1. BMI2 SS08 – Class 6 “functional MRI” Slide 1 Biomedical Imaging 2 Class 6 – Magnetic Resonance Imaging (MRI) Functional MRI (fMRI): Magnetic Resonance Angiography (MRA), Diffusion-weighted MRI (DWI) 02/26/08

2. BMI2 SS08 – Class 6 “functional MRI” Slide 2 MRI Physics

3. BMI2 SS08 – Class 6 “functional MRI” Slide 3 Magnetic Resonance in a Nutshell Hydrogen Nuclei (Protons) Axis of Angular Momentum (Spin), Magnetic Moment

4. BMI2 SS08 – Class 6 “functional MRI” Slide 4 Magnetic Resonance in a Nutshell Spins PRECESS at a single frequency (f 0 ), but incoherently − they are not in phase External Magnetic Field

5. BMI2 SS08 – Class 6 “functional MRI” Slide 5 Magnetic Resonance in a Nutshell Irradiating with a (radio frequency) field of frequency f 0, causes spins to precess coherently, or in phase ↓ ROTATING REFERENCE FRAME

6. BMI2 SS08 – Class 6 “functional MRI” Slide 6 Primary (Static) Magnetic Field N S magnetic field lines By staying in the interior region of the field, we can ignore edge effects.

7. BMI2 SS08 – Class 6 “functional MRI” Slide 7 Typical Magnetic Resonance Imager http://www.radiologyinfo.org/en/photocat/photos_pc.cfm?Image=si-symphony.jpg&pg=bodymr&bhcp=1 http://www.radiologyinfo.org/en/photocat/photos_pc.cfm?Image=si-symphony.jpg&pg=bodymr&bhcp=1 (Radiological Society of North America, Inc.)

8. BMI2 SS08 – Class 6 “functional MRI” Slide 8 Generating the Primary Magnetic Field http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html (Georgia State University)

9. BMI2 SS08 – Class 6 “functional MRI” Slide 9 Gradient coils 1 z -gradient: Anti-Helmholtz coils

10. BMI2 SS08 – Class 6 “functional MRI” Slide 10 Gradient coils 2 Gradients perpendicular to z

11. BMI2 SS08 – Class 6 “functional MRI” Slide 11 Alignment of 1 H Nuclei in a Magnetic Field m mzmz m mzmz B0B0 Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions What about direction of m? mzmz Correct quantum mechanical description is that m does not have an orientation, but is delocalized over all directions that are consistent with fixed value of m z. For the purpose of predicting/interpreting the interaction of m with radiation, we can think of m as a well-defined vector rapidly precessing about z-direction. mzmz What is the precession frequency?

12. BMI2 SS08 – Class 6 “functional MRI” Slide 12 Orientational Distribution of 1 H Nuclei What fraction of nuclei are in the “up” state and what fraction are “down”? m mzmz m mzmz B0B0 Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions The orientation with m z aligned with B 0 has lower potential energy, and is favored (North pole of nuclear magnet facing South pole of external field). The fractional population of the favored state increases with increasing |B 0 |, and increases with decreasing (absolute) temperature T. Boltzmann distribution:

13. BMI2 SS08 – Class 6 “functional MRI” Slide 13 Transitions Between Spin States (Orientations) I QM result: energy difference between the “up” and “down” states of m z is Δ E 0 =  h|B 0 | As always, frequency of radiation whose quanta (photons) have precisely that amount of energy is f 0 = Δ E 0 /h So, f 0 =  |B 0 | Different nuclei have different values of . (Units of  are MHz/T.) 1 H:  = 42.58; 2 H:  = 6.53; 3 H:  = 45.41 13 C:  = 10.71 31 P:  = 17.25 23 Na:  = 11.27 39 K:  = 1.99 19 F:  = 40.08

14. BMI2 SS08 – Class 6 “functional MRI” Slide 14 Transitions Between Spin States II The frequency f 0 that corresponds to the energy difference between the spin states is called the Larmor frequency. The Larmor frequency f 0 is the (apparent) precession frequency for m about the magnetic field direction. (In QM, the azimuthal part of the proton’s wave function precesses at frequency f 0, but this is not experimentally observable.) Three important processes occur: +  + +  + +  + hf 0 2hf 0 Absorption Stimulated emission Spontaneous emission (Relaxation)

15. BMI2 SS08 – Class 6 “functional MRI” Slide 15 Transitions Between Spin States III The number of 1 H nuclei in the low-energy “up” state is slightly greater than the number in the high-energy “down” state. Irradiation at the Larmor frequency promotes the small excess of low-energy nuclei into the high-energy state. When the nuclei return to the low-energy state, they emit radiation at the Larmor frequency. The radiation emitted by the relaxing nuclei is the NMR signal that is measured and later used to construct MR images. +  + +  + +  + hf 0 2hf 0 Absorption Stimulated emission Spontaneous emission (Relaxation)

16. BMI2 SS08 – Class 6 “functional MRI” Slide 16 Saturation Suppose the average time required for an excited nucleus to return to the ground state is long (low relaxation rate, long excited-state lifetime) If the external radiation is intense or is kept on for a long time, ground-state nuclei may be promoted to the excited state faster than they can return to the ground state. Eventually, an exact 50/50 distribution of nuclei in the ground and excited states is reached At this point the system is saturated. No NMR signal is produced, because the rates of “up”→“down” and “down”→“up” transitions are equal.

17. BMI2 SS08 – Class 6 “functional MRI” Slide 17 Relaxation I What are spin-lattice relaxation and spin-spin relaxation? What do time constants T 1 and T 2 mean? “Lattice” means the material (i.e., tissue) the 1 H nuclei are embedded in 1 H nuclei are not the only things around that have magnetic moments Other species of nuclei Electrons A 1 H magnetic moment can couple (i.e., exchange energy) with these other moments

18. BMI2 SS08 – Class 6 “functional MRI” Slide 18 Spin-Lattice Relaxation I Spin-lattice interactions occur whenever a physical process causes the magnetic field at a 1 H nucleus to fluctuate Spin-lattice interactions cause the perturbed distribution of magnetic moments (i.e., tipped bulk magnetization) to return to equilibrium more rapidly Types of spin-lattice interaction Magnetic dipole-dipole interactions Electric quadrupole interactions Chemical shift anisotropy interactions Scalar-coupling interactions Spin-rotation interactions What is the T 1 time constant associated with these processes? Look ’em up!

19. BMI2 SS08 – Class 6 “functional MRI” Slide 19 x׳x׳ y׳y׳ z׳z׳ B0B0 Spin-Lattice Relaxation II What is the T 1 time constant associated with spin-lattice interactions? At equilibrium, M point in z׳ direction Recall that static field direction defines z, z׳

20. BMI2 SS08 – Class 6 “functional MRI” Slide 20 x׳x׳ y׳y׳ z׳z׳ B0B0 Spin-Lattice Relaxation III What is the T 1 time constant associated with spin-lattice interactions? Now impose a transverse magnetic field …and tip the magnetization towards the x׳-y׳ plane Then turn the transverse field off

21. BMI2 SS08 – Class 6 “functional MRI” Slide 21 Spin-Lattice Relaxation IV What is the T 1 time constant associated with spin-lattice interactions? x׳x׳ y׳y׳ z׳z׳ B0B0 In the laboratory frame, M takes a spiralling path back to its equilibrium orientation. But here in the rotating frame, it simply rotates in the y׳-z׳ plane. The z component of M, M z, grows back into its equlibrium value, exponentially: M z = |M|(1 - e -t/T 1 ) MzMz M

22. BMI2 SS08 – Class 6 “functional MRI” Slide 22 Relaxation II What are spin-lattice relaxation and spin-spin relaxation? What do time constants T 1 and T 2 mean? A 1 H magnetic moment can couple (i.e., exchange energy with) the magnetic moments of other 1 H nuclei in its vicinity These are called “spin-spin coupling” Spin-spin interactions occur when the magnetic field at a given 1 H nucleus fluctuates Therefore, should the rates of these interaction depend on temperature? If so, do they increase or decrease with increasing temperature?

23. BMI2 SS08 – Class 6 “functional MRI” Slide 23 Spin-Spin Relaxation I What is the T 2 time constant associated with spin-spin interactions? x׳x׳ y׳y׳ z׳z׳ B0B0 M MzMz M tr If there were no spin-spin coupling, the transverse component of M, M tr, would decay to 0 at the same rate as M z returns to its original orientation What are the effects of spin-spin coupling?

24. BMI2 SS08 – Class 6 “functional MRI” Slide 24 Spin-Spin Relaxation II W hat are the effects of spin-spin coupling? Because the magnetic fields at individual 1 H nuclei are not exactly B 0, their Larmor frequencies are not exactly f 0. x׳x׳ y׳y׳ z׳z׳ B0B0 MzMz But the frequency of the rotating reference frame is exactly f 0. So in this frame M appears to separate into many magnetization vectors the precess about z׳. Some of them (f f 0 ) precess clockwise.

25. BMI2 SS08 – Class 6 “functional MRI” Slide 25 Spin-Spin Relaxation III W hat are the effects of spin-spin coupling? Within a short time, M is completely de-phased. It is spread out over the entire cone defined by cosθ = M z /|M| x׳x׳ y׳y׳ z׳z׳ B0B0 MzMz When M is completely de- phased, M tr is 0, even though M z has not yet grown back completely: M tr = 0, M z < |M| M tr decreases exponentially, with time constant T 2 : M tr = M tr 0 e -t/T 2 This also shows why T 2 can not be >T 1. It must be the case that T 2  T 1. In practice, usually T 2 << T 1.

26. BMI2 SS08 – Class 6 “functional MRI” Slide 26 Relaxation III In this example, T 1 = 0.5 s In this example, T 2 = 0.2 s

27. BMI2 SS08 – Class 6 “functional MRI” Slide 27 Contrast Intrinsic : Relaxation times T1, T2, proton density, chemical shift, flow Extrinsic: TR, TE, flip angle Contrast in T1: Contrast in T2:

28. BMI2 SS08 – Class 6 “functional MRI” Slide 28 T1-weighting Short TR: Maximizes T1 contrast due to different degrees of saturation Short TE: Minimizes T2 influence, maximizes signal T1 T2

29. BMI2 SS08 – Class 6 “functional MRI” Slide 29 T1 T2 T2 weighting Long TR: Reduces saturation and minimizes influence of different T1 Long TE: Maximizes T2 contrast Relatively poor SNR

30. BMI2 SS08 – Class 6 “functional MRI” Slide 30 T1 T2 Spin density weighting Long TR: Minimizes effects of different degrees of saturation (T1 contrast) Maximizes signal Short TE: Minimizes T2 contrast Maximizes signal

31. BMI2 SS08 – Class 6 “functional MRI” Slide 31 Effect of B 0 Field Heterogeneity W hat is the common element in spin-spin and spin-lattice interactions? They require fluctuations in the strength of the magnetic field in the immediate environment of a 1 H nucleus If the static B 0 field itself is not perfectly uniform, its spatial heterogeneity accelerates the de-phasing of the bulk magnetization vector The net, or apparent, decay rate of the transverse magnetization is 1/T 2 *  1/T 2 +  |B 0 |. T 2 * (“tee-two-star”) has a spin-spin coupling contribution and a field inhomogeneity contribution T 2 * < T 2 always, and typically T 2 * << T 2

32. BMI2 SS08 – Class 6 “functional MRI” Slide 32 MRI contrast mechanisms

33. BMI2 SS08 – Class 6 “functional MRI” Slide 33 MR Imaging Principles

34. BMI2 SS08 – Class 6 “functional MRI” Slide 34 Free induction decay (FID) Basic MRI measurement: Homogeneous static magnetic field (B 0 ) RF pulse generator Antenna (coil) for sending and receiving Free induction decay (FID) signal Free: No external RF field during detection Exponential decay at rate T2* due to spin-spin relaxation (dephasing) and local field inhomogeneities

35. BMI2 SS08 – Class 6 “functional MRI” Slide 35 Spin echo Inversion pulse after time   phase recovery at 2  Corrects for dephasing due to static B inhomogeneities x y x y 180 degree spin flip

36. BMI2 SS08 – Class 6 “functional MRI” Slide 36 Spin echo sequence Multiple  pulses create “Carr-Purcell-Meiboom-Gill (CPMG)” sequence Decays with time constant T2

37. BMI2 SS08 – Class 6 “functional MRI” Slide 37 Gradient fields in MRI 1 Strength of B z component varies linearly in space

38. BMI2 SS08 – Class 6 “functional MRI” Slide 38 Gradient fields in MRI 2 Larmor frequency varies linearly in space:

39. BMI2 SS08 – Class 6 “functional MRI” Slide 39 1 st Dimension (z): Slice selection Slice position: z 0 ~ f 0 Slice thickness: Slice profile:profile ~ FT (pulse shape) d (Frequency f 0 bandwidth B, pulse length T)

40. BMI2 SS08 – Class 6 “functional MRI” Slide 40 Slice selection cont. Pulse sequence (PS) for slice selection (TR = repetition time, TE = echo time)

41. BMI2 SS08 – Class 6 “functional MRI” Slide 41 Frequency encoding The NMR signal from each x-position contains a specific center frequency The over-all NMR signal is the sum of signals along x FT recovers signal contribution at each frequency, i.e. x -location Resulting spectrum is a projection Frequency spectrum

42. BMI2 SS08 – Class 6 “functional MRI” Slide 42 Frequency encoding cont. Pulse sequence: two gradients for x and z

43. BMI2 SS08 – Class 6 “functional MRI” Slide 43 3 rd Dimension (y) How to achieve y-localization? Frequency encoding will always produce iso-lines of resonance frequencies Solution: Reconstruction from projections Phase encoding

44. BMI2 SS08 – Class 6 “functional MRI” Slide 44 Phase encoding Pulse sequence: TP

45. BMI2 SS08 – Class 6 “functional MRI” Slide 45 2D FT pulse sequence (spin warp) Most commonly employed pulse sequence

46. BMI2 SS08 – Class 6 “functional MRI” Slide 46 A Closer Look at the Phase-Encoding Gradient y G(y)G(y)

47. BMI2 SS08 – Class 6 “functional MRI” Slide 47 A Closer Look at the Phase-Encoding Gradient y G(y)G(y)

48. BMI2 SS08 – Class 6 “functional MRI” Slide 48 A Closer Look at the Phase-Encoding Gradient y G(y)G(y)

49. BMI2 SS08 – Class 6 “functional MRI” Slide 49 A Closer Look at the Phase-Encoding Gradient time gradient

50. BMI2 SS08 – Class 6 “functional MRI” Slide 50 A Closer Look at the Phase-Encoding Gradient time gradient

51. BMI2 SS08 – Class 6 “functional MRI” Slide 51 k-space map The 2D array of NMR signals obtained from repeated pulse sequences is referred to as the k-space map. k x (Frequency encoding) FT k y (Phase encoding) FT K-space

52. BMI2 SS08 – Class 6 “functional MRI” Slide 52 From Structure to Function

53. BMI2 SS08 – Class 6 “functional MRI” Slide 53 MRI vs. fMRI

54. BMI2 SS08 – Class 6 “functional MRI” Slide 54 fMRI investigation of hemodynamics

55. BMI2 SS08 – Class 6 “functional MRI” Slide 55 Magnetic Resonance Angiography (MRA)

56. BMI2 SS08 – Class 6 “functional MRI” Slide 56 Arterial Spin Labeling (Perfusion MRI) HOW?

57. BMI2 SS08 – Class 6 “functional MRI” Slide 57 Basic Idea #1: Time-of-Flight (TOF) Step 1: Select this slice Step 2: Saturate this slice (TR <<T1) Step 3: Excite this region Step 4: Apply phase- and frequency-encoding gradients, record FIDs and/or this one Step 1: Select this slice Step 2: Saturate this slice (TR <<T1) Step 1: Select this slice Step 2: Saturate this slice (TR <<T1) Step 3: Excite this region and/or this one

58. BMI2 SS08 – Class 6 “functional MRI” Slide 58 Basic Idea #2: Phase Contrast Bipolar Field Gradients

59. BMI2 SS08 – Class 6 “functional MRI” Slide 59 Bipolar Gradient Effects Static (not moving) stuff Stuff that moves First gradient Second gradient

60. BMI2 SS08 – Class 6 “functional MRI” Slide 60 Examples of Phase-Contrast MRA

61. BMI2 SS08 – Class 6 “functional MRI” Slide 61 fMRI vs. Nuclear Imaging (PET)

62. BMI2 SS08 – Class 6 “functional MRI” Slide 62 Diffusion-weighted MRI (DWI) Stronger bipolar gradients → lower tissue velocities detectable Blood flow velocities: ~(0.1 – 10) cm-s -1 Water diffusion velocity: ~200 μm-s -1 Using the same basic strategy as phase-contrast MRA, can image “apparent diffusion coefficient” (ADC) Useful for diagnosing and staging conditions that significantly alter the mobility of water e.g., cerebrovascular accident (“stroke,” apoplexy)

63. BMI2 SS08 – Class 6 “functional MRI” Slide 63 Examples of Diffusion-weighted images

64. BMI2 SS08 – Class 6 “functional MRI” Slide 64 Examples of Diffusion-weighted images