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Introduction to Medical
Imaging
Oleh Tretiak
Drexel University
Imaging and Computer Vision Center
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Introduction
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Medical Imaging is part of the Health Care process.
Diversity. Medical Imaging includes a broad range or
processes and procedures.
This seminar focuses on basics and on most
commonly used techniques. The main question:
“How does it work?”
Ecology of Medical Imaging. Question : “What
makes a given technique successful?”
Tutorial is designed for scientists and engineers
active in image and signal processing, but not familiar
with Medical Imaging.
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Agenda
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Outline
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Introduction
X-ray imaging
Tomography
Isotope imaging
Magnetic resonance
Ultrasound
Issues in image quality
References
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Overview
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Medical Care is a major economic activity
» About 15% of US Gross Natural Product is devoted to health care.
» Most medical interactions follow a “diagnosis — therapy” model.
» Medical imaging focuses is primarily part of diagnosis, but to an increasing
extent, it is part of therapy.
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Most Imaging Procedures are performed in a Radiology department of a
Hospital
Two settings for medical imaging
» Differential diagnosis
» Screening
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Components of an imaging session:
» Instrument
» Procedure
» Diagnosis
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X-Ray
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Schematic of x-ray imaging
X-rays were discovered in November 1895.
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X-Ray physics
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Generation
Propagation
Detection
Imaging
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X-Ray Generation
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X-rays are electromagnetic waves, same as radio
and light
X-ray quality is specified in terms of photon energy in
kEv
 c/ f
E  h f
Diagnostic energy range is 20-100 kEv
X-ray generators produce polychromatic energy
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X-Ray Propagation
I0
t
I1
I1  I0 e t
- attenuation coefficient, depends on material and
photon energy.
Example: For soft tissue, E = 30 kEv,  = 0.365cm-1.
T  I1 / I0  e3.65  0.026
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X-Rays in complex object
 ( x,y,z)dz
I(x, y)  I0e 
Example: Bone or calcified tissue in soft tissue. We
compute T the difference in transmission between the
particle and the surrounding soft tissue.
For bone,   1.53,1mm of boneT  0.85.
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Scattered X-rays
X-rays are either absorbed (attenuated) or scattered.
Scattered x-rays are not parallel: they add to noise, but not
to the image. They also reduce contrast.
Most common device for reducing scatter is a Bucky-Potter
grid. It consist of parallel metal slats that absorb (most)
oblique rays.
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Recording X-rays
Most devices that record light also record X-rays. However, film
emulsion layers and electronic photodetectors are so thin that
only a small fraction of the energy is absorbed so that they have
very low efficiency.
The commonly used method for detecting x-rays is to convert Xrays to light with an intensifying screen, and to detect the light.
X-ray
Film
Light
Screen
Example: Screen-film combination
for recording x-rays. Thicker
screen increases X-ray detection
efficiency, but produces lower
resolution.
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X-ray imaging systems
An imaging system consists of a generator (source), a
subject, and a recorder.
x-ray
generator
depth-dependent
blurring
The performance of the system depends on the
combination of all devices.
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Issues in X-ray imaging
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Types of studies:
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Still pictures — radiography
Moving pictures — cine radiography
Real time — fluoroscopy
Contrast radiography (invasive)
Recording systems:
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Direct film
Screen-film combination.
Television
Digital radiography
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Summary of X-ray imaging
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Mature field (100 years of development)
In many cases, systems operate at limits imposed by
physics.
There is continued progress, driven primarily through
Information technology.
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Tomography
General imaging/display strategies:
» Surface displays
» Projection (shadow) displays
» Sectional (tomographic) displays
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Old and new tomographies
Mathematics
Instrumentation
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Conventional (analog) tomography.
Source and recorder move in opposite directions. Only one
plane remains in focus. Other planes are recorded, but are
blurry.
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Transverse (computer) tomography
Only one plane is illuminated. Source subject motion
provides added information.
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Algebraic Reconstruction
a
b
c
d
e
f
g
h
i
y
r
u s
v
t
x
w
r abc
s de f
t ghi
u  c ...
Given: Values of measurements r, s, t, ...
Find: Sectional image (a, b, c, d, ...)
Method: Solve system of equations.
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Analytic Reconstruction
I1
Linearization: p(t,  )  ln(I0 / I1 )
Tomography equation (Radon transform).
p(t, )   (t cos  l sin  ,t sin   l cos )dl
y
t
l
x
I0

Solution:
1. Convolution.
p1(t,  )   p(s,  )h(t  s)ds
2. Backprojection.

 (x, y)   p1 (x cos  ysin  ,  )d
0
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X-ray CT scanner
Fan beam scanner. Use analytic fan-beam inversion
algorithm.
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Summary, Computed
Tomography
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Dramatic impact of Image Processing on Medicine.
Led to a Nobel Prize.
Stable field (more than 20 years old). Performance
of X-ray CT scanners nearly optimal.
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Isotope Imaging
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Basic Idea
Gamma Camera
Tomography
Basic idea: A substance (drug) labeled with a radioactive
isotope is ingested. The drug goes to selective sites.
We can locate these site
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Imaging Principle
If gamma rays were light photons,
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Gamma Rays are Straight
There are no lenses for gamma rays
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Pinhole Camera
A “pinhole” camera forms images. Magnification
depends on object plane.
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Collimator
The magnification of a parallel hole collimator is independent of depth.
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Scatter, Revisited
c
d
b
a
e
a – primary photon
accepted by collimator
b – primary photon stopped
by collimator
c - absorbed photon
d – scattered photon misses
image
e – scattered photon
accepted by collimator
Scatter in scintigraphy is more severe than in X-ray
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Compton scattering
Photons and electrons bounce like billiard balls
after
before
h
h
–
–

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Electronic Gamma
Spectroscopy
h
pulse of current
gamma photon
scintilator light
Q 
detector
Charge in a pulse from a scintillation detector is
proportional to photon energy
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Anger Positional Decoding
Q2
gamma
photon
x2
Q1
h  Q1  Q2
x1 Q1  x2 Q2
x
Q1  Q2
x
x1
An Anger camera computes photon energy and location. Events
with low energy are rejected (scattered photons).
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Gamma Camera
Crystal
To energy and position
computer
Collimator
Photodetectors
A gamma camera outputs a sequence
of gamma ray locations. These are
processed to produce a picture.
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Ga
cammma
e
ra
a
m
m
Ga mera
ca
SPECT
Gamma
camera
Single Photon Emission Computed Tomography. Shown here is a
three-headed tomography system. The cameras rotate on a gantry.
A three-dimensional tomography volume is imaged.
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PET
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Positron Emission Tomography
Most positron emitting isotopes have a very short half
life.
On-site cyclotron and radiochemistry facilities (and
staff) are required.
PET is used mostly for research.
Technology is continuously evolving. New 3-D PET
systems place challenges for algorithm and computer
development.
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Isotope Imaging Overview
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Functional Imaging
» Heart muscle integrity
» Local Cerebral Glucose Utilization
» Neurotransmitter Imaging
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Isotope imaging systems make intensive use of
information processing
Show continuing promise for future improvement.
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Magnetic Resonance Imaging
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Nuclear Magnetism
Imaging Principles
Slice Selection
Contrast Mechanisms
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Nuclear Magnetism
No magnetic field
Strong magnetic field
Atomic nuclei have intrinsic quantized magnetic moments
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Nuclear Susceptibility
N(2h )2 I(I  1)
M  0 H0 
H0
3kT
M – sample magnetization
N – number of nuclei
h – Planck’s constant
 – gyromagnetic ratio
I – net magnetic moment
k – Bolzman’s constant
T – absolute temperature
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Nuclear Magnetic Resonance
 0  H0
When a nuclear magnet is tilted
away from the external magnetic
field it rotates (precesses) at the
Larmour frequency. For hydrogen,
the Larmour frequency is 42.6 MHz
per Tesla.
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External Signal from Resonance
H0
0
s(t)
Spinning magnetization induces a voltage in external
coils, proportional to the size of magnetic moment and
to the frequency.
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Bloch Equation
Mx i  My j (Mz  M0 )k
dM
 M  H 

dt
T2
T1
Motion of the magnetization vector is described by the
Bloch equation. The cross product term leads to
magnetic resonance, while T1 and T2 terms lead to
relaxation (decay) of transient effects. For living
tissues, T1 ~ 0.2 to 1 sec, T2 ~ 0.02 to 0.1 sec.
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Imaging: two boxes.
s(t)
2
1.5
1
a
b
3.9
3.6
3.3
3
2.7
2.4
2.1
1.8
1.5
1.2
0.9
0.6
-0.5
-1
0.3
0
0.5
0
-1.5
-2
Assume the ‘body’ consists of two samples, a in stronger field,
b in a weaker field. s(t) is the sum of sinewaves at the two
frequencies. The Fourier transform of s(t) will have two lines
corresponding to the frequencies (locations) of the two
samples. The strength of each line is proportional to the
amount of material in each location.
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Imaging: linear object
Fourier transform
of s(t)
Tube, parts are narrow, parts
are wide
‘Map’ of tube thickness
Tube of nonuniform thickness in linearly varying
magnetic field. The Fourier transform of the resonance
signal is proportional to the tube thickness.
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Imaging: two-dimensional object
Hz  H0  Gx x  Gy y
s(t)  Ke i 0 t  m(x, y)e
 Ke
i 0 t
i (Gx x Gy )t
FT [m(x, y)]( x  Gx t,  y  Gyt)
Given a thin plate of magnetic moments in the x-y
plane. The magnetic fields has linear variation
(gradients) in the x and y directions. The resulting total
magnetic resonance signal is proportional to the Fourier
transform of m(x, y) along a line in the Fourier plane.
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Diagram of Fourier plane path
y
y

x
m(x, y)
x
Gx  Gcos 
Gy  Gsin 
By successively applying different combinations of
gradients we can measure the Fourier transform over
the whole plane. Then take the inverse transform to
compute m(x, y).
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Excitation of Spins
In a static field, the spins line up with the magnetic field. There is
no external magnetic signal.
If a magnetic nucleus is in field strength H0 (Larmour frequency 0),
and a RF field normal to H0 and at frequency 0 is applied, the
magnetic moments move away (tip away) from the direction of Ho.
Tip angle is proportional to the magnitude and duration of the
exciting field (RF field).
This is a resonance phenomenon. If , the RF field frequency, is
very different from 0, the tip angle is equal to 0.
The motion of the magnetization is described by the Bloch
equation.
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Excitation of Spins
H0
  AT / 
H1  Acos 0 t
0tT
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Slice Selection
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If the external field is equal to Hz(x, y, z) = H0 + zGz,
and an exciting field at frequency w0 is applied, the
slice z=0 is selected. That is, spins in that plane are
tipped, while other planes are not affected.
Slice profile is proportional to the Fourier transform of
the RF field envelope. Short, strong pulse — thick
plane. Weak, long pulse — thin plane.
The plane can be selected by field gradients.
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Contrast Mechanisms
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Intrinsic contrast mechanisms: m, proton density; T1
and T2, relaxation times.
Chemical environment affects signals and can
produce contrast. For example, resonant frequencies
for fat and muscle are different.
Motion affects MRI signal. Flow and diffusion can be
measured.
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Summary of MRI
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Rich set of contrast mechanisms.
Versatile slice selection. Tomographic and projection
images are possible.
Non-ionizing. No known harmful effects, except
heating.
Resolution not as good as in X-ray.
Expensive and slow.
New technique. Rapid and continuing progress.
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Ultrasound
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How it works
Limitations
Contrast mechanisms
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Echography
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Acoustic Equation. Wave propagation is (largely)
restricted to soft tissues. Bone and air (lung) are
opaque.
Many methods have been investigated:
transmission, holography, impediography. Practical
systems use echo imaging.
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Scanning
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In essence, the transducer sends a ‘ball’ of sonic
energy, and receives echoes. Each pulse produces a
line in the image.
A picture is built up from scanned lines. Both parallel
and radial ray patterns are used. Scanning can be
mechanical or electronic.
Echosonography is intrinsically tomographic.
An image is acquired in milliseconds, so that real
time imaging is the norm.
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Resolution Limitations
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Resolution is limited by sound wavelength and
transducer aperture. Great instrumentation effort is
involved in obtaining optimal results. There are three
parameters: slice thickness, longitudinal resolution,
and transverse resolution.
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In the spatial Fourier domain
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Ewalt sphere.
Transmission imaging
Reflection imaging
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Doppler Ultrasound
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Signal processing allows real-time Doppler imaging.
This is a unique advantage of Ultrasound
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Contrast Mechanisms
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Density
Velocity (motion)
Soft-tissue echoes
Attenuation
Speed of sound
Nonlinear effects (frequency conversion)
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Summary of Acoustical
Imaging
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Rich set of contrast mechanisms (including Doppler)
Inexpensive
Intensive use of real-time broad-band signal
processing
Incomplete information
Access to only some body regions
Safe
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Medical Imaging Evaluation
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Stages of Evaluation
» I like it
» My doctor friend likes it
» Objective evaluation
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Objective Evaluation Setting
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A set of positive (sick) and (negative) cases
“Gold standard”, reliable actual finding.
Contingency table.
Problem: how do you compare results?
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Principles of ROC studies
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ROC, a tradeoff curve between False Positive and
True Positive findings.
Category scale reporting “Definitely Negative”,
“Probably Negative”, “Equivocal”, “Probably Positive”,
“Definitely Positive”.
Statistical analysis software.
Report includes quality measure with confidence
interval.
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Technical Evaluation of Image
Quality
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Resolution and S/N ratio
Detection and Estimation perspectives.
Analysis and Search
Each technique must be evaluated in its own setting
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Medical Efficacy
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Value of a diagnostic procedure depends on outcome
as well as on accuracy.
What is the value of an expensive technique?
What risks should be taken to obtain a diagnosis.
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Case Load at a Large Teaching
Hospital
Number of Studies
X-Ray
CT
Nuc Med
MRI
Ultrasound
1993
1994
159,976 157,958
12,803 14,343
11,546 10,772
12,046 12,380
16,629 15,844
Subdivisions
X-Ray
Chest
Bone
GI
GU
GU Inter.
Neurology
Neurosurg
Neuro Inv.
Angio
Angio Inv.
Mammo
XCT
Nuc. Med.
Body CT
Nuc. Med.
Imatron
Neuro CT
MRI
MRI
Ultrasound
General
Ultr. Uro
Ult. Qnt.
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Future Prospects
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Better Mousetrap? There are many Medical Imaging
systems.
Current techniques have technical and informational
limitations.
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Summary
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Many Medical Imaging modalities: X-ray, ultrasound,
radionuclide, magnetic resonance.
Variety of Imaging Methods: tomography,
transmission.
Room for improvements and new ideas.
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