Principles of the MRI Signal Contrast Mechanisms MR Image Formation John VanMeter, Ph.D. Center for Functional and Molecular Imaging Georgetown University Medical Center
Jan 14, 2016
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
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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