MRI Physics: Just the Basics
An Introduction to MRI Physics and Analysis
Michael Jay Schillaci, PhDMonday, February 4th, 2008
Overview Background
Forces Causes and Effects of MagnetismQuantum Theory - Larmor FrequencyBrain Physiology
Magnetic Fields in an MR SystemMain and Gradient CoilsRF Coils and Spatial EncodingGradient and Spin Echo Sequences
Background
Fields in General: Gravity
ssftGgrM //322
*Actual cause is force of attraction of the mass of ball to the mass of Earth through the “field of gravity”…
gmFg
Fields are covariates of motionWhen a ball falls… We refer to “gravity”…
Fields in General: Electricity
dV
r
QkE 2
*Actual cause is force of attraction of the charge of particle to the charge of Capacitor through the “field of electricity”…
EqFE
EdV
When a particle rises… We refer to “electricity”…
The Causes of Magnetism
Macroscopic ViewCurrent in wireField is “around” wire
Depends on current Depends on distance
Microscopic ViewMoment of atomField is “about” nucleus
Depends on material
r
IB
2
0
cosAB
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.
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
Protons align with a magnetic field…
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
BvqFM
2
02
1BM
Radiation is absorbedEnergy increases
Radiation is emittedEnergy decreases
Lower
Higher
Basic Quantum Theory
Static Field “splits” states Zeeman splits high/low
energy states
RF Field “rotates” moments Precession Frequency
Magnetic Precession
00 B m
qg
42
B0
B0
B0 J
dJ / dt = × × BBo
d/dt = ( × Bo)* For comparison: In the Earth’s magnetic field ( 0.00005 T ), hydrogen precesses at ~2100 Hz.
NMR Parameters B0=1T*
~ 1 ppm excess in spin-up state creates the net Magnetization…
M = net (bulk) magnetizationM
Energy Difference
FrequencyEquate differences
Larmor Frequency
E = Eup – Edown
= z Bo - (-z Bo )z Bo
E = hv0 = z Bo
h B0
002 Bv
Larmor Equation
Quantum Mechanics governs state transitions Energy of transition
Planck’s constant
Energy valuesMRI
X-Ray, CT
Electromagnetic Energy
hE
seVh 15101357.4
eVOE RayX 100102
eVOEMRI 10001910
Excites Electrons
Excites Protons
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
0
2
2B
Volume
Energy
WavelengthEnergy
Material Dependence Magnetization varies with field,
temperature and material
Magnetic susceptibility alters the local field
T
B
kVT
BcM
B
z 02
0 1
0
20
0
11 B
TVkMB
B
zmmLocal
Conductivity
Susceptibility
Brain Physiology – Empirical Brain Conductivity
Measure conductivity of 20 human brainsLess than 10 hours after death
ResultsConductivity 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
Brain Physiology – Measures
Energy Density
Conductivity
Relationship
2ESAR
2
02
1BM
202 cSAR
M
Magnetic Fields in an MR System
USC Trio – Siemens 3T MRI
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).
Transverse Magnetization
Bo
Bo
Longitudinal Axis (z
direction)
Transverse Plane (xy plane)
B is used for magnetic fields.
B0 is the scanner’s main field.
In a magnetic field, protons can take either high- or low-energy states
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.
002 Bv
Main Field Field Characteristics Generated by Helmholtz Coils
— Currents are parallel (same direction)
Field along MRI axis
a
a
22
222
2
20 11
2 azaz
aINB
aa
MMM
Coil 1
Coil 2
B M
Gradient Field Field Characteristics Created by Maxwell Pair
— currents are anti-parallel (opposite direction)
Field along MRI axis
b
b
22
222
2
20 11
2 bzbz
bINB
bb
GGG
Coil 1
Coil 2
BG
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
Gradient field decreases total
Gradient field increases total
ΔB0 ~ 1mT
Spatial Encoding - Gradient Field varies (almost) linearly Change in field = B0
Frequency depends on position (z) Field depends on material
zz
BBz 0
00 2)(
Image Resolution Strong Gradient → High Resolution Weak Gradient → Low Resolution
B0= 0.018 T
z = 0.16 m
Galois Coils Transverse RF Field
— Radio Frequency Transmitter, 0
Rotating frame— Total field given by
— Receiver currents are anti-parallel — Induced field is perpendicular
RF Fields - Generation
tII C sin2
tII C cos1
zBBB C ˆ00
BC-z
r
+x
tt
oo
= 1/ t= 1/ t
FTFT
BC
oo
Transmitter
Receiver
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)
Origin of the MR SignalBefore Excitation
After Excitation
Excitation tips the net magnetization (M) down into the transverse plane, where it
can generate current in detector coils (i.e., via induction).
During Excitation (to)
During Excitation (t1)
The amount of current oscillates at the (Larmor) frequency of the net
magnetization.
1. Assume perfect “spoiling” -transverse magnetization is zero before each excitation:
2. Spin-Lattice (T1) Relaxation occurs between excitations:
3. Assume steady state is reached during repeat time:
4. Spoiled gradient rephases the FID signal at echo time:
Gradient Echo Imaging
coszAzB MM
11 10
TTR
TTR
zBzC eMeMM*2
1
1
cos1
1sin0
TTE
TTR
TTR
Spoil ee
eMS
*2sin T
TE
zASpoil eMS
zAzC MM
1cos TTR
E e
Maximize signal: Ernst Angle
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
Basic Spin Echo Sequences (SE) The refocusing pulse allows us to recover true T2. Image from
http://www.e-mri.org/cours/ Includes interactive adjustment of T1/T2
T2
T2*
The Spin Echo Sequence
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.
Sig
na
lTime
0
1
T2
T2*
0.5 TE 0.5 TE
Actual Signal
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
dxdyetyxMtSArea
dtyGxGi
XY
t
YX
0,,)(
Horizontal density
Ver
tica
l de
nsit
y
T1 & T2 Weighting
T1 Contrast 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
T2 Contrast Weighting
TE
TR TE
TR
Min T2 Contrast Max T1 Contrast
Max T2 Contrast Min T1 Contrast
decay
T
TE
eryre
T
TR
XY eeMM
2
cov
10 1
Static Contrast Images
T2 Weighted Image (T2WI)(Gray Matter – CSF Contrast)
T1 Weighted Image (T1WI)(Gray Matter – White Matter)
Examples from the Siemens 3T T1 and T2 Weighted Images
RF pulse determines “flip angle” Rotation determines amount
of magnetization measured
Field strength determines resolution Increased magnetization
leads to increased signal
Pulse and Field Effects
cosMM Z
Images adapted from: http://www.mri.tju.edu/phys-web/1-T1_05_files/frame.htm
sinMM XY
Muscle
Tissue
Difference
B0= 0.2 T
B0 = 1.5 T