february 20, 2003francisco m. martinez magnetic resonance for bme 458 francisco (paco) martinez
TRANSCRIPT
February 20, 2003 Francisco M. Martinez
MR Principle
Magnetic resonance is based on the absorption and emission of energy in the radio frequency range of the
electromagnetic spectrum.
February 20, 2003 Francisco M. Martinez
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
1970’s MRI mainly in academia
1980’s Industry joined forces
February 20, 2003 Francisco M. Martinez
MRI Timeline1946 MR phenomenon - Bloch & Purcell1950 Spin echo signal discovered - Erwin Hahn1952 Nobel Prize - Bloch & Purcell1950 - 1970 NMR developed as analytical tool1972 Computerized Tomography1973 Backprojection MRI - Lauterbur1975 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 - Edelstein1986 Gradient Echo Imaging
NMR Microscope 1988 Angiography - Dumoulin1989 Echo-Planar Imaging (images at video rates = 30 ms / image)1991 Nobel Prize - Ernst1993 Functional MRI (fMRI)1994 Hyperpolarized 129Xe Imaging2000? Interventional MRI
February 20, 2003 Francisco M. Martinez
MR PhysicsBased 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
February 20, 2003 Francisco M. Martinez
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 )
February 20, 2003 Francisco M. Martinez
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.
February 20, 2003 Francisco M. Martinez
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
February 20, 2003 Francisco M. Martinez
/ (2)
Nucleus MHz / T 1H - 42.575 13C - 10.705 19F - 40.054 23Na- 11.262 31P - 17.235
February 20, 2003 Francisco M. Martinez
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.
February 20, 2003 Francisco M. Martinez
Spins and Magnetic Fields
The AVERAGE behavior of many spins (many magnetic moments) results in a NET MAGNETIZATION of a sample (substance/tissue)
Randomly orientedOriented parallel
or antiparallel
Net magnetization(Up/Down 0.999993)
Bo
February 20, 2003 Francisco M. Martinez
Bloch Equation
Says that the magnetization M will precess around a B field at frequency = B
BγMdt
Md
Vs.
February 20, 2003 Francisco M. Martinez
NomenclatureB0 = 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
zzyyxx aMaMaMM
yyxxxy aMaMM
zzyyxx aBaBaBB
zM
Detectedsignal
February 20, 2003 Francisco M. Martinez
Solution to Bloch Eq.
Jump to Matlab simulations that solve the Bloch Equation
- Observe “Rotating Frame of Reference”
February 20, 2003 Francisco M. Martinez
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
yRF1xRF11 at)sin(ωBat)cos(ωBB
February 20, 2003 Francisco M. Martinez
Resonance
If RF = 0 Resonance
Excitation is effective
If RF 0 Excitation occurs
but it is not optimal
Matlab simulation
February 20, 2003 Francisco M. Martinez
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
February 20, 2003 Francisco M. Martinez
T1 - relaxationLongitudinal magnetization (Mz) returns to steady state (M0) with time constant T1
Spin gives up energy into the surrounding molecular matrix as heatFactors
Viscosity Temperature State (solid, liquid, gas) Ionic content Bo Diffusion etc.
February 20, 2003 Francisco M. Martinez
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
February 20, 2003 Francisco M. Martinez
Typical T1’s, T2’s, 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
February 20, 2003 Francisco M. Martinez
Bloch Eq. Revised
20z
2y
x
z
y
x
z
y
x
z
y
x
T
1
MM
0
0
T
1
0
M
M
B
B
B
γ
M
M
M
M
M
M
dt
d
11M)(M 0zT
t
et
20x M)(M T
t
et
20y M)(M T
t
et
Solution on the rotating frame of reference
February 20, 2003 Francisco M. Martinez
Pulse Sequences 90° - 90° - 90° - …
- - - - - …
180° - 90° - 180° - 90° … (Inversion recovery)
90° - 180° - 180° - 180° - 180° …
90° - 180° - 90° - 180° … (Spin echo)
February 20, 2003 Francisco M. Martinez
HardwareFor the BME458 laboratory
PERMANENTPulse
ProgrammerRF Synthesized
Oscillator
Receiver
Mixer
RF AmplifierDetector
MAGNET
RF Amp.
Oscilloscope
Sync. CH1 CH2
RF Transmitting coil
Sample
RF Receiving coil
February 20, 2003 Francisco M. Martinez
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)
February 20, 2003 Francisco M. Martinez
15 MHz Osc/Amp/MixerTunable oscillator Display Coarse/fine adjustment
Power amplifier Amplifies pulses to
produce 12 gauss
(Max 150W)
Mixer Multiplies CW-RF with
received signal
February 20, 2003 Francisco M. Martinez
15 MHz Osc/Amp/MixerMixerMultiplies CW-RF with received signal
CW
FID
Mix
February 20, 2003 Francisco M. Martinez
Imaging
Requires magnetic fields as a function of position
Therefore frequency of oscillation is a function of position