2. Lecture 1: Introduction (1/2) – History, basic principles, modalities
Class consists of:
1) Deterministic Studies
- distortion
- impulse response
- transfer functions
All modalities are non-linear and space variant to some degree.
Approximations are made to yield a linear, space-invariant system.
2) Stochastic Studies
SNR (signal to noise ratio) of the resultant image
- mean and variance
3. Course Objectives
• Learn basics of 2D to n-dimensional system
theory and signal processing
– Emphasis on duals between space and frequency
domain
– Emphasis on intuitive understanding
• Understand underlying physics of medical
imaging modalities
• Study the deterministic and stochastic descriptions
of medical imaging systems
– Theory is applicable beyond medical imaging
4. Prerequisites and Postrequisites
• System Theory
– ECE 330, BME/MP 573
• Statistics Helpful but Not Required
– Mean and variance of stochastic processes
– ECE 331, BME/MP 574, ECE 730
• Other Courses
• Microscopy of Life
• BME 568/ MP 568 MRI ( less math)
5. Nov. 1895 – Announces X-ray discovery
Jan. 13, 1896 – Images needle in patient’s hand
– X-ray used presurgically
1901 – Receives first Nobel Prize in Physics
– Given for discovery and use of X-rays.
Wilhelm Röntgen, Wurtzburg
Radiograph
of the hand of
Röntgen’s
wife, 1895.
6. Röntgen detected:
• No reflection
• No refraction
• Unresponsive to mirrors or lenses
His conclusions:
• X-rays are not an EM wave
• Dominated by corpuscular behavior
Röntgen’s Setup
7. Projection X-Ray
Disadvantage: Depth information lost
Advantage: Cheap, simple
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z
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,
,
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μ density
electron ,
z
y
x
attenuation
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Measures line integrals of attenuation
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o
d I
I
x,y,z
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Film shows intensity as a negative ( dark areas, high x-ray detection
9. Early Developments
• Intensifying agents, contrast agents all developed within
several years.
• Creativity of physicians resulted in significant
improvements to imaging.
- found ways to selectively opacify regions of interest
- agents administered orally, intraveneously, or via catheter
10. Later Developments
More recently, physicists and engineers have initiated new
developments in technology, rather than physicians.
1940’s, 1950’s
Background laid for ultrasound and nuclear medicine
1960’s
Revolution in imaging – ultrasound and nuclear medicine
1970’s
CT (Computerized Tomography)
- true 3D imaging
(instead of three dimensions projected down to two)
1980’s
MRI (Magnetic Resonance Imaging)
PET ( Positron Emission Tomography)
2000’s
PET/ CT
11. Computerized Tomography (CT)
1972 Hounsfield announces findings at British Institute of Radiology
1979 Hounsfield, Cormack receive Nobel Prize in Medicine
(CT images computed to actually display attenuation coefficient m(x,y))
Important Precursors:
1917 Radon: Characterized an image by its projections
1961 Oldendorf: Rotated patient instead of gantry
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,
(
)
,
(
ID y
x
μ
y
x
Result:
12. First Generation CT Scanner
Acquire a projection (X-ray)
Translate x-ray pencil beam and
detector across body and record
output
Rotate to next angle
Repeat translation
Assemble all the projections.
13. Reconstruction from Back
Projection
1.Filter each projection to account for sampling data on polar grid
2. Smear back along the “line integrals” that were calculated by
the detector.
17. Nuclear Medicine
- Grew out of the nuclear reactor research of World War II
- Discovery of medically useful radioactive isotopes
1948 Ansell and Rotblat: Point by point imaging of thyroid
1952 Anger: First electronic gamma camera
a) Radioactive tracer is selectively taken up by organ of interest
b) Source is thus inside body!
c) This imaging system measures function (physiology)
rather than anatomy.
18. Nuclear Medicine, continued
Very specific in imaging physiological function - metabolism
- thyroid function
- lung ventilation: inhale agent
Advantage: Direct display of disease process.
Disadvantage: Poor image quality (~ 1 cm resolution)
Why is resolution so poor?
Very small concentrations of agent used for safety.
- source within body
Quantum limited:
CT 109 photons/pixel
Nuclear ~100 photons/pixel
Tomographic systems:
SPECT: single photon emission computerized tomography
PET: positron emission tomography
20. Necessary Probe Properties
Probe can be internal or external.
Requirements:
a) Wavelength must be short enough for adequate
resolution.
bone fractures, small vessels < 1 mm
large lesions < 1 cm
b) Body should be semi-transparent to the probe.
transmission > 10-1 - results in contrast problems
transmission < 10 -3 - results in SNR problems
λ > 10 cm - results in poor resolution
λ < .01Å - negligible attenuation
Standard X-rays: .01 Å < λ < .5 Å
corresponding to ~ 25 kev to 1.2 Mev per photon
22. Probe properties of different modalities
NMR
• Nuclear magnetic moment ( spin)
• Makes each spatial area produce its own signal
• Process and decode
Ultrasound
• Not EM energy
• Diffraction limits resolution
• resolution proportional to λ
