1. MRI Physics: Just the Basics
An Introduction to MRI Physics and Analysis
Michael Jay Schillaci, PhD
Monday, February 4th, 2008

2. Overview Background Magnetic Fields in an MR System Forces
Causes and Effects of Magnetism
Quantum Theory - Larmor Frequency
Brain Physiology
Magnetic Fields in an MR System
Main and Gradient Coils
RF Coils and Spatial Encoding
Gradient and Spin Echo Sequences

3. Background

4. Fields in General: Gravity
Fields are covariates of motion
When a ball falls…
We refer to “gravity”…
*Actual cause is force of attraction of the mass of ball to the mass of Earth through the “field of gravity”…

5. Fields in General: Electricity
When a particle rises…
We refer to “electricity”…
*Actual cause is force of attraction of the charge of particle to the charge of Capacitor through the “field of electricity”…

6. The Causes of Magnetism
Macroscopic View
Current in wire
Field is “around” wire
Depends on current
Depends on distance
Microscopic View
Moment of atom
Field is “about” nucleus
Depends on material

7. Properties of Atomic Nuclei
Nuclei have two properties:
Spin (conceptual, not literal)
Charge (property of protons)
Nuclei are made of protons and neutrons
Both have spin values of ½
Protons have charge
Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin
A nucleus has the NMR Property if it has both angular momentum and a magnetic moment. Such nuclei have an odd number of protons or an odd number of neutrons.

8. Kinds of Magnetism Ferromagnetic materials (e.g., Iron)
Both attract and repel other magnets
Create own field
Paramagnetic materials (e.g., Gadolinium)
Attracted toward magnets
Align with other fields
Diamagnetic materials (e.g., Water)
Repelled by magnets
Anti-align with other fields

9. Protons align with a magnetic field…

10. The Effects of Magnetism
Two ways to assess effects of magnetic fields:
Determine Magnetic Force
Forces move objects
Field is a covariate of force
Determine Magnetic Energy Density
Energy heats objects
Field is correlated with energy

11. Basic Quantum Theory Radiation is absorbed Radiation is emitted
Energy increases
Radiation is emitted
Energy decreases
Lower
Higher

12. Magnetic Precession Static Field “splits” states
Zeeman splits high/low energy states
RF Field “rotates” moments
Precession Frequency
M = net (bulk)
magnetization M B0 m
~ 1 ppm excess
in spin-up state
creates the net
Magnetization… B0 m
NMR Parameters B0=1T* B0
m = g J
dJ / dt = m × Bo
dm/dt = g (m × Bo)
* For comparison: In the Earth’s magnetic field ( T ), hydrogen precesses at ~2100 Hz.

13. Larmor Frequency Energy Difference Frequency Equate differences
E = Eup – Edown
= mz Bo - (-mz Bo )
= 2 mz Bo B0 m B0 m
Larmor Equation
E = hv0 = 2 mz Bo
= 2(1/2 h /2p g) B0

14. Electromagnetic Energy
Quantum Mechanics governs state transitions
Energy of transition
Planck’s constant
Energy values
X-Ray, CT
Excites Electrons
MRI
Excites Protons

15. Brain Physiology - Chemistry
Energy of Fields
Heats Brain Tissue
Drives Chemistry
Energy covaries with the wavelength
Higher energy breaks bonds
Medium energy vibrates molecules
Lower energy rotates molecules

16. Material Dependence
Magnetization varies with field, temperature and material
Magnetic susceptibility alters the local field
Conductivity
Susceptibility

17. Brain Physiology – Empirical
Brain Conductivity
Measure conductivity of 20 human brains
Less than 10 hours after death
Results
Conductivity depends on frequency:
1.39 S/m (0.14 S/m) at 900 MHz
1.84 S/m (0.16 S/m) at 1,800 MHz
fmri-fig jpg

18. Brain Physiology – Measures
Energy Density
Conductivity
Relationship

19. Magnetic Fields in an MR System

20. USC Trio – Siemens 3T MRI

21. Protons in no magnetic field
In the absence of a strong magnetic field, the spins are oriented randomly.
Thus, there is no net magnetization (M).

22. Transverse MagnetizationBo Bo
Longitudinal Axis (z direction)
B is used for magnetic fields.
B0 is the scanner’s main field.
Transverse Plane (xy plane)

23. In a magnetic field, protons can take either high- or low-energy states

24. The difference between the numbers of protons in the high-energy and low-energy states results in a net magnetization (M) and gives rise to the Larmor Equation.

25. Main Field Field Characteristics Generated by Helmholtz Coils
B M
Field Characteristics
Generated by Helmholtz Coils
Currents are parallel (same direction)
Field along MRI axis a a
Coil 2
Coil 1

26. Gradient Field Field Characteristics Created by Maxwell PairBG
Field Characteristics
Created by Maxwell Pair
currents are anti-parallel (opposite direction)
Field along MRI axis b b
Coil 2
Coil 1

27. Total (Static) Field Total Field Sum of Main and Gradient Fields
In practice a “shim” field is also used to “flatten” the field.
B0=BM+BG
ΔB0 ~ 1mT
Gradient field decreases total
Gradient field increases total

28. Spatial Encoding - Gradient
Field varies (almost) linearly
Change in field = DB0
Frequency depends on position (z)
Field depends on material
Image Resolution
Strong Gradient → High Resolution
Weak Gradient → Low Resolution
DB0= T
Dz = 0.16 m

29. RF Fields - Generation Galois Coils Transverse RF Field Rotating frame
Radio Frequency Transmitter, w0
Rotating frame
Total field given by
Receiver currents are anti-parallel
Induced field is perpendicular BC
Receiver BC -z r +x
Transmitter wo wo FT t
Dw = 1/ t

30. Radiofrequency Coils Defined by their function:
Transmit / receive coil (most common)
Transmit only coil (can only excite the system)
Receive only coil (can only receive MR signal)
Defined by geometry
Volume coil (low sensitivity but uniform coverage)
Surface coil (High sensitivity but limited coverage)
Phased-array coil (High sensitivity, near-uniform coverage)

31. Origin of the MR Signal During Excitation (to) During Excitation (t1)
The amount of current oscillates at the (Larmor) frequency of the net magnetization.
Before Excitation
After Excitation
fmri-fig jpg
Excitation tips the net magnetization (M) down into the transverse plane, where it can generate current in detector coils (i.e., via induction).

32. Gradient Echo Imaging
Assume perfect “spoiling” -transverse magnetization is zero before each excitation:
Spin-Lattice (T1) Relaxation occurs between excitations:
Assume steady state is reached during repeat time:
Spoiled gradient rephases the FID signal at echo time:
Maximize signal: Ernst Angle

33. Pulse Sequence Parameters
GE imaging
complex effects
maximum SNR typically between 30 and 60 degrees
long TR sequences (2D)
increase SNR with increased flip angle
short TR sequences (TOF & 3D)
decreased SNR with increased flip angle

34. Basic Spin Echo Sequences (SE)
The refocusing pulse allows us to recover true T2.
Image from
Includes interactive adjustment of T1/T2 T2
T2*

35. The Spin Echo Sequence
Actual Signal 1
Spin echo sequence applies a 180º refocusing pulse half way between 90º pulse and measurement.
This pulse eliminates phase differences due to artifacts, allowing measurement of pure T2.
Dramatically more signal with Spin Echo. T2
Signal
T2*
0.5 TE
0.5 TE
Time

36. Image Formation   Integrate magnetization to get MRI signal
Select a z “slice” and form image of XY plane variations
Contrast from difference in magnetization
Image at several times
Scanner acquires K-Space weights
Construct image and average slices
Horizontal density
Vertical density  

37. T1 & T2 Weighting T1 Contrast T2 Contrast Magnetization is given by
Echo (TE) at T2 min
Repeat (TR) at T1 max
T2 Contrast
Echo (TE) at T2 max
Repeat (TR) at T1 min
Magnetization is given by
T1 Contrast Weighting TR TE
Max T1 Contrast
Min T2 Contrast
T2 Contrast Weighting TE TR
Min T1 Contrast
Max T2 Contrast

38. Static Contrast Images
Examples from the Siemens 3T
T1 and T2 Weighted Images
T1 Weighted Image (T1WI)
(Gray Matter – White Matter)
T2 Weighted Image (T2WI)
(Gray Matter – CSF Contrast)

39. Pulse and Field Effects
Images adapted from:
Pulse and Field Effects
RF pulse determines “flip angle”
Rotation determines amount of magnetization measured
Field strength determines resolution
Increased magnetization leads to increased signal q
B0 = 1.5 T
Muscle
Tissue
Difference
B0= 0.2 T