Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography:...
Transcript of Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography:...
![Page 1: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/1.jpg)
Computed Tomography: Introduction and Instrumentation
Primary Source: Medical Imaging Signals and Systems
By Jerry Prince and Jonathan Links
![Page 2: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/2.jpg)
![Page 3: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/3.jpg)
![Page 4: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/4.jpg)
CT: Physics
• Same as x-ray radiography: – Image contrast from photoelectric effect
– Image blurring from compton scatter
Particulate ionizing radiation: Electromagnetic ionizing radiation:
![Page 5: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/5.jpg)
CT: Physics – radiation sidenote • http://www.dotmed.com/news/story/11025
• http://emf.mercola.com/sites/emf/archive/2010/09/25/high-ct-scan-radiation-is-deadly.aspx
![Page 6: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/6.jpg)
CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each exposure • Shield all of x-ray beam but slice • Obtain1D projections of 2D axial cross section • A Radon transform takes 1D projections of a 2D object over many angles
and it has an inverse
“raw data” (indirect and tomographic modality)
![Page 7: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/7.jpg)
• The Radon Transform: the integral transform consisting of the integral of a function over straight lines
Projections – general definition/concepts
x
y
θ
l l
l
θ=45o
θ=90o
θ=135o
l θ=0o
θ=179o
l
dxdyyxyxfg )sincos(),(),(
where δ(xcosθ+ysinθ-l) is a line impulse that exists along a line normal to
θ a distance l from the origin.
δ(xcosθ+ysinθ-l)
f(x,y)
g(l,θ), the Radon Transform:
![Page 8: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/8.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1
NS2
NS3
NS4
NS5
NS6
NS7
NS8
NS9
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Battleship:
New Rules
Old way
EW 2/ NS 3 Hit!
EW 5/ NS 6 Miss!
![Page 9: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/9.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1
NS2
NS3
NS4
NS5
NS6
NS7
NS8
NS9
1 0 4
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Battleship:
New Rules
Tell the other
player how
many times you
see a battleship in
a square along
each column.
![Page 10: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/10.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1
NS2
NS3
NS4
NS5
NS6
NS7
NS8
NS9
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Battleship:
New Rules
Here it is finished.
![Page 11: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/11.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1
NS2
NS3
NS4
NS5
NS6
NS7
NS8
NS9
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
If this is all your
opponent told you,
could you find
where the
battleships were?
Need more info.
Repeat the
procedure for
rows.
![Page 12: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/12.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1 1
NS2
1
NS3 4
NS4 1
NS5 0
NS6 0
NS7 3
NS8 0
NS9 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Here are all the
answers.
![Page 13: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/13.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1 1 1 1 0 1 1 1 4 0 1
NS2
1 1 1 0 1 1 1 4 0 1
NS3 1 1 1 0 1 1 1 4 0 4
NS4 1 1 1 0 1 1 1 4 0 1
NS5 1 1 1 0 1 1 1 4 0 0
NS6 1 1 1 0 1 1 1 4 0 0
NS7 1 1 1 0 1 1 1 4 0 3
NS8 1 1 1 0 1 1 1 4 0 0
NS9 1 1 1 0 1 1 1 4 0 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Can you find the
ships now if you just
knew the gray squares?
One idea:
Smear the East West
numbers all the way
up the columns.
This tells us that we
should not spend much
time looking along
EW4 or EW9.
But there is something
probably up in EW8
![Page 14: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/14.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1 1+1
=2
4+1
=5 1
NS2
1
NS3 4
NS4 1
NS5 0
NS6 0
NS7 3+1
=4 3
NS8 0
NS9 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Next, smear the
North/ South
numbers to the left
and add them
to what was in the
grid before.
Where do you
think the ships are?
By the biggest
numbers?
Is this always true?
![Page 15: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/15.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1 2 2 2 1 2 2 2 5 1 1
NS2
2 2 2 1 2 2 2 5 1 1
NS3 5 5 5 4 5 5 5 8 4 4
NS4 2 2 2 1 2 2 2 5 1 1
NS5 1 1 1 0 1 1 1 4 0 0
NS6 1 1 1 0 1 1 1 4 0 0
NS7 4 4 4 3 4 4 4 7 3 3
NS8 1 1 1 0 1 1 1 4 0 0
NS9 1 1 1 0 1 1 1 4 0 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Here I finished
smearing the
north/south
numbers to the left
and adding them to
the east/west
numbers.
Where do you
think the ships are?
By the biggest
numbers?
Is this always true?
![Page 16: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/16.jpg)
EW
1
EW
2
EW
3
EW
4
EW
5
EW
6
EW
7
EW
8
EW
9
NS1 2 2 2 1 2 2 2 5 1 1
NS2
2 2 2 1 2 2 2 5 1 1
NS3 5 5 5 4 5 5 5 8 4 4
NS4 2 2 2 1 2 2 2 5 1 1
NS5 1 1 1 0 1 1 1 4 0 0
NS6 1 1 1 0 1 1 1 4 0 0
NS7 4 4 4 3 4 4 4 7 3 3
NS8 1 1 1 0 1 1 1 4 0 0
NS9 1 1 1 0 1 1 1 4 0 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
East - West Data
N
o
r
t
h
/
S
o
u
t
h
D
a
t
a
Next, smear the
North/ South
numbers to the left
and add them
to what was in the
grid before.
Are the battleships
where the biggest
numbers are?
All of the time?
Some of the time?
![Page 17: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/17.jpg)
1 2 3 4 5 6 7 8 9
A
B
C
D
E
F
G
H
I
BATTLESHIP
0
0
1
1
1
0
0
0 1 1 2 1 1
1
0 0 0
What if we can measure along the diagonals?
![Page 18: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/18.jpg)
1 2 3 4 5 6 7 8 9
A 2 2 3 2 3 2 2 6 2 1
B
2 3 3 2 2 2 3 6 2 1
C 6 6 6 4 5 6 6 9 6 4
D 3 3 2 1 3 3 3 7 2 1
E 2 1 1 1 2 2 3 5 1 0
F 1 1 2 1 2 3 2 5 0 0
G 4 5 5 4 6 5 5 7 3 3
H 2 2 2 2 2 2 1 4 0 0
I 2 2 3 1 2 1 1 4 0 0
1 1 1 0 1 1 1 4 0
BATTLESHIP
Now add the
diagonal
information to our
totals.
Are we doing any
better?
Are the battleships
where the biggest
numbers are more
often?
![Page 19: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/19.jpg)
How is “BMEN 420 Battleship” similar to what we do in CT?
http://www.colorado.edu/physics/2000/index.pl
≈
![Page 20: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/20.jpg)
• Step 1: Backprojection – form 2D images (in (x,y) Cartesian space) from your 1D projections (collected in (ℓ,θ) polar space)
Examples of backprojecting: “smearing” your 1-D projection data collected at
an angle back into x-y space
Image Reconstruction from Projections Backprojection Summation
),sincos(),( yxgyxb
b0 (x,y)
b90 (x,y)
b35 (x,y) x
y
θ
l
![Page 21: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/21.jpg)
• Step 1: Backprojection – form 2D images (in (x,y) Cartesian space) from your 1D projections (collected in (ℓ,θ) polar space)
Examples of backprojecting: “smearing” your 1-D projection data collected at
an angle back into x-y space
Image Reconstruction from Projections Backprojection Summation
),sincos(),( yxgyxb
b0 (x,y)
b90 (x,y)
b35 (x,y)
![Page 22: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/22.jpg)
• Step 1: Backprojection – form 2D images (in (x,y) Cartesian space) from your 1D projections (collected in (ℓ,θ) polar space)
Examples of backprojecting: “smearing” your 1-D projection data collected at
an angle back into x-y space
Image Reconstruction from Projections Backprojection Summation
),sincos(),( yxgyxb
b0 (x,y)
b90 (x,y)
b35 (x,y)
![Page 23: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/23.jpg)
• Step 2: Summation – sum the backprojections from step 1 to obtain the reconstructed object fbs(x,y).
Image Reconstruction from Projections Backprojection Summation
tionbackprojec theis ),sincos(),( yxgyxbwhere
0
sincos0
0
),(),sincos(),(),( dlgdyxgdyxbyxf yxlbs
*how many projections you “need” depends on what you want to see
![Page 24: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/24.jpg)
• Step 2: Summation – sum the backprojections from step 1 to obtain the reconstructed object fbs(x,y).
Image Reconstruction from Projections Backprojection Summation
tionbackprojec theis ),sincos(),( yxgyxbwhere
0
sincos0
0
),(),sincos(),(),( dlgdyxgdyxbyxf yxlbs
*how many projections you “need” depends on what you want to see
![Page 25: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/25.jpg)
CT & General Radiography: Broad Comparisons
Advantages Disadvantages
General Radiography - Inexpensive -“fast” (motion not as big an issue) - no computational power necessary -Broad coverage -Very good resolution
-overlaying structures (projection) -lower contrast
CT -tomography (no overlaying structures) -higher contrast
-more radiation -motion artifacts -expensive -computationally challenging -narrow coverage -big, cumbersome -no long-axis images
Disappearing with computation power, 3D data blocks (allows for reformatting) from spiral, helical, and multislice
![Page 26: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/26.jpg)
CT: Instrumentation – 1st Generation
From Webb, Physics of Medical Imaging
0-D projection of 1-D object (pencil beam) Translate then rotate
![Page 27: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/27.jpg)
CT: Instrumentation – 2nd Generation
From Webb, Physics of Medical Imaging
Eliminate some of translation steps… Still have to translate + rotate
![Page 28: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/28.jpg)
1G and 2G – how large is the time savings?
Consider a 1G or 2G scanner whose source detector apparatus can move linearly at a speed of 1.0 m/sec and the field-of-view has a diameter of 0.5m. Suppose that 360 projections over 180o are required and that it takes 0.5 sec for the source-detector apparatus to rotate one angular increment, regardless of the angle.
-What is the scan time for a 1G scanner?
-What is the scan time for a 2G scanner having 9 detectors
spaced 0.5o apart?
![Page 29: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/29.jpg)
1G and 2G – how large is the time savings?
Consider a 1G or 2G scanner whose source detector apparatus can move linearly at a speed of 1.0 m/sec and the field-of-view has a diameter of 0.5m. Suppose that 360 projections over 180o are required and that it takes 0.5 sec for the source-detector apparatus to rotate one angular increment, regardless of the angle.
-What is the scan time for a 1G scanner?
-What is the scan time for a 2G scanner having 9 detectors
spaced 0.5o apart?
Example 6.1 in MISS - ans: 6 mins versus 40 secs
![Page 30: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/30.jpg)
CT: Instrumentation – 3rd Generation
Eliminate translation Just rotate
![Page 31: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/31.jpg)
CT: Instrumentation – 4th Generation
Eliminate rotation of detectors. Now just source rotates. NO DETECTOR COLLIMATION => More efficient, but more blurring
![Page 32: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/32.jpg)
• Generations 1-4 – Single x-ray tube (bulky, expensive, difficult to calibrate)
– Moving the source limits scan speed
• Generation 5: electron beam computed tomography (EBCT) – Source: Flying electron beam, steered electromagnetically,
to hit one of four tungsten anode strips. X-rays generated are collimated into a fan beam and detection is as with 4G
– Extremely fast (stop action cardiac without gating)
CT: Instrumentation – 5th ,6th , and 7th Generations
![Page 33: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/33.jpg)
• Generation 6: helical CT – 3G/4G continuously rotating with moving patient
for 3D volumetric acquisition • 60cm torso scan, 30 secs
• 24cm lung scan, 12 secs
• 15cm angio scan, 30 secs
• Generation 7: multislice CT – “thick” fan beam, parallel rows of detectors
– Collects multiple (up to 64, 256) 1-D projections at one time
• Multislicehelical = larger pitch on helix:
CT: Instrumentation – 5th ,6th , and 7th Generations
![Page 34: Computed Tomography: Introduction and Instrumentation · CT: Introduction • Computed Tomography: slice picture • Take a series of conventional projection x-rays, rotate b/t each](https://reader036.fdocuments.us/reader036/viewer/2022062508/600169e38099f96ae65155a4/html5/thumbnails/34.jpg)
CT: Instrumentation
• Instrumentation developments (engineering) have paved the way for modern CT: – Fan beam collimation: 2 pieces of lead with a slit 1-10mm between them,
as close as possible to patient. Controls slice thickness. Done at console. – Copper followed by aluminum filtration to “harden” the beam (make it
more monoenergetic) – Solid state detectors, xenon gas detectors (3G), multiple solid state
detector array – Gantry: holds the x-ray tube, detectors, so can rotate around patient
rapidly and repeatedly : movie of Philips Brilliance 16 slice http://www.youtube.com/watch?v=YAqK-huXQoI http://www.youtube.com/watch?v=2CWpZKuy-NE&feature=related – Slip ring: brush system to deliver power to x-ray tube – Patient table: must account for patient loading and continuous controlled
movement (if helical)