Magnetic Resonance for BME 458 Francisco (Paco) Martinez

1
Magnetic Resonancefor BME 458 Francisco
(Paco) Martinez
2
MR Principle

• Magnetic resonance is based on the absorption and
  emission of energy in the radio frequency range
  of the electromagnetic spectrum.

3
Historical Notes

• Discovered independently by Felix Bloch
  (Stanford) and Edward Purcell (Harvard)
• Initially used in chemistry and physics for
  studying molecular structure (spectrometry) and
  diffusion
• In 1973 Paul Lauterbur obtained the 1st MR image
  using linear gradients
• 1970s MRI mainly in academia
• 1980s Industry joined forces

4
MRI Timeline

• 1946 MR phenomenon - Bloch Purcell
• 1950 Spin echo signal discovered - Erwin Hahn
• 1952 Nobel Prize - Bloch Purcell
• 1950 - 1970 NMR developed as analytical tool
• 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 - Dumoulin
• 1989 Echo-Planar Imaging (images at video rates
  30 ms / image)
• 1991 Nobel Prize - Ernst
• 1993 Functional MRI (fMRI)
• 1994 Hyperpolarized 129Xe Imaging
• 2000? Interventional MRI

5
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

6
Properties of Spin

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

7
Properties of Spin

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

8
Spins and Magnetic Fields

• When placed in a magnetic field of strength B, a
  particle with a net spin can absorb a photon, of
  frequency ?. The frequency depends on the
  gyromagnetic ratio ?, of the particle
• Larmor relationship
• ? ? B
• ? Resonant Frequency (rad/s)
• ? Gyromagnetic ratio
• B magnitude of applied magnetic field

9
? / (2?)

• Nucleus MHz / T
• 1H - 42.575
• 13C - 10.705
• 19F - 40.054
• 23Na - 11.262
• 31P - 17.235

10
Biological abundances

• Hydrogen (H) 63
• Sodium (Na) 0.041
• Phosphorus (P) 0.24
• Carbon (C) 9.4
• Oxygen (O) 26
• Calcium (Ca) 0.22
• Nitrogen (N) 1.5

Calculated from M.A. Foster, Magnetic Resonance
in Medicine and Biology Pergamon
Press, New York, 1984.
11
Spins and Magnetic Fields

• The AVERAGE behavior of many spins (many magnetic
  moments) results in a NET MAGNETIZATION of a
  sample (substance/tissue)

Bo
Net magnetization (Up/Down ? 0.999993)
Randomly oriented
Oriented parallel or antiparallel
12
Bloch Equation

• Says that the magnetization M will precess around
  a B field at frequency ? ? B

Vs.
13
Nomenclature

• B0 External magnetic field normally on the z
  direction
• Magnetization
• Longitudinal magnetization
• Transverse magnetization
• Magnetic Field
• M0 Initial magnetization
• B0 Magnitude of main magnetic field
• B1 Magnitude of RF field

Detected signal
14
Solution to Bloch Eq.

• Jump to Matlab simulations that solve the Bloch
  Equation
• Observe Rotating Frame of Reference

15
Excitation

• Recall that the net magnetization (M) is aligned
  to the applied magnetic field (B0).
• Q. How can we rotate M so that it becomes
  perpendicular to B0?
• A. RF Excitation
• Rotating magnetic fields (B1) applied in the
  plane transverse to B0

16
Tip angle

• Tip angle

17
Resonance

• If ?RF ?0 Resonance
• Excitation is effective
• If ?RF ? ?0 Excitation occurs
• but it is not optimal
• Matlab simulation

18
Relaxation

• There are thermal processes that will tend to
  bring M back to its equilibrium state
• T1 recovery Spin-lattice relaxation
• T2 relaxation Spin-Spin relaxation

19
T1 - relaxation

• Longitudinal magnetization (Mz) returns to steady
  state (M0) with time constant T1
• Spin gives up energy into the surrounding
  molecular matrix as heat
• Factors
• Viscosity
• Temperature
• State (solid, liquid, gas)
• Ionic content
• Bo
• Diffusion
• etc.

20
T2 - relaxation

• Transverse magnetization (Mxy) decay towards 0
  with time constant T2
• Factors
• T1 (T2 ? T1)
• Phase incoherence
• Random field fluctuations
• Magnetic susceptibility
• Magnetic field inhomogeneities (RF, B0,
  Gradients)
• Chemical shift
• Etc.
• Matlab simulations of T1 and T2

21
Typical T1s, T2s, and Relative Density for
brain tissue

• T1 (sec) T2 (sec) ?R
• Distilled Water 3 3 1
• CSF 3 0.3 1
• Gray matter 1.2 0.06 - 0.08 0.98
• White matter 0.8 0.045 0.8
• Fat 0.15 0.035 1

22
Bloch Eq. Revised
Solution on the rotating frame of reference
23
Pulse Sequences

• 90 - 90 - 90 -
• ? - ? - ? - ? - ? -
• 180 - 90 - 180 - 90 (Inversion recovery)
• 90 - 180 - 180 - 180 - 180
• 90 - 180 - 90 - 180 (Spin echo)

24
Hardware

• For the BME458 laboratory

RF Amp.
PERMANENT
Pulse Programmer
RF Synthesized Oscillator
RF Transmitting coil
Oscilloscope Sync. CH1 CH2
Sample
Receiver
Mixer
RF Receiving coil
MAGNET
RF Amplifier Detector
25
Receiver

• High gain
• Linear
• Low noise
• Centered at 15 MHz

26
Pulse programmer

• Pulse generator that
• creates the pulse
• sequences.
• Pulses can be varied in
• Duration (1 30 ?s)
• Spacing (10 ?s 9.99 s)
• Number of B pulses (0 99)
• Repetition time (1 ms 10 s)

27
15 MHz Osc/Amp/Mixer

• Tunable oscillator
• Display
• Coarse/fine adjustment
• Power amplifier
• Amplifies pulses to
• produce 12 gauss
• (Max 150W)
• Mixer
• Multiplies CW-RF with
• received signal

28
15 MHz Osc/Amp/Mixer

• Mixer
• Multiplies CW-RF with received signal

CW
FID
Mix
29
Imaging

• Requires magnetic fields as a function of
  position
• Therefore frequency of oscillation is a function
  of position

30
Gradients
31
Gradients

• Recall that
• Now

32
Hardware
33
Pulse sequences

• Spin echo
• Gradient echo
• EPI
• Spiral
• 100s

34
References

• http//www.cis.rit.edu/htbooks/mri/
• Principles of magnetic resonance imaging.
• Dwight G. Nishimura, 1996