Outline
6.1 MR Image Formation
Matrix, Gradients & Signals
Image formation & k-pace
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
Carolyn Kaut Roth, RT (R)(MR)(CT)(M)(CV) FSMRT
CEO Imaging Education Associates
candi@imaginged.com
www.imaginged.com
Slide # 2
Objectives
Imaging Matrix
Upon completion of this course, the
attendee should…
1. Learn about the matrix.
2. Understand the MR signals and how they
are affected by gradients
3. Learn the concept phase, frequency &
amplitude.
4. Understand image formation, slice
selection, phase encoding, frequency
encoding
5. Understand the concept of k-space.
• Digital images
are created with
a matrix
• Smallest unit of
the digital image
is a pixel
3x3
6x6
Slide # 3
Slide # 4
Pixel , Voxel
What makes up a digital image?
• In MRI slices are
acquired
• The voxel is a 3d
volume element
•The face of the voxel
is the pixel
Voxel
Slice
Thickness
• The size of the area
imaged in MRI is the
field of view (FOV)
• The number of pixels
(rows x columns) is the
matrix
• The depth is the slice
thickness
matrix
matrix
Pixel
Slide # 5
Slice
Thickness
FOV
Slice
Thickness
FOV
Slide # 6
1
Calculating pixel size
Calculating pixel & voxel size
• Isotropic voxel
• to calculate the
pixel size
• to calculate the
voxel size
FOV
FOV
=
= Thickness
Matrix
Matrix
equals
matrix FOV
Voxel
equals
• Pixel size
FOV
x
Matrix
FOV
Matrix
by
FOV
Matrix
Pixel
• Area of the Pixel (mm2)
FOV
Matrix
Slice
Thickness
Pixel
Slice
Thickness
FOV
x
Matrix
times
FOV
Matrix
• Voxel Volume (mm3)
FOV x
Matrix
FOV
Matrix
FOV
Matrix
Slice
Thickness
times
Voxel
FOV x
Thickness
Matrix
times
Slide # 7
Slide # 8
Pixel Size and FOV
Pixel Size and Matrix
• higher matrix
• smaller pixel
• less tissue in the
pixel
• higher resolution
• smaller FOV
• smaller pixel
• less tissue in the
pixel
• higher resolution
3x3
6x6
Pixel
Larger FOV
Smaller FOV
Pixel
Pixel
Slide # 9
Pixel
Slide # 10
Pixel Size and Slice thickness
Imaging Planes
• smaller thickness
• smaller pixel
• less tissue in the
pixel
• higher resolution
• What Views (Planes)
Smaller thickness
Larger thickness
– Sagittal
– Axial
– Coronal
– Oblique
Sagittal
•What Contrast (Planes)
Pixel
Pixel
Slide # 11
– TR
– TE
Axial
Slide # 12
Coronal
2
Timing Diagrams – RF & Gradient Pulses
To Create MR Images
TR (Repetition Time)
TR, is the time
between 900
RF pulses
• The patient is placed in
the magnetic field
RF Pulse
Slice
selection gradient
–to align the spins
Phase
Encoding gradient
These
lines
represent
gradient
pulses
• The RF pulse is applied
–to excite the spins
–at the Larmor Frequency
Frequency
encoding gradient
MR signal
induced in the
receiver coil
MR signal
TE (Echo Time)
Slide # 13
Slide # 14
Short & Long TR Imaging
MR Excitation Relaxation
Short TR
Bo
1800
900 RF Pulse
Z
Z
Z
Mz
900
Mxy
X
X
MR Signal
FID
Long TR
1800
Y
Y
Alignment
RF
Receiver
coil
Excitation
900
Relaxation
Slide # 15
Slide # 16
Timing Diagram
Timing Diagram -TE
TR (Repetition Time)
1800
1800
900
Proton density-TE1
T2WI-TE2
T2 decay
TE (Echo Time)
FID
echo
TE 1
Image with artifact
Slide # 17
echo
TE 2
Cleaned up the “SIC”
Slide # 18
3
Imaging Planes
Imaging Planes
• What Views (Planes)
– Sagittal
– Axial
– Coronal
– Oblique
Sagittal
•What Contrast (Planes)
– TR
– TE
Axial
Sagittal
Slide # 19
Coronal
Slice
selection gradient
Phase
Encoding gradient
PE (Y)
FE (X)
Oblique
Slice Selection
• If the magnetic field is
homogeneous, the
frequency is the same
… head to feet
• If the RF is applied…
in this case the entire
body would be excited
RF Pulse
SS (Z)
Axial (Transverse)
Slide # 20
Timing Diagram – Gradients- logical coordinate system
Gradients
Coronal
Frequency
encoding gradient
MR signal
Slide # 21
Homogeneous magnetic field
The frequency is the same
from the head to the feet
Slide # 22
Selecting an Axial Slice – Physical Coordinate System
Selective Excitation
•To excite a location
within the imager, within
the body..
• A magnetic field
gradient is applied
• The RF pulse is applied
that matches a location
Homogeneous magnetic field
gradient
Axial slice
Z gradient
Superior to Inferior
Slide # 23
Homogeneous magnetic field
With a linear gradient field applied
Slide # 24
4
Selecting a Coronal Slice - Physical Coordinate System
Selecting a Sagittal Slice - Physical Coordinate System
X gradient
Right to Left
Y gradient
Anterior to Posterior
Coronal slice
Sagittal slice
Slide # 25
Slide # 26
Phase & Frequency Encoding
Outline
Gradient
S to I
• Once the slice is selected…
• Encoding along the other
axes,
–With gradients
•R to L
•A to P
Axial slice selection
Gradient
R to L
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
Gradient
A to P
–For encoding
•Phase encoding
•Frequency encoding
Axial slice
Slide # 27
Periodic signals
Slide # 28
Amplitude
wavelength
Low Amplitude Signal
Phase
Frequency
Medium Amplitude Signal
Amplitude
Wavelength
Enhanced Brain Image
High Amplitude Signal
Slide # 29
Slide # 30
5
Frequency
Phase
1 second
Periodic signal
Sine wave
Frequency = # times it repeats in a period of time
cycles per second or Hertz (Hz)
or million cycles per second , or megahertz (MHz)
What phase of the precession
where along the precessional path
In phase
Out of phase
1 cycles per second
Revolutions along the precessional path
In Phase
Out of phase
2 cycles per second
4 cycles per second
Slide # 31
Slide # 32
Phase & Frequency
Phases of Periodic Signals
90 degrees
0 degrees
180 degrees
360 degrees
0 degrees
90 degrees
180 degrees
270 degrees
270 degrees
Frequency is the rate of precession
Phase is a positionSlide
along
a precessional path
# 33
Changing the Frequency and Phase
Steep Gradient
High Amplitude Gradient
High changes in frequencies
Big changes in phase
De phased
Low signal
Low amplitude signal
Low Gradient
Low Amplitude Gradient
Small changes in frequencies
Small changes in phase
In phase
High signal
High amplitude signal
Slide # 35
Slide # 34
Signal Amplitude
Phase & Frequency = Where
Amplitude = What color
Black – Low Amplitude
Gray – Medium Amplitude
White – High amplitude
Slide # 36
6
Phase & Frequency
K-Space & MR Imaging
Phase & Frequency = Where
Same frequency – different phase
Amplitude = What color
Black, low
K-space (raw signal data)
Gray, med
White, high amplitude signal
Phase & Frequency = Where
Phase lines in k-space
Freqency – points along each line
Same phase different frequency
Same phase and frequency,
different ampltude
Slide # 37
MR Image)
Slide # 38
CT Image Acquisition
Back Projection
Phantom
X-ray
Xray
Water
Projection
Detectors
Water
Projection
In CT, the xray tube rotates around the “phantom”
In this case the x-ray beam is attenuated by the water in the phantom,
and therfore “projects” a “shadow” within the detectors…
Slide # 39
Slide # 40
Back Projection - Reconstruction
MR Image Formation
• In order to define a point
in space, we need three
coordintes X, Y & Z
Where the lines intersect,
there could be water in the phantom
Two projections are not enough!
Projection #1
Projection #3
He third projection allowed for the image!
Projection #2
Slide # 41
• To define these three
coordinates, we do 3 jobs
- slice selection
- phase encoding
- frequency encoding
3 x 3 Matrix
Slide # 42
7
Timing Diagram - Logical Coordinate System
Outline
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
RF Pulse
Gradients
SS (Z)
Slice
selection gradient
Phase
Encoding gradient
PE (Y)
FE (X)
Frequency
encoding gradient
MR signal
Slide # 43
Slide # 44
Slice Selection
Selective Excitation
• If the magnetic field is
homogeneous, the
frequency is the same
… head to feet
• If the RF is applied…
in this case the entire
body would be excited
Homogeneous magnetic field
The frequency is the same
from the head to the feet
Slide # 45
•To excite a location
within the imager, within
the body..
• A magnetic field
gradient is applied
• The RF pulse is applied
that matches a location
Slide # 46
Homogeneous magnetic field
gradient
Homogeneous magnetic field
With a linear gradient field applied
Slice Thickness & Transmitter Bandwidth
Slice Thickness & Gradient Amplitude
•If only one frequency is “sent in”
or transmitted for excitation, we
get a slice as thin as tissue paper.
•Steep Gradients (high amplitude)
slice selection gradient, produce thin
slices.
With a given BW, a steep gradient
produces a thinner slice
This radiofrequency matches the location in the mid
section of this patient, hence a thin axial slice in the belly
•For a thicker slice a range of
frequencies is “transmitted” known
as the Transmit Bandwidth
FYI… This is not the bandwidth that we typically
“set” during image acquisition. That is the
receiver bandwidth. Receive bandwidth will be
discussed later in this section
This range of radiofrequencies (or Bandwidth) matches the location
47this patient, hence a thin axial slice in the belly
in the mid Slide
section# of
•Flatter Gradients (low amplitude)
slice selection gradient, produce
thicker slices.
•“Steep things make skinny things!”
With a given BW, a flatter gradient
produces a thicker slice
Slide # 48
8
Imaging Planes & Slice Selection Gradients
Physical vs Logical Gradients
Logical Gradients
RF pulses
for spin echo
Z gradient
Physical Gradients
•Slice Selection
Z (runs superior to inferior) (axial)
Y (A-P) (coronal)
X (R-L) (sagittal)
Z
Slice Selection
Axial slice
Z gradient
Superior to Inferior
Sagittal slice
X gradient
Right to Left
•Phase Encoding
-Depends upon the plane
smaller word
smaller anatomy (motion)
smaller matrix (time)
Y
Phase Encoding
X
Frequency Encoding
Phase
Phase
•Frequency Encoding
-Depends upon the plane
Frequency
Z & Y gradient
Anterior to Posterior
Slide # 49
Frequency
The gradient used for
oblique depend upon
the oblique desired
Coronal slice
Y gradient
Anterior to Posterior
motion
Slide # 50
Spatial Encoding within the Slice
Spatial Encoding within the Slice
Gradient
S to I
• Once the slice is selected
• Encoding along the other axes,
–With gradients
Axial slice selection
•R to L
•A to P
Gradient
A to P
–For encoding
•Phase encoding
•Frequency encoding
Gradient
R to L
Fourier states that any “shape” can be reconstructed by periodic signals
Slide # 51
Slide # 52
Fourier Transformation – Step #1
Fourier Transformation – Step #2
Step #2
•Let’s take another sine wave
with lower amplitude and
higher frequency
•And try again
Step #1
•Let’s take one sine wave and
•Try to produce a “ramp”
Sine wave
Ramp
Sine wave
•Not Even close…
Ramp
•Better…
Step #1
Storage space
K-space
Slide # 53
? Image
Storage space
K-space
? Image
Slide # 54
9
Fourier Transformation – Step #3
Fourier Transformation – step #4
Step #3
•Let’s take another sine wave
with lower amplitude and
higher frequency
•And try again
Sine wave
Ramp
Step #4
•Let’s take another sine wave
with lower amplitude and
higher frequency
•And try again
Sine wave
Ramp
•Better but no cigar!
The Ramp
Storage space
K-space
•Not Bad!
? Image
The Ramp
Storage space
Slide # 55
K-space
? Image
Slide # 56
Truncation Artifact – 2D Fourier Tranform (2DFT)
K-space - Sampling
Center of K-space for
Contrast
Signal to Noise
Edges of K-space
Detail
Resolution
K-space
Brain image
128 phase matrix
Brain image
256 phase matrix
Image Matrix
Edge
Center
Virtually no visible
truncation Artifact
Truncation Artifact
Less Samples
Edge
More Samples
Storage space
Slide # 57
Image Formation & K-space filling
K-space for Mona Lisa
All lines filled
Image
Slide # 58
Image Formation & K-space filling
K-space for Mona Lisa
Edges Filled
Slide # 59
K-space
Resolution
But no contrast…
Slide # 60
10
Fourier Transformation
Image Formation & K-space filling
Ft
K-space for Mona Lisa
Center lines filled
Contrast but
No resolution…
K-space for Mona Lisa
All lines filled
Fourier transformer will do FT, one at a time
Array processor will to an “array” of FT’s
Slide # 61
Slide # 62
Let’s Make an MR Image…
Outline
Gradient
S to I
• Select a slice
• Encode along the other axes,
–With gradients
Axial slice selection
•R to L
•A to P
Gradient
A to P
–Encoding Steps
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
•Phase encoding
•Frequency encoding
Gradient
R to L
Slide # 63
Slide # 64
Image Acquisition & Image Formation
Sampling MR Signal
• Signals are created by a 900 and a 1800 pulse
• Signals are sampled during “readout” at TE
• Points are “stored” in k-space for until enough
points are sampled to create an MR Image
RF
SS (Z)
Phase matrix & FOV
PE (Y)
K-space sampling points
K-space sampling points
signals in K-space
Readout
Frequency Encoding Gradient
Frequency matrix & FOV
FE (X)
Signal
Signal
Timing Diagram
K-space
Not the image (raw data)
Slide # 65
Image
matrix (# phase & # frequency steps)
TE
Slide # 66
11
Nyquist Therum
Aliasing
• Signals must be samples at
least twice per cycle
• This means that they must be
sampled at the highest
frequency
• Sampling is performed at a
given time interval (t) based on
the frequency
t
Signals sampled at a given time interval
• If signals are not sampled at
the appropriate time interval
• Signals are not sampled
properly
• This results in aliasing
t
Signals sampled at a given time interval
Aliasing
Signals reproduced from sampling points
Undersampled signals, reproduce the wrong frequency
Signals reproduced from sampling points
Slide # 67
Undersampled
signals
Slide # 68
K-Space
K-Space
• K-space has lines, # Phase encoding steps
• And points along each line, # Frequency steps
•Steep (-) phase encoding gradient
•Sample the echo
•“Store” in k-space
Steep negative gradient
Phase
Phase matrix & FOV
Steep negative gradient
Phase
Frequency matrix & FOV
Frequency
Sample points along the echo
Slide # 69
Frequency
Points stored in the bottom line of k-space
Slide # 70
Image Formation
K-Space
• Less Steep (-) phase encoding gradient
•Sample the echo
•“Store” in k-space
Less Steep negative gradient
Phase
Less Steep negative gradient
Steep negative gradient
Sample points along the echo
Slide # 71
Frequency
Points stored in the bottom of k-space
Edges only
Center only
Slide # 72
12
Image Formation
Image Formation
•Less Steep (-) phase encoding gradient
•Sample the echo
•“Store” in k-space
Less Steep negative gradient
•Flat phase encoding gradient
•Sample the echo
•“Store” in k-space
Flat gradient
Flat gradient
Less Steep negative gradient
Less Steep negative gradient
Steep negative gradient
Sample points along the echo
Phase
Phase
Less Steep negative gradient
Less Steep negative gradient
Steep negative gradient
Frequency
Points stored in the bottom of k-space
Sample points along the echo
Slide # 73
Frequency
Points stored in the middle of k-space
Slide # 74
Image Formation
Image Formation
•Low amp (+) phase encoding gradient
•Sample the echo
•“Store” in k-space
Less Steep positive gradient
•Steeper (+) phase encoding gradient
•Sample the echo
•“Store” in k-space
Steeper positive gradient
Higher positive amplitude positive
Low amplitude positive
Flat gradient
Less Steep negative gradient
Less Steep negative gradient
Steep negative gradient
Sample points along the echo
Phase
Phase
Low amplitude positive
Flat gradient
Less Steep negative gradient
Less Steep negative gradient
Steep negative gradient
Frequency
Points stored in the top of k-space
Slide # 75
Sample points along the echo
Frequency
Points stored in the top of k-space
Slide # 76
Image Formation
K-space & Image Formation
•Steep (+) phase encoding gradient
•Sample the echo
•“Store” in k-space
Steepest positive gradient
Phase
Highest positive amplitude positive
Higher positive amplitude positive
Low amplitude positive
Flat gradient
Less Steep negative gradient
Less Steep negative gradient
Steep negative gradient
Sample points along the echo
Slide # 77
Frequency
Points stored in the top line of k-space
Scan Time
TR x # of Phase Views x NSA
Slide # 78
13
Motion Artifact
Outline
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
• k-space manipulation
Slide # 79
Filling k-space
Slide # 80
*Assume 256 phase matrix for this entire module
Remember:
The amplitude of the phase encoding gradient applied during the FID "encodes" the
sampled echo for a particular phase "line" or "profile" in k-space
+ 128 ky
Linear Filling
Fills from "bottom" up
ky
0 ky
+ 128 ky
0 ky
kx
- 128 ky
kx
These red arrows represent
the echoes sampled
following a given phase
gradient applied during the
FID
- 128 ky
If we desire a final image with 256 pixel resolution in the phase direction
of our FOV, then we will need to acquire 256 distinctive lines of acquisition
filling the data points in k-space
-128, -127, -126....-1, 0, +1, +2 ... +126, +127, +128
Slide # 81
Slide # 82
Centric Filling
Elliptic Filling
This technique acquires
high signal data "lines" first
Fills from "Middle" out
+ 128 ky
ky
Remember:
X = Frequency
Y = Phase
Z = Slice
ky
0 ky
Often used in Contrast
Enhanced MRA studies
kx
- 128 ky
This technique acquires
the most "central" data
points first
Fills from "Center" out
+ 128 ky
ky
*The center data points
in k-space contribute 0 ky
most to the final images
signal (contrast)
3D acquisition used for
Contrast Enhanced MRA to
minimize venous filling
kz
- 128 ky
0, +1, -1, +2, -2, +3, -3..............+128, -128
Slide # 83
These techniques fill k-space in either a "symmetrical" fashion as shown
here, or in a random pattern from the center data points outward
Slide # 84
14
Number of Signals Averaged (NSA)
Reducing NSA
Scan Time = TR x Ny x NSA
Scan Time = TR x Ny x NSA
+ 128 ky
1 NSA
1 NSA
ky
Reducing NSA
2 NSA
0 ky
3 NSA
- 128 ky
2 NSA
Reduces scan time
DOES NOT reduce
spatial resolution
Increases noise
(reduces SNR)
Increased flow/motion
artifacts
4 NSA
Think of the NSA as "coats of paint"
It's the number of times each "line" or "phase view"
of k-space is sampled
Image courtesy Dr. Val Runge
4 NSA
Image courtesy Dr. Val Runge
Slide # 85
Slide # 86
Partial Fourier
Reducing Phase Matrix
Scan Time = TR x Ny x NSA
Scan Time = TR x Ny x NSA
Ky
3 NSA
Ky
+y
Interpolated
Data
-y
Partial Fourier reduces scan time at the cost of increased noise (reduced SNR)
Spatial Resolution is Unaffected
“Physics of Clinical MR Taught Through Images”
V. Runge, Thieme Medical Publishers, 2005
Slide # 87
Slide # 88
Zero Fill
Zero Fill
Scan Time = TR x Ny x NSA
Scan Time = TR x Ny x NSA
Ky
256x 128y
256x 256y
Ky
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000
Reducing Ny
Reduces Scan Time
Reduces Spatial Resolution
Increased SNR
Increases Truncation Artifact
* Note: the number of phase encodings
may be selected by scan percentage
Image courtesy Dr. Val Runge
Slide # 89
Slide # 90
15
Rectangular FOV
Rectangular FOV
Scan Time = TR x Ny x NSA
Scan Time = TR x Ny x NSA
Standard Acquisition
+ 128 ky
50% Rectangular FOV
ky
+ 128 ky
ky
Phase
0 ky
0 ky
- 128 ky
- 128 ky
240 FOV / 256p
120 FOV / 128p
rFOV reduces scan time at the cost of
increased noise (reduced SNR)
Reduces Ny - reducing scan time
Increasing "step" between phase views
reduces pFOV
Slide # 91
Slide # 92
Parallel Imaging
Conventional Spin Echo
•Scan time is reduced by using a
Image courtesy Dr. Val Runge
rectangular FOV (therefore spatial
resolution is maintained)
•Data from multi-channel / phased-array
coils is used the image reconstruction
process
•Some techniques require a "reference" or
"calibration" scan prior to the actual scan
•Image is reconstructed with the
prescribed FOV
+ 128 ky
Gy
0 ky
kx
Gx
- 128 ky
-128, -127, -126....-1, 0, +1, +2 ... +126, +127, +128
Slide # 93
Slide # 94
Fast Spin Echo
Scan Time
Conventional Spin Echo
4 ETL Example
Fast Spin Echo
TR x Ny x NSA
+ 128 ky
0 ky
ETL
128 phase
160 phase
192 phase
256 phase
Gy
•Conventional Spin Echo fills one
"line" of k-space per repetition of the
pulse sequence
•Fast Spin Echo fills multiple lines of
k-space per repetition of the pulse
sequence
•The number of lines filled per
repetition period is determined by the
Echo Train Length (ETL)
•The TE most effecting image
contrast is placed in the more central
"lines" (effective TE)
TR x Ny x NSA
kx
10 ETL
14 ETL
17 ETL
25 ETL
Scan time increases
with increasing spatial
resolution (phase)
Scan time shortens
with increasing ETL
Scan time shortens
with reduction in spatial
resolution (phase)
Image "blurring" can increase
with increasing ETL
- 128 ky
Image Courtesy Siemens Medical Systems
Slide # 95
Slide # 96
16
Echo Planar Imaging (EPI)
Benefits of Fast Spin Echo
Sample Scan Time
TR x Ny x NSA
3000 TR x 256 phase x 2 NSA = 25.6 minutes !
Same scan with FSE and ETL of 16 = 1.6 minutes !!
500 TR
1500 TR
3000 TR
5000 TR
Images with bright
fluid often show pathology
best due to presence of water
The long T1-relaxation time
of water requires longer TR times
to obtain images with bright fluid
Scan time increases
with increasing TR
Slide # 97
Slide # 98
EPI Speed Compared to FSE
Summary
Scan Time = TR x Ny x NSA
FSE
FSE
180
180
echo
echo
180
180
echo
echo
180
180
echo
echo
180
180
echo
echo
90
90
How many lines of acquisition?
Zero-fill
EPI
EPI
180
180
echo
echo
echo
echo
echo
echo
echo
echo
echo
echo
echo
echo
echo
echo
Reduced NSA
Partial Fourier
90
90
Rectangular FOV
(Parallel Imaging)
SS-EPI
4 sec
whole brain
(1.5T)
FSE
25 sec
whole brain
(3T)
Reducing scan time by altering the way k-space is filled
typically reduces either spatial resolution or SNR
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Slide # 99
Since reduced spatial resolution is almost always
undesirable, therefore, most advanced imaging
techniques are SNR starved
6
Slide # 100
6
Outline
• Imaging Matrix
• Gradients & Signals
• Phase, Frequency and Amplitude
• Slice selection
• Phase encoding
• Frequency encoding
6.1 MR Image Formation
Matrix, Gradients & Signals
Image formation & k-space
Thank you for your attention!
Click to take your post test and get your credits
Carolyn Kaut Roth, RT (R)(MR)(CT)(M)(CV) FSMRT
CEO Imaging Education Associates
candi@imaginged.com
www.imaginged.com
Slide # 101
17