i.e. relaxatin s b. Enables estimatin f systematic errrs in parameter measurement c. Enable crrectin f spatial sensitivity variatin using reciprcity 5 6 B Field Mapping - Methds a. One-pulse read M x,y Venkatsen et al. Magn Resn Med 998; 4:59 b. Spin Ech (bth pulses altered) Barker et al. BJR 998; 7: 59-67 c. One-pulse read M z Vaughn et al. Mgn Resn Med ; 46: 4 B Field Mapping One-pulse M x,y methd Hard 8 pulse preceding D field ech sequence Bright center is maximum B Ring pattern ccurs at every 5% change in B -field 7 8 Deichmann R et al. Magn Resn Med ; 47: 398 G.D. Clarke, UTHSCSA 3
Dielectric Resnance Effect Fields inside a sample f diameter, d, can be resnant when d = nλ This can make the B field at the center f the sample larger than at the edges This effect is dampened as the cnductivity f the sample increases 9 Image Unifrmity at 3 Tesla.5T 3 T B field maps in a saline phantm (8 cm diameter) RL Greenman et al. JMRI 3, 7(6): 648-655 Dielectric Resnance Spin-Ech Sequence TX RX rf rf Spin Ech G sl G r G pe Symblizes gradient increment frm excitatin t excitatin Hult DI, J Magn Resn Imag, ; :46-67 Gradient Subsystems One Dimensinal FT B (x) x Mag FT ν 3 4 G.D. Clarke, UTHSCSA 4
MRI Gemetric Distrtins ω = γ ( B + xg ) Machine dependent Patient-dependent Accessry device dependent x MRI Gradient Fields Surces f Errr: Gradient Amplitude Calibratin Best abut % errr Gradient Nn-linearities Eddy Currents 5 6 Eddy Currents Accelerating current in gradient cils (gradient pulse) causes induced currents in nearby metallic structures. These currents prduce magnetic fields which, in turn, ppse the magnetic fields f the gradient cils Eddy Currents The magnetic field prduced by Eddy Currents have tw -dependent cmpnents: An ffset f the B field An additinal gradient field B ec ( r, t) = Δg( r, t) + ΔB 7 8 Eddy Current Pre-emphasis Gradient Current Eddy Current Actual Gradient Field Gradient Wavefrms Gradient t Magnet Rati G/R=.8 G/R=.6 In free space In magnet In magnet In free space Gradient Current with Pre-Emphasis Actual Gradient Field 9 A. Whle bdy system. B. Whle bdy, G/R=.6 In magnet In free space In magnet In free space ms ms A. Micrscpy system. B. Micrscpy system 3 G.D. Clarke, UTHSCSA 5
Actively Screened Gradients Reduce gradient field strength utside f gradient cil frmer - Current in shield is ppsite plarity Reduces gradient field in imaging vlume als - Imprves magnet hmgeneity Each gradient cil is assciated with a screen cil - Twice as many amplifiers required 3 Measuring Eddy Currents 3 De Deene Y et a. Phys Med Bil ; 45:87-83 Eddy Currents Time curse f eddy current field ffset fllwing different numbers f gradient pulse units MRI Gradient Fields Gradient Nnlinearities are ften tlerated as part f trade-ffs with gradient field strength r cil size Manufacturers ften apply gradient distrtin crrectins in rder t make images appear t be distrtin free Influences image quality parameters (SNR, spatial reslutin, etc.) 33 De Deene Y et a. Phys Med Bil ; 45:87-83 34 http://www.nbirn.net Brain Vlume Measurement Brain Vlume Relatinships White Matter Basal Gray Cerebellum High agreement between qmri vlumetry and physical sectins qmri vlumetry is susceptible t high inter-bserver variability Prblems greatest in thse regins where tissue margins are prly defined 35 Jelsing J NeurImage 5; 6: 57-65 36 Jelsing J NeurImage 5; 6: 57-65 G.D. Clarke, UTHSCSA 6
Cartilage MRI Relaxatin Times T : lngitudinal relaxatin defines recvery f ptential fr next signal (T =/R ) T : transverse relaxatin defines rate f dephasing f MRI signal due t micrscpic prcesses (T =/R ) T *: transverse relaxatin with B inhmgeneity effects added; defines rate f dephasing f MRI signal due t macrscpic and micrscpic prcesses (T * =/R * ) Accuracy f 3T high and tends t be mre reprducible than.5 T 37 Eckstein F et al. Arth & Rheum 5; 5: 33-336 38 Lngitudinal Relaxatin M = M (- exp(-tr/t) M Transverse T* Decay T T 3T 4T τ 39 4 Applicatins fr T Images Tissue characterizatin Cntrast agent uptake studies Measurement f Tissue Perfusin Measurement f Bld Vlume Factrs Influencing T Macrmlecular cncentratin in cytsl Water binding Water cntent Gd and Fermxide Cntrast Agents 4 4 G.D. Clarke, UTHSCSA 7
T Measurement Sequences Inversin Recvery 8-9 -8 ; the gld standard Inversin Recvery 8 9 8 Spin Ech 8 Saturatin Recvery 9-8 Stimulated Ech 9-9 -9 Lk-Lcker Sequence (see belw) 43 TI TE TR Inversin Excitatin Refcusing +M M = M ( - exp[-ti/t ]) TI -M 44 Lk-Lcker Sequence 8 α α α α α Saturatin Recvery fr CMRI Encde Encde Encde Encde Encde τ τ τ Very sensitive t RF pulse errrs recvery rate, T * : T * τ = τ ln T τ ( csα ) τ 45 46 Higgins DM, Med Phys 5; 3(6):738-746 (a) T Map f tubes f gel dped with Gd-DTPA T Parametric Maps (b) T-weighted image f heart in shrt axis (c) T parametric map image f heart in (b) T s calculated frm shrt-acquisitin perid T sequence (SAP-T) with varying delay s 47 Higgins DM, Med Phys 5; 3(6):738-746 Fr Accurate & Precise T Never Assume RF Flip Angle is Crrect Varies ver imaged slice due t slice prfile Flip angle must be calibrated acrss slice Be careful in assuming magnetizatin has reached steady state between acquisitins Optimize sequence acquisitin parameters t ensure maximal SNR Always check that fitted cnfrms t assumed mdel 48 G.D. Clarke, UTHSCSA 8
Signal Strength Multi-Ech with 8 Pulses 9 8 8 SE 8 TE SE *TE M exp(-te/t ) M exp (-TE/T * ) 3*TE SE3 TE >> T * Signal Strength G slice G read G phase Multi-Ech Acquisitins M exp(-te/t ) M exp (-TE/T * ) 9 8 8 SE 8 SE TE *TE 3*TE SE3 49 5 Time Scale f Relaxatin Calculatin f T Lngitudinal Transverse M exp (-TE/T * ) - exp (-TR / T ) s f ms s f ms M ln M ln( M T xy = M xy xy ' t / T e = / T / M ' ) = = / slpe t + ln M ' slpe = / T 5 5 Gel Dsimeters Used fr 3D Radiatin Dsimetry QC Relies n direct relatinship between relaxatin rate, R (R =/T ) f gel fllwing expsure and dse Eddy Current Effects n Slice a b c Ideal n eddy currents wrst case pre-gradient train RF pulse prfiles used fr T-relaxmetry a) Ideal prfile calculated frm Blch equatins b) prfile shwing the influence f eddy currents; c) pre-gradient pulse train establishes steady-state which regularizes the RF pulse prfile 53 www.mgsresearch.cm 54 De Deene Y et a. Phys Med Bil ; 45:87-83 G.D. Clarke, UTHSCSA 9
B Changes with Slice Psitin Effective Flip Angles Average transverse magnetizatin within a slice as a fractin f M fr varius slice psitins fr flip angles ranging frm t 36 55 De Deene Y et a. Phys Med Bil ; 45:85-839 56 De Deene Y et a. Phys Med Bil ; 45:85-839 R Calibratin T* Parametric Imaging M xy = M ' e t / T * Similar t T measurements but use gradient ech imaging with varying TE 57 58 Cntrast Agent Maps Transfer Cntrast Multislice FSE: T-weighted image Parametric map f R * Transfer Cntrast Enhances T - Weighted Appearance 59 http://www.research.philips.cm/ 6 G.D. Clarke, UTHSCSA
Transfer PROTON SPECTRUM Frequency (Hertz) Free Water Lipids Bund Water 7 Hz 5 Hz Frequency (Hertz) 6 Transfer Rati MTR = M M M Transfer Rati (MTR) the difference f the saturated versus nn-saturate images relative t the signal in the nrmal (nnsaturated images) s 6 MTR and Aging Gray matter and white matter MTR images reveal a quadratic change with age that is primarily attributed t nrmal demylenatin Physilgical Measurements Flw bulk mtin f bld and ther fluids within bdy Perfusin amunt f bld traveling thrugh capillaries in ml/s/gm f tissue Diffusin randm mtin f spins in a hmgeneus slutin Apparent Diffusin Cefficient measured diffusin rate f water thrugh tissue 63 Inglese & Ge, Tp Magn Resn Imag 4; 5:355-363 64 Attenuatin Due t Diffusin A( TE) = A() exp[ γ G Dappδ α ( Δ )] 4 δ Where: α=π/; G is amplitude f diffusin sensitive gradient pulse; δ is duratin f diffusin sensitive gradient; Δ is between diffusin sensitive gradient pulses; D app is the apparent diffusin cefficient 65 DWI Basic Pulse Sequence 9 8 G G δ δ Δ b = γ G δ ( Δ ) δ 66 Stejskal EO & Tanner JE, J Chem Phys 965. 4: 88-9 3 G.D. Clarke, UTHSCSA
The b-value Cntrls amunt f diffusin weighting in image The greater the b-value the greater the area under the diffusin-weighted gradient pulses lnger TE strnger and faster ramping the gradients 67 Anistrpic Diffusin H O H O Restricted diffusin alng neural fibers 68 Diffusin-Weighted MRI Hemispherical Hypperfusin Images acquired 55 minutes after nset f aphasia, hemiplegia, and hemiparesis. b = s/mm Tp. Cnventinal -sht EPI DWI B. SENSE EPI-DWI with R=3 shws reduced susceptibility artifacts in frntal brain 69 Bammer R, Schenberg SO. Tp Magn Resn Imag 4; 5: 9-58 T -weighted Diffusin Time-t-peak Weighted Perfusin 7 Sunshine JL et al. Radilgy 999; : 35-33. Diffusin Fiber Tracking Diffusin-Weighted Breast MRI Diffusin tracks (red and blue) in the splenium f the crpus callsum selected with ellipsid filtering vlumes (black) Parametric maps calculated frm bimdal expnential decay mdel: I I = P ' ' ' ( bd ) + P ( bd ) ' exp exp 7 Cntur et al. PNAS 999; 96:44. 7 Paran Y et al. NMR Bimed 4; 7:7-8 G.D. Clarke, UTHSCSA
Diffusin Tensr Imaging Dephasing Due t Mtin In anistrpic tissues (neural fibers, muscle fibers) scalar ADC depends n directin f diffusin sensitizing gradient G slice +8 BLOOD: phase nt zer Diffusive transprt f water can be characterized by an effective diffusin tensr Directin f diffusin can be used t create a map shwing rientatin f mycardial fibers. PHASE -8 t = Phase Shift Due t Mtin in a Gradient Field TISSUE: phase equals zer 73 Tseng et al., Radilgy ; 6: 8-39. 74 PHASE -8 +8 PHASE -8 Phase Cntrast Imaging +8 Velcity Encded Image TISSUE: phase equals zer in BOTH images Velcity Cmpensated Image Phase Difference Mtin Cmpensatin Gradient (Biplar) Applied Velcity Encded Image BLOOD: phase is DIFFERENT in each image 75 Phase Cntrast Images Tw Signals: S = S s + S m ;S = S s + S m e(iϕ m ) where ϕ m = γδm υ (υ = velcity) Cmplex difference - ΔS =S -S =S m [e(iϕ m )-] =is m sin(ϕ m /) Phase difference - Δϕ = arg S -arg S, then υ = Δϕ / (γ ΔM ) 76 Phase Cntrast Velcity Velcity Encding (V enc ) Magnitude Phase Cntrast +V enc 8 N Flw Flw Velcity 9 cm/s Statinary In Out In Out MRI Velcity (cm/s) -V enc True Flw Velcity (cm/s) Phase Difference (degrees) -8 77 78 G.D. Clarke, UTHSCSA 3
5 45 4 35 3 5 5 5 Anterir Anterseptal Inferseptal Inferir Inferlateral Anterlateral 5 5 5 3 5 45 4 35 3 5 5 5 Anterir Anterseptal Inf ersept al Inf erir Inferlateral Anterlateral 5 5 5 3 AAPM 6 - MRI Physics & Partial Vlume Effect Cardiac Output 5 S ttal φ S static S mving φ mving S ttal φ S static S mving φ mving Asc. Arta Flw (l/min) 5 5-5 4 8 6 Cine Frame Number Cardiac Output = 4. L/min Strke Vlume = 68 ml 79 8 Crnary Artery Flw Gadlinium Uptake A B C D 8 8 Nnunifrmity Crrectin Real- TrueFISP cine study with GRAPPA was perfrmed between tw perfusin scans SI nrmalizatin = SI SI crrectin = SI SI perf /SI cine SI nrmalizatin -SI base Crrect fr verall effects Crrect fr baseline signal Max Upslpe Parametric Map SI (A.U.) SI (A.U.) Time (sec) Time (sec) 83 MRI perfusin image Maximum upslpe parametric map 84 G.D. Clarke, UTHSCSA 4
Data Analysis Results SUMMARY MPRI 3 anterir anterseptal inferseptal inferir inferlateral anterlateral Mycardial perfusin reserve index (MPRI) is nt significantly different between segments in asymptmatic individuals after crrectins Bullseye display depicts segmental MPRI frm mst apical slice (center ring) t mst basal slice (uter ring) Befre undertaking qmri: Check gradient calibratins Understand gradient nn-linearities Evaluate eddy currents Measure RF pulse changes in space Determine RF receive nnunifrmities 85 86 Quantitative MRI Methds Learn Mre Details Measuring things with MRI: Diffusin Cefficients Frequency f a signal Relaxatin rates (T, T, MTC) Velcity f mtin Vlumes f tissues 87 88 G.D. Clarke, UTHSCSA 5