Introduction to Magnetic Resonance Imaging

Benjamin M Ellingson, MS Marquette University 21 February 2007

Quantum Theory of Magnetic Resonance

Quantum Theory of Magnetic Resonance Angular Momentum Magnetic Moment, M 0 Low Energy = Parallel High Energy = Antiparallel

Quantum Theory of Magnetic Resonance

Quantum Theory of Magnetic Resonance  So, B 0 (static magnetic field) causes some particles to align antiparallel, but most align parallel 

Classical View

: Vector sum of all magnetization is parallel to B 0 M 0 B 0 Classical View is easier to conceptualize…however some quantum restraints…

Theory of Magnetic Resonance

 Because of the

Uncertainty Principle

, spins cannot completely align with B 0 because the momentum of the particle cannot be defined completely, instead they precess or wobble around B 0 at the Larmor Frequency.

Magnetic Field Larmor Frequency Gyromagnetic Ratio

(specific to atom; 1 H  42.6 MHz/T

Theory of Magnetic Resonance

Laboratory Frame of Reference

: See m rotating about

B 0

in z-direction,

M z

. The time average value of M xy is 0. with net magnetization

M z

m

M xy

Rotating Frame of Reference

: Observer is rotating at the precession frequency, such that m is not moving. All we see all the components of m . In rotating frame of reference we will call this M 0 . So, placing many 1 H atoms in a static magnetic field  M 0 = M z .

Perturb Magnetic Equilibrium

   By applying a horizontal oscillating field at Larmor frequency (

B 1

) produces a torque on the magnetization vector, M 0 .

Since |B 1 | << |B 0 | the net field is still in z-dir Causes M 0 to “tip” into xy-plane.

RF Excitation

Laboratory Frame of Reference: Rotating Frame of Reference:

RF Excitation: Effect of Frequency

Static B 1

:

B 1 (t) = B 1 cos (0.5

w

t) B 1 (t) = B 1 cos (

w

t) B 1 (t) = B 1 cos (1.5

w

t) B 1 (t) = B 1 cos (2

w

t)

Relaxation

 After excitation, if B 1 field is turned off the spins undergo relaxation in both transverse and longitudinal directions at different rates.  

Transverse Relaxation = T2-relaxation = Spin-Spin Relaxation

 Corresponds to dephasing of neighboring spins  Causes decrease in M xy

Longitudinal Relaxation = T1-relaxation = Lattice Relaxation

 Causes increase in M z after excitation

MR Signal

 If we have

a lot

of 1 H excited such that they are spinning

in phase

in the xy-plane (i.e. changing magnetic field) we can detect this with an

antenna

due to Faraday’s Law of Induction: Antenna Total Magnetization

MR Signal: Free Induction Decay

 As T2 relaxation occurs (M xy decreasing), sinusoidal signal at antenna decays with T2 envelope 

Free Induction Decay (FID)

Localization via Magnetic Field Gradients  In a static magnetic field, we have no way of knowing where MR signal is coming from (i.e. all 1 H are precessing at same frequency):

Localization via Magnetic Field Gradients   To solve this problem we introduce a

GRADIENT FIELD

Gradient magnetic fields add to or subtract from the main magnetic field in a controlled and predictable pattern so the field is no longer homogeneous.

Localization via Magnetic Field Gradients

Localization via Magnetic Field Gradients

FREQUENCY ENCODE

Localization via Magnetic Field Gradients 

Frequency Encoding

causes 1-D localization but what about other dimensions?  Use field gradients to

Phase Encode

signal  By pulsing a gradient in another direction we can speed up or slow down spins

Localization via Magnetic Field Gradients

Same frequency but different phase!

2-D Spatial Frequency Domain: k-space

The FID Echo

   We get

maximum

signal when all spins are

in phase

and

no signal

when spins are

dephased

. Just as we used a pulsed gradient to phase encode, we can use pulsed gradients to rephase after dephasing has occurred.

The process of rephasing spins causes a symmetric FID with maximum at time when spins are completely rephased.

Slice Selection

   The previous RF excitation was applied to all 1 H-spins in the body because they were all at the Larmor Frequency ( w 0 = g B 0 ).

If we apply a gradient, G ss , while applying RF excitation at a very specific frequency we can excite an infinitely thin layer of spins.

Practically, we want to excite a “slab” of spins so we have high signal, therefore we envelope the RF excitation in a

sinc function

.

The MRI Pulse Sequence

Ideal Gradient Recalled Echo (GRE)

Slice Selection Phase Encode Frequency Encode

K-space

FID Echo FID

MRI Pros & Cons

  Pros     Non-ionizing radiation Limitless Contrast Possibilities (based on Pulse Sequence Design) Can image in any plane (vs. Axial only for CT) Exquisite Resolution & Soft Tissue Contrast Cons  Relatively Slow (changing due to better hardware and sequence design such as EPI)   No metal (although most implants are now MR compatible) Claustrophobia & Loud

Clinical Applications

 Too Numerous to list them all  Angiography  Diffusion  fMRI (BOLD & ASL)  Cardiac

Medical Imaging & Computing

 Making information accessible  CAD, 3D Visualization, Modality Registration  Reconstruction & Processing Algorithms  Novel Pulse Sequence Image Reconstruction  Real-time Image Reconstruction  Code optimization for fast imaging sequences  Archival & Storage  DICOM, PACs, Image Compression

Additional Info & References

     Additional Information  http://www.ellingsonbiomedical.com/MRI/Lectures/Intro_to_ MRI.htm

Medical College of Wisconsin Biophysics  http://www.mcw.edu

NIH Image Processing Interest Group  http://image.nih.gov

Johns Hopkins Biophysics Group  http://biophysics.jhu.edu

Stanford Magnetic Resonance Laboratory  http://smrl.stanford.edu