Textbook for the Statistical Parametric Mapping (SPM) class

1. Textbook for the Statistical Parametric Mapping (SPM) class

2. Statistical Parametric Mapping Chapter 3 Principles of Nuclear Magnetic Resonance and MRI Many thanks to those that share their MRI slides online

3. Engineering Computer Science Physics Statistics Cognitive Science Physiology Medicine Physical Science Technology Methodology Neuroscience Interpretation Applications Peter Bandettini NIH

4. MRI Has Many Layers Of Complexity Even subdivisions below have multiple layers of complexity … Physics … Engineering … Technology … Applications … Interpretation …

5. History: MRI • 1940s – Bloch & Purcell: Nuclear Magnetic Resonance • Paul Lauterbur and Peter Mansfield won the Nobel Prize in Physiology/Medicine (2003) for their pioneering work in MRI • 1973 - Lauterbur: gradients for spatial localization of images • 1977 – Mansfield: first image of human anatomy, first echo planar image (a fast imaging technique) • 1990s - Discovery that MRI can be used to distinguish oxygenated blood from deoxygenated blood. Leads to Functional Magnetic Resonance imaging (fMRI)

6. Venography Fiber Track Imaging Anatomy Angiography Perfusion Peter Bandettini NIH

7. fMRI R P Peter Bandettini NIH

8. Basic Physics of MRI • All magnetic fields are the result of charge in motion • Nucleus of an atom has a magnetic moment when it has an odd number of protons (or neutrons). Single proton in Hydrogen yields strongest magnetic effect. Model of spin as motion • Why does neutron have magnetic properties? • What about electron(s) magnetic properties?

9. Basic Physics of MRI • The orientation of nuclear magnetic moments are affected by an external magnetic field (that not due to the local nuclear magnetic moments). External magnetic field B0. Orientation follows direction of external magnetic field. No external magnetic field. Orientation is random.

10. Basic Physics of MRI • Nuclei line up with magnetic moments either in a parallel or anti-parallel configuration. • In body tissues more line up in parallel creating a small additional magnetization M in the direction of B0. Nuclei spin axis not parallel to B0 field direction. Nuclear magnetic moments precess about B0.

11. Field Strength and the Net Magnetization (M) .. NU = 1,000,000 - 5 ... NU = 1,000,000 ΔE3.0T = 2*ΔE1.5T ΔE1.5T ... NL ~ 1,000,000 + 10 NL ~ 1,000,000 + 15 ... M 1.5 T 3.0 T M NL = # /volume in low energy state NU = # /volume high energy state M(NL - NU) Lowering temperature increases M – Any volunteers?

12. Basic Physics of MRI • Frequency of precession of magnetic moments given by Larmor relationship f = g x B0 f = Larmor frequency (mHz) g = Gyromagnetic ratio (mHz/Tesla) B0 = Magnetic field strength (Tesla) g~ 43 mHz/Tesla Larmor frequencies of RICs MRIs 3T ~ 130 mHZ 7T ~ 300 mHz 11.7T ~ 500 mHz

13. NMRable Nuclei Basic Physics of MRI • Body 1H content is high due to water (>67%) • Hydrogen protons in mobile water are primary source of signals in fMRI and aMRI

14. Basic Physics of MRI • M is parallel to B0 since transverse components of magnetic moments are randomly oriented. • The difference between the numbers of protons in the parallel (up here) and anti-parallel states leads to the net magnetization (M). • Proton density relates to the number of parallel states per unit volume. • Signal producing capability depends on proton density. B0

15. Proton Signal • 6.023x1023 molecules in 18 gm of H2O • 3.35x1022 molecules in 1 gm (1 cc ~ cm3) • 3.35x1019 molecules in 1 mg (1 mm3) • 7.70x1019 hydrogen atoms/mm3 • 7.70x1014signal producing protons/mm3 So the approximately 1 in 105 signal producing protons is still a lot. Note: The number of protons contributing to signal will depend on volume from which the signal arises (voxel size).

16. Radio Frequency (RF) B1(f) is magnetic field rotating at frequency = f Resonance Condition:f = Larmor frequency Basic Physics of MRI NOTE: coordinate system B1 is rotating magnetic field associated with the RF pulse. RF at Larmor frequency will cause M to rotate about B1 in rotating frame of reference. Rotating B1 from RF pulse?

17. Basic Physics of MRI Frequency of rotation of M about B1 determined by the magnitude (strength) of B1. RF pulse duration and strength determine flip angle Basic RF Pulse Concepts RF Pulse strength duration

18. Bo: magnetic field B1: generated by the RF coil RF coil Sample Flip AngleRotation of Net Magnetization (M) Bo α: flip angle Mo M0: depends on proton density α B1 y’ x’ When α = 90° then Mxy = M0 and Mz = 0 When α = 180° then Mxy = 0 and Mz = - M0

19. Basic Physics of MRI FID = Free Induction Decay • 90° RF pulse rotates M into transverse (x-y) plane • Rotation of M within transverse plane induces signal in receiver coil at Larmor frequency. • Magnitude signal dependent on Mxy. FID magnitude decays in an exponential manner with a time constant T2. Decay due to ‘spin-spin’ relaxation.

20. Need for 180° Pulse - Spin Echo • FID also diminishes due to local static magnetic field inhomogeneity • Some spins precess faster and some slower than those due to B0 90° 0 180° time TE/2- TE/2+ • 180 ° RF pulse reverses dephasing at TE (echo time) • Residual decay due to T2 Spin Echo Signal TE

21. Nuclear Magnetic Resonance (NMR) Signal: Spin Echo (SE) TR (repetition time) = time between RF excitation pulses 90o 90o 180o FID Spin Echo TE/2 TE/2 TE = time from 90o pulse to center of spin echo

22. MRI Scanner Anatomy • A helium-cooled superconducting magnet generates the static field. • Always on: only quench field in emergency. • niobium titanium wire. • Coils allow us to • Make static field homogenous (shims: solenoid coils) • Briefly adjust magnetic field (gradients: solenoid coils) • Transmit, record RF signal (RF coils: antennas)

23. Superconductor Magnet

24. 3T magnet RF Coil gradient coils (inside) Necessary Equipment Magnet Gradient Coils RF Coil

25. Gradient Coils Sounds generated during imaging due to mechanical stress within gradient coils.

26. MRI Scanner Components

27. RF Coil • RF Coils can transmit and receive RF signals (i.e. apply B1 and monitor Mxy) • A typical coil is a tuned LC circuit and may be considered a near-field antenna

28. www.fmrib.ox.ac.uk/~karla/ RF Coils or Antennas • The MRI antenna is called a coil. • Use different coils for different body parts. • For brains, the most common antenna is the head coil (surrounds the volume of interest) • S coils: better signal for a small region near the coil. Head coil Surface coil Volume coil Surface coil

29. Comprehensive Receiving coils • 7 standard configuration： QD head coil QD Neck Coil QD Body Coil NSM-P035 Permanent Magnet MRI QD Extremity Coil Flat Spine Coil Breast Coil

30. Signal and Field Strength • In theory: • Signal increases with square of field strength • Noise increases linearly with field strength • A 3T scanner should have twice SNR of 1.5T scanner; 7T should have ~4.7 times SNR of 1.5T. • Unfortunately, physiological artifacts also increase, so advantage is less in practice. • Benefits: speed, resolution • Costs: Artifacts, RF heating, wavelength effects, auditory noise, $

31. Making Images of the NMR Signal • Uniform magnetic field to set the stage (Main Magnet) • Gradient coils for positional information • RF transceiver (excite and receive) • Digitizer (convert received analog to digital) • Pulse sequencer (controls timing of gradients, RF, and digitizer) • Computer (FFT to form images, store pulse sequences, display results, archive, etc.)

32. Role of Gradient Coils • Coils that produce magnetic field gradients along x-,y-,and z-directions to encode spatial information • Selective excitation: (during RF) excite those spins within a thin “slice” of the subject • Frequency encoding: (during readout) make the signal’s frequency depend on position • Phase encoding: (between excitation and readout) make the signal’s phase depend on position

33. Coil 2 Coil 1 Gradient Magnetic Fields for Gz • Field Characteristics • Gradient field direction parallel to B0 • Created by Maxwell Pair • currents are anti-parallel (opposite direction) BG

34. Total Field • Total Field • Sum of Main Magnet and Gradient Fields • In practice a “shim” field is also used to “flatten” the field. B0=BM+BG DB0 ~ 1mT Gradient field decreases total Gradient field increases total

35. Spatial Encoding by Gradient Fields • Field varies (almost) linearly • Field magnitude changes with z here • Frequency changes with z • Delta B0 = 0 at z = 0 for balanced system • Gradient units (T/m) DB= 0.001 T • Dz = 0.25 m • DB/ Dz = 0.004 T/m • ~ 172 kHz/m

36. Slice Selection During RF excitation, a linear gradient is applied. Only a “slice” of the sample is excited. f f=(B0 + Gss) Thickness TH = BWRF/ Gs Slice Location center of RF frequency range s

37. RF Field Generation • RF Coils • Transmit RF Field (B1) • Transmitter at frequency f0with bandwidth= Df • Receive signal from Mxy • Receiver tuned to frequency f0 Head Transmitter/Receiver Body Transmitter/Receiver fo fo Df= 1/ t t FT

38. Mxy f(x) Frequency encoding During signal readout, a gradient is applied in one direction: B(x) = B0 + Gxx f(x) = {B0 + Gxx} D f(x) =  Gxx The precession frequency of the net magnetization Mxy depends on x-location. A Fourier transform of the time signal can determine where the nuclei are along the x-direction.

39. Mxy f (y) Phase encoding Between excitation and readout a gradient is applied in one direction. This is done in small increments (once per TR) such that the summed effect is similar to frequency encoding. • B(y) = B0 + Gyy • f(y) = {B0 + Gyy} • f (y) =  Gyy The phase difference depends on y-location. When phase encoding is complete a Fourier transform of the signal tells us where the nuclei are along the y-direction.

40. Frequency and Phase Encoding for a 2D MRI RF Excitation Select slice (Gs) Repeat this many times with Gp changed each time Phase Encode (Gp) Frequency encode (Gf) Readout Slice Select for Brain Orientation: Gx – sagittal; Gy – coronal; Gz - axial

41. Making an Image k-space (frequency domain)A k-space domain image is formed using frequency and phase encoding

42. k-space Image space ky y kx x Acquired Data Final Image Two Spaces FT-1 FT MRI task is to acquire k-space image then transform to a spatial-domain image. kx is sampled (read out) in real time to give N samples. ky is adjusted before each readout. MR image is the magnitude of the Fourier transform of the k-space image

43. The k-space Trajectory Equations that govern 2D k-space trajectory kx = g 0tGx(t) dt if Gx is constant kx = gGxt ky = g 0t’Gy(t) dt if Gy is constant ky = gGyt’ The kx, ky frequency coordinates are established by durations (t) and strength of gradients (G).

44. Simple MRI Frequency Encoding: RF Excitation Slice Selection (Gz) Frequency Encoding (Gx) digitizer on Readout Exercise drawing k-space manipulation

45. The k-space Trajectory Frequency Encoding Gradient (Gx) Move to left side of k-space. (0,0) ky Digitizer records N samples along kx where ky = 0 kx

46. Simple MRI Frequency Encoding: Spin Echo Excitation Slice Selection Frequency Encoding (Gx) digitizer on Readout Exercise drawing k-space representation

47. The K-space Trajectory 180 pulse Digitizer records N samples of kx where ky = 0

48. 90 180 Excite Slice Select Frequency Encode Phase Encode digitizer on Readout Frequency and Phase Encoding for 2D Spin Echo Imaging kx ky

49. The 2D K-space Trajectory 180 pulse Digitizer records N samples of kx and N samples of ky

50. Raw 2D k-space data Processed data Magnitude of Fourier transform 2D Fourier Imaging Imaging time - Np TR