Principles of the MRI Signal

Contrast Mechanisms
MR Image Formation
John VanMeter, Ph.D.
Center for Functional and Molecular Imaging
Georgetown University Medical Center

Outline
Physics behind MRI
Basis of the MRI signal
Tissue Contrast
Examples
Spatial Localization

Properties of Electrical
Fields
S

+
N

Properties of Magnetic
Fields
S

Magnetic Resonance
Imaging
Hydrogen protons spin

producing a magnetic
field

A magnetic field
spinning
proton

creates an electrical
charge when it rotates
past a coil of wire

N
S

bar
magnet

Similarity between a
proton and a bar magnet

Randomly oriented
protons

Protons aligned with a

strong magnetic field

Bo

net magnetic
moment is zero

Mo

net magnetic
moment is
positive

The
MRI
Measurement
S
N

Effect of Static Field on

Protons

Bo

Net magnetization

Precession in Magnetic
Field

Bo

Head Coil (Birdcage)

Spin Excitation

Tipping Protons into the Imaging

Plane

90o pulse

Flip Angle - Degree of

Deflection from Z-axis
z
y
x

90o Radiofrequency Pulse used

to tip protons into X-Y plane.

Magnetic Moment
Measurable After RF Pulse

Bo

Following an RF pulse the

protons precess in the x-y
plane

Mo

The MRI Measurement

(Up to this point)

In the presence of the static magnetic

field
Protons align with the field
Protons precess about the magnetic

Briefly turn on RF pulse

Provides energy to tip the protons at least
partially into the imaging plane

What happens to the protons next?

Types of Relaxation
Longitudinal precessing protons are pulled back
into alignment with main magnetic field of the
scanner (Bo) reducing size of the magnetic moment
vector in the x-y plane
Transverse precessing protons become out of
phase leading to a drop in the net magnetic moment
vector (Mo)
Transverse relaxation occurs much faster than
Longitudinal relaxation
Tissue contrast is determined by differences in these
two types of relaxation

Longitudinal Relaxation in
3D

Longitudinal Relaxation in
2D
90o

z
y
x

Free Induction Decay

Transverse
Relaxation

Wait time TE after excitation before

measuring M when the shorter T2 spins have
dephased.
z

z
y

y
vector
sum

initially

at t= TE

Transverse Relaxation

Bo

Mo

Transverse Relaxation

Bo

Mo

Transverse Relaxation

Bo

Mo

T1 and T2 relaxation

The MRI Measurement

RF

(Sans Spatial Localization)

time

Bo

z
z
Mo

y
x

Voltage
(Signal)

90
y

Mo

x
Mo

V(t)
time

ty
x

Main Tissue Contrast

Controls
Echo Time (TE) time after 90o RF
pulse until readout. Determines how
much transverse relaxation will occur
before reading one row of the image.
Repetition Time (TR) time between
successive 90o RF pulses. Determines
how much longitudinal relaxation will
occur before constructing the next row
of the image.

Tissue Contrast

Intensity

Intensity

Every tissue has a different affect

on longitudinal (T1) and transverse
(T2) relaxation.

Time

Time

T1 Curve

T2 Curve

Contrast in MRI: T1-Weighting

1.0

Signal

0.8

white matter
T1 = 600

gray matter
T1 = 1000

0.6
CSF
T1 = 3000

0.4

0.2

0.0
0

1000

2000

TR (milliseconds)

3000

Optimizing TR Value for T1

Contrast

Effect of Varying TR

T1-Weighting

CSF dark
WM bright
GM gray

Contrast in MRI: T2-Weighting

10

50
TE (milliseconds)

Optimizing TE Value for T2

Contrast

Effect of Varying TE

T2-Weighting

CSF (fluid)
bright
GM gray
WM dark

Contrast in MRI: Proton Density

Tissue with most protons
has highest signal and is
thus brightest in the
image
Proton Density Weighted
aka PDW

Summarizing Contrast
Two main knobs:
TR controls T1 weighting
TE controls T2 weighting

Longitudinal relaxation determines T1

contrast
Transverse relaxation determines T2
contrast

But Wait
How do you set TE to generate a
T1 weighted image?
How do you set TR to generate a
T2 weighted image?
How do you set TR & TE to
generate a proton density
weighted image?

Mixing T1 & T2 Contrast

What do you get if you use the
optimal TR setting for T1 contrast
and the optimal TE setting for T2
contrast?
T3 contrast?
No contrast!!

(time in 1000s of ms)

Tissue Contrast Dependence on TR, TE

Long

PDW

T2

TR
Short

T1

poor!

Short

TE

Long

(time in 10s of ms)

Damadians Discovery
Differential longitudinal relaxation
between healthy and tumorous
tissue in the rat
Walker sarcoma had longer T1
relaxation time than healthy brain
Novikoff Hepatoma had shorter T2
relaxation time than healthy liver

Two Main Classes of Pulse

Sequence
Spin Echo (SE) - uses a second RFpulse to refocus spins
TR & TE control T1 and T2 contrast

Gradient Echo (GE) - uses a gradient to

refocus spins
Flip Angle & TE control T1 and T2* contrast
Used in EPI (fMRI) sequences

T2*-Weighting (GE)
Refer to T2-weighting in a gradient
echo sequence as T2*-weighting
Because of inhomogeneities in the B0
magnetic field T2 relaxation occurs
faster using a gradient echo sequence
than true T2 relaxation as measured
with a spin-echo sequence
The greater the inhomogeneity the
faster T2 decay occurs

T2*-Weighting (GE) vs
T2-Weighting (SE)

T2* Effect

Well shimmed

Poorly shimmed

Venous Infarct

T1Weighted

T2Weighted

PDWeighted

Glioblastoma Multiforme

T1-Weighted

T2-Weighted

Cerebral Lymphoma

T1-Weighted

T2-Weighted

Anaplastic Astrocytoma

T1-Weighted

T2-Weighted

Multiple Sclerosis

The MRI
Experiment
time

RF
Voltage
(Signal)

time

Mo

Bo

90

z
Mo

y
x

Mo

V(t)

The MRI Sequence

(Sans Spatial
Localization)

1) Equilibrium (magnetization points along Bo)

2) RF Excitation
(tip magnetization away from equilibrium)
3) Precession produces signal, dephasing
starts
4) Readout signal from precession of the
magnetization vector (TE)
5) Return to equilibrium and reapply RF
Excitation (TR)

Spatial Localization
Gradients, linear change in magnetic
field, will provide additional information
needed to localize signal
Makes imaging possible/practical
Remember the Indomitable?
Couldnt spatially localize MRI signal instead
moved subject to get each voxel

Nobel prize awarded for this idea!

Larmor Equation
Frequency (rate) of precession is
proportional to the strength of
magnetic field

=*B

Dissecting Larmor
Equation

=*B

Rate of
precession

Magnetic field

Gyromagnetic Constant

Center Frequency
Center frequency is the frequency
(i.e. rate) at which protons spin
(precess) with just the static
magnetic field
If the center frequency of a 1.5T
scanner is 63MHz what it the
center frequency of our 3.0T
scanner?

Center Frequency
B
63MHz

If B = 1.5T

2 * 63MHz

If B = 3.0T

126MHz

Gradients
A gradient is simply a deliberate change in
the magnetic field
Gradients are used in MRI to linearly modify
the magnetic field from one point in space to
another
Gradients are applied along an axis (i.e. Gx
along the x-axis, Gy along the y-axis, Gz along
the z-axis)
What happens to the frequency at which the
precess when we turn on a gradient?

Effect of Gradient on Rate

of Precession

B= B0+ B1
-r

0 1 2 3 4 5 6 7 8 9 +r

Effect of a Gradient

From Proton Signal to

Pixel Intensities
Amplitude of the sinusoidal wave
at a pixel used to determine the
brightness of the pixel (i.e. color)

Signal from Multiple Pixels

Pixel 1
.
.
.

Pixel n

Net
Signal
at Coil

Decomposing Received
Signal
Left unchanged the signal received
cannot be broken down by location of
individual pixels
Need method for efficiently pulling out
the signal from many pixels at once
Gradients used to relate where a
particular signal is coming from

Frequency Encoding
Use a gradient to modify the rate
at which the protons spin based on
location of the proton
Requires the gradient to remain on

Uniform
Field

Col 1

Col 2

Col 3
Uniform
Field

Prior to Gradient

Lower
Field

Col 1

Col 2

Col 3
Higher
Field

Gradient Applied

Frequency Encoding
Apply gradient in one direction and
leave it on
Result:
Protons that experience a decrease in
the net magnetic field precess slower
Protons that experience an increase
in the net magnetic field precess
faster

Side-Effect of Gradient
Gradient also
causes phase of
the protons to
change
Application of a
second gradient of
opposite polarity
will undo this

Frequency Encode
Gradient
The area
under the
second
gradient
must be
equal to that
of the first
gradient

Phase Encoding
Turn gradient on briefly then turn it off
Turning on the gradient will cause some
protons to spin faster others to spin
slower depending on where they are
located
Turning off the gradient will make them
all spin at the same rate again
BUT they will be out of phase with one
another based on where they are located

Phase Encoding

Uniform
Field

Row 1

Row 2

Row 3
Uniform
Field

Prior to Gradient

Lower
Field

Row 1

Row 2

Row 3
Higher
Field

Gradient Applied

Uniform
Field

Row 1

Row 2

Row 3
Uniform
Field

Gradient Turned Off

Phase Encoding
Apply gradient in one direction briefly
and then turn off
Result:
Protons initially decrease or increase their
rate of precession
After the gradient is turned off all of the
protons will again precess at the same rate
Difference is that they will be out phase
with one another

Combining Phase &

Frequency Encoding
Row 1,
Col 1
Row 2,
Col 2
Row 3,
Col 3

Sum Corresponds to
Received Signal

Row 1, Col
1

Row 2, Col
2

Row 3, Col
3

+
+

Converting Received
Signal into an Image
Signal produced using both
frequency and phase encoding can
be decomposed using a
mathematical technique called the
Inverse Fourier Transform
Result is the signal (sinusoidal
squiggles) produced at each
individual pixel

Row 1, Col
1

Row 2, Col
2

Row 3, Col
3

From Signal to Image

Inv FFT
Pixels

Lauterburs Insight
Use of gradients to provide spatial
encoding
Frequency and Phase - was
Lauterburs contribution
Awarded Nobel prize for this work

k-space

Pseudo
Time

Components of Frequency
Domain
Three components to a signal in the
frequency domain:

Amplitude
Frequency
Phase

comes from contrast

rate at which protons spin
direction of protons spin

Inverse Fourier Transform (IFT) is a

mathematical tool for converting data from
frequency domain to image domain

k-space
Frequency increases
from the center out
in all directions
Phase varies by
angle

Images From k-space

K-space is turned into an image
using a Fourier Transformation
2D-IFT

Center of k-space

2D-IFT

Everything Else

2D-IFT

Full Frequency Half

Phase

2D-IFT

Selecting a Slice
Again use gradient to modify frequency of the
protons spin
Slice select gradient is positive on one side of the
slice and negative on the other side
At the desired slice location the slice select
gradient is zero
Thus, protons in this slice and only this slice will be
spinning at the center frequency of the scanner!
If this gradient is on when we apply RF pulse only
protons in the slice will be tipped into x-y plane
and thus measurable

Slice Select Gradient

Slice Thickness vs
Gradient Strength

Slice Orientation

Putting it All Together

Basic Pulse Sequence Diagram

EPI pulse sequence and kspace trajectory

Signal loss due to

susceptibility artifacts in
GRE EPI images

Magnetic Susceptibility Greater on T2*

than T2 Images
Spin
Echo (T2)

Gradient
Echo (T2*)
Oxygenated
Hemoglobin

Deoxygenated
Hemoglobin

Effects of field variation

upon EPI images

Effects of field variation

upon EPI images

Spiral imaging

Susceptibility artifacts in
spiral images

Effects of field variation on

spiral images

Effects of field variation on

spiral images

Acquisition Matrix
Size

64 x 64 Matrix

64 x 128 Matrix

128 x 128 Matrix

Isotropic (square)

Anisotropic
(oblong)

Isotropic (square)

Relative SNR = 1

Relative SNR =
0.5

Relative SNR =
0.25

MRI Image
Acquisition
Constraints
Signal
to Noise Ratio

Spatial
Resolution

Temporal
Resolution