From Radio Astronomy to
Image-guided Surgery
Terry Peters
Robarts Research Institute
University of Western Ontario
Toronto
LONDON
Detroit
Cleveland
How I became a medical imager....
• 1966: Began BE in EE
at University of
Canterbury
• 1970: Entered PhD
program
• EE and Medicine
My professor
•
•
•
•
•
•
Engineer
Physicist
Mathematician
Radio astronomer
Optical astronomer
Biomedical
researcher
• Chess player
• Musician
• Former President
ACPSEM
Richard Bates DSc,
FIEEE,FRSNZ (1929-1990)
Professor of EE,
U Canterbury, Christchurch NZ
My project(s)
Which project led to CT research?
•Electromagnetic scattering?
•Bone Density with Ultrasound?
…and don’t forget to
use the Fourier
Transform!
Why Fourier?
• Prof Bates “lived in Fourier Space”
– Radio Astronomy
– Optics
– Image processing
• Inspired by
– Ronald Bracewell – Sydney/Stanford
– Interferometric reconstructions of celestial radio sources*
• Similar maths applied to CT and MRI
• Fourier reconstruction
– Central slice theorem: CT/MR
– Filtered back projection: CT
– K-space sampling: MR
* Fourier transforms with mechanical calculator
The Fourier Integral
…and its 2D equivalent…
 
f ( x, y ) 

F
(
u
,
v
)
e

  
i 2 ( ux  vy )
dudv
A powerful technique!
Bracewell’s Radio Astronomy Problem
A source distribution f(x,y) of outer diameter D and its
two-dimensional Fourier Transform.
From Bracewell, R.N. Strip integration in radio astronomy. Aust. J.
Phys., 9, 198, 1956, and Bracewell and Riddle. Inversion of Fan
beams in Radio Astronomy, Astrophys J 1967.
The CT reconstruction problem
X-ray density distribution f(x,y) of outer diameter D and
its two-dimensional Fourier Transform.
Central Slice Theorem
Horizontal Projection
2-D Inverse FT
1-D Fourier Transform
Vertical Projection
Interpolate in Fourier
Transform Space
1-D Fourier Transform
2-D Fourier Transform
Filtered Back Projection
Back-project filtered
projections (at all angles)
Cross-section of head
FT

Inv FT
Or convolve with
Vertical projection
of this cross-section
Modified (filtered) projection
A Son Reminiscences
Jason HT Bates PhD DSc, U Vermont
1971……
• We set out to test theories on real data
• Borrowed x-ray tube/film
• Jig to rotate object and acquire images
• Scanning densitometer
• Manually digitize graphs onto punch cards
…but we needed an object to scan!
A plentiful source….
The “Object”
The “Reconstruction” 1972
• 20 radiographs;
• 20 mins recon IBM 360
• “Pretty pictures, but
they will never replace
radiographs” –Senior NZ
Neuroradiologist
• Hounsfield reports
on invention of EMI
scanner!
Sir Godfrey Hounsfield
• Engineer for EMI PLC
• UK Patent 1968-72
• Nobel Prize 1979 (with
Alan Cormack)
• Bracewell sadly omitted
from recipients
• Knighted 1981
And how did EMI fund this work?
Getting real…
Xenon ionization chamber
The Christchurch CT Scanner ca 1978
….and all for $20K!
Then…….
• 1974
•
•
•
•
80 x 80 image
3 mm pixels
13 mm thick slices
Two simultaneous
slices!!!
• 80 sec scan time
per slice
• 80 sec recon time
• EMI – “should be a
world demand for
~6 machines”
…..……………and now
• 2009
• 1024 x 1024 image
• <1mm slice
thickness
• <0.5mm pixels
• 0.25 sec rotation
• 0.1 sec recon per
slice
• Isotropic resolution
• Volume scanning up to 320 slices in
350ms
CT in Robotically-Assisted Heart Surgery
Planning Robotic Heart Surgery
Planning Robotic Heart Surgery
Magnetic Resonance Imaging
MRI (formally NMR imaging)
• Paul Lautebur 1975
Projections from multiple angles
– Presented at Stanford CT
meeting
– “Zeugmatography”
• Raymond Damadian
1977
– relaxation times and
cancer
• Sir Peter Mansfield late
1970’s
– Echoplanar imaging
sequences
Lautebur and Mansfield
shared 2003 Nobel Prize in
Medicine for MRI
Object
Reconstruction
MRI Scanner
The Fourier Connection
1
0.8
0.6
FID
z
1
H precessing nucleus
Signal
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
0.8
1
Time
FT
x
60
50
spectrum
40
Signal
0
30
y
20
stationary (lab) frame of reference
10
0
0
0.2
0.4
0.6
Frequency
0.8
1
Lower mag field
Lower prec freq
Higher mag field
Higher prec freq
NMR
B0
Real
Gx
Project
Imag
FT
time
frequency
Measured RF signal
B0 +
B0 -
B0
Gx
B0 B0
Measured RF signal
Gy B
0+
There’s much more than this!
• MR scanner:
– “Spatial-frequency sieve”
• Gradient sequences
– impose controlled spatial-frequency pattern in object
• Arbitrary image:
– arbitrary pattern of spatial frequencies
• Orthogonality:
– signal received from object only when spatial frequency
imposed by gradient=spatial frequency in object
• Gradients:
– Driven to cover all possible spatial frequencies in object
• Amplitude of evoked rf signal
~ strength of that spatial frequency in object.
Just like a lens!
Fourier
Transform
Input
Image
Output
Image
#
#
Lens
f
Lens
f
SCANNING
f
f
RECONSTRUCTION
ky
y
DFT
kx
magnitude raw data
x
magnitude reconstructed image
Gradients drive k-space sampling
• Gradients change instantaneous phase of
spins
• Combine gradients to impose and desired
spatial frequency pattern on sample
• Orthogonality: Signal only produced when
imposed pattern matches a fequency in
object.
• Can pick off k-space samples one by one.
Rectilinear sequence
ky
RF
Gx
kx
Gy
Repeat with changing Gy
“Echo-planar” sequence
ky
RF
Gy
Gx
kx
Spiral sequence
ky
RF
Gx
Gy
kx
Fourier Transform and Image
2D (3D) signal data are samples of a 2D (3D) Fourier
Transform of the image
a
35 Years of MRI
First brain MR image
2009
image
MRI7T
Today
• “Interesting
images,
but will never be as
useful as CT”
MRI Today
– A different
Neuroradiologist,
1982
– He rapidly changed his
tune!!
Typical T2-weighted MR image
Functional MRI (fMRI)
• Active brain regions demand more fuel
(oxygen)
• Extra oxygen in blood changes MRI
signal
• Activate brain regions with specific tasks
• Oxygenated blood generates small (~1%)
signal change
• Correlate signal intensity change with
task
• Represent changes on anatomical
images
digitalspotlight.files.wordpress.com
Diffusion Tensor Imaging
• MR pulse sequence sensitive to slow
water flow (diffusion)
• Water diffuses preferentially along
nerve fibres
• Scan session creates series of
images that indicate preferential
direction of flow
• “Tractography” algorithm joins up
flow direction vectors slice–to-slice
Combining it all in “Slicer”
Ultrasound
Ultrasound …..then
…and now
Putting it all together…
• How do you perform surgery on beating
heart?
• Insert instruments into heart through rib
spaces
• Register 3D MRI or CT to patient
• Use ultrasound in during surgery
• Display it all in Virtual Reality
Intra-cardiac intervention
Intra-cardiac intervention
Intra-cardiac intervention
Coming full circle
Images displayed in
3D Slicer
– Medical Visualization platform
The take-home message(s)
• Don’t get discouraged when you get
scooped!
• Don’t always believe the experts|
• You never know where a journey
through Fourier space may lead!
Thanks to my “productive” lab!
Thank you