Principles of Magnetic Resonance Imaging

1、Principles of Magnetic Resonance ImagingJ. Peter Mustonen(from David J. Michalak)Presentation for Physics 25005/01/2008MotivationPrinciples of NMRInteractions of spins in B0 fieldPrinciples of 1D-MRIPrinciples of 2D-MRISummaryOutlineMagnetic Resonance Imaging provides a non-invasive imaging techniqu

2、e.Pros: -No injection of potentially dangerous elements (radioactive dyes)-Only magnetic fields are used for imaging no x-raysCons:-Current geometries are expensive, and large/heavyMotivationB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a ne

3、t magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0M = SMiRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0Applicatio

4、n of a rf pulse w0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M right on xy planeM = SMiMRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetizati

5、on, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M = SMiM precesses in the transverse plane. In the absence of any disturbances, M continues to rotate indefinitely in xy plane.MMTimeApplication of a rf pulse w0=2pf0 along the x-axis will provide a torque that displaces M

6、 from the z axis towards y axis. A certain pulse length will put M right on xy planeexp-iw0tRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M

7、 = SMiM precesses in the transverse plane. In the absence of any disturbances, M continues to rotate indefinitely in xy plane.DetectorMMTimeApplication of a rf pulse w0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M righ

8、t on xy planeexp-iw0tRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M = SMiM precesses in the transverse plane. In the absence of any distur

9、bances, M continues to rotate indefinitely in xy plane.DetectorMMTimeAssume: All spins feel same B0.No other forces on Mi (including detection).Application of a rf pulse w0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M

10、right on xy planeexp-iw0tRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M = SMiDetectorMMTimetime, tsignal, sr(t)Application of a rf pulse w

11、0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M right on xy plane(w0/2p)-1exp-iw0tRFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M

12、 rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M = SMiDetectorFTMMTimesr(t)sr(w)tApplication of a rf pulse w0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M right on xy planew0 = 2pf0w exp-iw0t(w0/

13、2p)-1RFPulseB0Principles of NMRApplication of prepolarizing magnetic field, B0, aligns the spins in a sample to give a net magnetization, M. M rotates about B0 at a Larmor precession frequency, w0 = gB0yxzB0yxzB0M = SMiDetector(w0/2p)-1FTMMTimeBoring Spectrum!w0 = 2pf0sr(t)sr(w)tw Application of a r

14、f pulse w0=2pf0 along the x-axis will provide a torque that displaces M from the z axis towards y axis. A certain pulse length will put M right on xy planeexp-iw0tPrinciples of NMRyxzB0In Reality:Relaxation (Inherent even if B0 is homogeneous) T1: Spins move away from xy plane towards z. T2: Spins d

15、ephase from each other.B0 inhomogeneity.Chemical Shift.Complexity Makes Things InterestingPrinciples of NMRyxzB0T1 Spin Relaxation: return of the magnetization vector back to z-axis.Spin-Lattice Time Constant: Energy exchange between spins and surrounding lattice. Fluctuations of B field (surroundin

16、g dipoles receivers) at w0 are important. Larger E exchange necessary for larger B0 longerT1.Math: dM/dt = -(Mz-M0)/T1Solution: Mz = M0 + (Mz(0)-M0)exp(-t/T1)After 90 pulse: Mz = M0 1-exp(-t/T1)M0 = net magnetization based on B0.Mz = component of M0 along the z-axis.t = timeT1 Spin RelaxationPrincip

17、les of NMRyxzB0T2 Spin Relaxation: Decay of transverse magnetization, Mxy.T1 plays a role, since as Mxy Mz, Mxy 0But dephasing also decreases Mxy: T2 T1.T2: Spin-Spin Time Constant Variations in Bz with time and position. Pertinent fluctuations in Bz are those near dc frequencies (independent of B0)

18、 so that w0 is changed. Molecular motion around the spin of interest.Liquids: High Temp more motion, less DB, high T2Solids: slow fluctuations in Bz, extreme T2.Bio Tissues: spins bound to large molecules vs. those free in solution.yxzB0+DB(r,t)T2 Spin RelaxationMxyPrinciples of NMRyxzB0Comparison o

19、f T1 and T2 Spin Relaxation:yxzB0+DB(r,t)TissueT1 (ms)T2 (ms)Gray Matter950100White Matter60080Muscle90050Fat25060Blood1200100-200*200 for arterial blood, 100 for venous blood.B0 = 1.5 T, 37 degC (Body Temp)Magnetic Resonance Imaging: Physical Principles and Sequence Design, Haacke E.M. et al., Wile

20、y: New York, 1999.T1/T2 Spin RelaxationMath: dM/dt = -Mxy/T2After 90 pulse: Mxy = M0 exp(-t/T2)Principles of NMRyxzB0Comparison of T1 and T2 Spin Relaxation:yxzB0+DB(r,t)TissueT1 (ms)T2 (ms)Gray Matter950100White Matter60080Muscle90050Fat25060Blood1200100-200*200 for arterial blood, 100 for venous b

21、lood.Magnetic Resonance Imaging: Physical Principles and Sequence Design, Haacke E.M. et al., Wiley: New York, 1999.FIDw0SpectrumT2 T1Mxy decaysexp(-t/T2)DetectorFT2/T2Because T2 is independent of B0, higher B0 gives better resolutionT1/T2 Spin Relaxationsr(t)tPrinciples of NMRyxzB0yxzB0+DB(r,t)Incl

22、usion of T1 and T2 Spin Relaxation:Inclusion of mathematical expression:Bloch Equationg = gyromagnetic ratioT1 = Spin-Lattice (longitudinal-z) relaxation time constantT2 = Spin-Spin (transverse-x/y) relaxation time constantM0 = Equilibrium Magnetization due to B0 field.i, j, k = Unit vectors in x, y

23、, z directions respectively.T1/T2 Spin RelaxationPrinciples of NMRyxzB0yxzB0+DB(r,t)Inclusion of T1 and T2 Spin Relaxation:Inclusion of mathematical expression:Bloch Equationg = gyromagnetic ratioT1 = Spin-Lattice (longitudinal-z) relaxation time constantT2 = Spin-Spin (transverse-x/y) relaxation ti

24、me constantM0 = Equilibrium Magnetization due to B0 field.i, j, k = Unit vectors in x, y, z directions respectively.PrecessionTransverseDecayLongitudinalGrowthNet magnetization is not necessarily constant: e.g., very short T2, long T1.T1/T2 Spin RelaxationPrinciples of NMRyxzB0Chemical Shift: Nuclei

25、 are shielded (slightly) from B0 by the presence of their electron clouds.Effective field felt by a nuclear spin is B0(1-s).Larmor precession freq, w = gB0(1-s).Shift is often in the ppm range.500,000 precessions before Mxy = 0Chemical environment determines amount of s.H2O vs. Fat (fat about 3.5 pp

26、m lower w0)yxzB0(1-s)Discrete ShiftHHOd+d+2d-HHCDetectorLess ShieldingMore ShieldingChemical ShiftPrinciples of NMRyxzB0Chemical Shift: Nuclei are shielded (slightly) from B0 by the presence of their electron clouds.yxzB0(1-s)Discrete Shiftw02/T2Because T2 is independent of B0, higher B0 gives bette

27、r resolutionDetectorw0(1-s)Ability to resolve nuclei in different chemical environments is key to NMRChemical ShiftPrinciples of NMRyxzB0T2*: B0 Inhomogeneity: Additional decay of Mxy.In addition to T2, which leads to Mxy decay even in a constant B0, application of dB0(x, y, z, t) will cause increas

28、ed dephasing: 1/T2* = 1/T2 + 1/T, where T is the dephasing due only to dB0(x, y, z, t). T2* T2, and depends on dB0(x, y, z, t). Additional loss of resolution between peaks.yxzB0+dB(r,t)time, tField InhomogeneityPrinciples of NMRyxzB0T2*: B0 Inhomogeneity: Additional decay of Mxy.In addition to T2, w

29、hich leads to Mxy decay even in a constant B0, application of dB0(x, y, z, t) will cause increased dephasing: 1/T2* = 1/T2 + 1/T, where T is the dephasing due only to dB0(x, y, z, t). T2* T2, and depends on dB0(x, y, z, t). Additional loss of resolution between peaks.If dB0(x, y, z) is not time depe

30、ndent, then it can be corrected by an echo pulse.yxzB0+dB(r,t)time, tField InhomogeneityPrinciples of NMRyxzB0T2*: B0 Inhomogeneity: Additional decay of Mxy.In addition to T2, which leads to Mxy decay even in a constant B0, application of dB0(x, y, z, t) will cause increased dephasing: 1/T2* = 1/T2

31、+ 1/T, where T is the dephasing due only to dB0(x, y, z, t). T2* Image size!Prevent AliasingPrinciples of 2DMRIkxkySampling rate of k-spacexyDkyDkxFOVy=1/(Dky)FOVx = 1/(Dkx)FOV Image size!Prevent Aliasing(Image Overlap)Aliasing IssuesAliasing: If sampling rate is not sufficient, the Field of view wi

32、ll overlap. Principles of 2DMRIResolutionResolution: Resolution in the object-oriented domain is determined by the extent of k-space measured.kxkySampling rate of k-spacexyDkyNpeDkxNreaddy = FOVy/Npe=(DkyNpe)-1dx = FOVx/Nread=(DkxNread)-1Field of View/Resolution # points need to sample(e.g., 25.6 cm image, 1mm resolution:256 points/dimension, 65.5k points)Nread: # of readout points during FIDNpe: # of phase encoding stepsSummar