Magnetic Resonance for BME 458 Francisco (Paco) Martinez

February 20, 2003 Francisco M. Martinez

Magnetic Resonancefor

BME 458

Francisco (Paco) Martinez


MR Principle

Magnetic resonance is based on the absorption and emission of energy in the radio frequency range of the

electromagnetic spectrum.


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


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


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


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 )


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.


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


/ (2)

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


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.


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


Bloch Equation

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

BγMdt

Md

Vs.


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


Solution to Bloch Eq.

Jump to Matlab simulations that solve the Bloch Equation

- Observe “Rotating Frame of Reference”


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


Tip angle

Tip angle = dt(t)Bγα 1


Resonance

If RF = 0 Resonance

Excitation is effective

If RF 0 Excitation occurs

but it is not optimal

Matlab simulation


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


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.


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


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


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


Pulse Sequences 90° - 90° - 90° - …

- - - - - …

180° - 90° - 180° - 90° … (Inversion recovery)

90° - 180° - 180° - 180° - 180° …

90° - 180° - 90° - 180° … (Spin echo)


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


Receiver

High gain

Linear

Low noise

Centered at 15 MHz


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)


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


15 MHz Osc/Amp/MixerMixerMultiplies CW-RF with received signal

CW

FID

Mix


Imaging

Requires magnetic fields as a function of position

Therefore frequency of oscillation is a function of position


Gradients


Gradients

Recall that:

Now:

zzyyxx aBaBaBB

0zyxz BzGyGx GB


Hardware


Pulse sequences

Spin echo

Gradient echo

EPI

Spiral

… 100’s


References

http://www.cis.rit.edu/htbooks/mri/

Principles of magnetic resonance imaging.

Dwight G. Nishimura, 1996

Magnetic Resonance for BME 458 Francisco (Paco) Martinez

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