Biomedical Imaging 2

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. MRI Physics

3. Magnetic Resonance in a Nutshell Hydrogen Nuclei (Protons) Axis of Angular Momentum (Spin), Magnetic Moment

4. Spins PRECESS at a single frequency (f0), but incoherently − they are not in phase External Magnetic Field Magnetic Resonance in a Nutshell

5. Magnetic Resonance in a Nutshell Irradiating with a (radio frequency) field of frequency f0, causes spins to precess coherently, or in phase ↓ ROTATING REFERENCE FRAME

6. Primary (Static) Magnetic Field S magnetic field lines By staying in the interior region of the field, we can ignore edge effects. N

7. Typical Magnetic Resonance Imager http://www.radiologyinfo.org/en/photocat/photos_pc.cfm?Image=si-symphony.jpg&pg=bodymr&bhcp=1 (Radiological Society of North America, Inc.)

8. Generating the Primary Magnetic Field http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html (Georgia State University)

9. Gradient coils 1 • z-gradient: Anti-Helmholtz coils

10. Gradient coils 2 • Gradients perpendicular to z

11. B0 mz m m mz mz 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 mz. 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. mz Alignment of 1H Nuclei in a Magnetic Field 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? What is the precession frequency?

12. B0 mz m m mz Boltzmann distribution: Orientational Distribution of 1H Nuclei Protons must orient themselves such that the z-components of their magnetic moments lie in one of the two permissible directions What fraction of nuclei are in the “up” state and what fraction are “down”? The orientation with mz aligned with B0 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 |B0|, and increases with decreasing (absolute) temperature T.

13. Transitions Between Spin States (Orientations) I • QM result: energy difference between the “up” and “down” states of mz is ΔE0 = h|B0| • As always, frequency of radiation whose quanta (photons) have precisely that amount of energy is f0 = ΔE0/h • So, f0 = |B0| • Different nuclei have different values of . (Units of  are MHz/T.) • 1H:  = 42.58; 2H:  = 6.53; 3H:  = 45.41 • 13C:  = 10.71 • 31P:  = 17.25 • 23Na:  = 11.27 • 39K:  = 1.99 • 19F:  = 40.08

14. hf0 hf0  + +   + + + + 2hf0 Spontaneous emission (Relaxation) Stimulated emission Absorption Transitions Between Spin States II • The frequency f0 that corresponds to the energy difference between the spin states is called the Larmor frequency. • The Larmor frequency f0 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 f0, but this is not experimentally observable.) • Three important processes occur:

15. hf0 hf0  + +   + + + + 2hf0 Spontaneous emission (Relaxation) Stimulated emission Absorption Transitions Between Spin States III • The number of 1H 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.

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. Relaxation I • What are spin-lattice relaxation and spin-spin relaxation? • What do time constants T1 and T2 mean? • “Lattice” means the material (i.e., tissue) the 1H nuclei are embedded in • 1H nuclei are not the only things around that have magnetic moments • Other species of nuclei • Electrons • A 1H magnetic moment can couple (i.e., exchange energy) with these other moments

18. Look ’em up! Spin-Lattice Relaxation I • Spin-lattice interactions occur whenever a physical process causes the magnetic field at a 1H 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 T1 time constant associated with these processes?

19. Recall that static field direction definesz, z׳ B0 z׳ At equilibrium, M point in z׳ direction y׳ x׳ Spin-Lattice Relaxation II • What is the T1 time constant associated with spin-lattice interactions?

20. B0 z׳ Now impose a transverse magnetic field Then turn the transverse field off y׳ …and tip the magnetization towards the x׳-y׳ plane x׳ Spin-Lattice Relaxation III • What is the T1 time constant associated with spin-lattice interactions?

21. 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. Spin-Lattice Relaxation IV • What is the T1 time constant associated with spin-lattice interactions? B0 z׳ Mz M y׳ x׳ The z component of M, Mz, grows back into its equlibrium value, exponentially: Mz = |M|(1 - e-t/T1)

22. Relaxation II • What are spin-lattice relaxation and spin-spin relaxation? • What do time constants T1 and T2 mean? • A 1H magnetic moment can couple (i.e., exchange energy with) the magnetic moments of other 1H nuclei in its vicinity • These are called “spin-spin coupling” • Spin-spin interactions occur when the magnetic field at a given 1H nucleus fluctuates • Therefore, should the rates of these interaction depend on temperature? If so, do they increase or decrease with increasing temperature?

23. Spin-Spin Relaxation I • What is the T2 time constant associated with spin-spin interactions? B0 z׳ Mtr If there were no spin-spin coupling, the transverse component of M, Mtr, would decay to 0 at the same rate as Mz returns to its original orientation Mz M y׳ What are the effects of spin-spin coupling? x׳

24. Spin-Spin Relaxation II • W hat are the effects of spin-spin coupling? Because the magnetic fields at individual 1H nuclei are not exactly B0, their Larmor frequencies are not exactly f0. B0 z׳ But the frequency of the rotating reference frame is exactly f0. So in this frame M appears to separate into many magnetization vectors the precess about z׳. Mz y׳ Some of them (f < f0) precess counterclockwise (viewed from above), others (f > f0) precess clockwise. x׳

25. Spin-Spin Relaxation III • W hat are the effects of spin-spin coupling? B0 z׳ Within a short time, M is completely de-phased. It is spread out over the entire cone defined by cosθ = Mz/|M| When M is completely de-phased, Mtr is 0, even though Mz has not yet grown back completely: Mtr = 0, Mz < |M| Mz y׳ Mtr decreases exponentially, with time constant T2: Mtr = Mtr0 e-t/T2 x׳ This also shows why T2 can not be >T1. It must be the case that T2 T1. In practice, usually T2 << T1.

26. Relaxation III In this example, T1 = 0.5 s In this example, T2 = 0.2 s

27. Contrast • Intrinsic : Relaxation times T1, T2, proton density, chemical shift, flow • Extrinsic: TR, TE, flip angle • Contrast in T1: Contrast in T2:

28. T1 T2 T1-weighting • Short TR: • Maximizes T1 contrast due to different degrees of saturation • Short TE: • Minimizes T2 influence, maximizes signal

29. T2 T1 T2 weighting • Long TR: • Reduces saturation and minimizes influence of different T1 • Long TE: • Maximizes T2 contrast • Relatively poor SNR

30. T2 T1 Spin density weighting • Long TR: • Minimizes effects of different degrees of saturation (T1 contrast) • Maximizes signal • Short TE: • Minimizes T2 contrast • Maximizes signal

31. Effect of B0 Field Heterogeneity • What 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 1H nucleus • If the static B0 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/T2*  1/T2 + |B0|. • T2* (“tee-two-star”) has a spin-spin coupling contribution and a field inhomogeneity contribution • T2* < T2 always, and typically T2* << T2

32. MRI contrast mechanisms

33. MR Imaging Principles

34. Basic MRI measurement: Homogeneous static magnetic field (B0) 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 Free induction decay (FID)

35. Inversion pulse after time t phase recovery at 2t Corrects for dephasing due to static B inhomogeneities x x y y Spin echo 180 degree spin flip

36. Spin echo sequence • Multiple p pulses create “Carr-Purcell-Meiboom-Gill (CPMG)” sequence • Decays with time constant T2

37. Gradient fields in MRI 1 • Strength of Bz component varies linearly in space

38. Gradient fields in MRI 2 • Larmor frequency varies linearly in space:

39. 1st Dimension (z): Slice selection • Slice position: z0 ~ f0 • Slice thickness: • Slice profile: profile ~ FT (pulse shape) (Frequency f0 bandwidth B, pulse length T) d

40. Slice selection cont. • Pulse sequence (PS) for slice selection (TR = repetition time, TE = echo time)

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. Frequency encoding cont. • Pulse sequence: two gradients for x and z

43. 3rd Dimension (y) • How to achieve y-localization? Frequency encoding will always produce iso-lines of resonance frequencies • Solution: • Reconstruction from projections • Phase encoding

44. Phase encoding • Pulse sequence: TP

45. 2D FT pulse sequence (spin warp) • Most commonly employed pulse sequence

46. G(y) y A Closer Look at the Phase-Encoding Gradient

47. G(y) y A Closer Look at the Phase-Encoding Gradient

48. G(y) y A Closer Look at the Phase-Encoding Gradient

49. time gradient A Closer Look at the Phase-Encoding Gradient

50. time gradient A Closer Look at the Phase-Encoding Gradient