MRI Physics I: Spins, Excitation, Relaxation

Transcription

1 MRI Physics I: Spins, Excitation, Relaxation Douglas C. Noll Biomedical Engineering University of Michigan

2 Michigan Functional MRI Laboratory

3 Outline Introduction to Nuclear Magnetic Resonance Imaging NMR Spins Excitation Relaxation Contrast in images

4 MR Principle Magnetic resonance is based on the emission and absorption of energy in the radio frequency range of the electromagnetic spectrum by nuclear spins

5 Historical Notes Discovered independently by Felix Bloch and Edward Purcell Initially used in chemistry and physics for studying molecular structure (spectrometry) and diffusion In 1973 Paul Lauterbur obtained the 1 st MR image using linear gradients 1970 s MRI mainly in academia 1980 s MRI was commercialized

6 MRI Timeline 1946 MR phenomenon - Bloch & Purcell 1950 Spin echo signal discovered - Erwin Hahn 1952 Nobel Prize - Bloch & Purcell NMR developed as analytical tool 1963 Doug Noll born 1972 Computerized Tomography 1973 Backprojection MRI - Lauterbur 1975 Fourier Imaging - Ernst (phase and frequency encoding) 1977 MRI of the whole body - Raymond Damadian Echo-planar imaging (EPI) technique - Peter Mansfield 1980 MRI demonstrated - Edelstein 1986 Gradient Echo Imaging NMR Microscope 1988 Angiography O Donnell & Dumoulin 1989 Echo-Planar Imaging (images at video rates = 30 ms / image) 1991 Nobel Prize - Ernst 1992 Functional MRI (fmri) 1994 Hyperpolarized 129 Xe Imaging 2003 Nobel Prize Lauterbur and Mansfield

7 MR Physics Based on the quantum mechanical properties of nuclear spins Q. What is SPIN? A. Spin is a fundamental property of nature like electrical charge or mass. Spin comes in multiples of 1/2 and can be + or -. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2

8 Properties of Nuclear Spin Nuclei with: Odd number of Protons Odd number of Neutrons Odd number of both exhibit a MAGNETIC MOMENT (e.g. 1 H, 2 H, 3 He, 31 P, 23 Na, 17 O, 13 C, 19 F )

9 Properties of Spin Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin. (e.g. 4 He, 16 O, 12 C) In nuclear magnetic resonance, it is unpaired nuclear spins that are of importance.

10 Bar Magnet Bar Magnets North and South poles

11 A Spinning Proton A spinning proton generates a tiny magnetic field Like a little magnet + angular momentum

12 NMR Spins B 0 B 0 In a magnetic field, spins can either align with or against the direction of the field

13 NMR Spins B 0 Zeeman splitting!e= "!B 0 =!# 0 B 0 These two states represent 2 energy levels. Transitions must involve absorption/emission at # 0 $ " B 0 Larmor Frequency

14 Common NMR Active Nuclei Spin % natural " elemental Isotope I abundance MHz/T abundance of isotope in body 1 H 1/ % % 2 H % % 13 C 1/ % % 14 N % % 15 N 1/2 0.37% % 17 O 5/ % % 19 F 1/2 100% % 23 Na 3/2 100% % 31 P 1/2 100% %

15 Protons in the Human Body The human body is made up of many individual protons. Individual protons are found in every hydrogen nucleus. The body is mostly water, and each water molecule has 2 hydrogen nuclei. 1 gram of your body has ~ 6 x protons

16 Spinning Protons in the Body Spinning protons are randomly oriented. No magnetic field - no net effect

17 Protons in a Magnetic Field Spinning protons become aligned to the magnetic field. On average - body become magnetized. M

18 Magnetization of Tissue M

19 A Top in a Gravitational Field L L % r F=mg A spinning top in a gravitational field is similar to a nuclear spin in a magnetic field (classical description)

20 A Top in a Gravitational Field L L % r F=mg Gravity exerts a force on top that leads to a Torque (T): dl + rm ( T $ $ L, ) & g dt * L '

21 A Top in a Gravitational Field z TOP VIEW L L dl dl dl dl x y This causes the top to precess around g at frequency: - $ r g m L

22 Spins in a Magnetic Field Spins have both magnetization (M)( and angular momemtum (L): M $ " L B 0 Applied magnetic field (B( 0 ) exerts a force on the magnetization that leads to a torque: dl T $ $ M, dt B 0 M, L

23 Spins in a Magnetic Field This can be rewritten to yield the famous Bloch Equation: dm dt $ M," B 0 B 0 which says that the magnetization will precess around the applied magnetic field at frequency: # 0 M # 0 $ " B 0 Larmor Frequency

24 Spins in a Magnetic Field Three spins with different applied magnetic fields.

25 The NMR Signal z v(t) B v(t) #0 M y t x The precessing magnetization generates the signal in a coil we receive in MRI, v(t)

26 Frequency of Precession For 1 H, the frequency of precession is: T (B 0 = 1.5 Tesla) T T

27 Excitation The magnetization is initially parallel to B 0 M z But, we need it perpendicular in order to generate a signal v(t) #0 M B y x

28 The Solution: Excitation RF Excitation (Energy into tissue) Magnetic fields are emitted

29 Excitation Concept 1: Spin system will absorb energy at!e corresponding different in energy states Apply energy at # 0 = " B 0 (RF frequencies) Concept 2: Spins precess around a magnetic field. Apply magnetic fields in plane perpendicular to B 0.

30 Excitation Try this: Apply a magnetic field (B 1 ) rotating at # 0 = " B 0 in the plane perpendicular to B 0! Magnetization will tip into transverse plane Applied RF

31 Rotating Frame of Reference It is much easier to see the rotation of the magnetization around the B1 field by rotating the frame of reference at the rotation rate of the RF pulse Lab Frame Rotating Frame

32 Resonance Phenomena Excitation in MRI works when you apply magnetic fields at the resonance frequency. Conversely, excitation does not work when you excite at the incorrect frequency.

33 Off-Resonance Excitation Excitation only works when B 1 field is applied at # 0 = " B 0 (wrong!e) This will allows us the select particular groups of spins to excite (e.g. slices, water or fat, etc.)

34 90 Degree Flip Excitation routinely stops with the magnetization is fully tipped into the transverse plane Signal reception can then begin Typical strength is B 1 = 2 x 10-5 T 90 degree tip takes about 300.s v(t) #0 x M z B y

35 What next?! Relaxation Excitation z v(t) B M #0 M y x Spins relax back to their equilibrium state

36 Relaxation The system goes back to its equilibrium state Two main processes: Decay of traverse (observable) component Recovery of parallel component

37 T 1 - relaxation Longitudinal magnetization (M z ) returns to steady state (M 0 ) with time constant T 1 Spin gives up energy into the surrounding molecular matrix as heat Factors Viscosity Temperature State (solid, liquid, gas) Ionic content Bo Diffusion etc.

38 T1 Recovery Tissue property (typically 1-3 seconds) Spins give up energy into molecular matrix Differential Equation: dm dt ( M M 0) $ / T1 z z / M 0 M z t

39 T 2 - relaxation Transverse magnetization (M xy ) decay towards 0 with time constant T 2 Factors T 1 (T 2 0 T 1 ) Phase incoherence» Random field fluctuations» Magnetic susceptibility» Magnetic field inhomogeneities (RF, B 0, Gradients)» Chemical shift» Etc.

40 T2 Decay Tissue property (typically 10 s of ms) Spins dephase relative to other spins Differential Equation: dm dt xy $ / M xy T 2 M xy t

41 Steps in an MRI Experiment 0. Object goes into B 0 1. Excitation 2a. T 2 Relaxation (faster) 2b. T 1 Relaxation (slower) 3. Back to 1.

42 Excitation

43 Relaxation

44 Resting State

45 Excitation

46 Excitation

47 T 2 Relaxation

48 T 1 Relaxation

49 T 1 Relaxation

50 T 1 Relaxation

51 Typical T 1 s, T 2 s, and Relative Spin Density for Brain Tissue at 3.0 T T 1 (ms ) T 2 (ms) 1 R Distilled Water CSF Gray matter White matter Fat

52 The Pulsed MR Experiment MRI uses a repeated excitation pulse experimental strategy RF pulses Data acquisition TR (Repetition Time) TE (Echo Time) time

53 Contrast TR mainly controls T1 contrast Excitation or flip angle also contributes TE mainly controls T2 contrast

54 T1 Contrast and TR TR

55 T1 Contrast and TR TR

56 T1 Contrast and TR TR

57 T1 Contrast and TR TR

58 T1 Contrast and TR TR

59 T1 Contrast and TR TR

60 T1 Contrast For short TR imaging, tissues with short T1 s (rapidly recovering) are brightest Fat > brain tissue White Matter > Grey Matter Gray Matter > CSF Spin Density T1 Weighting

61 T2 Contrast and TE TE

62 T2 Contrast and TE TE

63 T2 Contrast and TE TE

64 T2 Contrast and TE TE

65 T2 Contrast and TE TE

66 T2 Contrast For long TE imaging, tissues with short T2 s (rapidly recovering) are darkest Fat < brain tissue White Matter < Grey Matter Gray Matter < CSF Spin Density T2 Weighting

67 Contrast Equation For a 90 degree flip angle, the contrast equation is: Signal 2 1(1 / e / TR / T1 ) e / TE / T 2

68 Can the flip angle be less than 90? Of course, but the contrast equation is more complicated. Flip angle can be chose to maximize signal strength: Ernst Angle

69 Next Step Making an image!! First some examples of MR Images and Contrast

70 Supratentorial Brain Neoplasm T1-weighted image with contrast T2-weighted image

71 Cerebral Infarction MR Angiogram T2-weighted image

72 Imaging Breast Cancer

73 Imaging Joints

74 Imaging Air Passages

75

76 Tagging Cardiac Motion

77 Diffusion and Perfusion Weighted MRI

78 fat Coke Air/ CO 2 mixture fries spleen burger