Principles of the MRI SignalContrast MechanismsMR Image Formation

John VanMeter, Ph.D.

Center for Functional and Molecular ImagingGeorgetown University Medical Center

Outline

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

Properties of Electrical Fields

N

S+

-N

S

Properties of Magnetic Fields

N

S

N

S

+

spinningproton

barmagnet

•Hydrogen protons spin producing a magnetic field

•A magnetic field creates an electrical charge when it rotates past a coil of wire

Magnetic Resonance Imaging

Similarity between a proton and a bar magnet

net magnetic moment is zero

Randomly oriented protons

Bo

net magnetic moment is

positive

Protons aligned with a strong magnetic field

Mo

N

SThe MRI Measurement

+

Bo

Effect of Static Field on Protons

Net magnetization

Precession in Magnetic Field

Bo

Head Coil (Birdcage)

Spin ExcitationTipping Protons into the Imaging

Plane

90o pulse

90o Radiofrequency Pulse usedto “tip” protons into X-Y plane.

x

y

z

Flip Angle - Degree of Deflection from Z-axis

Following an RF pulse the protons precess in the x-y plane

Bo Mo

Magnetic Moment Measurable After RF Pulse

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

Free Induction Decay

x

y

z90o

Longitudinal Relaxation in 2D

Transverse Relaxation

Wait time TE after excitation before measuring M when the shorter T2 spins have dephased.

x

y

z

x

y

z

x

y

z

vectorsum

initially at t= TE

Transverse Relaxation

MoBo

Transverse Relaxation

MoBo

Transverse Relaxation

MoBo

T1 and T2 relaxation

The MRI Measurement (Sans Spatial Localization)

RF

time

Voltage(Signal)

time

Mo

t

x

y

z

x

y

z

x

y

z

Mo

90°

V(t)

Bo

Mo

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.

T1 Curve T2 Curve

Inte

nsi

ty

Inte

nsi

ty

Time Time

Tissue ContrastEvery tissue has a different affect on longitudinal (T1) and transverse (T2) relaxation.

30002000100000.0

0.2

0.4

0.6

0.8

1.0

TR (milliseconds)

Sig

nal

gray matterT1 = 1000

CSFT1 = 3000

white matterT1 = 600

Contrast in MRI: T1-Weighting

Optimizing TR Value for T1 Contrast

Effect of Varying TR

T1-Weighting

•CSF dark

•WM bright

•GM gray

TE (milliseconds)

5010

Contrast in MRI: T2-Weighting

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!!

Tissue Contrast Dependence on TR, TE

TR

Long

Short

Short LongTE

PDW

T1 poor!

T2

(time in 10’s of ms)

(tim

e in

10

00

’s o

f m

s)

Damadian’s 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 RF-pulse 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

T2-Weighted

T1-Weighted

PD-Weighted

Venous Infarct

Glioblastoma Multiforme

T2-WeightedT1-Weighted

Cerebral Lymphoma

T2-WeightedT1-Weighted

Anaplastic Astrocytoma

T2-WeightedT1-Weighted

Multiple Sclerosis

The MRI Experiment

x

y

z

RF

time

x

y

z

Voltage(Signal)

time

Mo

t

x

y

z

Mo

90°

V(t)

Bo

Mo

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?– Couldn’t 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

Gyromagnetic Constant

Rate of precession

Magnetic field

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?

BB= B0+ B1

+r0-r 1 2 3 4 5 6 7 8 9

Effect of Gradient on Rate of Precession

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)

Net Signal at Coil

Signal from Multiple Pixels

Pixel 1

.

.

.

Pixel n

+

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

Prior to Gradient

Col 1

Col 2

Col 3

Uniform Field

Uniform Field

Gradient Applied

Col 1

Col 2

Col 3

Lower Field

Higher Field

Frequency Encoding

• Apply gradient in one direction and leave it on

• Result:Protons that experience a decrease in

the net magnetic field precess slowerProtons 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

Prior to Gradient

Row 1

Row 2

Row 3

Uniform Field

Uniform Field

Gradient Applied

Row 1

Row 2

Row 3

Lower Field

Higher Field

Gradient Turned Off

Row 1

Row 2

Row 3

Uniform Field

Uniform Field

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 rateDifference 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

From Signal to Image

Row 1, Col 1

Row 2, Col 2

Row 3, Col 3

Inv FFTPixels

Lauterbur’s Insight

• Use of gradients to provide spatial encoding

• Frequency and Phase - was Lauterbur’s contribution

• Awarded Nobel prize for this work

PseudoTime

k-space

Components of Frequency Domain

• Three components to a signal in the frequency domain:– Amplitude comes from contrast– Frequency rate at which protons spin– Phase direction of proton’s 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 outin 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 proton’s 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 k-space trajectory

Signal loss due to susceptibility artifacts in

GRE EPI images

Magnetic Susceptibility Greater on T2* than T2 Images

OxygenatedHemoglobin

DeoxygenatedHemoglobin

Spin GradientEcho (T2) Echo (T2*)

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

Isotropic (square)

Relative SNR = 1

64 x 128 Matrix

Anisotropic (oblong)

Relative SNR = 0.5

128 x 128 Matrix

Isotropic (square)

Relative SNR = 0.25

Signal to Noise Ratio

Spatial Resolution

TemporalResolution

MRI Image Acquisition Constraints