Transcript MRI Physics: Image Acquisition

Fundamental Physics of MRI
Introduction to Cardiovascular Engineering
Michael Jay Schillaci, PhD
Managing Director, Physicist
Thursday, September 11th, 2008
Overview

Theoretical Background



Magnetism and Matter
MR Safety and Brain Physiology
MR Fields and Coils

Main and Gradient Fields


Spatial Encoding
Radio Frequency Coils


M
RF Field Mechanics
R
Image Formation


Basic Pulse Sequences
RF Fields and Timing


Growing (T1) and Decaying (T2)
Repeating (TR) and Listening (TE)
I
Magnetic Resonance Imaging
The Siemens Magnetom Trio
Total Body Imaging System
Magnetic Resonance Imaging
(MRI) technology allows total
body imaging using many
modalities and advanced
analysis techniques.
Theoretical Background
The Causes of Magnetism

Macroscopic View



Current in wire
Field is “around” wire

Depends on current

Depends on distance
B
0 I
2 r
Microscopic View


Moment of atom
Field is “about” nucleus


Depends on material
Depends on angle
B  A cos
Magnetism in Matter

Field Effects




Electric field is “out”
Magnetic field is “around”
Forces are “orthogonal”
Material Effects

Insulators – charges “stuck”


Fields are very weak
Conductors – charges “free”

Fields may be very strong
Material Dependence

Net Magnetization

varies with field, temperature and material
2
B0 1  B0
M c

T V kB T
Conductivity
Susceptibility
In Absence of External Field Moments Align Randomly

Local Field

Susceptibility alters the local field
BLocal  1   m 0 M z

1   m 0  z2

B
Vk BT
0
The Effects of Magnetism

Two ways to assess effects of magnetic fields:


Determine Magnetic Force

Forces move objects

Field is a covariate of force

 
FM  qv  B
Determine Magnetic Energy Density


Energy heats objects
Field is correlated with energy
M 
1 2
B
20
State Transitions

RF Waves are Absorbed

Energy increases
Lower
Higher

RF Waves are Emitted

Energy decreases
Lower
Higher
Electromagnetic Energy

Quantum Mechanics governs state transitions
 Energy of transition
E  h
X-Ray, CT

Planck’s constant
h  4.13571015 eV  s

Excites Electrons
MRI
Energy values
 
EX Ray  O 102  100eV
Excites Protons
 
EMRI  O 109  neV
International Electrotechnical
Commission (IEC)

MRI Safety
Food and Drug
Administration (FDA)
The FDA and IEC place limits on SAR and
How a Scanner Estimates SAR
Determines energy for 90 and 180 degree flip
Adds up energy of all RF pulses divides by TR
Divides by patient weight to get whole body SAR
Peak SAR estimated as 2.5 times higher on most scanners
IEC/FDA Limits for Whole Body Heating
Normal mode limit (suitable for all patients): 2 W/kg
First level controlled mode (medical supervision): 4 W/kg
Second level controlled mode (requires IRB approval): 4 W/kg
IEC/FDA Limits for Localized Heating
Head normal mode limit (averaged over head): 3.2 W/kg
Torso normal mode limit: 10 W/kg
No first level for head, torso or extremities
B
B
t
 c
 b1  
t
 d
b  20 Ts 
Brain Physiology

Energy Density
1
M 
B2
20

Conductivity
 2
SAR  E


Relationship
SAR
M

20c 2

Empirical Methods

Brain Conductivity



Conductivity of 20 brains
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
MR Fields and Coils
Magnetization Directions
+z
Bc
Longitudinal
(Z Axis)
Bo
Bo
+y
+x
B0 is Total Static Field
BC is Dynamic RF Field
Transverse
(XY Plane)
Magnetic Precession

Static Field “splits” states

Zeeman splits high/low energy states
M

B0

B0

M = net (bulk)
magnetization
~ 1 ppm excess
in spin-up state
creates the net
Magnetization…
NMR Parameters B0=1T*
RF Field “rotates” moments

Precession Frequency
dJ / dt =  × Bo
d/dt =  ( × Bo)
 0  B0
B0
J
* For comparison: In the Earth’s magnetic field
( 0.00005 T ), hydrogen precesses at ~2100 Hz.

q

g
2
4m
Magnetic Precession
In the absence of a strong magnetic field, the spins are oriented randomly.
Thus, there is no net magnetization (M).
NO FIELD
0  B0
HIGH FIELD
The difference between the number of protons in the high-energy and low-energy states
results in a net magnetization (M) and gives rise to the Larmor Equation.
The Larmor Frequency

Energy Difference
E = Eup – Edown
= z Bo - (-z Bo )
 2 z Bo

Frequency
E = hv0 = 2 z Bo
 21/2 h /2  B0
B0

B0

Larmor Equation
 0  B0
Main Field

Field Characteristics

Generated by Helmholtz Coils
—

Currents are parallel (same direction)
Field along MRI axis
a
a
Coil 2
Coil 1
BM 
0 N M I M a 2 
2

1
1



2
a 2
z  a2 2  a 2 
 z  2   a
BM
Gradient Field

Field Characteristics

Created by Maxwell Pair
—

currents are anti-parallel (opposite direction)
Field along MRI axis
b
b
Coil 2
Coil 1
BG 
0 N G I G b 2 
2

1
1



2
b 2
z  b2 2  b 2 
 z  2   b
BG
Total (Static) Field

Main Field
 Helmholtz Coils

(Currents in same direction)
B0
Gradient Field
 Maxwell Pair
(Currents in opposite direction)
B0=BM+ BG
Spatial Encoding

The Magnetic Field varies


Frequency depends on position (z)
Field depends on the material (tissue)
 0 ( z) 
B0= 0.018 T
z = 0.16 m

2
B0

B

 0
z


z

By choosing a frequency we
can select a “slice” of the brain.
Slice Selection Gradients
Slope of gradient slice thickness

Position of gradient determines slice selection
Change currents to move zero point of field
Field Strength
Field Strength

Z Position
Z Position
Field Strength

Field strength limits minimum slice thickness
Field Strength

Z Position
Z Position
Radio Frequency (RF) Coils
 Galois Coils


Head Coil is Transmitter and Receiver
RF Transmitter sends frequency
RF Receiver encodes signal
o
BC
+y
BC
t
Fourier
Transform
o
 = 1/ t
+z
I 2  IC sin t 
I1  IC cos t 
  
 
B  BC   B0  0  zˆ
 

+x
Origin of the MR Signal
Before
Excitation
During
Excitation (to)
After
Excitation
During
Excitation (t1)
Excitation tips the net magnetization (M) down
into the transverse plane, where it can generate
current in detector coils (i.e., via induction).
The amount of current oscillates at the (Larmor)
frequency of the net magnetization.
Rotation and Excitation
Net Magnetization M0
Naturally Rotates Around
Applied Field B0
An RF Pulse Causes the
Net Magnetization M0 to
Rotate Away From B0
RF Field - Mechanics

An RF pulse (excitation) rotates the total
magnetization M away from axis
 The torque depends on the total field

 
dM
 M  B
dt
B0
+x
In the laboratory frame the total field is

B  Bc cost xˆ  Bc sint yˆ  B0 zˆ

In the rotating frame the total field is
M
M0
BC





B  BC   B0   zˆ
 

+z
+y
MXY
MZ
T1 - Definition

Spin-Lattice Relaxation Time (T1)

Net magnetization M0 is sum along external field, B0
B0
+z
M
M0
+y
 t

T1 
M z t   M 0 1  e



+x

T1 measures amount of M0 aligned with field

T1 is time for ~63% of M0 to realign with B0
T2 - Definition

Spin-Spin Relaxation Time (T2)

Transverse magnetization MXY is perpendicular to B0
+z
B0
M0
BC
+x

MZ
+y
M XY t   M 0e
it
e
 t
T2
MXY
T2 measures amount of MXY perpendicular to field

T2 is time for ~39% of MXY to remain in transverse plane
Simulated MRI
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Image Formation
Image Formation


Integrate Magnetization to get the MRI signal
 Select a z “slice”; tissue differences in slice give contrast
Scanner acquires K-Space weights
 Image at several times; reconstruct and average slices
t
S (t ) 
 M x, y, t e
i
 xGX   yGY  dt
0
XY
Area

dxdy
Gradient Echo Imaging
1. Assume perfect “spoiling” transverse magnetization is
zero before each excitation:
M zB  M zA cos
2. Spin-Lattice (T1) Relaxation
occurs between excitations:
M zC  M zB e
TR
T1
TR

 M 0 1  e T1




1. Assume steady state is reached
during repeat time (TR):
S Spoil
TR 

T
1  e 1  TE *
 e T2
 M 0 sin  
TR
1  cose T1
M zC  M zA
2. Spoiled gradient rephases the
FID signal at echo time (TE):
SSpoil  M zA sin e
TE
T2*
T1 and T2 Recovery Times

Determine Mz at
half-multiples of T1
MZ 
n
 1  e 2 100%  39%,63%,

M0 

Determine Mxy at
half-multiples of T2
M XY   n 2 
  e 100%  61%,37%,

M0 
T1 and T2 Values

Equilibrium or Net Magnetization Values


Depends directly (linearly) on field strength
Depends (roughly) on percentage of H20 content in tissue
N  z2
M0 
B0  % H 2O B0
V k BT
T1 and T2 Values for Various Tissues and Fields1
Material
% H2O2,3
T1 ( ms )4
B0 = 0.5 T
T2 ( ms )4
B0 = 1.5 T
B0 = 0.5 T
B0 = 1.5 T
White matter
84.3
500
600
74
80
Grey Matter
70.6
650
900
87
100
CSF
99.0
1800
4000
600
2000
1Table Adapted from: http://members.lycos.nl/mri/Nieuw/T1eng.htm
Matter: http://www.fmrib.ox.ac.uk/~stuart/lectures/lecture4/sld004.htm
3CSF Value: http://www.ivis.org/special_books/Braund/tipold/chapter_frm.asp?LA=1
4Values From: Huettel Chapter 5 and http://members.lycos.nl/mri/Nieuw/T1eng.htm
2White/Grey
T1 - Characteristics

A Greater value for T1

Means a lesser amount of M0 has “recovered” at a given time
B0 = 1.5 T
White Matter
Gray Matter
CSF
B0 = 0.5 T
T2 - Characteristics

A greater value for T2

Means a greater amount of M0 has recovered at a given time
CSF
B0 = 1.5 T
White Matter
Gray Matter
B0 = 0.5 T
T1 and T2 Weighted Images

Measuring Magnetization



Send RF at TR (repeat)
Listen for signal at TE (echo)
M XY
TR
TE






T
1
T
2
 e

 M 0 1  e







re cov ery
T1 WEIGHTED IMAGE


Echo at T2 min
Repeat at T1 max
TR
TE
Max T1 Contrast

Min T2 Contrast
T2 WEIGHTED IMAGE


Echo at T2 max
Repeat at T1 min
TR
Min T1 Contrast
TE
Max T2 Contrast
decay